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Glossary

Every term the site defines, collected from the definition boxes in the articles themselves. A term is defined in exactly one place, and this is the link to it.

A

A posteriori
Knowledge or justification that depends on experience for its warrant. Also called empirical knowledge.Defined in A Priori and A Posteriori · Epistemology · Intermediate
A priori
Knowledge or justification that does not depend on experience for its warrant. Experience may be needed to acquire the concepts involved, but plays no part in supporting the claim once the concepts are in hand.Defined in A Priori and A Posteriori · Epistemology · Intermediate
A priori argument
An argument whose premises can be known without appeal to experience of how the world happens to be, resting instead on concepts, definitions, or truths of reason.Defined in Ontological Arguments · Theism · Intermediate
Abduction
An inference from a body of evidence to a hypothesis on the grounds that the hypothesis would explain the evidence better than the alternatives. Also called inference to the best explanation.Defined in Deductive and Inductive Support · Logic · Beginner
absolute creationism
The thesis that abstract objects exist and are created by God, so that numbers, properties, propositions, and possible worlds are among the things brought into being by divine creative activity. It preserves aseity by refusing to make an exception for the abstract: everything distinct from God depends on God, without qualification.Defined in Aseity and the Bootstrapping Problem · Theism · Advanced
Abstract object
An object of the sort that has no such place: the number seven, the proposition that grass is green, the game of chess as distinct from any particular playing of it.Defined in Abstract and Concrete · Metaphysics · Beginner
Access consciousness
The property a mental state has when its content is available to the rest of the system: poised for use in reasoning, for the direct control of action, and for report.Defined in Consciousness Versus Cognition · Philosophy of Mind · Beginner
Access internalism
The view that a factor can justify a belief only if the believer has reflective access to it, so that on reflection alone the believer could become aware of what justifies them.Defined in Internalism versus Externalism · Epistemology · Intermediate
Accessibility relation
A two-place relation on the set of worlds, written $R$, where $Rwv$ says that $v$ is accessible from $w$. The clauses for the operators are then relativised to it: $\Box \varphi$ is true at $w$ when $\varphi$ is true at every world accessible from $w$, and $\Diamond \varphi$ is true at $w$ when $\varphi$ is true at at least one world accessible from $w$. Worlds not accessible from $w$ are simply not consulted in evaluating a modal formula at $w$.Defined in Modal Logic: Possible Worlds Semantics · Logic · Intermediate
accidental necessity
The kind of necessity a proposition acquires simply by being about the past. A proposition can be contingent in itself, in the sense that things could have gone otherwise, while being accidentally necessary now, because there is no longer anything anyone can do to make it false. That Caesar crossed the Rubicon was once an open question and is now beyond anyone's power to affect, including God's. The name marks that the necessity is not built into the content of the proposition but attaches to it by the accident of its subject matter having become past.Defined in Divine Foreknowledge and Freedom · Theism · Advanced
Accidental property
A property a thing has but could have lacked. Nearly everything true of an ordinary object is accidental to it in this sense.Defined in Essence and Accident · Metaphysics · Beginner
Accuracy dominance
One credence function accuracy-dominates another if it is at least as accurate at every possible world and strictly more accurate at some. It strictly dominates if it is strictly more accurate at every world.Defined in Accuracy-First Epistemology · Epistemology · Advanced
Accuracy-first epistemology
The programme of deriving norms for credences from a single underlying value: accuracy, or closeness to the truth. It holds that the only fundamental epistemic good is having credences close to the truth values of the propositions they concern, and that all other norms of credence are justified by showing that obeying them promotes accuracy.Defined in Accuracy-First Epistemology · Epistemology · Advanced
Acts and omissions doctrine
The claim that there is a moral difference between performing an act that produces a result and omitting an act that would have prevented that result, so that the two can differ in permissibility even where the result and the agent's state of mind are the same.Defined in Doing, Allowing, and Double Effect · Applied Ethics · Beginner
Actual infinite
A completed totality with infinitely many members, as distinct from a potential infinite, which is a process or collection that can always be extended further without ever being finished.Defined in Cosmological Arguments · Theism · Intermediate
Adams' thesis
The claim that the assertibility of an indicative conditional goes by the conditional probability of the consequent given the antecedent, rather than by the probability of any proposition the conditional expresses. Proposed by Ernest Adams in 1965 and 1975.Defined in Conditionals and the Triviality Results · Logic · Advanced
adaptive but false belief
A belief that contributes to the survival and reproduction of the organism that holds it while being false. Its possibility is the pivot of the evolutionary argument: if a system of largely false beliefs could generate the same fitness-enhancing behaviour as a system of largely true ones, then selection for behaviour does not amount to selection for truth, and the adaptiveness of our faculties gives no direct evidence of their accuracy.Defined in The Evolutionary Argument Against Naturalism · Theism · Advanced
Adequate set
A set of connectives that is functionally complete. The two terms are used interchangeably, with "adequate set" more common when the set itself is the subject and "functional completeness" more common when the property is.Defined in Truth-Functional Completeness · Logic · Intermediate
Affirming the consequent
The invalid form that takes a conditional and the truth of its consequent, and concludes the truth of its antecedent: from $P \rightarrow Q$ and $Q$, to $P$.Defined in Common Formal Fallacies · Logic · Beginner
Agnosticism
Either the condition of a person who suspends judgement about whether God exists, or the claim that nobody is justified in believing either that God exists or that God does not.Defined in Theism, Atheism, and Agnosticism · Theism · Beginner
Agrippa's trilemma
The claim that any attempt to justify a belief must end in an infinite regress, in a circle, or in an unsupported assumption, and that none of the three delivers justification.Defined in The Regress Problem · Epistemology · Beginner
Ampliative inference
An inference whose conclusion says more than its premises do, so that the conclusion could be false even if every premise is true. Every inductive inference is ampliative, and no valid argument is.Defined in Deductive and Inductive Support · Logic · Beginner
analogy of being
The doctrine that terms applied to God and creatures are used neither in the same sense nor in unrelated senses, but in related senses, because of a real relation between God and creatures. On the analogy of attribution, a term applies primarily to one thing and derivatively to others related to it, as "healthy" applies primarily to an organism and derivatively to a diet that produces health. On the analogy of proportionality, a term applies to each thing in the way proper to what that thing is, so that God's wisdom is to God as human wisdom is to a human. Aquinas develops the account in the first part of the Summa Theologiae, question 13, arguing that names are said of God and creatures analogically, and that the perfection named exists more properly in God, though our understanding of it begins from creatures.Defined in Religious Language · Theism · Advanced
Analysis of knowledge
The project of stating conditions that are individually necessary and jointly sufficient for someone to know that something is the case, thereby saying what knowing consists in.Defined in The JTB Analysis · Epistemology · Beginner
Analytic truth
A proposition true solely in virtue of the meanings of its constituent terms, so that understanding it is sufficient for seeing that it is true. Standard examples are that all bachelors are unmarried and that no square is round.Defined in The Analytic/Synthetic Distinction and Quine's Attack · Epistemology · Intermediate
Anarchism
The position that the state is unjustified and should be abolished or dispensed with, and that the goods it supposedly provides can be secured by voluntary and non-coercive association instead.Defined in What a State Is For · Political Philosophy · Beginner
Annihilationism
The view that those not finally united with God simply cease to exist, so that immortality is a gift conditional on that union rather than a property everyone has.Defined in Death and the Afterlife · Theism · Intermediate
Anthropic principle
The principle that our observations of the universe are inevitably restricted to conditions compatible with the existence of observers, so that finding conditions suitable for us carries a built-in selection effect.Defined in Design and Fine-Tuning Arguments · Theism · Intermediate
anthropomorphism objection
The charge that a conception of God has been built by taking human characteristics and enlarging them, so that what the conception describes is a magnified person rather than the ultimate reality it claims to describe. Directed against theistic personalism, the objection is that its God differs from us only in scale, and that a difference of scale is not the difference religion has always claimed. The objection is old: Xenophanes observed in the sixth century that people picture the gods with their own features, and remarked that horses and oxen would draw gods shaped like horses and oxen.Defined in Classical Theism Against Theistic Personalism · Theism · Advanced
Anti-luminosity argument
Williamson's argument that no non-trivial condition is luminous, where a condition is luminous if, whenever it obtains, one is in a position to know that it obtains. The argument uses a margin-for-error principle for knowledge, applied to a gradual series of cases, to show that even conditions like feeling cold can obtain without one's being in a position to know it.Defined in Knowledge-First Epistemology and Anti-Luminosity · Epistemology · Advanced
Anti-reductionism about testimony
The view that testimony is a basic source of justification in its own right. A hearer is entitled to accept what they are told without positive reasons for trusting the speaker, provided they have no reasons against doing so.Defined in Testimony and Disagreement · Epistemology · Intermediate
anti-theism
The view that God's existence would make things worse, or does make things worse, than they otherwise would be. It is not the claim that God does not exist, and it is not the claim that God is not good. An anti-theist may accept that God is perfectly good and still hold that certain goods available in a godless world are unavailable in a world with God, so that something of value is lost. The position was named and developed by Kahane, taking its cue from remarks by Thomas Nagel.Defined in The Axiology of Theism · Theism · Advanced
anti-theodicy
The position that the project of justifying God's permission of evil should not be undertaken, rather than merely that it has not yet succeeded. Its proponents, among them Kenneth Surin in Theology and the Problem of Evil (Basil Blackwell, 1986), Terrence Tilley in The Evils of Theodicy (Georgetown University Press, 1991), and D. Z. Phillips in The Problem of Evil and the Problem of God (SCM Press, 2004), hold that theodicy misconceives what religious belief is, treats suffering as a theoretical problem when it is a practical and moral one, and produces a distorted relation to the suffering of others in those who practise it.Defined in Horrendous Evils and Anti-Theodicy · Theism · Advanced
apophatic theology
Theology conducted through denial, on which what can be known about God is what God is not. Positive statements are treated as at best provisional and at worst misleading, because every affirmative predicate carries a creaturely condition that God does not satisfy. The apophatic theologian regards the sequence of denials as itself a form of knowledge, a progressive refusal to rest in any concept, rather than as an admission that theology has nothing to work with.Defined in Religious Language · Theism · Advanced
Applied ethics
The part of moral philosophy that addresses particular practical questions, asking what may or must be done in a specified kind of situation rather than what makes actions right in general.Defined in From Theory to Cases · Applied Ethics · Beginner
Argument
A set of statements, one of which (the conclusion) is presented as being supported by the others (the premises).Defined in What an Argument Is · Logic · Beginner
Argument from analogy
The inference that since one's own mental states are correlated with certain bodily conditions and behaviour, and other creatures exhibit relevantly similar bodies and behaviour, they probably have similar mental states.Defined in The Problem of Other Minds · Philosophy of Mind · Beginner
Argument from design
The argument that certain features of the natural world exhibit the marks of contrivance found in artefacts, and are therefore best explained by a designer.Defined in Design and Fine-Tuning Arguments · Theism · Intermediate
argument from divine hiddenness
J. L. Schellenberg's argument that the existence of nonresistant nonbelief is incompatible with the existence of a perfectly loving God. If perfect love entails openness to relationship, and openness to relationship entails ensuring that the person is able to believe, then a perfectly loving God would see to it that no nonresistant person lacks belief. Since some nonresistant people do lack belief, there is no perfectly loving God, and therefore, on any conception of God on which God is perfectly loving, no God.Defined in The Problem of Divine Hiddenness · Theism · Advanced
argument from pain and pleasure
Draper's argument that the observed facts about the distribution and biological integration of pain and pleasure are antecedently much more probable on the hypothesis of indifference than on theism, and that they therefore constitute significant evidence against theism. The conclusion is that theism is less probable than it would otherwise have been, not that theism is false, and Draper explicitly allows that other evidence might outweigh it.Defined in Draper's Argument from Pain and Pleasure · Theism · Advanced
Arithmetical completeness
The property a modal system has when it derives exactly those formulas all of whose arithmetical interpretations are provable in Peano arithmetic. Solovay proved in 1976 that $\mathsf{GL}$ has it.Defined in Provability Logic and Löb's Theorem · Logic · Advanced
Arithmetical comprehension
The principle asserting the existence of every set definable by a formula containing no set quantifiers, though possibly containing set parameters. Added to the base theory it gives the system ACA-zero, whose first-order consequences are exactly those of Peano arithmetic.Defined in Reverse Mathematics · Logic · Advanced
Arithmetical interpretation
An assignment of a sentence of arithmetic to each propositional variable of the modal language, extended to all formulas by commuting with the connectives and by sending $\Box A$ to the arithmetised statement that the sentence assigned to $A$ is provable in Peano arithmetic. Every modal formula thereby becomes a sentence of arithmetic, one for each choice of assignment.Defined in Provability Logic and Löb's Theorem · Logic · Advanced
aseity
The property of existing from oneself, of having one's existence and nature from no source outside oneself. A being with aseity does not depend on anything for existing, for being the kind of thing it is, or for having the features it has. The doctrine that God has aseity is the strongest form of the independence claim: everything other than God depends on God, and God depends on nothing.Defined in Aseity and the Bootstrapping Problem · Theism · Advanced
aseity bootstrapping problem
The objection that God cannot create the properties his own creative activity presupposes. To create anything, God must already be omnipotent, must already have the property of being a creator, and must already be the kind of thing that can act. If those properties are among the things God creates, then God must have them before he creates them, and the account is circular. If they are not, then some properties are uncreated and aseity fails in the way absolute creationism was introduced to prevent.Defined in Aseity and the Bootstrapping Problem · Theism · Advanced
Assumption
A formula written down without justification, for the sake of argument, opening a subproof in which it and everything derived from it are available. An assumption differs from a premise in that it carries no commitment: the argument does not claim it is true, only that something follows from it.Defined in Natural Deduction · Logic · Intermediate
Atheism
The proposition that God does not exist: the denial of theism.Defined in Theism, Atheism, and Agnosticism · Theism · Beginner
Atomic formula
A sentence letter standing alone. Atomic formulas have no connectives and no proper parts that are themselves formulas, which is what makes them the base case of the grammar. A formula that is not atomic is compound, and every compound formula has exactly one main connective.Defined in Propositional Logic and Well-Formed Formulas · Logic · Intermediate
Attribute incompatibility
An argument that two or more of the properties ascribed to God cannot both be instantiated by the same being, so that nothing answers to the description and God as classically conceived does not exist.Defined in Divine Attributes and Their Tensions · Theism · Intermediate
axiology of theism
The study of what difference in value God's existence would make, as distinct from whether God exists. The question was given its modern form by Guy Kahane in "Should We Want God to Exist?" in Philosophy and Phenomenological Research in 2011, and the literature that followed treats the existential question and the axiological question as fully independent: one can hold that God exists and that this is in some respect regrettable, or that God does not exist and that this is a loss.Defined in The Axiology of Theism · Theism · Advanced
Axiom schema
A pattern with metalinguistic variables in place of formulas, every uniform substitution of formulas for which is an axiom. A schema stands for infinitely many axioms, so a system described as having three axioms in fact has infinitely many, arranged in three families. The alternative is to state finitely many axioms and add a rule permitting substitution, which shifts the same work from the axioms to the rules.Defined in Axiomatic Systems and the Deduction Theorem · Logic · Intermediate

B

Barcan formula
The schema $\Diamond \exists x\, \varphi \rightarrow \exists x\, \Diamond \varphi$, equivalently $\forall x\, \Box \varphi \rightarrow \Box \forall x\, \varphi$. It says that if there might have been something satisfying a condition, then something actually existing might have satisfied it, and it is valid on exactly the models whose domains do not grow along the accessibility relation.Defined in Quantified Modal Logic and the Barcan Formulas · Logic · Advanced
Basic belief
A belief that is justified without deriving its justification from other beliefs. If there are such beliefs, the chain of reasons can stop at one without stopping arbitrarily.Defined in The Regress Problem · Epistemology · Beginner
Bayes factor
The factor by which a body of evidence multiplies the prior odds to give the posterior odds. For two hypotheses that each fix a definite probability for the evidence, it is identical to the likelihood ratio.Defined in Bayesian Natural Theology · Theism · Advanced
Bayes's theorem
The result that $P(h \mid e) = P(e \mid h) \cdot P(h) / P(e)$, which expresses the probability of a hypothesis given evidence in terms of the probability of that evidence given the hypothesis, the prior probability of the hypothesis, and the overall probability of the evidence.Defined in Bayesian Confidence and Credence, Introduced · Epistemology · Intermediate
Bayesian theodicy
A theodicy assessed not as a demonstration that some good justifies the evil, but as a hypothesis that raises the probability of the observed evils given theism. Its function within a probabilistic argument is to narrow the likelihood gap, and it can perform that function without being known to be true, since what matters is the probability it confers rather than its establishment. The trade-off is that a theodicy specific enough to raise the likelihood substantially is a further claim, so the conjunction of theism with it has a lower prior than theism alone.Defined in The Probabilistic Problem of Evil · Theism · Advanced
Behavioural evidence
The observable facts about a creature that bear on what mental states it has: what it does, how it responds, what it says, and how its body is built and behaves.Defined in The Problem of Other Minds · Philosophy of Mind · Beginner
Being
The condition of being something at all, as opposed to nothing. In most contemporary writing "being" and "existence" are used interchangeably; a minority tradition keeps them apart, so that some things can have being without existing.Defined in What 'Exists' Means · Ontology · Beginner
being among beings
The status classical theism denies to God: membership in the class of existing things, alongside stars, numbers, and people, differing from other members in degree rather than in kind. On the classical view God is not the greatest item in the inventory of what exists but the source of there being an inventory at all. Aquinas marks this by identifying God with subsistent existence itself rather than with something that has existence, which is the doctrinal use of the essence-existence distinction.Defined in Classical Theism Against Theistic Personalism · Theism · Advanced
Belief
Taking something to be the case. To believe that P is to hold P as true, which is compatible with being wrong, being unsure, and never having examined the matter.Defined in Knowledge, Belief, and Opinion · Epistemology · Beginner
Benardete paradox
Any of a family of cases in which infinitely many agents or objects are each conditioned to act only if no earlier one has acted, and in which there is no earliest, so that the situation is inconsistent although each agent's own instruction is unobjectionable.Defined in Grim Reaper Paradoxes and Causal Finitism · Theism · Advanced
Benefit
A change that leaves a being better off in some respect it has a stake in: the mirror image of a setback to its interests.Defined in Harm, Benefit, and Consent · Applied Ethics · Beginner
Bergmann's skeptical theses
Michael Bergmann's formulation of what the skeptical theist is committed to, given in "Skeptical Theism and Rowe's New Evidential Argument from Evil" in Noûs in 2001 and extended in "Skeptical Theism and the Problem of Evil" in The Oxford Handbook of Philosophical Theology (Oxford University Press, 2009). The theses deny that our samples are representative: that the goods we know of are representative of the goods there are, that the evils we know of are representative of the evils there are, that the entailment relations we grasp between goods and the permission of evils are representative of those that obtain, and, in the extended version, that our grasp of the total moral value of possible states of affairs is representative of the whole.Defined in Skeptical Theism and Its Costs · Theism · Advanced
Bertrand's paradox
A demonstration, due to Joseph Bertrand in 1889, that the principle of indifference gives different answers to a single question depending on which quantity is treated as uniformly distributed. The standard version asks for the probability that a chord drawn at random in a circle is longer than the side of the inscribed equilateral triangle, and three equally natural constructions give three different values.Defined in Probability as an Extension of Logic · Logic · Intermediate
best possible world
The world, among all the worlds an omnipotent being could bring about, that is better than every other. Leibniz argued in the Théodicée of 1710 that since God is omnipotent, omniscient, and perfectly good, God surveys all the possibilities and brings about the best of them, from which it follows that this world, whatever its apparent defects, is the best available. The phrase has since become detached from Leibniz's system and is used for the general assumption that there is such a world to be chosen.Defined in The No-Best-World Problem · Theism · Advanced
BHK interpretation
The Brouwer-Heyting-Kolmogorov reading of the connectives in terms of proofs rather than truth: a proof of $\varphi \land \psi$ is a pair of proofs; a proof of $\varphi \lor \psi$ is a proof of one disjunct together with an indication of which; a proof of $\varphi \rightarrow \psi$ is a construction transforming any proof of $\varphi$ into one of $\psi$; a proof of $\exists x\, \varphi$ is an object together with a proof that it satisfies $\varphi$; and $\neg \varphi$ abbreviates $\varphi \rightarrow \bot$.Defined in Intuitionistic Logic and Kripke Semantics · Logic · Advanced
Biconditional
The truth function written $P \leftrightarrow Q$ and read "$P$ if and only if $Q$": true when the two parts have the same truth value, and false when they differ.Defined in Statements and Connectives · Logic · Beginner
Binary truth function
A truth function taking two arguments. Since two arguments admit four combinations of truth values and each combination can be sent to either value independently, there are exactly sixteen binary truth functions, and each corresponds to one possible filling of the four-row output column of a truth table.Defined in The Sixteen Binary Connectives · Logic · Intermediate
biological role of pain
The fact that pain and pleasure in living organisms are systematically integrated into goal-directed biological systems: they are triggered by conditions that bear on survival and reproduction, they motivate behaviour that tends to preserve the organism, and their intensity and duration track biological stakes rather than moral ones. Tissue damage hurts, nutrition and mating are pleasant, and the correlation is not incidental but is what one would expect of a trait shaped by differential reproductive success.Defined in Draper's Argument from Pain and Pleasure · Theism · Advanced
Bodily resurrection
The view that persons do not survive death at all, and that God restores them to existence embodied at some later time.Defined in Death and the Afterlife · Theism · Intermediate
Bound variable
An occurrence of a variable that falls within the scope of a quantifier using that same variable. A bound occurrence contributes nothing on its own and could be replaced throughout by any other unused variable without changing what the formula says, so $\forall x Fx$ and $\forall y Fy$ are the same claim differently written.Defined in Predicate Logic · Logic · Intermediate
Brain in a vat
The modern version of the deceiver hypothesis: that you are a disembodied brain in a nutrient bath, receiving electrical stimulation that produces exactly the experiences you are now having.Defined in Skepticism, First Encounter · Epistemology · Beginner
Branch closure
The state of a branch that contains both some formula and its negation. Such a branch describes an impossible interpretation and is marked closed, and no further work is done on it. A tableau all of whose branches are closed is itself closed, and a branch on which every formula has been decomposed and which has not closed is open.Defined in Semantic Tableaux · Logic · Intermediate
Burden of proof
The obligation, in a dispute, to make the case for one's position, borne by whichever party would lose if no argument at all were offered.Defined in Theism, Atheism, and Agnosticism · Theism · Beginner

C

Canonical model
An interpretation built directly out of a maximal consistent set, in which the truth values of the atomic formulas are read off membership in the set. The defining property of such a model, established by induction over formulas, is that a formula is true in it exactly when the formula belongs to the set that generated it.Defined in Soundness and Completeness Proofs · Logic · Advanced
Canonicity
A modal logic is canonical when its canonical frame, whose worlds are the maximal consistent sets of formulas of the logic and whose accessibility relation holds between two sets when everything necessitated in the first belongs to the second, validates all the logic's axioms. A canonical logic is complete with respect to the class of frames its axioms define.Defined in Correspondence Theory · Logic · Advanced
Cardinality
The size of a set, understood so that two sets have the same cardinality exactly when there is a bijection between them. For finite sets this agrees with counting. For infinite sets it is the definition rather than an approximation to one, since there is nothing else available, and it has consequences that finite intuition does not prepare anyone for.Defined in Basic Set Theory for Logicians · Logic · Intermediate
Cartesian doubt
The procedure of provisionally rejecting any belief that admits of the slightest doubt, in order to find out what survives. The doubts are deliberately extreme, because the point is to test the foundations rather than to describe anyone's actual uncertainty.Defined in Skepticism, First Encounter · Epistemology · Beginner
Casuistry
Moral reasoning that works outward from settled paradigm cases, deciding a new case by comparing it with cases already resolved and judging how far the differences between them matter.Defined in From Theory to Cases · Applied Ethics · Beginner
Categoricity
The property a theory has, relative to a cardinal, when all of its models of that cardinality are isomorphic. A theory categorical in some infinite cardinal and having no finite models is complete, since two models of a sentence-disputing pair could be brought down or up to that cardinality and would then have to be isomorphic.Defined in Model Theory: Types, Quantifier Elimination, Categoricity · Logic · Advanced
Category
One of the most general kinds a thing can belong to, such that everything falls under some category and the categories are not themselves species of anything more general.Defined in What Metaphysics Asks · Metaphysics · Beginner
Causal chain
A sequence of occurrences in which each depends on the one before it. Causation is then taken to hold between the ends of such a chain, not only between adjacent links.Defined in Causation, First Pass · Metaphysics · Beginner
Causal finitism
The thesis that nothing can be affected by infinitely many causes, so that every event has only finitely many causal antecedents.Defined in Grim Reaper Paradoxes and Causal Finitism · Theism · Advanced
Causal inefficacy
The inability to cause anything or to be affected by anything: standing outside the causal order entirely.Defined in Abstract and Concrete · Metaphysics · Beginner
Causal series per se
A causal series in which each member's causing depends on the simultaneous causing of the member before it, so that the later members have no causal power of their own but only what is being conferred on them.Defined in Cosmological Arguments · Theism · Intermediate
Causation
The relation that holds between one occurrence and another when the first brings about, produces, or is responsible for the second.Defined in Causation, First Pass · Metaphysics · Beginner
Cause
The occurrence that does the bringing about: the striking of the match, the impact of the ball, the passing of the law.Defined in Causation, First Pass · Metaphysics · Beginner
Change
A persisting thing having a property at one time and lacking it at another. Change requires numerical identity across the two times, since otherwise there is no one thing that has altered.Defined in Change and Identity Over Time · Metaphysics · Beginner
Church-Turing thesis
The claim that the functions computable by any effective procedure whatever are exactly the recursive functions. It is not a theorem and cannot be one, since one side of the identification is an informal notion and no proof can connect an informal notion to a mathematical one. It is supported by the convergence of independently motivated analyses on the same class, by the failure of every attempt to define a procedure falling outside it, and by ninety years of use.Defined in Computability, Decidability, and Church's Theorem · Logic · Advanced
Church's theorem
The result that the set of valid first-order sentences is not decidable: no procedure takes an arbitrary sentence of first-order logic and determines in finitely many steps whether it is valid. The set is recursively enumerable, since completeness allows the derivations to be listed, so the failure is exactly the failure of the complement to be listable.Defined in Computability, Decidability, and Church's Theorem · Logic · Advanced
Claim right
A right that another party has a duty to you: you have a claim right that someone do or refrain from something exactly when they have a duty to you to do or refrain from it.Defined in Rights, Introduced · Political Philosophy · Beginner
Classical theism
The conception of God developed in Jewish, Christian, and Islamic philosophical theology, on which God is one, without a body, the creator of everything other than himself, and possessed of every perfection to the highest degree.Defined in What God Is Claimed to Be · Theism · Beginner
Close possible world
A way things might have been that differs minimally from how they actually are. Modal epistemology uses closeness as a measure of how easily something could have happened: an outcome that occurs in a close world is one that could easily have occurred.Defined in Safety and Sensitivity Conditions · Epistemology · Intermediate
Closure denial
The position that knowledge is not always preserved under known entailment, so that one may know an ordinary proposition without knowing the denial of a sceptical hypothesis it entails.Defined in Epistemic Closure and Its Denial · Epistemology · Intermediate
Coercion
Getting someone to act by threatening them with a consequence they will want to avoid, so that the option they would otherwise have taken is made unattractive or removed.Defined in Authority and Legitimacy · Political Philosophy · Beginner
Cognition
The mind's information-handling: taking in, storing, representing, transforming, and using information to guide behaviour. Perception, memory, inference, categorisation, and language use are cognitive processes.Defined in Consciousness Versus Cognition · Philosophy of Mind · Beginner
Cognitive science of religion
The research programme explaining religious belief as a by-product of ordinary cognitive systems that evolved for other purposes, rather than as an adaptation for religion or as a product of reasoning.Defined in Natural Explanations of Religious Belief · Theism · Intermediate
Coherence
The relation among the members of a set of beliefs consisting in logical consistency together with positive relations of explanation, inference, and mutual support, and the absence of unexplained anomalies.Defined in Foundationalism, Coherentism, Infinitism · Epistemology · Intermediate
Coherentism
The view that no belief is justified independently of others, and that justification is a property a body of beliefs has in virtue of how its members fit together. It takes the second horn and denies that the circularity involved is vicious.Defined in Foundationalism, Coherentism, Infinitism · Epistemology · Intermediate
Compactness theorem
The result that a set of first-order sentences has a model if and only if every finite subset of it has a model. One direction is immediate, since a model of the whole set is a model of each part. The other direction is the substantial one: satisfiability, which is a condition on an infinite collection, is settled entirely by conditions on its finite parts.Defined in Compactness and Löwenheim-Skolem · Logic · Advanced
Complete type
A maximal consistent set of formulas in a fixed finite number of free variables, consistent with a given theory. A type is realised in a model when some tuple of elements satisfies every formula in it, and omitted when no tuple does.Defined in Model Theory: Types, Quantifier Elimination, Categoricity · Logic · Advanced
Completeness theorem
The claim that every semantic consequence is derivable: whenever every interpretation making a set of premises true makes a conclusion true, a derivation of that conclusion from those premises exists. A proof system with this property leaves no valid argument out, so the failure to find a derivation is evidence that none exists rather than a comment on the searcher.Defined in Soundness and Completeness, Informally · Logic · Intermediate
Comprehension schema
The schema asserting, for each formula $\varphi$ of the language, that there exists a relation holding of exactly the tuples satisfying it: $\exists X\,\forall \bar{x}\,(X\bar{x} \leftrightarrow \varphi(\bar{x}))$. Full comprehension permits $\varphi$ to contain second-order quantifiers, in which case the schema is impredicative, since the relation asserted to exist is in the range of quantifiers occurring in the condition defining it.Defined in Second-Order and Higher-Order Logic · Logic · Advanced
Conceptual truth
A truth held to follow from the content of the concepts involved rather than from empirical fact. Often used interchangeably with analytic truth, though writers who distinguish them treat conceptual truth as the broader notion, covering cases where the connection between concepts is not a matter of definition.Defined in The Analytic/Synthetic Distinction and Quine's Attack · Epistemology · Intermediate
Conciliationism
The view that on discovering that an epistemic peer disagrees with you, you should move your credence substantially towards theirs. In its strongest form, the equal weight view, each peer's opinion counts for the same, and each should adopt the average or suspend judgement.Defined in Testimony and Disagreement · Epistemology · Intermediate
Conclusion
The statement an argument is trying to establish, on the strength of its premises.Defined in What an Argument Is · Logic · Beginner
Concrete object
An object of the sort that has a place in the world's causal and spatial order: the mug, the mountain, the electron, the eruption.Defined in Abstract and Concrete · Metaphysics · Beginner
concurrentism
The position that God does more than sustain creatures: he concurs immediately in every creaturely act, so that each natural effect is produced by God and by the creature together, and neither would produce it alone. The creature's contribution is genuine and specific, determining what sort of effect occurs, while God's contribution is general and required for any effect to occur at all. This is the mainstream scholastic view, developed with most care by Francisco Suárez.Defined in Existential Inertia and Divine Conservation · Theism · Advanced
Conditional probability
The probability of one proposition on the supposition that another holds, written $P(h \mid e)$ and defined as $P(h \wedge e) / P(e)$ whenever $P(e) > 0$.Defined in Bayesian Confidence and Credence, Introduced · Epistemology · Intermediate
Conditional proof
The introduction rule for the conditional. Assume the antecedent, derive the consequent within the subproof, then discharge the assumption and write the conditional at the outer level. The rule is what makes the conditional provable at all, since without it a conditional could only ever be carried down from a premise.Defined in Natural Deduction · Logic · Intermediate
Conditionalization
The rule that when an agent learns a proposition $E$ with certainty and learns nothing stronger, their new credence in any proposition $H$ should equal their old conditional credence in $H$ given $E$. In symbols, $c_{\text{new}}(H) = c_{\text{old}}(H \mid E)$.Defined in Formal Epistemology: Probabilism and Updating · Epistemology · Advanced
Confabulation
The production of a sincere, confident report that is not based on the process it purports to report, and which the subject does not recognise as invented.Defined in Introspection and Its Limits · Philosophy of Mind · Beginner
Confirmation
The relation that holds between a piece of evidence and a hypothesis when the evidence supports the hypothesis, making it more credible than it would otherwise be. Confirmation can be qualitative (whether E supports H at all) or quantitative (how much E supports H).Defined in Confirmation Theory, Ravens, and Grue · Epistemology · Advanced
Confirmation holism
The thesis that empirical evidence bears on bodies of belief as wholes rather than on individual statements, so that no single statement has its own confirming or disconfirming observations.Defined in The Analytic/Synthetic Distinction and Quine's Attack · Epistemology · Intermediate
Conflicting claims objection
The argument that since religious experiences across different traditions support incompatible claims about what is experienced, they cannot all be veridical, and no way of privileging one tradition's experiences is available that does not assume what is in question.Defined in Religious Experience · Theism · Intermediate
Conjunction
The truth function written $P \land Q$ and read "$P$ and $Q$": true when both parts are true, and false otherwise.Defined in Statements and Connectives · Logic · Beginner
Conjunction closure
The principle that if it is rational to believe $p$ and rational to believe $q$, it is rational to believe $p \land q$. A system of rational belief closed under conjunction permits one to combine any beliefs into a single belief.Defined in Lottery, Preface, and the Threshold View of Belief · Epistemology · Advanced
Consciousness
An umbrella term covering several distinct phenomena: a creature's being awake and responsive, a creature's being aware of something, a mental state's being available to the rest of the mind, and there being something it is like to undergo a state.Defined in Consciousness Versus Cognition · Philosophy of Mind · Beginner
Consequentialism
The family of theories on which the rightness of an action is determined entirely by its outcomes. Nothing about an act matters morally except the state of the world it brings about.Defined in Consequences, Rules, and Character · Ethics · Beginner
Consistency
The property a set of formulas has when no contradiction is derivable from it. This is a syntactic condition, concerning what can be written down, and it is to be distinguished from satisfiability, which is the semantic condition of having a model. A set with a model is consistent in any sound system, since a contradiction derived from it would have to be true on that model.Defined in Soundness and Completeness, Informally · Logic · Intermediate
Constant domain semantics
The interpretation on which every world of a model shares a single domain of quantification, so that the same objects exist at every world. Quantifiers are evaluated against that fixed domain regardless of which world is under consideration.Defined in Quantified Modal Logic and the Barcan Formulas · Logic · Advanced
Constitutionalism
The doctrine that the powers of government should be defined and limited by fundamental law, so that there are things the state may not do however it decides to do them and whatever majority supports it.Defined in Law and the Rule of Law · Political Philosophy · Beginner
Constructive proof
A proof that exhibits what it asserts to exist. A constructive proof of a disjunction specifies a true disjunct and a constructive proof of an existential specifies a witness, so the proofs are algorithms in a sense that can be made exact.Defined in Intuitionistic Logic and Kripke Semantics · Logic · Advanced
Contextualism
The view that the truth conditions of knowledge attributions vary with the context of the attributor. A sentence of the form "S knows that p" can be true as uttered in one conversation and false as uttered in another, about the same subject at the same time, because the word "knows" picks out different relations in different contexts.Defined in Contextualism, Invariantism, and Pragmatic Encroachment · Epistemology · Advanced
Contingency
A formula whose truth table column is true in at least one row and false in at least one row. Its value depends on how things stand, not on its form alone.Defined in Truth Tables · Logic · Beginner
Contingent truth
A truth that is not necessary: something that is the case but could have failed to be the case.Defined in Possibility and Necessity, Informally · Metaphysics · Beginner
Continuum of inductive methods
The one-parameter family of confirmation functions introduced by Carnap in 1952, in which the probability that the next individual has a property observed in $n_{i}$ of $n$ cases, with $k$ properties in the language, is $(n_{i} + \lambda / k) / (n + \lambda)$. The parameter $\lambda$ measures how much weight is given to the language's structure as against the observed frequency.Defined in Inductive Logic and the Carnap Programme · Logic · Advanced
Contraction
The structural rule permitting two occurrences of the same formula to be identified: from $\Gamma, \varphi, \varphi \vdash \psi$ infer $\Gamma, \varphi \vdash \psi$. It expresses the assumption that having a premise once is having it as many times as needed, and it is the rule that makes the Curry paradox derivable in a theory with naive comprehension.Defined in Substructural Logics · Logic · Advanced
Contradiction
A formula whose truth table column is false in every row. A contradiction cannot be true, whatever the letters in it stand for.Defined in Truth Tables · Logic · Beginner
Contrary-to-duty paradox
The difficulty of representing an obligation conditional on the violation of another obligation. Chisholm's 1963 example, that one ought to go to the neighbours' assistance, that if one goes one ought to tell them one is coming, that if one does not go one ought not to tell them, and that one does not go, is consistent and intuitively independent, and every natural formalisation in the standard system is either inconsistent or renders one premise redundant.Defined in Temporal, Deontic, and Epistemic Logic · Logic · Advanced
Converse Barcan formula
The schema $\exists x\, \Diamond \varphi \rightarrow \Diamond \exists x\, \varphi$, equivalently $\Box \forall x\, \varphi \rightarrow \forall x\, \Box \varphi$. It is valid on exactly the models whose domains do not shrink along the accessibility relation, and it follows from the ordinary quantifier axioms together with necessitation in any system with the distribution schema.Defined in Quantified Modal Logic and the Barcan Formulas · Logic · Advanced
CORNEA
Wykstra's Condition on Reasonable Epistemic Access: one is entitled to claim, on the basis of some situation one has examined, that it appears there is no such-and-such, only if it is reasonable to believe that if there were such a thing, the situation would likely have looked different in some way one could detect. The condition is not specific to religion; it is offered as a general constraint on when the failure to observe something counts as evidence of its absence.Defined in The Probabilistic Problem of Evil · Theism · Advanced
Corrective justice
Justice in the rectification of a wrong: restoring the injured party, so far as possible, to the position they would have occupied had the wrong not been done.Defined in What Justice Requires · Political Philosophy · Beginner
Correspondence
A modal formula and a condition on the accessibility relation correspond when the formula is valid on exactly the frames satisfying the condition. The correspondence is a biconditional between a modal fact and a relational one, proved in both directions.Defined in Correspondence Theory · Logic · Advanced
Cosmological argument
An argument from the existence of the universe, or from some completely general feature of it, to a cause or explanation lying outside it.Defined in Cosmological Arguments · Theism · Intermediate
Countability
The feature a kind has when it makes sense to ask how many of them there are, and there is a determinate answer.Defined in Identity and Individuation · Ontology · Beginner
Countable set
A set that is either finite or can be put into a bijection with the natural numbers. A countable infinite set can be arranged in a list with a first member, a second, and so on, such that every member appears somewhere in the list. A set that cannot be so arranged is uncountable.Defined in Basic Set Theory for Logicians · Logic · Intermediate
Counterexample
A possible situation in which all of an argument's premises are true and its conclusion is false. An argument is invalid exactly when it has one.Defined in Validity and Soundness · Logic · Beginner
Counterfactual
A conditional whose antecedent is supposed for the sake of argument, typically contrary to fact, and which asserts that the consequent holds under that supposition. The standard semantics evaluates it by considering the most similar situations in which the antecedent is true.Defined in Safety and Sensitivity Conditions · Epistemology · Intermediate
Counterfactual account of harm
The view that an act harms a person when it leaves them worse off than they would have been had the act not been performed, so that harm is measured against what would otherwise have happened.Defined in Harm, Benefit, and Consent · Applied Ethics · Beginner
counterfactuals of freedom
The propositions middle knowledge is knowledge of: conditionals stating what a particular creature would freely do if placed in a particular fully specified circumstance. They are contingent, since the creature could have done otherwise in that circumstance, and they are not up to God, since the freedom of the act requires that the creature and not God settles it. If such propositions are true prior to creation, they constitute a fixed landscape that God must work with rather than a set of options God can select among.Defined in Divine Foreknowledge and Freedom · Theism · Advanced
Countermodel
An interpretation on which every premise of an argument is true and its conclusion false. An argument is invalid precisely when it has one, and exhibiting a countermodel is the standard way of establishing invalidity, since it settles the matter outright rather than reporting a failure to find a proof.Defined in Semantic Tableaux · Logic · Intermediate
Cox's theorem
The result that any measure of plausibility satisfying a short list of structural requirements is a rescaling of a probability measure. The requirements are that degrees of plausibility be represented by real numbers, that the plausibility of a conjunction depend in a fixed way on the plausibility of one conjunct and of the other given the first, that the plausibility of a negation depend in a fixed way on the plausibility of what is negated, and that the assignment be consistent, in that two routes to the same value must agree. Cox published the argument in 1946.Defined in Probability as an Extension of Logic · Logic · Intermediate
Creation ex nihilo
The doctrine that God brings things into existence without working on any pre-existing material and without producing them out of God's own substance.Defined in Creation, Conservation, and Providence · Theism · Beginner
Credence
A degree of belief represented numerically on a scale from 0 to 1, where 0 is certainty that the proposition is false and 1 is certainty that it is true.Defined in Bayesian Confidence and Credence, Introduced · Epistemology · Intermediate
Credibility deficit
The condition of being given less credibility than one's evidence and competence warrant. A credibility deficit is not unjust merely by being mistaken; it becomes unjust when it results from prejudice.Defined in Epistemic Injustice · Epistemology · Intermediate
Criterion of identity
A principle stating, for things of a given kind, the condition under which one of them is the same as another. Sets have a well-known one: the same set when the same members.Defined in Identity and Individuation · Ontology · Beginner
Criterion of the mental
A condition whose satisfaction counts as grounds for applying a mental term, in virtue of what the term means rather than in virtue of an empirical correlation.Defined in The Problem of Other Minds · Philosophy of Mind · Beginner
culpable nonbelief
Nonbelief for which the nonbeliever is responsible, because it arises from some form of resistance: refusal to attend to the evidence, unwillingness to accept the moral demands belief would bring, or a disposition of the will turned against God. The theist who denies the hiddenness argument's third premise holds that all nonbelief is of this kind, and so that the category of nonresistant nonbelief is empty.Defined in The Problem of Divine Hiddenness · Theism · Advanced
Cumulative case argument
An argument that no single consideration establishes a conclusion, while several independent considerations, each inconclusive by itself, together support it.Defined in How Arguments About God Work · Theism · Beginner
Curry-Howard correspondence
The identification of proofs with terms and propositions with types, under which a proof of a formula is a term whose type is that formula, and reduction of terms corresponds exactly to the simplification of proofs. Observed by Haskell Curry for the implicational fragment in the 1930s and extended by William Howard in a 1969 manuscript circulated for a decade before its 1980 publication.Defined in The Curry-Howard Correspondence · Logic · Advanced
Cut elimination
Gentzen's Hauptsatz: every proof in the sequent calculus can be transformed into a proof of the same sequent that uses no cuts. The cut rule is therefore admissible rather than necessary, adding nothing to what the system proves, and the transformation is effective, taking a given proof to a cut-free one by a procedure that terminates.Defined in Sequent Calculus and Cut Elimination · Logic · Advanced
Cut rule
The rule permitting a formula proved on the right of one sequent to be discharged on the left of another: from a proof of Δ together with φ, and a proof that φ together with Γ yields Δ, infer that Γ yields Δ with φ gone. The formula cut away appears in both premises and in neither conclusion, which distinguishes cut from every other rule in the system.Defined in Sequent Calculus and Cut Elimination · Logic · Advanced

D

Debunking argument
An argument that a belief is unjustified because the best explanation of why people hold it makes no reference to the belief's being true.Defined in Natural Explanations of Religious Belief · Theism · Intermediate
Decidability
The property a set has when some procedure determines membership in it: given any object, the procedure halts and answers correctly, yes or no. A property is decidable when the set of things having it is, and a theory is decidable when the set of its theorems is. The requirement that the procedure halt on every input is what distinguishes this from mere search.Defined in Computability, Decidability, and Church's Theorem · Logic · Advanced
Decision-making capacity
The ability to make a particular decision at a particular time: to understand the relevant information, appreciate how it applies to oneself, reason with it, and express a choice.Defined in Harm, Benefit, and Consent · Applied Ethics · Beginner
Deduction theorem
The result that if $\varphi$ can be derived from a set of premises together with $\psi$, then $\psi \rightarrow \varphi$ can be derived from that set alone. Written with the turnstile: if $\Gamma, \psi \vdash \varphi$ then $\Gamma \vdash \psi \rightarrow \varphi$. It is a theorem about the system rather than a rule within it, and it holds despite the system having no assumptions and no discharge.Defined in Axiomatic Systems and the Deduction Theorem · Logic · Intermediate
Deductive argument
An argument put forward as valid: one whose premises are meant to guarantee the conclusion, so that accepting the premises and rejecting the conclusion would be inconsistent. A deductive argument that fails its own standard is not a weak argument, it is an invalid one.Defined in Deductive and Inductive Support · Logic · Beginner
Defeasibility analysis
The proposal that knowledge is justified true belief for which there exists no true proposition that, had the believer been aware of it, would have destroyed the justification. Such a proposition is a defeater.Defined in Gettier Cases and Post-Gettier Repairs · Epistemology · Intermediate
defeat within a life
The relation that must hold between a horrendous evil and the goods of the life containing it if that life is to be a great good to the person whose life it is. Following Roderick Chisholm's "The Defeat of Good and Evil" in the Proceedings and Addresses of the American Philosophical Association in 1968, a bad thing is balanced off when some separate good outweighs it in a sum, and defeated when it is integrated into a larger whole whose value depends on its presence, so that the whole is better for containing it than it would be without. Adams argues that horrendous evils require defeat within the individual's own life and that balancing off is not enough.Defined in Horrendous Evils and Anti-Theodicy · Theism · Advanced
defeater
Something a person acquires that removes the warrant a belief would otherwise have. A rebutting defeater is evidence that the belief is false. An undercutting defeater does not indicate falsity but removes the connection between the belief and its ground, as learning that the lighting is coloured undercuts a belief about an object's colour without showing the belief wrong. A belief can be properly basic and warranted at one time and lose that status when a defeater is acquired, which is why proper basicality is not immunity.Defined in Reformed Epistemology and Proper Function · Theism · Advanced
Defence
A response to the problem of evil that describes a way in which God's permitting evil could be consistent with God's goodness, without claiming that this is in fact God's reason.Defined in The Problem of Evil · Theism · Intermediate
Definite description
A phrase of the form "the such-and-such", which purports to pick out exactly one thing by describing it rather than by naming it. Definite descriptions behave like names in a sentence, occupying the same positions and appearing to refer, and the question of whether they really are a kind of name is the question this article turns on.Defined in Identity and Definite Descriptions · Logic · Intermediate
Degree of belief
The strength with which a person holds a proposition, understood as admitting of gradations rather than being all or nothing.Defined in Bayesian Confidence and Credence, Introduced · Epistemology · Intermediate
deism
The view that a creator brought the world into being and established its order but does not intervene in it, perform miracles, issue revelations, or respond to prayer. It was the dominant heterodox position of the seventeenth and eighteenth centuries, argued for in John Toland's Christianity Not Mysterious of 1696 and Matthew Tindal's Christianity as Old as the Creation of 1730, both published anonymously, which held that reason establishes everything in religion worth having and that revelation adds nothing.Defined in Philosophy of Religion Beyond Monotheism · Theism · Advanced
Demonstrative argument
An argument whose premises are held to be certain and whose conclusion follows from them necessarily, so that anyone who accepts the premises cannot consistently deny the conclusion.Defined in How Arguments About God Work · Theism · Beginner
Denying the antecedent
The invalid form that takes a conditional and the falsity of its antecedent, and concludes the falsity of its consequent: from $P \rightarrow Q$ and $\neg P$, to $\neg Q$.Defined in Common Formal Fallacies · Logic · Beginner
Deontic logic
The modal treatment of obligation and permission, with the box read as what ought to be the case and the accessibility relation running to the deontically ideal alternatives. The standard system, usually called SDL, is the normal modal logic D, whose characteristic axiom says that what is obligatory is permitted.Defined in Temporal, Deontic, and Epistemic Logic · Logic · Advanced
Deontology
The family of theories on which some actions are right or wrong in virtue of what they are, independent of their consequences. Certain acts are constrained or required whatever the outcomes.Defined in Consequences, Rules, and Character · Ethics · Beginner
Derivation
A finite sequence of formulas in which each member is an axiom, a premise, or follows from earlier members by a rule of the system. The last member is the formula derived. Nothing may be assumed temporarily and nothing is ever discharged, so every line of a derivation is asserted outright and depends on the premises alone.Defined in Axiomatic Systems and the Deduction Theorem · Logic · Intermediate
Descriptive claim
A claim about how things are, were, or will be. It reports, predicts, or explains, and it is assessed by finding out whether the world matches it.Defined in Descriptive and Normative Claims · Ethics · Beginner
Desert
What a person is owed in virtue of something they have done or some way they have been: their effort, their contribution, their conduct, or their character.Defined in What Justice Requires · Political Philosophy · Beginner
Designated value
A truth value counted as success for the purposes of defining validity. An argument is valid when every assignment giving all premises a designated value gives the conclusion one, so the choice of designated values fixes the consequence relation independently of the truth tables.Defined in Many-Valued Logics · Logic · Advanced
Desire
A propositional attitude whose content specifies a way the world is to be made, rather than a way the world is taken to be. Desires motivate action, and they are satisfied or frustrated rather than true or false.Defined in What a Mental State Is · Philosophy of Mind · Beginner
Diagonal lemma
The result that for any formula ψ with one free variable, in a theory capable of representing the recursive functions, there is a sentence φ such that the theory proves φ if and only if it proves ψ applied to the code of φ. Every property expressible in the language has a sentence that ascribes that property to itself.Defined in Gödel's Incompleteness Theorems · Logic · Advanced
Dialetheism
The thesis that some contradictions are true, so that certain sentences are both true and false. Defended principally by Graham Priest, it is a metaphysical position, distinct from the logical thesis of paraconsistency, which concerns only the consequence relation and carries no commitment to any contradiction being true.Defined in Relevance Logic and Paraconsistency · Logic · Advanced
Discharge
The act of closing a subproof and drawing a conclusion that no longer depends on the assumption that opened it. The conclusion is written outside the subproof, and from that point on neither the assumption nor any line inside the subproof may be cited. Every rule that makes an assumption also discharges it, so no assumption is ever left standing at the end of a completed proof.Defined in Natural Deduction · Logic · Intermediate
Disjunction
The truth function written $P \lor Q$ and read "$P$ or $Q$": true when at least one part is true, and false only when both are false.Defined in Statements and Connectives · Logic · Beginner
Disjunctive normal form
A formula that is a disjunction of one or more disjuncts, each of which is a conjunction of one or more literals, where a literal is a sentence letter or the negation of one. Every truth function is expressed by some formula in this form, and the construction below produces one from a truth table directly.Defined in Truth-Functional Completeness · Logic · Intermediate
Disjunctive syllogism
The valid form that takes a disjunction together with the denial of one disjunct and yields the other: from $P \lor Q$ and $\neg P$, infer $Q$.Defined in Basic Inference Rules · Logic · Beginner
Dispositional state
A mental state a subject has without it being currently active: a standing belief or preference the subject would produce or act on given the right occasion, but which is doing nothing at present.Defined in What a Mental State Is · Philosophy of Mind · Beginner
Distributive justice
The question of how the benefits and burdens of social cooperation ought to be allocated among the people who take part in it: who is entitled to what, and on what basis.Defined in Liberty, Equality, and Justice as Three Demands · Political Philosophy · Beginner
Divine command theory
The view that moral obligations are constituted by God's commands, so that an action is obligatory because God commands it and wrong because God forbids it.Defined in Moral Arguments · Theism · Intermediate
divine conceptualism
The view that abstract objects are constituents of the divine mind rather than independent entities: propositions are God's thoughts, properties are God's concepts, and possible worlds are the ways God conceives things might be. Since they are not distinct from God, they do not need to be created, and aseity is preserved without any act of creation being required to explain them.Defined in Aseity and the Bootstrapping Problem · Theism · Advanced
Divine conservation
The action by which God maintains a thing in existence over time, so that the thing would cease to exist at once if the action stopped.Defined in Creation, Conservation, and Providence · Theism · Beginner
Divine freedom
The question whether God can act freely, given that a being who is essentially omnipotent and essentially perfectly good appears to have no alternative but to do the best available thing.Defined in Divine Attributes and Their Tensions · Theism · Intermediate
divine love thesis
The claim that a perfectly loving God would always be open to personal relationship with any finite person capable of such a relationship, so long as that person is not resisting it. The thesis is offered not as an empirical observation about God but as an analysis of what perfect love comes to, drawing on the least controversial features of love as it appears between persons: that a loving parent is available to a child, that unavailability requires justification, and that love which withholds itself without reason is not love.Defined in The Problem of Divine Hiddenness · Theism · Advanced
divine simplicity
The doctrine that God has no parts and no internal composition of any kind. God is not composed of matter and form, of a subject and its properties, of an essence and an existence that instantiates it, or of a genus and a differentia. The consequence usually drawn is the identity thesis: God's attributes are not distinct things God has but are identical with God and therefore with each other. God's goodness is God's power is God's knowledge is God.Defined in Simplicity, Timelessness, and Impassibility · Theism · Advanced
divine timelessness
The doctrine that God has no temporal location, no duration measured in earlier and later, and no succession of states. God does not exist at a time, was not around before the world, and will not still be around afterwards. On the traditional formulation God possesses the whole of his life at once rather than living through it in parts.Defined in Simplicity, Timelessness, and Impassibility · Theism · Advanced
Doctrine of double effect
The principle that an act with a foreseen bad effect may be permissible when the bad effect is not intended, either as an end or as a means, provided the act is otherwise acceptable and the good achieved is proportionate to the harm.Defined in The Trolley Problem as a Diagnostic · Ethics · Beginner
Doing and allowing
The distinction between bringing a harm about and failing to prevent one. It underlies the widely held view that killing is harder to justify than letting die, even when the outcome is the same.Defined in The Trolley Problem as a Diagnostic · Ethics · Beginner
Domain of discourse
The collection of objects that an interpretation of a formula is about, over which its quantifiers range. Every interpretation fixes one, and it is required to be non-empty. A claim that everything is thus and so is a claim about the domain and nothing outside it, so the same formula can be true under one interpretation and false under another purely because the domain has changed.Defined in Predicate Logic · Logic · Intermediate
Doxastic attitude
A stance a person can take toward a claim: believing it, disbelieving it, or suspending judgement about it. Suspension is a genuine third attitude rather than the absence of the first two.Defined in What Justification Is · Epistemology · Beginner
Doxastic basing
The relation between a belief and the reasons the believer actually holds it on. A belief is based on a reason when that reason is what sustains it, as opposed to merely being available to the believer or being a good reason that someone might give.Defined in Foundationalism, Coherentism, Infinitism · Epistemology · Intermediate
Doxastic voluntarism
The view that belief is subject to the will, so that a person can decide to believe a proposition and thereby believe it.Defined in Pragmatic Arguments for Belief · Theism · Intermediate
Dream argument
The argument that since dreaming can be qualitatively indistinguishable from waking, no present experience establishes that one is awake, and so no experience establishes that things are as they appear.Defined in Skepticism, First Encounter · Epistemology · Beginner
Dualism
The view that the mental and the physical are fundamentally different in kind, so that mental phenomena are not reducible to, or identical with, anything physical.Defined in The Mind-Body Problem Stated · Philosophy of Mind · Beginner
Dutch book
A set of bets, each of which an agent regards as fair given their credences, that together guarantee the agent a net loss however the world turns out.Defined in Formal Epistemology: Probabilism and Updating · Epistemology · Advanced
Duty of rescue
The obligation to assist a person in serious and immediate peril where one is in a position to help and the cost or risk to oneself is small.Defined in Rights, Duties, and Going Beyond Duty · Applied Ethics · Beginner

E

Effect
The occurrence brought about: the lighting, the breaking of the window, the fall in emissions.Defined in Causation, First Pass · Metaphysics · Beginner
Elementary equivalence
The relation holding between two structures when exactly the same first-order sentences are true in both. It is implied by isomorphism, since an isomorphism preserves every property expressible in the language, and it does not imply isomorphism, as the results above make plain.Defined in Compactness and Löwenheim-Skolem · Logic · Advanced
Elimination rule
A rule licensing an inference from a formula whose main connective is a given one to a formula in which it no longer appears as the main connective. The rule states what may be drawn from a compound of that kind, and so states what having asserted it commits one to.Defined in Natural Deduction · Logic · Intermediate
Empty domain
A model with no objects at all, excluded by the classical definition of a model and permitted in free logic. In such a model every universally quantified sentence is true and every existentially quantified one is false, and the logic that results is called universally free or inclusive.Defined in Free Logic · Logic · Advanced
Enumerative induction
The simplest inductive form: from the observation that all examined members of a class have a property, to the conclusion that all members do, or that the next one will.Defined in The Problem of Induction · Epistemology · Intermediate
Epistemic access
The relation a believer stands in to a justifying factor when that factor is available to them on reflection, without further investigation of the world.Defined in Internalism versus Externalism · Epistemology · Intermediate
Epistemic closure
The principle that knowledge is preserved under known entailment: if a person knows one proposition and competently deduces a second from it while retaining knowledge of the first, they know the second.Defined in Epistemic Closure and Its Denial · Epistemology · Intermediate
Epistemic injustice
A wrong done to someone specifically in their capacity as a knower. Fricker distinguishes two central forms: testimonial injustice, which occurs in the assessment of what someone says, and hermeneutical injustice, which occurs in the shared resources for making sense of experience.Defined in Epistemic Injustice · Epistemology · Intermediate
Epistemic logic
The modal treatment of knowledge and belief, with the box read as knowing and the accessibility relation running to the worlds an agent cannot distinguish from the actual one. Hintikka's Knowledge and Belief of 1962 is the founding work; knowledge is usually modelled by S4 or S5 and belief by KD45.Defined in Temporal, Deontic, and Epistemic Logic · Logic · Advanced
Epistemic luck
The condition of holding a true belief where the truth is not attributable to the believer's evidence, faculties, or competence. Knowledge is standardly taken to exclude it, though not every kind of luck in the neighbourhood is excluded.Defined in Gettier Cases and Post-Gettier Repairs · Epistemology · Intermediate
Epistemic peer
A person who is your equal with respect to a question: they have the same evidence, and they are as intelligent, careful, and free from bias in assessing it as you are.Defined in Testimony and Disagreement · Epistemology · Intermediate
Epistemic reason
A consideration that bears on whether a claim is true. Evidence, observation, testimony from someone in a position to know, and inference from other things believed are the usual sorts.Defined in What Justification Is · Epistemology · Beginner
Epistemic regress
The chain of supporting reasons generated when each justifying belief is itself asked to be justified, and the demand is repeated on whatever answers it.Defined in The Regress Problem · Epistemology · Beginner
Epistemic standards
The level of epistemic position a subject must meet for a knowledge attribution to count as true in a given context. On contextualist views these standards are set by features of the attributor's conversation, such as which possibilities of error have been mentioned or what depends on getting the answer right.Defined in Contextualism, Invariantism, and Pragmatic Encroachment · Epistemology · Advanced
Epistemic utility
The value of a credal state from a purely epistemic point of view. Epistemic utility theory treats the choice of credences as analogous to a practical decision, with epistemic utility in place of practical utility, and applies the principles of decision theory to determine which credences are rational. In accuracy-first epistemology, epistemic utility is accuracy.Defined in Accuracy-First Epistemology · Epistemology · Advanced
Epistemic value
The kind of value that belongs to cognitive states and achievements in virtue of their relation to cognitive goals such as truth, understanding and knowledge, as opposed to their practical, moral or aesthetic value.Defined in Epistemic Value and the Swamping Problem · Epistemology · Advanced
Epistemicism about vagueness
The theory that vague predicates have sharp boundaries and that vagueness is ignorance of where they lie. Defended by Timothy Williamson in 1994 and by Roy Sorensen, it retains classical logic and bivalence in full and locates the phenomenon in an epistemic principle rather than in semantics.Defined in Vagueness and the Sorites · Logic · Advanced
Epistemological disjunctivism
The view, developed by John McDowell and systematically defended by Duncan Pritchard, that in paradigm cases of perceptual knowledge the subject's rational support for their belief is both factive and reflectively accessible. The support consists in the subject's seeing that p, which entails p and is something the subject can know by reflection that they have.Defined in Epistemological Disjunctivism and the New Evil Demon · Epistemology · Advanced
Equality
The demand that people be treated as of equal standing, or that some benefit or burden be distributed evenly among them, depending on which respect is in question.Defined in Liberty, Equality, and Justice as Three Demands · Political Philosophy · Beginner
Essence
The collection of a thing's essential properties, taken as an answer to the question of what that thing is.Defined in Essence and Accident · Metaphysics · Beginner
Essential property
A property a thing could not have lacked while existing. If having it is necessary for that very thing to be, the property is essential to it.Defined in Essence and Accident · Metaphysics · Beginner
Euthyphro dilemma
The question, put to any view that grounds morality in a divine will, whether something is right because God commands it or God commands it because it is right, with each answer said to be unacceptable.Defined in Moral Arguments · Theism · Intermediate
Evaluative claim
A claim that something is good, bad, better, worse, admirable, or contemptible. It grades rather than instructs.Defined in Descriptive and Normative Claims · Ethics · Beginner
Event
A happening: something that occurs rather than something that persists. The eruption, the meeting, the collision of two cars at a particular time and place.Defined in Candidate Existents · Ontology · Beginner
Evidence as knowledge
Williamson's thesis, often written E = K, that a subject's evidence consists of exactly the propositions the subject knows. Something is part of your evidence if and only if you know it.Defined in Knowledge-First Epistemology and Anti-Luminosity · Epistemology · Advanced
Evidential aggregation
The combination of several independent pieces of evidence into a single verdict, by multiplying their individual Bayes factors together.Defined in Bayesian Natural Theology · Theism · Advanced
evidential atheology
Argument against the existence of God that proceeds by treating some feature of the world as evidence, and claiming that the evidence lowers the probability of theism, rather than by claiming that the feature is logically incompatible with theism. Its conclusion is comparative and defeasible: it says that the evidence counts against theism to some degree, which leaves open that other evidence counts in favour and that the total balance could go either way.Defined in Draper's Argument from Pain and Pleasure · Theism · Advanced
Evidential problem of evil
The argument that the amount, the kinds, and the distribution of suffering, while not logically incompatible with the existence of God, constitute strong evidence against it.Defined in The Problem of Evil · Theism · Intermediate
Evidentialism
The view that a belief is justified only in proportion to the evidence supporting it, so that religious belief is rational only if the available evidence supports it.Defined in Faith and Reason · Theism · Beginner
evolutionary argument against naturalism
Alvin Plantinga's argument that the conjunction of naturalism with the claim that human cognitive faculties arose through unguided evolution gives one no reason to think those faculties are reliable, and that recognising this gives the naturalist a defeater for all of their beliefs. Since the belief in naturalism is among them, the position defeats itself. Plantinga developed it in the final chapter of Warrant and Proper Function (Oxford University Press, 1993) and restated it at length in Where the Conflict Really Lies: Science, Religion, and Naturalism (Oxford University Press, 2011).Defined in The Evolutionary Argument Against Naturalism · Theism · Advanced
Exchange
The structural rule permitting the formulas in a sequent to be reordered. It expresses the assumption that premises form a set or multiset rather than a sequence, and dropping it leaves order significant, which is what a grammar needs.Defined in Substructural Logics · Logic · Advanced
Exchangeability
The property a probability assignment has when the probability of a sequence of outcomes depends only on how many of each kind occur, not on their order. De Finetti's representation theorem of 1937 shows that an exchangeable assignment is a mixture of independent identically distributed ones, so that a subjectivist who treats individuals symmetrically behaves as though estimating an unknown objective chance.Defined in Inductive Logic and the Carnap Programme · Logic · Advanced
Excluded middle
The schema $\varphi \lor \neg \varphi$. Classically valid because every sentence has one of two truth values, it is rejected by intuitionists on the ground that asserting a disjunction requires a method of determining which disjunct holds, and no such method is available in general.Defined in Intuitionistic Logic and Kripke Semantics · Logic · Advanced
Existence
What something has when it is one of the things there are. To say that a thing exists is to say that the world includes it. Whether saying so also describes the thing is a further question, taken up later in this tier.Defined in What 'Exists' Means · Ontology · Beginner
Existence as a predicate
The disputed claim that existing is a property a thing can have or lack, so that it may be included in or omitted from the concept of a thing.Defined in Ontological Arguments · Theism · Intermediate
Existence claim
A sentence asserting that there is at least one thing of a given kind, such as "there are prime numbers greater than a million" or "there is no largest prime".Defined in What 'Exists' Means · Ontology · Beginner
Existence predicate
The expression "exists" understood as a predicate. On the Fregean analysis it is not a first-order predicate at all: "there are horses" is regimented as saying that something is a horse, so "exists" disappears into the quantifier rather than surviving as a predicate of individuals.Defined in Is Existence a Property? · Ontology · Beginner
existential inertia thesis
The claim that things tend to persist in existence on their own, without needing a sustaining cause at each moment. On this view a cause is required to bring a thing into existence and a cause is required to destroy it, but no cause is required for it merely to continue. Persistence is the default, and what calls for explanation is change, not continuation.Defined in Existential Inertia and Divine Conservation · Theism · Advanced
Existential quantifier
The symbol $\exists$, read "for some" or "there is at least one". The formula $\exists x Fx$ is true under an interpretation when at least one object in the domain satisfies $F$, and false when none does. It renders "some", "there is", "at least one", and "a" in its general use.Defined in Predicate Logic · Logic · Intermediate
explanatory power
The extent to which a hypothesis makes the data expected: a hypothesis has high explanatory power with respect to some evidence when, if the hypothesis were true, that evidence is what one would anticipate finding. It is only one virtue among several, and it trades against others. A hypothesis specific enough to make the data highly expected is usually less probable in advance, since it says more and therefore has more ways of being wrong, and the assessment of any explanation requires weighing that trade rather than maximising either side.Defined in Naturalism and Supernaturalism as Frameworks · Theism · Advanced
Explosion
The principle that from $\varphi$ and $\neg \varphi$ any sentence whatever follows, known also by the medieval name ex contradictione quodlibet. It holds in classical and intuitionistic logic alike.Defined in Relevance Logic and Paraconsistency · Logic · Advanced
Externalism
The denial of internalism. On externalist views, what justifies a belief can include facts the believer has no awareness of, such as the reliability of the process that produced it or the believer's causal relation to what the belief is about.Defined in Internalism versus Externalism · Epistemology · Intermediate
Extrinsic property
A property a thing has partly in virtue of how other things are, or how it is related to them. Being the tallest mountain in Wales, being owned by Priya, and being three metres from the door are all extrinsic.Defined in Objects and Properties · Metaphysics · Beginner

F

Factive mental state
A mental state that one can be in with respect to a proposition only if that proposition is true. Seeing that it is raining, remembering that the door was locked, and knowing that the shop is closed are factive: none of them can obtain if the proposition is false. Believing and hoping are not factive.Defined in Knowledge-First Epistemology and Anti-Luminosity · Epistemology · Advanced
Factive reason
A reason whose possession entails the truth of what it supports. Seeing that there is a cup is a factive reason for believing there is a cup, since one cannot see that there is a cup unless there is one. Seeming to see a cup is not factive.Defined in Epistemological Disjunctivism and the New Evil Demon · Epistemology · Advanced
Faith
The attitude a religious believer takes toward what they believe, analysed variously as assent to propositions on the authority of the one who revealed them, as trust in a person, or as practical commitment held beyond what the evidence establishes.Defined in Faith and Reason · Theism · Beginner
Fideism
The position that religious faith does not answer to reason, either because it operates where reason has no jurisdiction or because it has standards internal to religious practice that external assessment cannot apply.Defined in Faith and Reason · Theism · Beginner
Field of events
A collection of subsets of a sample space that contains the whole space and is closed under complement and under finite union. Closure under complement and union guarantees closure under intersection as well, so the collection supports all the Boolean operations. Where the closure requirement is extended to countable unions, the collection is called a sigma-field, and that is the form the measure-theoretic treatment uses.Defined in Probability as an Extension of Logic · Logic · Intermediate
Final value
The value something has for its own sake, as an end rather than as a means. Final value is sometimes called intrinsic value, though the two can come apart: something might be valued for its own sake because of a relational property, such as being the first edition of a book.Defined in Epistemic Value and the Swamping Problem · Epistemology · Advanced
Fine-tuning argument
The argument that the constants and initial conditions of physics fall within extremely narrow ranges compatible with the existence of complex structures, and that this is better explained by design than by chance.Defined in Design and Fine-Tuning Arguments · Theism · Intermediate
Finite additivity
The requirement that for any two events that cannot both occur, the probability of their union is the sum of their probabilities, and by repetition the same for any finite collection of pairwise exclusive events. Kolmogorov's own formulation strengthens this to countable additivity, which extends the requirement to infinite sequences of exclusive events, and the two are not equivalent.Defined in Probability as an Extension of Logic · Logic · Intermediate
First incompleteness theorem
For any consistent, recursively axiomatizable theory that represents enough arithmetic, there is a sentence in its language that the theory neither proves nor refutes. No such theory is complete, and adding the undecided sentence as a new axiom yields a theory to which the theorem applies again.Defined in Gödel's Incompleteness Theorems · Logic · Advanced
First philosophy
Aristotle's own name for the enquiry now called metaphysics: the study of being as such, prior to and more general than the study of any particular kind of being.Defined in What Metaphysics Asks · Metaphysics · Beginner
First-order property
A property of individual things: being blue, having a mass of two kilograms, being a mountain. First-order properties are what objects instantiate.Defined in Is Existence a Property? · Ontology · Beginner
First-person authority
The thesis that a subject's sincere reports about their own mental states carry a special weight, so that they are ordinarily taken as settling the matter without needing support.Defined in Introspection and Its Limits · Philosophy of Mind · Beginner
Fixed-point theory of truth
Kripke's account, on which the truth predicate is interpreted by a pair of sets, its extension and its anti-extension, and the interpretation is grown in stages from the empty pair until it reaches a fixed point, a stage at which adding the sentences now settled adds nothing further. Sentences in neither set at the fixed point receive no truth value.Defined in Undefinability and the Theories of Truth · Logic · Advanced
Formal equality
The requirement that like cases be treated alike: that where two people do not differ in any relevant respect, they be treated the same.Defined in Liberty, Equality, and Justice as Three Demands · Political Philosophy · Beginner
Formal fallacy
An invalid argument form: a pattern of premises and conclusion that fails to guarantee its conclusion no matter what is substituted into it. An argument commits a formal fallacy when it instantiates such a pattern and its arguer takes the pattern to secure the conclusion.Defined in Common Formal Fallacies · Logic · Beginner
Foundationalism
The view that justified beliefs divide into basic beliefs, which are justified without deriving their justification from other beliefs, and non-basic beliefs, which are justified by inference from basic ones. It takes the third horn of the trilemma and denies that stopping is arbitrary.Defined in Foundationalism, Coherentism, Infinitism · Epistemology · Intermediate
Frame
A non-empty set of worlds together with an accessibility relation on that set, written $\langle W, R \rangle$. A frame contains no information about which formulas are true anywhere; it is pure structure, specifying only what points there are and which of them can see which.Defined in Modal Logic: Possible Worlds Semantics · Logic · Intermediate
Frame validity
A formula is valid on a frame when it is true at every world of every model built on that frame, that is, under every assignment of truth values to the atoms. Validity on a frame is therefore a second-order condition, since it quantifies over all subsets of the set of worlds.Defined in Correspondence Theory · Logic · Advanced
Free logic
A predicate logic free of existence assumptions with respect to its singular terms, in which a term may fail to denote and quantifiers range only over what exists. The rule of universal instantiation is restricted, requiring an additional premise asserting that the instantiated term denotes.Defined in Free Logic · Logic · Advanced
Free variable
An occurrence of a variable that is not bound by any quantifier. A formula containing one says nothing determinate, since the variable names nothing; it expresses a condition that objects may or may not satisfy rather than a claim that may be true or false. A formula with no free variables is a sentence, and only sentences have truth values.Defined in Predicate Logic · Logic · Intermediate
Free will defence
The response holding that God's creating agents with genuine freedom is a good sufficient to justify permitting the moral evil those agents choose, and that not even an omnipotent being could create freely choosing agents while guaranteeing what they choose.Defined in Theodicies and Defences · Theism · Intermediate
Function
A relation that assigns to each object in one set exactly one object in another. The set the function takes its inputs from is its domain and the set it delivers values into is its codomain, and the value it assigns to $a$ is written $f(a)$. A function is injective when distinct inputs always receive distinct values, surjective when every object in the codomain is the value of something, and bijective when it is both.Defined in Basic Set Theory for Logicians · Logic · Intermediate
Functional completeness
The property a set of connectives has when every truth function of every number of arguments can be expressed by some well-formed formula built using only connectives from that set. The property concerns expressive power alone and says nothing about convenience: a complete set may require enormous formulas for functions a richer set expresses briefly.Defined in Truth-Functional Completeness · Logic · Intermediate

G

Gaunilo's island
The original parody of the ontological argument: an island than which no greater can be conceived, which by Anselm's reasoning would have to exist, since an existing island is greater than an imaginary one.Defined in Modal Ontological Arguments and Their Parodies · Theism · Advanced
Generality problem
The difficulty that any token belief is produced by a process describable at many levels of generality, each with a different reliability, and that reliabilism must specify the right level without appealing to whether the resulting verdict is the intuitively correct one.Defined in Reliabilism and Virtue Epistemology · Epistemology · Intermediate
Genetic fallacy
The mistake of inferring that a claim is true or false from facts about how the claim came to be believed or proposed.Defined in Natural Explanations of Religious Belief · Theism · Intermediate
Gettier case
A case in which a person holds a belief that is true and justified but that intuitively fails to count as knowledge, because the feature that makes the belief justified is disconnected from the feature that makes it true.Defined in Gettier Cases and Post-Gettier Repairs · Epistemology · Intermediate
God
In the tradition this subject examines, the one personal being that is responsible for the existence of everything else and possesses power, knowledge, and goodness to the maximal degree, existing without depending on anything.Defined in What God Is Claimed to Be · Theism · Beginner
God of the gaps
The strategy of invoking divine action to account for whatever natural science has not yet explained, and, as a term of criticism, the charge that theistic explanation systematically occupies the shrinking territory of current ignorance. The concept was stated by Henry Drummond in the 1890s, criticising those who searched the sciences for unexplained gaps to fill with God, and the phrase is usually credited to Charles Coulson's Science and Christian Belief of 1955. Dietrich Bonhoeffer made the same complaint from a theological direction in the letters written during his imprisonment, arguing that a God found only at the limits of knowledge is a God being pushed steadily out of the world.Defined in Naturalism and Supernaturalism as Frameworks · Theism · Advanced
Gödel numbering
An assignment of distinct natural numbers to the symbols, formulas and finite sequences of formulas of a formal language, computable in both directions, so that syntactic operations on expressions correspond to arithmetical operations on their codes. Under such an assignment a sentence about numbers can be read as a sentence about the language it is written in.Defined in Gödel's Incompleteness Theorems · Logic · Advanced
Gradational accuracy
The idea that credences can be more or less accurate, depending on how close they are to the truth values of the propositions they concern. A credence of 0.9 in a truth is more accurate than a credence of 0.6, and a credence of 0.1 in a falsehood is more accurate than a credence of 0.4.Defined in Accuracy-First Epistemology · Epistemology · Advanced
Gratuitous evil
An instance of suffering that an omnipotent and omniscient being could have prevented without thereby losing some greater good or permitting some equally bad or worse evil.Defined in The Problem of Evil · Theism · Intermediate
Great Pumpkin objection
The charge that if belief in God can be properly basic without argument, so can anything. Plantinga named it after the character in the comic strip Peanuts who awaits the arrival of the Great Pumpkin each Halloween: if the theist may take belief in God as basic, the Great Pumpkin believer may take their belief as basic, and the account gives no way to distinguish them. Generalised, the worry is that a theory of proper basicality with no criterion licenses any belief whatever, which is not a defence of theism but an abandonment of epistemology.Defined in Reformed Epistemology and Proper Function · Theism · Advanced
Great-making property
A property that makes a thing greater than it would be without it, so that a being possessing it is, other things equal, greater than one lacking it.Defined in Ontological Arguments · Theism · Intermediate
Greater good
A good whose existence requires, or is made possible only by, the permitting of some evil, offered as the justifying reason for that evil.Defined in Theodicies and Defences · Theism · Intermediate
Grim Reaper paradox
The Benardete case in which infinitely many reapers are each set to kill a person at their appointed time if the person is still alive, with the appointed times having no earliest, so that the person must die and no reaper can be the one who kills them.Defined in Grim Reaper Paradoxes and Causal Finitism · Theism · Advanced
Groundedness
The property a sentence has when the fixed-point construction settles it at some stage, which happens when its value can be traced back through applications of the truth predicate to sentences not containing that predicate at all. "Snow is white is true" is grounded. The liar is not, and neither is the truth-teller, the sentence saying of itself that it is true.Defined in Undefinability and the Theories of Truth · Logic · Advanced
Grue
A predicate defined by Nelson Goodman in 1955: an object is grue if it is examined before a certain future time $t$ and is green, or is not examined before $t$ and is blue.Defined in Confirmation Theory, Ravens, and Grue · Epistemology · Advanced

H

Hallucination
An experience that is subjectively like perceiving an ordinary object, but in which no such object is being perceived.Defined in Sensation and Perception · Philosophy of Mind · Beginner
Halting problem
The problem of determining, given a procedure and an input, whether that procedure eventually halts on that input. The set of such pairs is recursively enumerable, since one can simply run the procedure and wait, and it is not decidable, so its complement is not recursively enumerable.Defined in Computability, Decidability, and Church's Theorem · Logic · Advanced
Harm
A setback to a being's interests: a change that leaves it worse off in some respect it has a stake in.Defined in Moral Status · Applied Ethics · Beginner
Henkin construction
The method of proving completeness by first enriching the language with new constants and adding, for every existential formula, an axiom saying that if something satisfies it then a specified new constant does. A set so extended has a name for a witness to each of its existential claims, and the model built out of its constants then satisfies the truth lemma at the quantifier cases as well as the others.Defined in Soundness and Completeness Proofs · Logic · Advanced
Henkin semantics
The interpretation on which a model specifies, alongside its domain, a collection of relations for the second-order variables to range over, required to be closed under the operations definable in the language. Second-order logic so interpreted is a two-sorted first-order logic in disguise.Defined in Second-Order and Higher-Order Logic · Logic · Advanced
Hermeneutical injustice
The wrong done when a gap in the collective interpretive resources of a society leaves someone unable to make sense of, or communicate, a significant area of their own experience, and the gap exists because their group has been excluded from the practices that generate shared meanings.Defined in Epistemic Injustice · Epistemology · Intermediate
Hick's pluralistic hypothesis
John Hick's proposal that there is a single ultimate reality, which he calls the Real, that is never encountered as it is in itself, and that the deities and absolutes of the various traditions are the Real as it appears through different historically conditioned human frameworks. The structure is borrowed from Kant: the Real in itself corresponds to the noumenon and the various described divinities to phenomena, so that no tradition's description applies to the Real as it is, and none is thereby refuted by another. Hick set the hypothesis out at length in An Interpretation of Religion in 1989, an expansion of his Gifford Lectures.Defined in Religious Pluralism and Exclusivism · Theism · Advanced
Higher-order vagueness
The vagueness of the boundary between the clear cases and the borderline cases. If there is no sharp line between the bald and the borderline bald, the classification into three categories is itself vague, and the difficulty reappears one level up without limit.Defined in Vagueness and the Sorites · Logic · Advanced
Hilbert system
A proof system with a small number of rules, often only one, and a stock of axioms carrying the weight the rules do not. The label is retrospective and honours the programme in foundations that Hilbert led rather than any single system he published; systems of this shape were standard well before the name attached to them.Defined in Axiomatic Systems and the Deduction Theorem · Logic · Intermediate
Hilbert's hotel argument
The argument that an actual infinite cannot be instantiated in the world, because a collection with infinitely many members would license operations whose results are absurd, such as adding members without increasing the total.Defined in Grim Reaper Paradoxes and Causal Finitism · Theism · Advanced
Hintikka systems
The family of confirmation functions introduced by Jaakko Hintikka in 1966, which assign positive prior probability to the constituents describing which combinations of properties are instantiated, and thereby give universal generalisations positive probability that rises with evidence. They show that the zero result is a consequence of Carnap's particular priors rather than of the probabilistic framework.Defined in Inductive Logic and the Carnap Programme · Logic · Advanced
horrendous evil
Marilyn McCord Adams's category for evils such that a person's participation in them, whether by suffering them or by doing them, gives that person reason at first sight to doubt whether their life could be a great good to them on the whole. The definition is indexed to the individual participant rather than to the world, and it covers agents as well as victims. Adams introduced the category in a 1989 symposium paper and developed it in Horrendous Evils and the Goodness of God (Cornell University Press, 1999).Defined in Horrendous Evils and Anti-Theodicy · Theism · Advanced
Human rights
Rights held by all human beings simply as such, taken to constrain what any state may do to anyone within its power, and asserted in international law and practice independently of any particular legal system's recognition of them.Defined in Rights, Introduced · Political Philosophy · Beginner
Hume's argument against miracles
The argument of Section X of Hume's Enquiry concerning Human Understanding that testimony can never make belief in a miracle reasonable, since the evidence for the law the miracle violates is always stronger than the evidence supporting any report.Defined in Miracles and Hume · Theism · Intermediate
Hume's problem of induction
The problem posed by the argument that inductive inference cannot be justified deductively, since its conclusions do not follow, nor inductively, since that would presuppose what is at issue.Defined in The Problem of Induction · Epistemology · Intermediate
Hyperactive agency detection
The proposed cognitive system that infers the presence of an agent from minimal cues, and that is biased toward over-detection because the costs of the two possible errors are unequal.Defined in Natural Explanations of Religious Belief · Theism · Intermediate
hypothesis of indifference
The hypothesis that neither the nature nor the condition of sentient beings on earth is the result of benevolent or malevolent actions performed by non-human persons. It is not the same as naturalism, and it is deliberately weaker: it does not deny that supernatural beings exist, and it does not deny that they act. It denies only that what happens to sentient creatures here is the product of their caring, one way or the other.Defined in Draper's Argument from Pain and Pleasure · Theism · Advanced
Hypothetical syllogism
The valid form that chains two conditionals sharing a middle term: from $P \rightarrow Q$ and $Q \rightarrow R$, infer $P \rightarrow R$.Defined in Basic Inference Rules · Logic · Beginner
Hypothetico-deductive method
The account of scientific reasoning on which a hypothesis is tested by deducing observable consequences from it, together with auxiliary assumptions, and checking whether they obtain. Evidence confirms a hypothesis if it is a deductive consequence of the hypothesis and the auxiliaries, and disconfirms it if the hypothesis and auxiliaries entail its negation.Defined in Confirmation Theory, Ravens, and Grue · Epistemology · Advanced

I

Identity
The relation each thing bears to itself and to nothing else. To say that a is identical with b is to say that a and b are one thing, not two.Defined in Identity and Individuation · Ontology · Beginner
Identity predicate
The two-place predicate written $=$ and read "is identical to", whose interpretation is fixed in advance rather than varying between interpretations. Where an ordinary predicate applies to whatever objects an interpretation assigns to it, $a = b$ is true exactly when $a$ and $b$ name the same object, on every interpretation without exception. It is conventionally written between its terms rather than in front of them.Defined in Identity and Definite Descriptions · Logic · Intermediate
Immanence
God's being present to and active in every part of the created order, sustaining it from within rather than operating on it from a distance.Defined in Creation, Conservation, and Providence · Theism · Beginner
Immortality of the soul
The view that a person's soul is a distinct thing from the body, capable of existing without it, and continuing after the body's death.Defined in Death and the Afterlife · Theism · Intermediate
Immutability
The doctrine that God cannot undergo change of any kind, since a perfect being could change only for the worse and a being that changes for the better was not perfect before.Defined in Divine Attributes and Their Tensions · Theism · Intermediate
impassibility
The doctrine that God cannot be acted upon by anything outside himself, and in particular cannot be caused to undergo emotional states by what creatures do. An impassible God is not made sorrowful by suffering or gratified by praise. The doctrine is compatible with God's being good and loving, provided love is understood as a settled disposition to will the good of another rather than as a feeling produced in the lover by the beloved.Defined in Simplicity, Timelessness, and Impassibility · Theism · Advanced
Impossible world
A world at which the truth conditions for the connectives do not hold, so that a contradiction may be true, or a classical tautology false. Impossible worlds are used to individuate propositions more finely than sets of possible worlds permit, since any two necessary truths hold at exactly the same possible worlds and are therefore the same proposition on the standard account.Defined in Non-Normal Modal Logics · Logic · Advanced
Imprecise probability
The representation of an epistemic state by a set of probability functions rather than a single one, so that a proposition receives an interval of values rather than a point. Developed systematically by Peter Walley in 1991, it is also known as the theory of lower and upper previsions.Defined in Probability Logic and Uncertain Premises · Logic · Advanced
Incorrigibility
The thesis that a subject cannot be mistaken about their own current mental states, so that a sincere first-person report about them cannot be false.Defined in Introspection and Its Limits · Philosophy of Mind · Beginner
Indicative conditional
A conditional in the indicative mood, whose antecedent is entertained as a live possibility. "If Oswald did not shoot Kennedy, someone else did" is indicative, and it is true, since someone shot him.Defined in Conditionals and the Triviality Results · Logic · Advanced
Individuation
Marking off one thing from another: determining where one individual ends and the next begins, and what makes it the individual it is rather than some other.Defined in Identity and Individuation · Ontology · Beginner
Induction
Inference from premises that do not entail the conclusion but are taken to support it, typically from observed cases to unobserved ones or from a sample to a population.Defined in The Problem of Induction · Epistemology · Intermediate
Inductive logic
The study of the confirmation relation as a formal relation between sentences, with degree of confirmation playing the role that truth preservation plays in deductive logic. Its central task on Carnap's conception is to select the correct confirmation function from among the infinitely many probability measures that meet the formal constraints.Defined in Inductive Logic and the Carnap Programme · Logic · Advanced
Inductive strength
The degree to which true premises would raise the probability of a conclusion without guaranteeing it. Inductive strength comes in degrees: an argument can be strong, moderate, or weak, and adding a premise can move it in either direction.Defined in Deductive and Inductive Support · Logic · Beginner
Inference
The step from premises to conclusion; the relation an argument claims holds between them.Defined in What an Argument Is · Logic · Beginner
inference to the best explanation
The pattern of reasoning on which, given some data, one accepts the hypothesis that would best explain them if true. It is not deductive, since the data are compatible with other hypotheses, and it is not simple enumerative induction, since it can conclude to entities and processes not observed. Gilbert Harman introduced the label in "The Inference to the Best Explanation", in the Philosophical Review in 1965, and Peter Lipton's Inference to the Best Explanation (Routledge, 1991) is the standard extended treatment.Defined in Naturalism and Supernaturalism as Frameworks · Theism · Advanced
Inferential justification
Justification a belief gets from other beliefs. A belief is inferentially justified when what supports it is something else the person believes, which is offered as a reason for it.Defined in The Regress Problem · Epistemology · Beginner
Infinitism
The view that justification requires an infinite and non-repeating series of reasons, and that having such a series available is what justification consists in. It takes the first horn and denies that endless chains fail to justify.Defined in Foundationalism, Coherentism, Infinitism · Epistemology · Intermediate
Informed consent
A person's authorisation of what is to be done to them, given with adequate disclosure of the material facts, with understanding of them, voluntarily, and with the capacity to decide.Defined in Harm, Benefit, and Consent · Applied Ethics · Beginner
Innate knowledge
Knowledge held to be present in the mind prior to any experience, rather than acquired from it. The traditional rationalist doctrine, argued for by Plato and Descartes and revived in altered form by Chomsky.Defined in A Priori and A Posteriori · Epistemology · Intermediate
Instantiation
The relation that holds in the world between a thing and a property it has, in virtue of which a predication is true. Also called exemplification, or having.Defined in Objects and Properties · Metaphysics · Beginner
Instrumental value
The value something has as a means to something else. Money has instrumental value because of what it can buy. A reliable thermometer has instrumental value because it tends to give accurate readings.Defined in Epistemic Value and the Swamping Problem · Epistemology · Advanced
Intellectual virtue
A stable excellence of a cognitive agent. On reliabilist versions this means a faculty that reliably produces truth, such as good eyesight or a sound memory. On responsibilist versions it means an acquired trait of character, such as open-mindedness, intellectual courage, or thoroughness.Defined in Reliabilism and Virtue Epistemology · Epistemology · Intermediate
Intention and foresight
The distinction between the effects an agent aims at, whether as an end or as a means to their end, and the effects the agent expects to result but does not aim at, which are side effects of what they are doing.Defined in Doing, Allowing, and Double Effect · Applied Ethics · Beginner
Interest
A stake in how things go: something a being has when it can be better or worse off, so that the world can go well or badly from its own point of view.Defined in Moral Status · Applied Ethics · Beginner
Internalism
The family of views on which whether a belief is justified is settled entirely by factors internal to the believer, so that two people alike in all internal respects are alike in what they are justified in believing.Defined in Internalism versus Externalism · Epistemology · Intermediate
Interpretation
An assignment of exactly one truth value to each sentence letter of the language. Since the connectives are truth functions, an interpretation fixes a truth value for every well-formed formula, computed from the values of its letters by the rules for the connectives. For a formula containing $n$ distinct letters, there are $2^n$ interpretations that differ on those letters, and these are the rows of its truth table. In propositional logic an interpretation is nothing more than this; in predicate logic, later in the tier, it becomes a considerably richer object.Defined in Semantic and Syntactic Consequence · Logic · Intermediate
Intrinsic property
A property a thing has purely in virtue of how it itself is, independently of what anything else is like. Having a mass of two kilograms, and being spherical, are the standard examples.Defined in Objects and Properties · Metaphysics · Beginner
Introduction rule
A rule licensing a formula whose main connective is a given one, on the basis of formulas that do not contain it. The rule states what has to be established in order to assert a compound of that kind, and so functions as an account of what the connective means in the system.Defined in Natural Deduction · Logic · Intermediate
Introspection
The process by which a subject comes to know about their own current mental states, apparently without observing their own behaviour and without inference from anything else.Defined in Introspection and Its Limits · Philosophy of Mind · Beginner
Intuitionistic logic
The logic obtained from classical logic by rejecting the law of excluded middle and the equivalent principles of double negation elimination and classical reductio, while retaining every other rule of natural deduction. It was formalised by Arend Heyting in 1930, following L. E. J. Brouwer's earlier informal criticism of classical reasoning about infinite totalities.Defined in Intuitionistic Logic and Kripke Semantics · Logic · Advanced
Invariantism
The view that "knows" has a single, context-invariant meaning, so that a knowledge attribution expresses the same proposition whoever utters it and wherever. Invariantists differ over what that proposition requires.Defined in Contextualism, Invariantism, and Pragmatic Encroachment · Epistemology · Advanced

J

Jeffrey updating
A generalisation of conditionalization, due to Richard Jeffrey, for cases in which experience changes one's credence in a proposition without making it certain. If experience shifts one's credence in $E$ to a new value, the new credence in $H$ is the old conditional credences in $H$ weighted by the new credences in $E$ and its negation. Also called Jeffrey conditionalization or probability kinematics.Defined in Formal Epistemology: Probabilism and Updating · Epistemology · Advanced
JTB analysis
The account on which a person knows that something is the case when three conditions hold: the claim is true, the person believes it, and the person is justified in believing it. Knowledge is justified true belief.Defined in The JTB Analysis · Epistemology · Beginner
Justification
The positive standing a doxastic attitude has when it is supported by epistemic reasons of sufficient strength. A justified belief is one the believer is, in this sense, entitled to.Defined in What Justification Is · Epistemology · Beginner

K

Kalam cosmological argument
The argument that whatever begins to exist has a cause, that the universe began to exist, and therefore that the universe has a cause of its beginning.Defined in Cosmological Arguments · Theism · Intermediate
Kant's objection
Kant's claim, directed at the ontological argument, that existence is not a determining property of things: saying that a thing exists adds nothing to the concept of it, and so cannot be one of the features a concept includes.Defined in Is Existence a Property? · Ontology · Beginner
Killing and letting die
The medical case at the centre of the dispute: whether ending a patient's life differs in moral character from withholding treatment that would have preserved it, holding the outcome, the motive, and the patient's wishes fixed.Defined in Doing, Allowing, and Double Effect · Applied Ethics · Beginner
Kleene logic
The three-valued scheme introduced by Stephen Kleene in 1938 for partial recursive predicates, in which the third value represents undefinedness. In the strong scheme a compound is defined whenever its value is settled by the defined parts, so a disjunction with a true disjunct is true even if the other is undefined; in the weak scheme any undefined part makes the whole undefined.Defined in Many-Valued Logics · Logic · Advanced
Knowledge
Belief that has both the required relation to truth and something further that a lucky guess lacks. What that further thing is, is the question the rest of this tier and the next builds toward.Defined in Knowledge, Belief, and Opinion · Epistemology · Beginner
Knowledge norm of assertion
The principle that one must assert that p only if one knows that p. Knowledge is the condition an assertion must meet to be proper, so that asserting what one does not know is a violation of the norm constitutive of assertion, even if the assertion is true or reasonable.Defined in Knowledge-First Epistemology and Anti-Luminosity · Epistemology · Advanced
Knowledge-first epistemology
The programme, associated principally with Timothy Williamson, that takes knowledge as explanatorily fundamental rather than as something to be analysed into belief, truth, justification and further conditions. Other epistemic notions, such as evidence, justification, and the norms of assertion and belief, are explained by reference to knowledge.Defined in Knowledge-First Epistemology and Anti-Luminosity · Epistemology · Advanced
Known entailment
The relation holding when a believer knows one proposition, knows that it entails a second, and is in a position to draw the inference. The qualification matters, since no principle is plausible for entailments the believer has not recognised.Defined in Epistemic Closure and Its Denial · Epistemology · Intermediate
Kolmogorov axioms
The three conditions defining a probability measure, given by Kolmogorov in 1933. Every event receives a non-negative value; the whole sample space receives the value one; and the value of a union of events that cannot occur together is the sum of their separate values. Everything else in the mathematical theory of probability is derived from these three.Defined in Probability as an Extension of Logic · Logic · Intermediate
Kripke model
A frame together with a valuation, which assigns to each atomic formula the set of worlds at which it is true. Written $\langle W, R, V \rangle$, a model contains everything needed to evaluate any formula of the language at any of its worlds, since the valuation settles the atomic cases and the clauses for the connectives and the operators settle the rest.Defined in Modal Logic: Possible Worlds Semantics · Logic · Intermediate

L

Lambek calculus
The substructural system obtained by dropping exchange as well as weakening and contraction, introduced by Joachim Lambek in 1958 for the analysis of syntax. Without exchange the antecedent is a sequence, and implication splits into a leftward and a rightward form according to which side the argument is sought on.Defined in Substructural Logics · Logic · Advanced
Law
A system of general rules issued and enforced by an authority claiming jurisdiction over a territory, which purport to bind those subject to them and which officials apply in deciding disputes.Defined in Law and the Rule of Law · Political Philosophy · Beginner
Law of nature
A true generalisation about how things behave that holds without exception, and that supports claims about what would have happened in circumstances that never arose.Defined in Miracles and Hume · Theism · Intermediate
Legal positivism
The position that what the law is depends on social facts alone, so that a rule's legal validity is determined by its sources and by the practices of officials, not by its moral merits.Defined in Law and the Rule of Law · Political Philosophy · Beginner
Legitimacy
The property a state or government has when its exercise of political power is morally justified, so that its claim to authority is a genuine right rather than a pretension.Defined in Authority and Legitimacy · Political Philosophy · Beginner
Leibniz's law
The principle that if a is identical with b, then everything true of a is true of b. Also called the indiscernibility of identicals.Defined in Change and Identity Over Time · Metaphysics · Beginner
Lewis systems
The five systems S1 to S5 developed by C. I. Lewis and C. H. Langford, axiomatising strict implication, defined as the necessity of the material conditional. S4 and S5 are normal and are the ones in wide use; S1, S2 and S3 are not, and S2 and S3 fail the rule of necessitation in the form normal systems require.Defined in Non-Normal Modal Logics · Logic · Advanced
Liberty right
A right consisting in the absence of a duty: you have a liberty right to do something exactly when you have no duty not to do it.Defined in Rights, Introduced · Political Philosophy · Beginner
Likelihood ratio
The ratio of how expected a body of evidence is on one hypothesis to how expected the same evidence is on a rival, written $P(e|h_1) / P(e|h_2)$.Defined in Bayesian Natural Theology · Theism · Advanced
Lindenbaum's lemma
The result that every consistent set of formulas is a subset of some maximal consistent set. The extension is not unique and no procedure picks out a canonical one, but at least one exists, which is all the completeness proof requires. The result is attributed to Adolf Lindenbaum, who published very little; it reached print through Tarski, who credited it to him in 1930.Defined in Soundness and Completeness Proofs · Logic · Advanced
Linear logic
The logic obtained by dropping weakening and contraction while retaining exchange, introduced by Jean-Yves Girard in 1987. Its formulas are read as resources consumed by use, and each classical connective splits into two: a multiplicative form combining separate resources and an additive form offering a choice between them.Defined in Substructural Logics · Logic · Advanced
Löb's theorem
The result that if Peano arithmetic proves $\Box A \rightarrow A$, then Peano arithmetic proves $A$. A theory can establish a reflection principle for a particular sentence only in the case where the sentence was available anyway, so the reflection principle is never a route to anything new.Defined in Provability Logic and Löb's Theorem · Logic · Advanced
Lockean thesis
The principle, so named by Richard Foley after a remark of John Locke's, that it is rational to believe a proposition if and only if it is rational to have a sufficiently high credence in it.Defined in Lottery, Preface, and the Threshold View of Belief · Epistemology · Advanced
Logic of paradox
The system LP, introduced by Graham Priest in 1979, sharing the strong Kleene tables but designating the third value as well as truth. It is paraconsistent, since a sentence and its negation can both be designated, and it has exactly the classical tautologies.Defined in Many-Valued Logics · Logic · Advanced
Logical constant
An expression held fixed in the definition of consequence, as against the non-logical vocabulary reinterpreted from model to model. The truth functional connectives, the quantifiers and identity are standardly counted logical; predicates, names and function symbols are not.Defined in What Makes a Constant Logical? · Logic · Advanced
Logical omniscience
The consequence of normality that an agent knows every logical truth and every consequence of what they know. It follows from necessitation and distribution together, and it is false of every actual agent.Defined in Temporal, Deontic, and Epistemic Logic · Logic · Advanced
Logical pluralism
The position that there is more than one correct consequence relation. In the version defended by JC Beall and Greg Restall, the generalised definition of validity, that the conclusion holds in every case in which the premises hold, admits several equally admissible specifications of a case, yielding classical, constructive and relevant consequence together.Defined in What Makes a Constant Logical? · Logic · Advanced
Logical possibility
Possibility judged by consistency alone. A claim is logically possible when it involves no contradiction, whatever else may stand in the way of its being true.Defined in Possibility and Necessity, Informally · Metaphysics · Beginner
Logical probability
A degree of confirmation holding between an evidence sentence and a hypothesis in virtue of their logical forms alone, conceived as the inductive analogue of entailment. Rudolf Carnap developed the notion systematically from the 1940s, following earlier work by Keynes and by W. E. Johnson.Defined in Inductive Logic and the Carnap Programme · Logic · Advanced
Logical problem of evil
The claim that the existence of God and the existence of any evil at all are logically inconsistent, so that theism is not merely improbable but impossible.Defined in The Problem of Evil · Theism · Intermediate
Lottery paradox
The paradox, due to Henry Kyburg in 1961, that in a large fair lottery with one winner, it is rational to believe of each ticket that it will lose, yet it is irrational to believe that every ticket will lose, which is known to be false. Given the Lockean thesis and conjunction closure, rational belief must include a known falsehood.Defined in Lottery, Preface, and the Threshold View of Belief · Epistemology · Advanced
Löwenheim-Skolem theorem
A pair of results about the sizes of models. The downward direction says that a satisfiable set of sentences in a countable language has a countable model. The upward direction says that a set with an infinite model has models of every infinite cardinality at least as large as the language. Together they say that no first-order theory with an infinite model controls how large its models are.Defined in Compactness and Löwenheim-Skolem · Logic · Advanced

M

Main connective
The connective in a formula that applies last, so that the rest of the formula falls inside one or another of its parts. Every formula that is not a single letter has exactly one.Defined in Translating English into Symbols · Logic · Beginner
Many-gods objection
The objection that the wager's reasoning applies equally well to any number of mutually incompatible religious hypotheses that promise an infinite reward, so it cannot single out the one its proponent has in mind.Defined in Pragmatic Arguments for Belief · Theism · Intermediate
Material conditional
The truth function written $P \rightarrow Q$: false in the single case where $P$ is true and $Q$ is false, and true in every other case. $P$ is the antecedent and $Q$ the consequent.Defined in Statements and Connectives · Logic · Beginner
Maximal consistent set
A consistent set of formulas that cannot be extended: adding any formula not already in it produces an inconsistent set. Equivalently, a consistent set containing, for every formula of the language, either that formula or its negation. Such a set decides every question the language can pose, and it decides them in a way that turns out to mirror the behaviour of a single interpretation.Defined in Soundness and Completeness Proofs · Logic · Advanced
Maximal greatness
The property of having maximal excellence, understood as omnipotence, omniscience, and moral perfection, in every possible world rather than merely in some.Defined in Ontological Arguments · Theism · Intermediate
meaningful life argument
The central argument for pro-theism, which holds that a range of goods bearing on the significance of human life are available only if God exists: that each person's existence is intended rather than accidental, that suffering is not finally wasted, that moral wrongs are not left permanently unaddressed, that death is not the end of the person, and that each person is known and loved by a being who understands them completely. The argument is not that a godless life is meaningless, which few defend, but that these particular goods are large and that their absence is a large loss.Defined in The Axiology of Theism · Theism · Advanced
Meinongianism
The view, after Alexius Meinong, that there are objects which do not exist, and that such objects genuinely have the properties their descriptions attribute to them.Defined in Existence and Non-Existence · Metaphysics · Beginner
Memory
The retention of information already acquired, and the source of belief when a person believes something because they remember it.Defined in Sources: Perception, Memory, Testimony, Reason · Epistemology · Beginner
Mental state
A condition a subject is in that is characterised in psychological terms: believing something, wanting something, being in pain, attending to something. Mental states are the items a psychological description of a person is made of.Defined in What a Mental State Is · Philosophy of Mind · Beginner
Mentalism
The view that justification supervenes on the believer's mental states, so that any two believers in exactly the same mental states are justified in exactly the same beliefs, whether or not those states are reflectively accessible.Defined in Internalism versus Externalism · Epistemology · Intermediate
mere conservationism
The position that God's causal role in the ordinary course of nature is limited to creating things and keeping them in existence with their powers intact. Given that a creature exists and has the power to do something, its doing it requires no further divine contribution. God sustains the fire; the fire does the burning, unaided. The medieval figure usually named as its representative is Durandus of Saint-Pourçain.Defined in Existential Inertia and Divine Conservation · Theism · Advanced
Merit
Fitness for a particular position or task: the qualities, skills, and capacities that make someone able to do well what the position requires.Defined in What Justice Requires · Political Philosophy · Beginner
Metaethics
The part of ethics that asks about moral claims rather than making them: what they mean, whether they can be true, what would make them true, and how anyone could know. Its output is claims about morality.Defined in What Metaethics Asks · Ethics · Beginner
Metalanguage
The language in which the object language is described. Here it is English supplemented with some notation, including the variables $\varphi$ and $\psi$ that range over formulas of the object language, and the symbols for the consequence relations introduced in the next article. Statements about which strings are wffs, or about what follows from what, are made in the metalanguage; they are not themselves formulas.Defined in Propositional Logic and Well-Formed Formulas · Logic · Intermediate
Metaphysical possibility
Possibility judged by the natures of things: what could have been the case given what the things involved actually are, whether or not the laws of nature or logic alone would have permitted it.Defined in Possibility and Necessity, Informally · Metaphysics · Beginner
Metaphysics
The study of the most general features of reality: what kinds of thing there are, what it is for something to be a thing at all, and how the categories we describe the world with fit together.Defined in What Metaphysics Asks · Metaphysics · Beginner
Method of cases
The practice of testing general moral claims against judgements about particular scenarios, treating a clash between a principle and a confident judgement about a case as evidence against the principle.Defined in Moral Intuitions and What to Do With Them · Ethics · Beginner
methodological naturalism
The working rule that scientific inquiry proceeds by seeking natural causes and does not admit supernatural ones among its candidate explanations. It is a constraint on method rather than a claim about what exists, and it is compatible with the truth of theism: a theist can hold that God created a law-governed order and that investigating that order means looking for its regularities rather than invoking its author. Metaphysical naturalism, by contrast, is the substantive claim that there is nothing beyond nature.Defined in Naturalism and Supernaturalism as Frameworks · Theism · Advanced
middle knowledge
God's knowledge of what any possible free creature would freely do in any possible set of circumstances. It is called middle because it falls between two other kinds. Natural knowledge is of necessary truths and of everything that could possibly happen, and God has it independently of any decision. Free knowledge is of what actually happens, and God has it as a consequence of deciding which world to make actual. Middle knowledge is of contingent truths that God does not decide, known prior to the creative decision and therefore available as input to it.Defined in Divine Foreknowledge and Freedom · Theism · Advanced
Mind-body problem
The problem of saying how mental states and processes are related to physical states and processes, and in particular to the body and the brain.Defined in The Mind-Body Problem Stated · Philosophy of Mind · Beginner
Miracle
An event that exceeds what nature can produce, brought about by the action of God, and standardly characterised as a violation of a law of nature by a divine volition.Defined in Miracles and Hume · Theism · Intermediate
modal collapse objection
The argument that divine simplicity entails that everything that exists exists necessarily. If God's act of creating is identical with God's essence, and God's essence exists of absolute necessity, then God's act of creating is absolutely necessary, and so is everything that act produces. The consequence is that God could not have refrained from creating this world, that no contingency survives anywhere, and that divine freedom is lost.Defined in Simplicity, Timelessness, and Impassibility · Theism · Advanced
Modal ontological argument
An argument that proceeds from the premise that a necessarily existing perfect being is possible to the conclusion that such a being actually exists, using the principle that what is possibly necessary is necessary.Defined in Ontological Arguments · Theism · Intermediate
Modality
The general topic of possibility and necessity, and of the related notions of impossibility and contingency. A modal claim is one that says how a thing is rather than merely that it is.Defined in Possibility and Necessity, Informally · Metaphysics · Beginner
Model
An interpretation on which a given formula, or every member of a given set of formulas, comes out true. A set of formulas that has at least one model is satisfiable, and one with no model is unsatisfiable. The word carries the same sense in the phrase model theory: the models of a set of sentences are the situations in which those sentences hold.Defined in Semantic and Syntactic Consequence · Logic · Intermediate
Model-theoretic consequence
The relation holding between a set of sentences and a sentence when every model of the set is a model of the sentence. Tarski's 1936 paper proposed this as the analysis of following from, replacing the proof-theoretic conception on which consequence is derivability in a system.Defined in What Makes a Constant Logical? · Logic · Advanced
Modus ponens
The valid form that takes a conditional together with its antecedent and yields its consequent: from $P \rightarrow Q$ and $P$, infer $Q$.Defined in Basic Inference Rules · Logic · Beginner
Modus tollens
The valid form that takes a conditional together with the denial of its consequent and yields the denial of its antecedent: from $P \rightarrow Q$ and $\neg Q$, infer $\neg P$.Defined in Basic Inference Rules · Logic · Beginner
Molinism
The account of providence built on middle knowledge, developed by Luis de Molina in the Concordia of 1588. God knows the complete set of counterfactuals of freedom, and with that knowledge chooses which total situation to actualise. What creatures then freely do is not caused by God, but God knew it before deciding, because God knew what they would do in whatever circumstances he might set up. Providence is exercised through the choice of circumstances rather than through the determination of acts, which is why Molinists claim to combine full divine control over history with libertarian freedom for creatures.Defined in Divine Foreknowledge and Freedom · Theism · Advanced
Monism
The view that reality is composed of one fundamental kind of thing, so that mental and physical phenomena are not two basic categories but aspects, arrangements, or instances of a single category.Defined in The Mind-Body Problem Stated · Philosophy of Mind · Beginner
Monopoly on force
The state's claimed exclusive right to authorise the use of physical force within its territory, such that any private use of force is permitted only on terms the state sets.Defined in What a State Is For · Political Philosophy · Beginner
Monotonicity
The requirement that a formula true at a stage remains true at every later stage. Imposed on atoms as a condition on models, it is provable for all formulas, and it encodes the thought that what has been established is not later lost.Defined in Intuitionistic Logic and Kripke Semantics · Logic · Advanced
Moral agent
A being capable of recognising moral reasons and acting on them, and so capable of being held responsible for what it does.Defined in Moral Status · Applied Ethics · Beginner
Moral argument
An argument from the existence or the character of moral facts to the existence of God, in either a theoretical form claiming God is the best explanation of those facts or a practical form claiming that moral commitment rationally requires belief in God.Defined in Moral Arguments · Theism · Intermediate
Moral epistemology
The study of how moral claims could be known or justified, and what the sources of moral knowledge are.Defined in What Metaethics Asks · Ethics · Beginner
Moral evil
Suffering or wrongdoing brought about by the free choices of responsible agents.Defined in The Problem of Evil · Theism · Intermediate
moral insensitivity objection
The charge that constructing justifications for suffering damages the moral perception of the person who constructs them. Someone practised at explaining why a given atrocity was permitted for the sake of a greater good has acquired a habit of looking at other people's worst experiences as instrumental, and that habit is held to be corrupting whether or not the explanations are true. The objection is directed at theodicy as an activity rather than at any particular theodicy's content.Defined in Horrendous Evils and Anti-Theodicy · Theism · Advanced
Moral intuition
A moral judgement about a case or principle that strikes a person as correct without being inferred from anything else. It is how the case seems on considering it, prior to any theory.Defined in Moral Intuitions and What to Do With Them · Ethics · Beginner
Moral metaphysics
The study of what would have to exist for moral claims to be true, and whether it does: whether there are moral properties and facts, and what sort of thing they could be.Defined in What Metaethics Asks · Ethics · Beginner
Moral obligation
A requirement to act that binds an agent whether or not the agent accepts it and whether or not acting on it serves the agent's interests.Defined in Moral Arguments · Theism · Intermediate
moral paralysis objection
The objection that skeptical theism, if accepted, undermines the reasoning by which we decide what to do. If I cannot tell whether preventing some suffering would forfeit a greater good beyond my grasp, then I cannot tell whether preventing it is the right thing to do, and the same doubt attends every action whose justification runs through its consequences. Michael Almeida and Graham Oppy pressed the objection in "Sceptical Theism and Evidential Arguments from Evil" in the Australasian Journal of Philosophy in 2003.Defined in Skeptical Theism and Its Costs · Theism · Advanced
Moral patient
A being that can be wronged, and to which duties are therefore owed, whether or not it is itself capable of having duties.Defined in Moral Status · Applied Ethics · Beginner
Moral principle
A general normative claim of the form that actions with some feature are right, wrong, or required, in virtue of having it. Principles are the components a theory is assembled from.Defined in What a Moral Theory Is · Ethics · Beginner
Moral semantics
The study of what moral claims mean and what kind of speech act is performed in making them: whether they state facts, express attitudes, issue prescriptions, or do something else.Defined in What Metaethics Asks · Ethics · Beginner
Moral status
The property a thing has when it matters morally for its own sake, so that there are reasons to treat it in some ways rather than others which are grounded in what it is or what things are like for it, rather than in anyone else's interests.Defined in Moral Status · Applied Ethics · Beginner
Moral theory
A systematic account of what makes actions right or wrong, stated generally enough to deliver verdicts on cases it was not built from.Defined in What a Moral Theory Is · Ethics · Beginner
Morley's theorem
The result that a countable first-order theory categorical in one uncountable cardinality is categorical in every uncountable cardinality. Proved by Michael Morley in 1965, it establishes that uncountable categoricity is a single property rather than a family of properties indexed by cardinals.Defined in Model Theory: Types, Quantifier Elimination, Categoricity · Logic · Advanced
Motivating reason
The consideration a person actually acts on, whatever its merits. It is the answer to why they did it, in the sense that identifies what they were going for.Defined in Reasons, Oughts, and Normative Force · Ethics · Beginner
Multiverse hypothesis
The hypothesis that our universe is one member of a very large or infinite ensemble of universes in which constants and initial conditions vary.Defined in Design and Fine-Tuning Arguments · Theism · Intermediate
Mystical experience
An experience characterised by a sense of unity, understood either as unity perceived in and through the world of ordinary objects or as unity found by emptying the mind of ordinary content, and typically reported as beyond adequate expression while carrying a conviction of insight.Defined in Religious Experience · Theism · Intermediate

N

Natural deduction
A proof system with no axioms, in which every step is licensed by a rule, and in which formulas may be assumed temporarily for the sake of argument and later set aside. The name records the design goal: the rules were chosen to match the moves that mathematical arguments actually make, rather than to minimise the number of primitives.Defined in Natural Deduction · Logic · Intermediate
Natural evil
Suffering brought about by the operation of the natural world, with no responsible agent choosing it.Defined in The Problem of Evil · Theism · Intermediate
Natural law theory
The position that law is connected to morality by more than accident, so that moral standards enter into what makes a rule a law at all rather than merely into whether it is a good law.Defined in Law and the Rule of Law · Political Philosophy · Beginner
Natural rights
Rights held in virtue of what a person is rather than in virtue of any law, agreement, or institution, and therefore held by people whether or not any legal system recognises them.Defined in Rights, Introduced · Political Philosophy · Beginner
Natural theology
The project of investigating claims about God using the faculties natural to human beings, principally reason, perception, and reflection, without appeal to revelation.Defined in Faith and Reason · Theism · Beginner
naturalism
The view that the natural world is all there is: there are no supernatural entities, no minds or agents that exist independently of physical processes, and no explanations that appeal to purposes outside those had by natural organisms. Stating it precisely is harder than it looks, because "natural" is usually explained as "of the kind studied by the natural sciences", which makes the thesis hostage to whatever the sciences turn out to study, and because a science that discovered an intelligent cosmic agent would presumably make that agent natural by definition.Defined in Naturalism and Supernaturalism as Frameworks · Theism · Advanced
Necessary and sufficient conditions
A condition is necessary for something when that thing cannot hold without it, and sufficient when its holding is enough. A set of conditions that are individually necessary and jointly sufficient picks out exactly the cases in question, admitting no others and excluding none.Defined in The JTB Analysis · Epistemology · Beginner
Necessary being
A being that could not have failed to exist, whose existing is explained by what it is rather than by anything outside it.Defined in Cosmological Arguments · Theism · Intermediate
Necessary condition
A condition without which something cannot occur. Oxygen is a necessary condition for the match to light: no oxygen, no lighting.Defined in Causation, First Pass · Metaphysics · Beginner
Necessity
The status of being unable to fail to be the case. A claim is necessary when there is no way for it to be false.Defined in Possibility and Necessity, Informally · Metaphysics · Beginner
Necessity of identity
The thesis that if $a$ and $b$ are identical, then necessarily they are identical: $a = b \rightarrow \Box\, a = b$. It follows from the reflexivity of identity, Leibniz's law and necessitation, and is therefore available in any quantified modal system retaining all three.Defined in Quantified Modal Logic and the Barcan Formulas · Logic · Advanced
Necessity operator
The one-place operator written $\Box$ and read "it is necessary that" or "necessarily", which attaches to a formula to make a longer formula. Where $\varphi$ is a well-formed formula, so is $\Box \varphi$, and the operator may be applied repeatedly and may occur inside the scope of connectives and quantifiers exactly as negation does.Defined in Modal Logic: Possible Worlds Semantics · Logic · Intermediate
Need
What a person requires in order to reach some threshold of functioning or well-being, independently of what they have done or what they can do.Defined in What Justice Requires · Political Philosophy · Beginner
Negation
The truth function written $\neg P$ and read "not $P$": true when $P$ is false, and false when $P$ is true.Defined in Statements and Connectives · Logic · Beginner
Negative duty
A duty not to do something to someone: an obligation discharged by refraining, which every person can satisfy toward every other person at the same time.Defined in Rights, Duties, and Going Beyond Duty · Applied Ethics · Beginner
Negative liberty
Freedom understood as the absence of interference: a person is free to the extent that no one else prevents them from doing what they might otherwise do.Defined in Liberty, Equality, and Justice as Three Demands · Political Philosophy · Beginner
Negative rights
Rights whose corresponding duty is a duty of restraint: that others not do something to the right-holder.Defined in Rights, Introduced · Political Philosophy · Beginner
Neighbourhood semantics
An interpretation assigning to each world a collection of sets of worlds, its neighbourhoods, with $\Box \varphi$ true at a world when the set of worlds satisfying $\varphi$ is one of that world's neighbourhoods. Introduced independently by Dana Scott and Richard Montague in 1970, it is also called Scott-Montague semantics.Defined in Non-Normal Modal Logics · Logic · Advanced
neo-classical theism
Charles Hartshorne's position, on which God has two aspects rather than one. In his abstract essence God is unchanging, necessary, and perfect in the classical way; in his concrete states God is affected by the world, grows in knowledge as events occur, and is enriched by what creatures do. The view is also called dipolar theism, and it is a form of panentheism, since the world is included in God through God's knowledge and love of it without being identical with God.Defined in Classical Theism Against Theistic Personalism · Theism · Advanced
New evil demon problem
The objection, due to Keith Lehrer and Stewart Cohen in 1983 and developed by Cohen in 1984, that externalist theories of justification give the wrong verdict about a subject who is internally identical to a normal perceiver but systematically deceived by a demon. The deceived subject seems just as justified as the normal one, but their belief-forming processes are unreliable, so reliabilism says they are not justified.Defined in Epistemological Disjunctivism and the New Evil Demon · Epistemology · Advanced
New riddle of induction
Goodman's problem of explaining why some predicates, such as green, support inductive generalisation from observed instances while others, such as grue, do not, when the observed instances fit both equally well.Defined in Confirmation Theory, Ravens, and Grue · Epistemology · Advanced
No false lemmas
The proposal that knowledge is justified true belief whose justification does not essentially depend on any false proposition. Smith fails the condition because his reasoning passes through the falsehood that Jones will get the job.Defined in Gettier Cases and Post-Gettier Repairs · Epistemology · Intermediate
no-best-world problem
The difficulty that arises if, for every world an omnipotent being could create, there is a better one that could have been created instead. The series of possible worlds would then be unbounded above, with no maximum, in the way the natural numbers are unbounded. Since perfect goodness is normally understood as requiring that one do the best one can, and there would be no best to do, either the standard for perfect goodness cannot be met or that standard is not the right one.Defined in The No-Best-World Problem · Theism · Advanced
Non-normal world
A world of a relational model at which $\Box \varphi$ is stipulated false for every $\varphi$, and correspondingly $\Diamond \varphi$ true for every $\varphi$, regardless of the accessibility relation. Validity is defined as truth at every normal world of every model, so a formula can fail to be valid by failing at a normal world that accesses a non-normal one.Defined in Non-Normal Modal Logics · Logic · Advanced
Nonexistent object
An object that has properties and can be referred to, described, and distinguished from other objects, while not being among the things that exist.Defined in Existence and Non-Existence · Metaphysics · Beginner
nonresistant nonbelief
Nonbelief in God that is not the result of the person's own resistance to relationship with God. It covers the lifelong seeker who investigates in good faith and finds nothing; the former believer who loses belief while wishing it were otherwise; the person raised in a tradition with no concept of the God in question; and anyone who would welcome the relationship if they took it to be available. Schellenberg's argument is stated in terms of this category rather than in terms of reasonable or justified nonbelief, in order to avoid disputes about the standards for rational belief.Defined in The Problem of Divine Hiddenness · Theism · Advanced
Nonstandard element
An element of a nonstandard model larger than the interpretation of every numeral. Such an element is not the value of any closed term of the language, and the model also contains the images of all the numerals, called its standard part.Defined in Nonstandard Models of Arithmetic · Logic · Advanced
Nonstandard model
A model of the first-order theory of the natural numbers that is not isomorphic to the natural numbers. Every such model satisfies exactly the same first-order sentences as the standard one, so no sentence of the language distinguishes it, and it is nonetheless a different structure.Defined in Nonstandard Models of Arithmetic · Logic · Advanced
nontheistic religion
A religious tradition that does not affirm a creator God and whose central claims are not about one. Theravada Buddhism analyses the human situation and prescribes a path without positing a creator, and treats the question as one that does not conduce to liberation. Jainism has no creator and holds the universe to be eternal. Within Indian philosophy, the Mimamsa school developed an elaborate defence of scriptural authority while arguing against the existence of a creator. The category is not a curiosity: it covers a substantial fraction of the world's religious life.Defined in Philosophy of Religion Beyond Monotheism · Theism · Advanced
Normal modal logic
A set of formulas containing every propositional tautology and every instance of the distribution schema, closed under modus ponens, closed under uniform substitution, and closed under the rule of necessitation, which permits inferring $\Box \varphi$ from $\varphi$ whenever $\varphi$ has itself been proved. Every system in this article is normal, and systems failing one of these conditions, which do exist and have uses, are treated in the advanced tier.Defined in The Normal Systems K, D, T, B, S4, S5 · Logic · Intermediate
Normative claim
A claim about how things ought to be, or about what someone has reason to do. It does not report the world; it says something about what the world calls for.Defined in Descriptive and Normative Claims · Ethics · Beginner
Normative ethics
The part of ethics that asks which actions are right, which things are good, and what makes them so. Its output is claims about conduct.Defined in What Metaethics Asks · Ethics · Beginner
Normative reason
A consideration that counts in favour of some action or attitude. It is a reason there is, whether or not anyone has noticed it, and whether or not it moves anyone.Defined in Reasons, Oughts, and Normative Force · Ethics · Beginner
Normative theory
A general account of what makes actions right or wrong, or of what a good life or a good character consists in, offered as the standard against which particular judgements are to be assessed.Defined in From Theory to Cases · Applied Ethics · Beginner
Normativity
The general feature shared by reasons, oughts, values, and standards: the property of favouring, requiring, or grading rather than merely describing.Defined in Reasons, Oughts, and Normative Force · Ethics · Beginner
noseeum inference
Wykstra's label, introduced in his 1996 essay "Rowe's Noseeum Arguments from Evil", for an inference from "so far as I can tell, there is no such thing" to "there is no such thing". Such inferences are ordinary and often good, but their strength depends entirely on a background assumption about detectability: that if the thing existed, one would probably have noticed. Where that assumption fails, the inference carries no weight at all.Defined in The Probabilistic Problem of Evil · Theism · Advanced
Number
A mathematical object such as 7 or π, if there are such objects: the sort of thing numerals appear to name and mathematical statements appear to be about.Defined in Candidate Existents · Ontology · Beginner
Numerical identity
The relation a thing bears to itself and to nothing else. Two names or descriptions pick out numerically identical things when there is one thing there, not two.Defined in Change and Identity Over Time · Metaphysics · Beginner

O

O-minimality
The property a structure with a linear order has when every definable subset of its universe is a finite union of points and open intervals with endpoints in the structure. Definable sets in one variable are as simple as the order permits, and by a theorem of Pillay and Steinhorn the property transfers to every structure elementarily equivalent to the given one.Defined in Model Theory: Types, Quantifier Elimination, Categoricity · Logic · Advanced
Object
A thing that has properties without being a property of anything else: the mug, the mountain, the electron, arguably the number nine. Also called a particular, an individual, or in the older vocabulary a substance.Defined in Objects and Properties · Metaphysics · Beginner
Object language
The language being studied. In propositional logic it contains exactly the sentence letters, the five connectives, and the parentheses, and nothing else. Its expressions are the wffs.Defined in Propositional Logic and Well-Formed Formulas · Logic · Intermediate
occasionalism
The position that creatures have no causal power whatever, and that what look like natural causes are only the occasions on which God produces the effects directly. The fire does not heat the water; God heats the water when the fire is present, and does so with such regularity that we mistake the pattern for a power. On this account there is exactly one cause in the universe.Defined in Existential Inertia and Divine Conservation · Theism · Advanced
Occurrent state
A mental state that is currently active in the subject: a thought being entertained, a pain being felt, a desire currently operating on behaviour.Defined in What a Mental State Is · Philosophy of Mind · Beginner
Ockhamism
The response that denies the second premise, holding that God's past beliefs about the future are not accidentally necessary because they are not really facts about the past alone. A hard fact about a time is one whose obtaining is settled by how things are at that time. A soft fact about a time is one that is partly about later times, as it was a fact in 1900 that a war would begin fourteen years later. Ockhamists argue that God's believing in 1000 that you would have coffee tomorrow is a soft fact about the year 1000, since its obtaining depends on what happens tomorrow, and soft facts about the past carry no accidental necessity.Defined in Divine Foreknowledge and Freedom · Theism · Advanced
Old evidence problem
The difficulty that evidence already known has probability one, so that conditioning on it cannot change any hypothesis's probability, even when that evidence is what convinced everyone in the first place.Defined in Bayesian Natural Theology · Theism · Advanced
Omnibenevolence
Perfect goodness: moral excellence that could not be surpassed, in what God wants, what God is like, and what God does.Defined in What God Is Claimed to Be · Theism · Beginner
Omnipotence
Maximal power: the property of a being whose power could not be exceeded by any other being.Defined in What God Is Claimed to Be · Theism · Beginner
Omnipresence
The property of being present everywhere, ascribed to God despite God's being immaterial and therefore not the kind of thing that occupies a region.Defined in Divine Attributes and Their Tensions · Theism · Intermediate
Omniscience
Maximal knowledge: for every proposition, if it is true then God knows it, and God believes nothing false.Defined in What God Is Claimed to Be · Theism · Beginner
Ontological argument
An argument from the concept or definition of God alone, without appeal to any observation, to the conclusion that God exists.Defined in Ontological Arguments · Theism · Intermediate
Ontological commitment
What a theory must say exists for its claims to be true. A theory is committed to entities of a kind when there is no way for what it asserts to be true unless there are entities of that kind.Defined in Ontological Commitment, Informally · Ontology · Beginner
Ontological inventory
The complete list of what a theory says there is: every kind of entity that has to be on the list for the theory's claims to come out true.Defined in Ontological Commitment, Informally · Ontology · Beginner
Ontology
The study of what there is: which things exist, what kinds they divide into, and what would settle a disagreement about existence when one arises.Defined in What 'Exists' Means · Ontology · Beginner
open theism
The view that the future is genuinely open, so that propositions about what free creatures will do are not yet true, and God therefore does not know them. God is held to know everything that is true, including every possibility and every probability, and to be unsurpassably wise in responding to what happens. What is denied is not omniscience but that infallible knowledge of future free acts is among the things omniscience covers, since there is nothing there to know.Defined in Divine Foreknowledge and Freedom · Theism · Advanced
Opinion
A belief held on grounds the holder does not regard as settling the matter, and about which reasonable disagreement is expected.Defined in Knowledge, Belief, and Opinion · Epistemology · Beginner
Other minds problem
The problem of saying what entitles anyone to believe that beings other than themselves have mental states, given that only behaviour and physical constitution are observable and mental states themselves are not.Defined in The Problem of Other Minds · Philosophy of Mind · Beginner
Ought
The word marking what a person is required or recommended to do. An ought-claim directs action, where an evaluative claim only ranks.Defined in Descriptive and Normative Claims · Ethics · Beginner
Outer domain
A second domain of a model, disjoint from or containing the domain of quantification, providing denotations for terms that do not denote anything existing. Quantifiers range over the inner domain only, while a predicate may hold of an object in the outer one, which is how a positive free logic makes a sentence about Pegasus true.Defined in Free Logic · Logic · Advanced
Overspill
The principle that a formula holding of every standard element of a nonstandard model holds of some nonstandard element. It follows because the set of elements satisfying the formula, if it contained exactly the standard elements, would give a definable set with no least element among the elements failing the formula, contradicting the least number principle that the model satisfies.Defined in Nonstandard Models of Arithmetic · Logic · Advanced

P

panentheism
The view that the world is contained within the divine, which is nonetheless more than the world. It is positioned deliberately between classical theism, which places God wholly outside the world, and pantheism, which identifies them, and it aims to keep divine immanence without surrendering transcendence. The most developed versions are the process theologies descending from Charles Hartshorne, on which God has two aspects: an abstract, unchanging character and a concrete, changing life that includes and is affected by what happens in the world.Defined in Philosophy of Religion Beyond Monotheism · Theism · Advanced
pantheism
The view that the divine is identical with the totality of what exists, so that there is no God distinct from the universe and no universe distinct from God. Spinoza's Ethics of 1677 is the canonical philosophical statement, and his formula Deus sive Natura, God or Nature, marks the identification. Pantheism is not the claim that nature is worthy of reverence, which an atheist may accept; it is the claim that the totality has a unity and a status that make the religious vocabulary appropriate to it.Defined in Philosophy of Religion Beyond Monotheism · Theism · Advanced
Paraconsistent logic
A logic whose consequence relation is not explosive, so that a theory may contain a contradiction without containing every sentence. Relevance logics are paraconsistent, and so are systems reached by other routes, including da Costa's C systems, Priest's logic of paradox and the discussive logic of Jaśkowski.Defined in Relevance Logic and Paraconsistency · Logic · Advanced
Paradox of the stone
The puzzle asking whether an omnipotent being can create a stone too heavy for it to lift, on the ground that either answer seems to identify something the being cannot do.Defined in Divine Attributes and Their Tensions · Theism · Intermediate
Paraphrase
A rewriting of a claim, intended to preserve what it says while removing an apparent commitment. A paraphrase succeeds when the rewritten version says what the original said and requires less.Defined in Ontological Commitment, Informally · Ontology · Beginner
Parody argument
An argument constructed to share the form of a target argument while reaching a conclusion its proponents reject, offered as evidence that the form is defective or that its premises are not as acceptable as they seem.Defined in Modal Ontological Arguments and Their Parodies · Theism · Advanced
Particular
A thing that is not repeatable: it is here rather than there, and it cannot be wholly present in two places at once. This mug, this mountain, and this electron are particulars.Defined in Candidate Existents · Ontology · Beginner
Pascal's wager
The argument that because the reward attached to belief in God is infinite and the cost is finite, wagering for God maximises expected value whatever the probability of theism, provided that probability is not zero.Defined in Pragmatic Arguments for Belief · Theism · Intermediate
Paternalism
Interference with a person's choices or liberty, without their consent, justified by the claim that it will protect them from harm or make them better off.Defined in Harm, Benefit, and Consent · Applied Ethics · Beginner
Peirce arrow
The binary connective false on every row except the one where both arguments are false, written $P \downarrow Q$ and read "neither". It is the negation of disjunction and is often called NOR. Like the Sheffer stroke, it is adequate on its own.Defined in The Sixteen Binary Connectives · Logic · Intermediate
Penumbral connection
A logical relation holding among borderline cases regardless of how the vagueness is resolved. If one man has strictly less hair than another, the sentence saying that the first is bald if the second is comes out true even when both are borderline, because every admissible precisification respects the ordering.Defined in Vagueness and the Sorites · Logic · Advanced
Perception
The uptake of information about the environment through the senses. Perceptual beliefs are those formed directly on the basis of how things look, sound, feel, taste, or smell.Defined in Sources: Perception, Memory, Testimony, Reason · Epistemology · Beginner
Perceptual experience
The conscious episode a subject undergoes when they perceive, or seem to perceive, their surroundings: how things look, sound, or feel to them on an occasion.Defined in Sensation and Perception · Philosophy of Mind · Beginner
Perfect being theology
The method of determining God's attributes a priori, by identifying God as the greatest possible being and then working out which properties such a being would have.Defined in Divine Attributes and Their Tensions · Theism · Intermediate
Permissibility
The status of an action that may be performed without doing anything wrong, whether or not it must be performed.Defined in What a Moral Theory Is · Ethics · Beginner
Permutation invariance
The criterion on which an expression is logical when its semantic value is unchanged by every permutation of the domain of a model. Suggested by Tarski in a 1966 lecture published posthumously in 1986 and developed by Gila Sher, it derives from Felix Klein's Erlangen programme, which characterised geometries by the transformations their notions are invariant under.Defined in What Makes a Constant Logical? · Logic · Advanced
Persistence
Existing at more than one time. A thing persists when it is there at an earlier time and there at a later one, and it is numerically the same thing on both occasions.Defined in Change and Identity Over Time · Metaphysics · Beginner
Personal autonomy
A person's capacity to govern themselves: to decide, on the basis of their own values and reasoning, how they will act and what shape their life will take.Defined in Harm, Benefit, and Consent · Applied Ethics · Beginner
Personal God
A God that has a mind: beliefs, intentions, and purposes, and the capacity to act for reasons and to stand in relationships with created persons.Defined in What God Is Claimed to Be · Theism · Beginner
Personal identity after death
The problem of specifying what would make a person existing after death the same person as one who died, rather than a duplicate, a successor, or something merely very like them.Defined in Death and the Afterlife · Theism · Intermediate
Phenomenal consciousness
The property a mental state has when there is something it is like to be in it: the experiential or felt character of the state, as distinct from anything it does.Defined in Consciousness Versus Cognition · Philosophy of Mind · Beginner
Physicalism
The view that everything is physical: that the world contains nothing over and above what a completed physics would describe, so that mental states and processes are either identical with physical ones or wholly fixed by them.Defined in The Mind-Body Problem Stated · Philosophy of Mind · Beginner
Political authority
The right to rule: the right to issue directives that are binding on those subject to them, and to enforce those directives, in a way that the directives of a private person are not.Defined in Authority and Legitimacy · Political Philosophy · Beginner
Political obligation
The moral duty of a person subject to a political authority to obey its directives, held in virtue of their relationship to it rather than in virtue of the content of any particular directive.Defined in Authority and Legitimacy · Political Philosophy · Beginner
polytheism
The view that there are several or many divine beings, none of which possesses every perfection and none of which is the sole ultimate. It is not merely a historical stage that monotheism superseded: as a philosophical position it has specific advantages, and it is the conclusion that several of the standard arguments actually support when they are read carefully.Defined in Philosophy of Religion Beyond Monotheism · Theism · Advanced
Popper function
A probability function taking conditional probability as primitive, axiomatised directly rather than defined as a ratio, and permitting conditional probabilities on conditions of probability zero to be well defined and non-trivial. Introduced by Karl Popper in 1955 and studied further by Rényi and by Alan Hájek.Defined in Probability Logic and Uncertain Premises · Logic · Advanced
Positive duty
A duty to do something for someone: an obligation to provide aid, resources, or protection, which cannot be discharged by refraining and which costs whoever bears it something.Defined in Rights, Duties, and Going Beyond Duty · Applied Ethics · Beginner
Positive liberty
Freedom understood as the presence of control: a person is free to the extent that they are the author of their own life, in command of themselves and able to act on their own purposes.Defined in Liberty, Equality, and Justice as Three Demands · Political Philosophy · Beginner
Positive rights
Rights whose corresponding duty is a duty of provision: that others supply the right-holder with something.Defined in Rights, Introduced · Political Philosophy · Beginner
Possibility
The status of being able to be the case. A claim is possible when there is no obstacle of the relevant kind to its being true, whether or not it is in fact true.Defined in Possibility and Necessity, Informally · Metaphysics · Beginner
Possibility operator
The one-place operator written $\Diamond$ and read "it is possible that" or "possibly", formed and used under the same syntactic rules as the box. In the standard systems the two operators are interdefinable, so a language containing either one and negation contains the other by abbreviation.Defined in Modal Logic: Possible Worlds Semantics · Logic · Intermediate
Possibility premise
The premise of a modal ontological argument stating that the property in question is instantiated in at least one possible world.Defined in Modal Ontological Arguments and Their Parodies · Theism · Advanced
Possible world
One of the points at which a formula is evaluated in a modal semantics. For the purposes of the logic a world is nothing but an element of a set, carrying no structure of its own; what makes it behave like a way things might have been is that each world assigns truth values to the atomic formulas, and different worlds may assign different ones. Whether worlds are anything more than this, and what they are if so, is a question of metaphysics rather than of logic.Defined in Modal Logic: Possible Worlds Semantics · Logic · Intermediate
Posterior probability
The credence assigned to a proposition after the evidence has been taken into account.Defined in Bayesian Confidence and Credence, Introduced · Epistemology · Intermediate
Power set
The set whose members are all the subsets of a given set, written $\mathcal P(A)$. It includes the empty set and the whole of $A$, since both are subsets. If $A$ has $n$ members then $\mathcal P(A)$ has $2^n$, since each member of $A$ may independently be included in a subset or left out.Defined in Basic Set Theory for Logicians · Logic · Intermediate
Practical reason
Reasoning about what to do, as opposed to reasoning about what is the case. Its conclusion is an action or an intention rather than a belief.Defined in Reasons, Oughts, and Normative Force · Ethics · Beginner
Practical stakes
What a subject stands to lose if they act on a belief and it turns out to be false. In the bank cases, the cost of a bounced cheque raises the stakes on the belief that the bank will be open.Defined in Contextualism, Invariantism, and Pragmatic Encroachment · Epistemology · Advanced
Pragmatic argument
An argument for adopting a belief that appeals to the consequences of holding it rather than to evidence that it is true.Defined in Pragmatic Arguments for Belief · Theism · Intermediate
Pragmatic encroachment
The thesis that practical factors, such as the costs of error, partly determine whether a subject knows or is justified, so that two subjects with the same evidence and the same reliability can differ in what they know because they differ in what hangs on being right.Defined in Contextualism, Invariantism, and Pragmatic Encroachment · Epistemology · Advanced
Predicate
An expression that becomes a sentence when supplied with the right number of names. A predicate taking one name expresses a property, one taking two expresses a relation between two things, and so on, with the number of names required called its arity. Predicates are written with capital letters, and the names they take are written after them, so that $Fa$ says that the object named by $a$ has the property expressed by $F$, and $Rab$ says that $a$ stands in the relation $R$ to $b$.Defined in Predicate Logic · Logic · Intermediate
Predication
The linguistic operation of applying a predicate to a subject: attaching "is chipped" to "the mug" to form a sentence that can be true or false.Defined in Objects and Properties · Metaphysics · Beginner
Preface paradox
The paradox, due to D. C. Makinson in 1965, that an author can rationally believe each claim in their book while also rationally believing, as they say in the preface, that the book contains at least one error.Defined in Lottery, Preface, and the Threshold View of Belief · Epistemology · Advanced
Premise
A statement offered as a reason for accepting the conclusion of an argument.Defined in What an Argument Is · Logic · Beginner
Presumption of atheism
The claim that inquiry into God's existence should start from the absence of belief, so that the theist bears the obligation to make a case and atheism stands if that case fails.Defined in How Arguments About God Work · Theism · Beginner
Primitive conditional probability
The treatment on which the two-place function is the basic notion and the one-place function is recovered by conditioning on a tautology. On this approach the ratio formula holds whenever the denominator is positive and is silent, rather than undefined, when it is not.Defined in Probability Logic and Uncertain Premises · Logic · Advanced
Principle of credulity
The principle that if it seems to a person that something is present, then probably it is present, in the absence of special considerations that would override the appearance.Defined in Religious Experience · Theism · Intermediate
Principle of indifference
The rule that when there is no reason to favour any one of several possibilities over the others, each should receive the same probability. It was standard in the classical period of the subject under the name principle of insufficient reason, and Keynes gave it the name now used in his treatise of 1921.Defined in Probability as an Extension of Logic · Logic · Intermediate
principle of plenitude
The principle that the fullness of being is itself a good, so that a reality containing every kind of thing that could exist is better than a sparser one. Arthur Lovejoy traced its history from the Greeks through the eighteenth century in The Great Chain of Being (Harvard University Press, 1936), where he identified it as one of the organising commitments of Western metaphysics. It functions in this debate as the premise that makes multiverse proposals attractive, since if variety and abundance are goods in themselves, a creator with unlimited power has a reason to make everything worth making.Defined in The No-Best-World Problem · Theism · Advanced
Principle of sufficient reason
The principle that there is an explanation for every fact, or for the existence of every thing, of why it is so rather than otherwise.Defined in Cosmological Arguments · Theism · Intermediate
Principle of testimony
The principle that, in the absence of special considerations, the reports people give of their experiences are probably accurate accounts of how things seemed to them.Defined in Religious Experience · Theism · Intermediate
Prior probability
The credence assigned to a proposition before the evidence in question is taken into account.Defined in Bayesian Confidence and Credence, Introduced · Epistemology · Intermediate
privacy and autonomy objection
The principal argument for anti-theism, which holds that certain goods are unavailable to any creature of an omniscient and omnipotent God. Complete privacy is impossible, since every thought is observed. Genuine independence is impossible, since one exists at every moment by another's sustaining will and one's projects unfold within another's plan. The status of being nobody's subordinate is unavailable, since one is permanently and necessarily in the position of a creature before its maker. The claim is not that these losses outweigh theism's goods but that they are genuine goods, so that even the best theistic world involves a cost.Defined in The Axiology of Theism · Theism · Advanced
Privation theory of evil
The view that evil has no positive existence of its own, and consists instead in the absence of some good that ought to be present, as blindness is the absence of sight rather than a thing in its own right.Defined in Theodicies and Defences · Theism · Intermediate
Privileged access
The thesis that a subject has a way of knowing their own mental states that no one else has and that does not rely on observation of behaviour.Defined in Introspection and Its Limits · Philosophy of Mind · Beginner
Pro tanto reason
A consideration that counts in favour of an action to some degree, and that can be outweighed by others without being cancelled. It contributes to the verdict rather than settling it.Defined in Reasons, Oughts, and Normative Force · Ethics · Beginner
pro-theism
The view that God's existence would make things better, or does make things better, than they otherwise would be. In its strong form it holds that a world with God is better in every respect that matters; in the more defensible weaker form it holds only that a world with God is better on balance, leaving room for particular respects in which it is worse.Defined in The Axiology of Theism · Theism · Advanced
Probabilism
The norm that a rational agent's credences at any time must satisfy the probability axioms. An agent whose credences violate the axioms is said to be incoherent.Defined in Formal Epistemology: Probabilism and Updating · Epistemology · Advanced
Probabilistic argument
An argument whose premises are held to raise or lower the probability of its conclusion without establishing it, so that the conclusion may remain deniable even when the premises are granted.Defined in How Arguments About God Work · Theism · Beginner
Probabilistic entailment interval
The interval of values the conclusion's probability may take, given the probabilities of the premises. Computing it is a linear programming problem, since the constraints are linear in the probabilities of the state descriptions, and the interval is generally wide.Defined in Probability Logic and Uncertain Premises · Logic · Advanced
Probabilistic validity
The property an argument has when the uncertainty of its conclusion cannot exceed the sum of the uncertainties of its premises, under every probability assignment. Adams proved that for arguments in the language of conditionals interpreted by his thesis, probabilistic validity coincides with classical validity for arguments without nested conditionals, which is a substantial vindication of classical logic in a probabilistic setting.Defined in Probability Logic and Uncertain Premises · Logic · Advanced
Probability axiom
One of the basic conditions defining a probability function. In the standard formulation due to Andrey Kolmogorov, a function $P$ from propositions to real numbers is a probability function if it satisfies non-negativity, normalisation and finite additivity.Defined in Formal Epistemology: Probabilism and Updating · Epistemology · Advanced
Probability measure
A function assigning to each event in a field a real number between zero and one, subject to the constraints below. It is a function in the sense defined in the previous article, with the field as its domain and the unit interval as its codomain, and the constraints are what distinguish a probability measure from an arbitrary such function.Defined in Probability as an Extension of Logic · Logic · Intermediate
Problem of evil
The difficulty of reconciling the existence of a God who is omnipotent, omniscient, and perfectly good with the existence, quantity, and distribution of suffering in the world.Defined in The Problem of Evil · Theism · Intermediate
Problem of hell
The argument that eternal punishment cannot be reconciled with perfect goodness, since no finite life could merit unending suffering and a being who loved everyone would not permit it.Defined in Death and the Afterlife · Theism · Intermediate
Problem of the priors
The difficulty that Bayes's theorem tells you how to revise a probability but not where the initial probability comes from, so that any posterior at all can be reached by choosing a prior to suit it.Defined in Bayesian Natural Theology · Theism · Advanced
Procedural justice
Justice understood as a property of the process by which an outcome was reached, rather than of the outcome itself.Defined in What Justice Requires · Political Philosophy · Beginner
Process reliabilism
The specific view, due to Alvin Goldman, that a belief is justified when it is produced by a cognitive process that tends to produce true beliefs, and unjustified when the process producing it does not.Defined in Reliabilism and Virtue Epistemology · Epistemology · Intermediate
Projectibility
The property a predicate has when its observed instances confirm generalisations involving it, so that it is legitimate to project it from observed to unobserved cases. Green is projectible; grue is not. Goodman's challenge was to say what projectibility consists in.Defined in Confirmation Theory, Ravens, and Grue · Epistemology · Advanced
Projection theory
The view that religious belief arises by taking human properties, needs, or social facts and projecting them outward as an independent divine being.Defined in Natural Explanations of Religious Belief · Theism · Intermediate
Proof normalization
The process of removing detours from a natural deduction proof, where a detour is an introduction rule immediately followed by the corresponding elimination. Under the correspondence it is exactly beta reduction of the associated term, so simplifying a proof and running a program are the same operation.Defined in The Curry-Howard Correspondence · Logic · Advanced
Proof system
A specification of three things: the language whose formulas the system operates on, a set of axioms taken as derivable without premises, and a set of rules permitting a formula to be written down given formulas already written. The relation of syntactic consequence is defined relative to such a specification, so that a claim of the form $\Gamma \vdash \varphi$ is incomplete until one is fixed.Defined in Natural Deduction · Logic · Intermediate
properly basic belief
A belief held without being inferred from other beliefs, and rationally so. Basicality is a structural matter, concerning where a belief sits in a person's noetic structure rather than what it is about. Propriety is the normative addition: a belief is properly basic when holding it immediately is appropriate rather than reckless. Perceptual, memorial, and other-minds beliefs are the standard examples, and the point of the category is that most of what anyone knows is held this way.Defined in Reformed Epistemology and Proper Function · Theism · Advanced
Property
A way a thing is: being chipped, having a mass of two kilograms, being taller than the fence. Properties are what predicates are true of things in virtue of, and are also called attributes, qualities, or in some contexts features.Defined in Objects and Properties · Metaphysics · Beginner
Proposition
What a declarative sentence says: the thing that is true or false. Two sentences express the same proposition when they say the same thing, and one sentence can express different propositions on different occasions of use.Defined in Statements and Connectives · Logic · Beginner
Propositional attitude
A mental state consisting of an attitude taken toward a proposition: believing that the bus is late, hoping that the bus is late, doubting that the bus is late. The state divides into a mode and a content.Defined in What a Mental State Is · Philosophy of Mind · Beginner
Propositional knowledge
Knowing that something is the case: that Ottawa is the capital of Canada, that the bridge will hold, that the patient has an infection. It takes a complete statement as its object rather than a person, a place, or a skill.Defined in Knowledge, Belief, and Opinion · Epistemology · Beginner
Propositions as types
The reading of a formula as the type of its proofs, so that provability is inhabitation: a formula is provable exactly when some closed term has it as a type. Under the reading, conjunction is the product type, disjunction is the sum type, the false constant is the empty type, and the universal quantifier is the dependent function type.Defined in The Curry-Howard Correspondence · Logic · Advanced
Provability logic
The study of the principles governing the formalised provability predicate of a theory of arithmetic, conducted in a modal language whose box is read as "is provable in the theory". The field is distinguished from modal logic generally by the fact that its intended reading is a single fixed predicate rather than a family of informal notions, so that the question of which principles are correct has a determinate answer.Defined in Provability Logic and Löb's Theorem · Logic · Advanced
Providence
God's governing of the created order toward the ends God intends for it, including what God brings about, what God permits, and what God arranges.Defined in Creation, Conservation, and Providence · Theism · Beginner
Public goods
Goods whose benefits cannot practicably be withheld from those who did not pay for them, and whose enjoyment by one person does not reduce what is available to anyone else.Defined in What a State Is For · Political Philosophy · Beginner

Q

Qualia
The introspectively accessible qualitative features of experience: the particular way red looks, the particular way a burn feels, what distinguishes one experience from another in respect of how it is.Defined in Consciousness Versus Cognition · Philosophy of Mind · Beginner
Qualitative identity
Exact similarity. Two things are qualitatively identical when they share all their relevant properties, and there are still two of them.Defined in Change and Identity Over Time · Metaphysics · Beginner
Quantifier elimination
The property a theory has when every formula is equivalent, modulo the theory, to a quantifier-free formula in the same free variables. Since quantifier-free formulas are boolean combinations of atomic ones, the definable sets of such a theory are exactly the boolean combinations of the sets defined by atomic formulas.Defined in Model Theory: Types, Quantifier Elimination, Categoricity · Logic · Advanced
Quantifier scope
The portion of a formula a quantifier governs, determined by the punctuation exactly as the scope of a connective is. A quantifier binds every occurrence of its variable within its scope and none outside it, and moving a quantifier across a connective can change the claim entirely.Defined in Predicate Logic · Logic · Intermediate
Quine's circularity argument
The argument that every proposed explanation of analyticity relies on a notion, such as synonymy, definition, or necessity, that can itself be explained only by appeal to analyticity, so that the family of terms is never anchored outside itself.Defined in The Analytic/Synthetic Distinction and Quine's Attack · Epistemology · Intermediate

R

Rational intuition
A non-sensory mental state in which a proposition strikes the thinker as true on the basis of understanding it, offered by rationalists as the source of a priori justification.Defined in A Priori and A Posteriori · Epistemology · Intermediate
Raven paradox
The paradox, formulated by Carl Hempel in 1945, that on apparently innocent principles of confirmation, the observation of a non-black non-raven, such as a white shoe, confirms the hypothesis that all ravens are black.Defined in Confirmation Theory, Ravens, and Grue · Epistemology · Advanced
RCA-zero
The recursive comprehension axiom, the base theory of reverse mathematics. It asserts the existence of sets definable by a condition expressible both with a bounded existential arithmetical formula and with a bounded universal one, which by Post's theorem means the recursive sets, together with induction for existential arithmetical formulas.Defined in Reverse Mathematics · Logic · Advanced
Reason
The capacity to arrive at beliefs by thinking rather than by observing: deriving conclusions from premises, and grasping truths whose warrant does not depend on any particular experience.Defined in Sources: Perception, Memory, Testimony, Reason · Epistemology · Beginner
Recursive axiomatizability
The property a theory has when its axioms form a decidable set, so that some effective procedure can determine of any given sentence whether it is one of the axioms. The condition is what distinguishes a theory that has been specified from a set of sentences that merely exists, and it is satisfied by every axiom system in ordinary use, including those with infinitely many axioms given by an axiom schema.Defined in Gödel's Incompleteness Theorems · Logic · Advanced
Recursive definition
A definition of a set given in three parts: a base clause listing the simplest members outright, a recursion clause specifying operations that build new members from members already obtained, and a closure clause stating that nothing else belongs. The closure clause is what makes the definition a definition rather than a partial description, since without it the base and recursion clauses would be satisfied by any larger set as well.Defined in Propositional Logic and Well-Formed Formulas · Logic · Intermediate
Recursive function
A function on the natural numbers built from the constant zero, the successor function, and the functions returning one of their arguments, by three operations: composing functions already built, defining a function by recursion on one argument in terms of its value at the predecessor, and searching upward for the least number satisfying a condition already built. The functions obtainable without the search operation are the primitive recursive ones, which are all total; the search operation is what allows a definition to fail to return a value.Defined in Computability, Decidability, and Church's Theorem · Logic · Advanced
Recursively enumerable set
The property a set has when some procedure lists its members, so that everything in the set eventually appears and nothing else does. Equivalently, when some procedure halts exactly on the members and runs forever on everything else. Such a set can be confirmed but not, in general, refuted: waiting is evidence of nothing.Defined in Computability, Decidability, and Church's Theorem · Logic · Advanced
Reductio ad absurdum
The pattern of assuming a formula, deriving a contradiction from it, and concluding its negation. In a natural deduction system it is the introduction rule for negation: assume $\varphi$, derive some formula together with its negation, discharge, and write $\neg \varphi$.Defined in Natural Deduction · Logic · Intermediate
Reductionism about testimony
The view that testimonial justification is not basic but reduces to other sources. A hearer is justified in accepting what a speaker says only when they have independent reasons, ultimately from perception, memory, and inference, for taking the speaker to be reliable on the matter.Defined in Testimony and Disagreement · Epistemology · Intermediate
Reflective access
The capacity to determine, by reflection alone, whether some condition obtains. Access internalists hold that the factors that make a belief justified must be reflectively accessible to the subject.Defined in Epistemological Disjunctivism and the New Evil Demon · Epistemology · Advanced
Reflective equilibrium
The state reached by adjusting principles and judgements against one another until they agree, revising a judgement when a principle is well supported and revising the principle when a judgement is more secure. The method is the process of mutual adjustment; the equilibrium is its endpoint.Defined in Moral Intuitions and What to Do With Them · Ethics · Beginner
Reformed epistemology
The position that belief in God can be properly basic, so that a person may be rational in believing in God without holding that belief on the basis of arguments or evidence. It is called Reformed because it draws on a strand in the Reformed theological tradition that was suspicious of natural theology, and its principal development is the work of Alvin Plantinga, with Nicholas Wolterstorff and William Alston as the other main figures. It does not claim that theistic arguments fail. It claims that their success or failure is not what belief in God stands or falls with.Defined in Reformed Epistemology and Proper Function · Theism · Advanced
Regress argument
The argument that since the chain of reasons must terminate in one of a small number of ways, and each way appears to fail, justified belief is impossible.Defined in The Regress Problem · Epistemology · Beginner
Regularity
The condition that no possible proposition receives probability zero. It secures that the ratio formula is always applicable and is unattainable in any space with uncountably many mutually exclusive possibilities, since only countably many can have positive probability.Defined in Probability Logic and Uncertain Premises · Logic · Advanced
Reincarnation
The view that a person, or a continuing series causally derived from them, is reborn into another life after death, with the conditions of each life bearing on the next.Defined in Death and the Afterlife · Theism · Intermediate
Relation
A set of ordered pairs. The pair $\langle a, b \rangle$ differs from $\langle b, a \rangle$ unless its two members are the same, which is what distinguishes a pair from a two-membered set. A relation holds between $a$ and $b$ exactly when the pair whose first member is $a$ and whose second is $b$ belongs to it, and the same construction with longer sequences gives relations of any number of places.Defined in Basic Set Theory for Logicians · Logic · Intermediate
Relevance logic
A family of systems requiring that the premises of a valid argument bear on its conclusion, developed principally by Alan Ross Anderson and Nuel Belnap from the 1950s and formalised in the systems E, R and their relatives. Relevance logics are substructural, obtained by dropping weakening, which is the rule licensing the introduction of premises that play no part.Defined in Relevance Logic and Paraconsistency · Logic · Advanced
Relevant alternatives
The view that knowing a proposition requires ruling out only those incompatible possibilities that are relevant in the context, rather than every possibility whatever.Defined in Epistemic Closure and Its Denial · Epistemology · Intermediate
Reliabilism
The family of externalist views on which the justification or warrant of a belief is a matter of its connection to truth, rather than of the believer's evidence or reasons.Defined in Reliabilism and Virtue Epistemology · Epistemology · Intermediate
reliability of cognitive faculties
The property a set of belief-forming faculties has when they produce a high proportion of true beliefs across the range of conditions in which they are used. Reliability in this sense is a matter of frequency rather than of infallibility, and it is domain-relative: a faculty can be reliable about the location of nearby solid objects and unreliable about the origins of the universe, and nothing in the concept requires that a creature's faculties be uniformly good or uniformly bad.Defined in The Evolutionary Argument Against Naturalism · Theism · Advanced
religious disagreement
The problem raised by the fact that religious beliefs are rejected by large numbers of people who appear to be as intelligent, as informed, as careful, and as sincere as those who hold them. The question is what, if anything, awareness of such disagreement does to the rationality of continuing to believe. It is a special case of a general problem in epistemology about disagreement among epistemic peers, and it is not confined to religion, though religion is where the disagreement is most persistent and least resolvable by shared method.Defined in Religious Pluralism and Exclusivism · Theism · Advanced
religious exclusivism
The view that the central claims of one tradition are true and that claims of other traditions incompatible with them are false. In its strict soteriological form it adds that the goods the tradition promises are available only through it. The two components are separable: one can hold that a tradition is uniquely correct about the facts while holding that its benefits are not restricted to its own adherents.Defined in Religious Pluralism and Exclusivism · Theism · Advanced
Religious experience
An experience that seems to the person having it to be of some objective reality, and that has religious significance either in its content or in the interpretation the person places on it.Defined in Religious Experience · Theism · Intermediate
religious inclusivism
The view that one tradition is uniquely correct or complete, but that the goods it identifies are available to people outside it, who may attain them through their own traditions without recognising the source. Karl Rahner's much-discussed notion of anonymous Christianity is the best-known version, and the Second Vatican Council's declaration Nostra Aetate of 1965 took the Catholic Church some distance in this direction while retaining the claim to uniqueness.Defined in Religious Pluralism and Exclusivism · Theism · Advanced
religious pluralism
The view that no tradition is uniquely correct, and that the major traditions are all authentic and roughly equally effective responses to the same ultimate reality, their apparent conflicts arising from differences in the human conceptual and cultural equipment through which that reality is encountered. The position denies exclusivism's uniqueness claim rather than affirming that all religious claims are true, which would be inconsistent on its face.Defined in Religious Pluralism and Exclusivism · Theism · Advanced
Resemblance
The relation of being alike in some respect. On resemblance-based accounts of properties, facts about which things resemble which are taken as basic, rather than being explained by an entity that the resembling things have in common.Defined in Universals and Instances · Ontology · Beginner
Revealed theology
Theology that proceeds from what is taken to have been divinely revealed, such as scripture, tradition, or direct communication, rather than from what unaided human faculties can establish.Defined in Faith and Reason · Theism · Beginner
Reverse mathematics
The programme of determining, for each theorem of ordinary mathematics, the weakest set-existence axioms sufficient to prove it, by establishing an equivalence between the theorem and those axioms over a fixed weak base theory. Initiated by Harvey Friedman in the 1970s and developed principally by Stephen Simpson and his collaborators.Defined in Reverse Mathematics · Logic · Advanced
Reverse ontological argument
An argument of exactly the same form as the modal ontological argument, starting from the premise that maximal greatness is possibly not instantiated, and concluding that it is necessarily not instantiated.Defined in Modal Ontological Arguments and Their Parodies · Theism · Advanced
Right action
An action that is morally in order: not wrong to perform. The term covers both what is required and what is merely allowed.Defined in What a Moral Theory Is · Ethics · Beginner
Rowe's evidential argument
The argument that there exist instances of intense suffering that an omnipotent and omniscient being could have prevented without losing some greater good or permitting some equally bad or worse evil; that such a being would prevent any suffering it could prevent without such a loss; and therefore that no such being exists. Its distinctive feature is that the first premise is offered as a reasonable inference from the evidence rather than as something known, which makes the conclusion probable rather than demonstrated.Defined in The Probabilistic Problem of Evil · Theism · Advanced
Rule of law
The ideal that public power be exercised through general, known, and stable rules applied by independent institutions, so that officials as well as citizens are bound by law and no one is subject to arbitrary command.Defined in Law and the Rule of Law · Political Philosophy · Beginner
Russell's theory of descriptions
The account, given in "On Denoting" of 1905, on which a sentence containing a definite description is not about any object named by the description but is instead a general claim with three parts: that something answers to the description, that at most one thing does, and that it has whatever the sentence goes on to attribute. On this account "the" is not a device of reference at all, and the description does not survive as a unit in the analysis.Defined in Identity and Definite Descriptions · Logic · Intermediate

S

Safety condition
The requirement that the believer could not easily have believed falsely. A belief is safe when in all or nearly all close worlds in which the believer forms that belief in the same way, the belief is true.Defined in Safety and Sensitivity Conditions · Epistemology · Intermediate
satisficing creation
The view that a perfectly good creator is required only to create a world that is good enough, rather than the best world available, so that any world above some threshold of value is a permissible choice. The position is what allows a theist to accept that there is no best possible world without concluding that God's goodness has been compromised, since a standard that can actually be met has replaced one that cannot.Defined in The No-Best-World Problem · Theism · Advanced
Saturation
The property a model has when it realises every type over every parameter set of size less than the model's own cardinality. A saturated model realises as many types as its size permits, and is correspondingly homogeneous: any two tuples satisfying the same formulas can be mapped to one another by an automorphism.Defined in Model Theory: Types, Quantifier Elimination, Categoricity · Logic · Advanced
Scope
The portion of a formula that a given connective applies to. Brackets fix scope, and a formula whose brackets are missing may have no determinate meaning at all.Defined in Translating English into Symbols · Logic · Beginner
Scoring rule
A function that measures the inaccuracy of a credence, or a whole credence function, at a given possible world. The most widely used is the Brier score, which sums the squared differences between each credence and the corresponding truth value.Defined in Accuracy-First Epistemology · Epistemology · Advanced
Second incompleteness theorem
No consistent, recursively axiomatizable theory that represents enough arithmetic proves the sentence expressing its own consistency. A theory strong enough to be worth worrying about is therefore not strong enough to settle the worry, and any proof of its consistency must use resources it does not itself contain.Defined in Gödel's Incompleteness Theorems · Logic · Advanced
Second-order logic
The extension of first-order logic with variables for relations and functions on the domain, and quantifiers binding them. A sentence may say that every property with a given closure condition holds universally, or that some relation with a stated feature exists, without the property or relation being named by a formula.Defined in Second-Order and Higher-Order Logic · Logic · Advanced
Second-order property
A property of a property or concept, rather than of an individual: being widely instantiated, being had by exactly nine things, being had by nothing at all.Defined in Is Existence a Property? · Ontology · Beginner
secondary causation
Causation exercised by creatures, so called because it operates under and through the primary causation exercised by God. To affirm secondary causation is to say that when a fire heats water, the fire genuinely does the heating, and not merely that God heats the water on the occasion of the fire being nearby. The term marks a position on which creatures have real causal powers of their own rather than being placeholders in a description of divine activity.Defined in Existential Inertia and Divine Conservation · Theism · Advanced
self-defeat
The condition of a position that, if accepted, supplies a reason to reject it. A self-defeating position is not thereby shown to be false, and this is what distinguishes self-defeat from self-contradiction: the position may be true, but it cannot be rationally believed by someone who sees what it implies. The verification principle of rung 9 failed in this way, and so, on this argument, does naturalism.Defined in The Evolutionary Argument Against Naturalism · Theism · Advanced
Semantic closure
The condition a language meets when it contains names for its own expressions, a predicate applying to those names to say that the sentence named is true, and the resources to assert every instance of the T-schema for its own sentences. Tarski's diagnosis of the liar is that semantic closure, together with ordinary logic, is inconsistent.Defined in Undefinability and the Theories of Truth · Logic · Advanced
Semantic consequence
The relation that holds between a set of formulas and a formula when every interpretation that makes all members of the set true also makes the formula true. It is written $\Gamma \vDash \varphi$, with the double turnstile, where $\Gamma$ is the set of premises. Equivalently, there is no interpretation making every premise true and the conclusion false, which is the beginner tier's account of validity stated exactly.Defined in Semantic and Syntactic Consequence · Logic · Intermediate
Semantic tableau
A tree of formulas built by decomposing a set of formulas into their components according to fixed rules, undertaken to determine whether the set has a model. The root holds the formulas being tested, each rule replaces a formula with the simpler formulas its truth would require, and branching records the alternatives that a formula leaves open. The method is also called the tree method or the method of analytic tableaux.Defined in Semantic Tableaux · Logic · Intermediate
sempiternity
Existence throughout all of time, without beginning or end, as opposed to existence outside time altogether. A sempiternal God has a past and a future, undergoes succession, and knows what time it is now. The position is also called everlastingness or temporal eternity, and it is compatible with God's never having come into being and never ceasing to be.Defined in Simplicity, Timelessness, and Impassibility · Theism · Advanced
Sensation
The raw registering of a stimulus, considered apart from any recognition or classification of what it is: a patch of colour, a pressure, a sound, before it is taken as anything in particular.Defined in Sensation and Perception · Philosophy of Mind · Beginner
Sense datum
An immediate object of perceptual awareness, understood as actually having the qualities the experience presents: a coloured, shaped item of which the perceiver is directly aware and which is distinct from the physical object.Defined in Sensation and Perception · Philosophy of Mind · Beginner
Sensitivity condition
The requirement that had the proposition been false, the believer would not have believed it. A belief meets the condition when it varies with the truth of what is believed.Defined in Safety and Sensitivity Conditions · Epistemology · Intermediate
sensus divinitatis
A supposed human cognitive faculty that produces belief in God directly, in response to circumstances rather than arguments: seeing the night sky, being confronted with the beauty or the scale of the natural world, feeling guilt, coming through danger. On this account belief in God is not the conclusion of an inference from those circumstances; the circumstances are the occasion on which the faculty operates, standing to theistic belief roughly as being appeared to in a certain way stands to perceptual belief.Defined in Reformed Epistemology and Proper Function · Theism · Advanced
Sentience
The capacity for felt experience, and in particular for experiences that feel bad or good to the being having them, such as pain, distress, and pleasure.Defined in Moral Status · Applied Ethics · Beginner
Sequent
An expression with two lists of formulas separated by an arrow, read as saying that if everything on the left holds then at least one thing on the right holds. The left list is the antecedent and the right list the succedent, and either may be empty. A sequent with an empty succedent says that the antecedent is contradictory; a sequent with an empty antecedent asserts the disjunction of the succedent outright.Defined in Sequent Calculus and Cut Elimination · Logic · Advanced
Set
A collection considered as a single object, determined entirely by which things belong to it. That an object $a$ belongs to a set $A$ is written $a \in A$. Two sets with the same members are the same set, so a set has no order and no repetition: nothing is a member twice, and there is no first member. The set with no members at all is the empty set, and there is only one of it.Defined in Basic Set Theory for Logicians · Logic · Intermediate
Sheffer stroke
The binary connective true on every row except the one where both arguments are true, written $P \mid Q$ and read "not both". It is the negation of conjunction and is often called NAND. It is one of only two binary connectives that form an adequate set on their own.Defined in The Sixteen Binary Connectives · Logic · Intermediate
Simplicity as a prior
The proposal that a hypothesis's probability before any evidence is fixed by how simple the hypothesis is, so that simpler hypotheses start out likelier.Defined in Bayesian Natural Theology · Theism · Advanced
Simply typed lambda calculus
A formal language of terms built from variables, abstraction and application, in which every term carries a type. Types are generated from base types by the arrow constructor, an abstraction $\lambda x^{A}.\, t$ has type $A \rightarrow B$ when $t$ has type $B$ under the assumption that $x$ has type $A$, and an application $t\,u$ has type $B$ when $t$ has type $A \rightarrow B$ and $u$ has type $A$.Defined in The Curry-Howard Correspondence · Logic · Advanced
skeptical spillover
The general worry that the scepticism skeptical theism requires cannot be confined to the case it was introduced for. The theses are about our grasp of value and of the relations between goods and permitted evils, and those matters are not sealed off from the rest of the theist's commitments, so a scepticism strong enough to block the inference from apparent pointlessness is likely to block other inferences the theist wants to keep.Defined in Skeptical Theism and Its Costs · Theism · Advanced
Skeptical theism
The response holding that our failure to identify a justifying reason for some evil is weak evidence that there is none, because our grasp of the available goods, evils, and connections between them is not a representative sample of what an omniscient being would grasp.Defined in Theodicies and Defences · Theism · Intermediate
Skepticism
The position that knowledge of some domain is not available. Global versions deny that anything at all is known; local versions target a particular area, such as the external world, other minds, or the past.Defined in Skepticism, First Encounter · Epistemology · Beginner
Skolem's paradox
The apparent contradiction that arises when the downward theorem is applied to set theory itself. The axioms of Zermelo-Fraenkel set theory are countably many first-order sentences, so if they are consistent they have a countable model. But among their consequences is Cantor's theorem, so that model contains a set it takes to be uncountable, and the model as a whole has only countably many elements.Defined in Compactness and Löwenheim-Skolem · Logic · Advanced
Social epistemology
The study of the social dimensions of knowledge: how knowledge is produced, transmitted, and distributed through relations between people and institutions, and how those relations can support or distort it.Defined in Epistemic Injustice · Epistemology · Intermediate
Sorites paradox
An argument from an evidently true base case and an evidently true tolerance premise, by a long chain of apparently valid steps, to an evidently false conclusion. Attributed to Eubulides of Miletus in the fourth century BC, its name comes from the Greek for heap, the original version concerning how many grains make one.Defined in Vagueness and the Sorites · Logic · Advanced
Sortal
A term or concept that supplies a way of dividing and counting: chair, cat, coin, symphony. A sortal answers what a thing is, and carries with it a way of telling one of them from another.Defined in Identity and Individuation · Ontology · Beginner
Soul-making theodicy
The view that God's purpose is not to maximise happiness but to develop moral and spiritual character, and that a world containing genuine risk, difficulty, and suffering is required for that development.Defined in Theodicies and Defences · Theism · Intermediate
Soundness
An argument is sound when it is valid and all of its premises are in fact true. An argument that is not sound is unsound.Defined in Validity and Soundness · Logic · Beginner
Soundness theorem
The claim that everything derivable is a semantic consequence: whenever a conclusion can be derived from a set of premises, every interpretation making those premises true makes the conclusion true. A proof system with this property never licenses an invalid argument, so a derivation is a guarantee and not merely an indication.Defined in Soundness and Completeness, Informally · Logic · Intermediate
Sovereignty
Supreme authority within a territory: authority not derived from and not answerable to any higher authority of the same kind.Defined in What a State Is For · Political Philosophy · Beginner
Spatiotemporal continuity
The condition of tracing a single unbroken path through space and time, with no gaps and no jumps: at every moment between two times the thing is somewhere, and it gets from each position to the next by passing through the positions in between.Defined in The Ship of Theseus · Metaphysics · Beginner
Spatiotemporal location
Having a position in space and time: being somewhere, at some time, with a determinate distance from other located things.Defined in Abstract and Concrete · Metaphysics · Beginner
Stalnaker-Lewis semantics
The treatment of the counterfactual on which it is true when the consequent holds at the antecedent worlds most similar to the actual world. Stalnaker's version, from 1968, assumes a unique closest antecedent world; Lewis's, from 1973, quantifies over a sphere of sufficiently close ones and does not assume uniqueness.Defined in Conditionals and the Triviality Results · Logic · Advanced
Standard semantics
The interpretation on which a second-order relation variable ranges over the full power set of the relevant product of the domain, so that every set of elements, definable or not, is in range. Under it, the second-order quantifier means what it appears to mean.Defined in Second-Order and Higher-Order Logic · Logic · Advanced
State
A political association that claims supreme authority over a defined territory and the people in it, exercised through permanent institutions that persist independently of whoever currently occupies them.Defined in What a State Is For · Political Philosophy · Beginner
Statistical independence
The relation two events bear when the probability of both occurring is the product of their separate probabilities. It is a definition rather than an intuitive notion made precise, and it is relative to the measure: two events independent under one probability measure may fail to be under another, with no change in the events themselves.Defined in Probability as an Extension of Logic · Logic · Intermediate
Steadfast view
The view that, at least in some cases, one may rationally maintain one's belief in the face of peer disagreement, because the first-order evidence continues to support it and the fact of disagreement does not cancel that support.Defined in Testimony and Disagreement · Epistemology · Intermediate
Strengthened liar
The sentence saying of itself that it is not true, considered in a setting that has assigned it no truth value. The setting's own verdict, that the sentence is not true, is precisely what the sentence says, so the theory appears committed to the sentence's truth at the same time as it denies the sentence a value.Defined in Undefinability and the Theories of Truth · Logic · Advanced
Strong atheism
The condition of a person who believes that God does not exist. Also called positive atheism.Defined in Theism, Atheism, and Agnosticism · Theism · Beginner
Structural rule
A rule that alters the arrangement of a sequent without mentioning any connective. There are three: weakening, which adds a formula to either side; contraction, which replaces two occurrences of the same formula on one side by one; and exchange, which reorders the formulas on a side. They say, respectively, that unused premises are harmless, that repetition carries no information, and that order carries none either.Defined in Sequent Calculus and Cut Elimination · Logic · Advanced
Subformula property
The feature a proof has when every formula occurring anywhere in it is a subformula of some formula in the sequent being proved. Cut-free proofs in the sequent calculus have it, since every rule other than cut carries its side formulas downward unchanged and introduces only a formula built from what its premises contain.Defined in Sequent Calculus and Cut Elimination · Logic · Advanced
Subject-sensitive invariantism
The view that "knows" is invariant in meaning, but that whether a subject knows depends partly on non-epistemic features of the subject's situation, principally their practical stakes. Also called interest-relative invariantism.Defined in Contextualism, Invariantism, and Pragmatic Encroachment · Epistemology · Advanced
Subjunctive conditional
A conditional whose antecedent is entertained counterfactually, typically marked in English by the subjunctive or by a past-tense construction. "If Oswald had not shot Kennedy, someone else would have" is subjunctive, and it is false unless one holds an unusual view about the assassination.Defined in Conditionals and the Triviality Results · Logic · Advanced
Substantive equality
Equality in the actual condition or outcome of people's lives, as against equality only in the rules applied to them.Defined in What Justice Requires · Political Philosophy · Beginner
Substructural logic
A logic obtained by restricting or removing one or more of the structural rules of the sequent calculus. Since the structural rules govern the treatment of premises as a collection rather than the behaviour of any connective, their removal changes what a premise is taken to be.Defined in Substructural Logics · Logic · Advanced
Subsystem of second-order arithmetic
An axiomatic theory in the two-sorted language of second-order arithmetic obtained by restricting the comprehension schema, and correspondingly the induction schema, to a limited class of formulas. Five such subsystems account for the overwhelming majority of the equivalences found.Defined in Reverse Mathematics · Logic · Advanced
Successive addition
The formation of a collection by adding one member at a time, so that at every stage of the process the collection has finitely many members.Defined in Grim Reaper Paradoxes and Causal Finitism · Theism · Advanced
Sufficient condition
A condition whose presence is enough for something to occur. Being decapitated is a sufficient condition for death.Defined in Causation, First Pass · Metaphysics · Beginner
Supererogation
The class of actions that are morally good and praiseworthy but not obligatory, so that performing them is admirable while failing to perform them is not a fault.Defined in Rights, Duties, and Going Beyond Duty · Applied Ethics · Beginner
supernaturalism
The view that there exists at least one thing that is not part of the natural order and that acts on it: minimally, a mind or agent whose existence does not depend on physical arrangement and whose activity is not the operation of a natural law. Theism is one form of it, but not the only one, and the two terms are not interchangeable: a supernaturalism with many limited spirits and no creator would still be supernaturalism.Defined in Naturalism and Supernaturalism as Frameworks · Theism · Advanced
Supertask
The completion of infinitely many tasks within a finite stretch of time.Defined in Grim Reaper Paradoxes and Causal Finitism · Theism · Advanced
Supervaluationism
The theory on which a vague sentence is true when it comes out true on every admissible way of making the language precise, false when it comes out false on every such precisification, and neither when precisifications disagree. Developed by Kit Fine in 1975, following van Fraassen's treatment of presupposition failure.Defined in Vagueness and the Sorites · Logic · Advanced
Swamping problem
The objection, pressed by Linda Zagzebski, Jonathan Kvanvig and others, that if the value of a reliable process lies wholly in the true beliefs it produces, then a true belief produced by a reliable process has no more value than the same true belief produced by an unreliable one. The value of the truth swamps the value of the reliability.Defined in Epistemic Value and the Swamping Problem · Epistemology · Advanced
Syntactic consequence
The relation that holds between a set of formulas and a formula when there is a finite sequence of formulas ending with that formula, each member of which is either a premise from the set, an axiom of the system, or the result of applying one of the system's rules to earlier members. It is written $\Gamma \vdash \varphi$, with the single turnstile. The relation is always relative to a specified proof system, so that strictly the turnstile should carry a subscript naming it, and does whenever more than one system is in play.Defined in Semantic and Syntactic Consequence · Logic · Intermediate
Synthetic truth
A proposition whose truth depends on how the world is and not on meanings alone, so that understanding it leaves open whether it is true.Defined in The Analytic/Synthetic Distinction and Quine's Attack · Epistemology · Intermediate
System B
T together with the schema $\varphi \rightarrow \Box \Diamond \varphi$, which corresponds to symmetry: whenever one world is accessible from another, the second is accessible from the first. The schema says that whatever is the case is necessarily possible, and the letter is inherited from a traditional association with Brouwer rather than from any doctrine of his about modality.Defined in The Normal Systems K, D, T, B, S4, S5 · Logic · Intermediate
System D
K together with the schema $\Box \varphi \rightarrow \Diamond \varphi$, which corresponds to seriality: every world has at least one world accessible from it, so there are no dead ends. Equivalently, D rules out the worlds at which every formula whatever is necessary.Defined in The Normal Systems K, D, T, B, S4, S5 · Logic · Intermediate
System GL
The normal modal logic obtained by adding to $\mathsf{K}$ the single axiom schema $\Box(\Box A \rightarrow A) \rightarrow \Box A$, known as the Löb axiom. Named for Gödel and Löb, it is also found in the literature as $\mathsf{G}$, $\mathsf{L}$, $\mathsf{KW}$ and $\mathsf{PrL}$.Defined in Provability Logic and Löb's Theorem · Logic · Advanced
System K
The smallest normal modal logic: propositional logic together with the distribution schema and the rule of necessitation, and nothing further. It is sound and complete for the class of all frames, so a formula is a theorem of K exactly when it is valid on every frame whatever, with no condition placed on the accessibility relation.Defined in The Normal Systems K, D, T, B, S4, S5 · Logic · Intermediate
System S4
T together with the schema $\Box \varphi \rightarrow \Box \Box \varphi$, which corresponds to transitivity: whenever one world sees a second and the second sees a third, the first sees the third. The name is inherited from the fourth of the five systems Lewis and Langford numbered in 1932, which is also why the schema is usually called 4.Defined in The Normal Systems K, D, T, B, S4, S5 · Logic · Intermediate
System S5
T together with the schema $\Diamond \varphi \rightarrow \Box \Diamond \varphi$, which corresponds to the euclidean condition: whenever a world sees two worlds, each of those sees the other. Combined with reflexivity this makes the accessibility relation an equivalence relation, so S5 contains both B and S4, and it is the strongest of the six.Defined in The Normal Systems K, D, T, B, S4, S5 · Logic · Intermediate
System T
K together with the schema $\Box \varphi \rightarrow \varphi$, which corresponds to reflexivity: every world is accessible from itself. T contains D, since a reflexive relation is automatically serial, and it is the weakest system in which necessity implies truth.Defined in The Normal Systems K, D, T, B, S4, S5 · Logic · Intermediate

T

T-schema
The schema whose instances take the form: the sentence "p" is true if and only if p, with one instance for each sentence of the language under description. Tarski treated the schema as a condition of adequacy rather than as a definition: any account of truth for a language must entail every instance, and an account that does is materially adequate whatever else it says.Defined in Undefinability and the Theories of Truth · Logic · Advanced
Tautology
A formula whose truth table column is true in every row. A tautology cannot be false, whatever the letters in it stand for.Defined in Truth Tables · Logic · Beginner
Teleological argument
Any argument from the apparent directedness of things toward ends, or from order suited to an outcome, to an intelligence responsible for it.Defined in Design and Fine-Tuning Arguments · Theism · Intermediate
Temporal logic
The modal treatment of tense, with operators for what will always be the case, what was always the case, and their duals. Developed by Arthur Prior from 1957, its accessibility relation is the earlier-than ordering on times.Defined in Temporal, Deontic, and Epistemic Logic · Logic · Advanced
Tennenbaum's theorem
The result that no countable nonstandard model of Peano arithmetic is recursive. There is no nonstandard model whose domain is the natural numbers and whose addition and multiplication are both computable functions, and indeed addition alone cannot be computable.Defined in Nonstandard Models of Arithmetic · Logic · Advanced
Testimonial injustice
The wrong done to a speaker when a hearer gives them a credibility deficit because of prejudice against a social group to which the speaker belongs. Fricker's central case is identity-prejudicial credibility deficit, where the prejudice is systematic and tracks the speaker through many areas of life.Defined in Epistemic Injustice · Epistemology · Intermediate
Testimony
The reports of others, taken as a source of belief. Almost everything anyone knows about history, science, geography, and other people's lives rests on it.Defined in Sources: Perception, Memory, Testimony, Reason · Epistemology · Beginner
The argument from illusion
The argument that since illusory experiences present objects as having qualities they do not have, the immediate object of awareness in illusion is not the ordinary object; and since illusory and veridical experiences are of the same kind, the immediate object of awareness is never the ordinary object.Defined in Sensation and Perception · Philosophy of Mind · Beginner
the deceptive appearances objection
The objection that if God may have reasons beyond our grasp for permitting terrible suffering, God may equally have reasons beyond our grasp for permitting us to be systematically deceived. Ordinary confidence that our senses and testimony are not being interfered with rests on the judgement that a good being would not allow large-scale deception without sufficient reason, and skeptical theism removes the basis for that judgement. The result is a general scepticism about appearances, arrived at from inside theism.Defined in Skeptical Theism and Its Costs · Theism · Advanced
The frames of GL
A modal formula is valid on a frame when it holds at every world under every assignment. The Löb axiom is valid on exactly the frames that are transitive and contain no infinite ascending chain of accessible worlds, a condition equivalent, for finite frames, to being transitive and irreflexive.Defined in Provability Logic and Löb's Theorem · Logic · Advanced
The numinous
The distinctive object of religious dread and attraction, described by Rudolf Otto as an overwhelming and wholly other mystery that at once terrifies and compels, and treated by him as a category that cannot be reduced to moral or rational terms.Defined in Religious Experience · Theism · Intermediate
The one over many
The argument that when several distinct things are the same in some respect, there must be a single thing they share, since otherwise their sameness has nothing to consist in.Defined in Universals and Instances · Ontology · Beginner
The ship of Theseus
The puzzle of whether an object that has had every one of its parts replaced, one at a time, is still the object it was.Defined in The Ship of Theseus · Metaphysics · Beginner
Theism
The proposition that God exists, where God is understood as in classical theism: one personal being, responsible for everything else, possessing maximal power, maximal knowledge, and perfect goodness.Defined in Theism, Atheism, and Agnosticism · Theism · Beginner
theistic activism
The more specific account of how that dependence works, on which abstract objects are the products of God's intellective activity. Numbers and propositions exist because God thinks them, and they exist necessarily and eternally because God thinks them necessarily and eternally. The position was developed by Thomas Morris and Christopher Menzel in "Absolute Creation", published in the American Philosophical Quarterly in 1986.Defined in Aseity and the Bootstrapping Problem · Theism · Advanced
theistic multiverse
The proposal that God creates every universe worth creating rather than selecting one, so that the totality of what God makes has no better alternative even though no single universe within it is best. Versions have been developed by Donald Turner, Klaas Kraay, and Timothy O'Connor. Kraay's formulation, in "Theism, Possible Worlds, and the Multiverse" in Philosophical Studies in 2010, holds that God actualises the unique possible world that contains all and only the universes worth creating, which restores a best choice at the level of worlds while denying one at the level of universes.Defined in The No-Best-World Problem · Theism · Advanced
theistic personalism
The family of views on which God is understood as a person, or as personlike, in a sense continuous with our ordinary concept of a person: a bodiless being with beliefs, intentions, and free choices, distinguished from us by having those attributes without limit rather than by belonging to a different order of reality. Brian Davies introduced the label in An Introduction to the Philosophy of Religion to name what he took to be the operating assumption of much analytic philosophy of religion, in contrast with the classical theism of Augustine, Maimonides, Avicenna, and Aquinas.Defined in Classical Theism Against Theistic Personalism · Theism · Advanced
Theodicy
A response to the problem of evil that identifies the reasons God actually has for permitting evil, and argues that those reasons are morally sufficient.Defined in Theodicies and Defences · Theism · Intermediate
theological fatalism
The thesis that divine foreknowledge of a future act is incompatible with that act being free, so that if God knows in advance everything anyone will do, nobody does anything freely. It is not the claim that God's knowledge causes the act. The claim is that a fixed past truth about the act removes the ability to do otherwise, which is what the relevant notion of freedom requires.Defined in Divine Foreknowledge and Freedom · Theism · Advanced
Threshold view
The view that binary belief just is credence above some threshold $t$, where $0.5 < t < 1$. On this view, to believe $p$ is to have credence in $p$ of at least $t$, and there is no further state of belief over and above the credence.Defined in Lottery, Preface, and the Threshold View of Belief · Epistemology · Advanced
Token
A particular instance of a type: the specific inscription of "the" third from the left on this line, tonight's performance of the Ninth, the coin in your pocket.Defined in Universals and Instances · Ontology · Beginner
total evidence requirement
The requirement that a probability judgement be made relative to all of one's relevant evidence, and not to some selected portion of it. It is a general constraint on probabilistic reasoning rather than a move within philosophy of religion, and it has an obvious rationale: a probability conditional on part of the evidence can be misleading about the probability conditional on the whole, and there is no rule that the omitted part must point in the same direction.Defined in The Probabilistic Problem of Evil · Theism · Advanced
Tracking account
Robert Nozick's analysis of knowledge, on which knowing requires that the belief be true, that it be sensitive, and that the believer would still believe it were it true but circumstances slightly different, all held fixed for the method actually used.Defined in Safety and Sensitivity Conditions · Epistemology · Intermediate
Transcendence
God's being wholly other than the created order: not an item within the world, not subject to its conditions, and not a member of any kind that its contents belong to.Defined in Creation, Conservation, and Providence · Theism · Beginner
Translation key
An explicit list pairing each capital letter with the English proposition it stands for. The key is written down before any translating begins and does not change while the argument is being handled.Defined in Translating English into Symbols · Logic · Beginner
Transworld depravity
The property an agent has if, in every possible world where that agent exists and is free with respect to morally significant actions, the agent goes wrong at least once.Defined in Theodicies and Defences · Theism · Intermediate
Triviality result
A theorem showing that no proposition can have, as its probability, the conditional probability of consequent given antecedent across all probability functions in any sufficiently rich class. Proved by David Lewis in 1976, with numerous strengthenings since.Defined in Conditionals and the Triviality Results · Logic · Advanced
Trolley problem
The problem of identifying a principle that permits diverting the trolley onto one person while forbidding pushing one person into its path, given that both save five at the cost of one.Defined in The Trolley Problem as a Diagnostic · Ethics · Beginner
Truth
The property a statement has when things are as it says they are. "Snow is white" is true when snow is white.Defined in Knowledge, Belief, and Opinion · Epistemology · Beginner
Truth function
A way of building a compound proposition whose truth value is fixed entirely by the truth values of its parts. Change the parts for others with the same truth values, and the value of the whole cannot change.Defined in Statements and Connectives · Logic · Beginner
Truth table
An exhaustive listing of the possible assignments of truth values to the letters in one or more formulas, with a column showing the value each formula takes under each assignment. A formula with $n$ distinct letters has $2^n$ rows.Defined in Truth Tables · Logic · Beginner
Truth value gap
The status of a sentence assigned neither truth nor falsity, used for presupposition failure, reference failure, future contingents and the borderline cases of vague predicates. The third value in a gap logic is undesignated, so a gappy premise supports nothing.Defined in Many-Valued Logics · Logic · Advanced
Truth value glut
The status of a sentence assigned both truth and falsity, used for the paradoxes by those prepared to accept them. The third value in a glut logic is designated, since a glutty sentence is true, among other things.Defined in Many-Valued Logics · Logic · Advanced
Type
A repeatable kind, of which there can be many instances: the word "the", the Ninth Symphony, the design of a particular coin.Defined in Universals and Instances · Ontology · Beginner
Type-token distinction
The difference between a repeatable kind and its particular instances: the word "the" as against each printed occurrence of it, the Ninth Symphony as against each performance.Defined in Abstract and Concrete · Metaphysics · Beginner

U

Uncertainty accumulation
The growth of uncertainty in the conclusion of a valid argument as a function of the uncertainty in its premises. Since the uncertainty of a conjunction can be as large as the sum of the uncertainties of its conjuncts, the conclusion of a valid argument from $n$ premises each of probability $1 - \varepsilon$ can have probability as low as $1 - n\varepsilon$.Defined in Probability Logic and Uncertain Premises · Logic · Advanced
Undefinability theorem
Tarski's result that the set of Gödel numbers of true sentences of arithmetic is not definable by any formula of the language of arithmetic. In the form applying to theories: no consistent theory interpreting enough arithmetic contains a predicate it proves to satisfy the T-schema for its own sentences.Defined in Undefinability and the Theories of Truth · Logic · Advanced
undercutting defeater
A consideration that removes the support one's ground gave to a belief without providing any reason to think the belief false. If you learn that the room you are in is lit by lights that make white objects look red, you no longer have grounds for believing the wall is red, but you have not acquired a reason for thinking it is not red. It is contrasted with a rebutting defeater, which supplies positive evidence against the belief itself.Defined in The Evolutionary Argument Against Naturalism · Theism · Advanced
Uniformity of nature
The supposition that unobserved cases resemble observed ones, or that the future will resemble the past. Every inductive inference requires something of this kind as a suppressed premise.Defined in The Problem of Induction · Epistemology · Intermediate
Universal
An entity that can be wholly present in more than one place at the same time, and that different particulars share when they are the same in some respect. Redness, if there is such a thing, is a universal.Defined in Universals and Instances · Ontology · Beginner
Universal quantifier
The symbol $\forall$, read "for all" or "for every". The formula $\forall x Fx$ is true under an interpretation when every object in the domain satisfies $F$, and false when at least one does not. It is the formal counterpart of "every", "all", "each", and "any" in their general uses.Defined in Predicate Logic · Logic · Intermediate
univocal predication
Using a term in exactly the same sense in both applications, so that "wise" means the same in "Solomon is wise" and "God is wise" and differs only in the degree or manner in which it holds. Univocity is what makes ordinary inference possible: if a word shifts sense between premises, the argument equivocates. Its cost in theology is that a term with a single sense across creatures and God appears to place God under a common concept, which is what the doctrine of simplicity was designed to prevent.Defined in Religious Language · Theism · Advanced

V

Validity
An argument is valid when there is no possible situation in which all of its premises are true and its conclusion is false. An argument that is not valid is invalid.Defined in Validity and Soundness · Logic · Beginner
Variable domain semantics
The interpretation on which each world carries its own domain, so that an object may exist at one world and not another. Quantifiers at a world range over that world's domain, and the domains may overlap, nest or be disjoint.Defined in Quantified Modal Logic and the Barcan Formulas · Logic · Advanced
Variable sharing
The necessary condition these systems impose: if $\varphi \rightarrow \psi$ is a theorem, then $\varphi$ and $\psi$ share a propositional variable. The condition rules out the paradoxes of material and strict implication, since $\varphi \rightarrow (\psi \rightarrow \psi)$ and $(\varphi \land \neg \varphi) \rightarrow \psi$ both fail it.Defined in Relevance Logic and Paraconsistency · Logic · Advanced
verification principle
The criterion of meaning proposed by the logical positivists, on which a statement is factually significant only if it is analytic, true or false by the meanings of its terms, or empirically verifiable, capable in principle of being confirmed or disconfirmed by observation. Statements meeting neither condition are not false but meaningless, in the sense of failing to express a proposition at all. Applied to theology, the principle classifies "God exists" and "God does not exist" as equally void of content.Defined in Religious Language · Theism · Advanced
Veritism
The view that truth is the fundamental epistemic good, so that all other epistemic goods, including justification, reliability and rationality, are valuable only as means to true belief and the avoidance of false belief. The term is Alvin Goldman's.Defined in Epistemic Value and the Swamping Problem · Epistemology · Advanced
via negativa
The specific procedure of apophatic theology: reaching a conception of God by removing from an initial description everything that belongs to creatures as such. God is not material, so not extended, not divisible, not located; not changeable, so not temporal; not limited, so not finite in power or knowledge. Each step subtracts rather than adds, and the resulting conception is defined by its exclusions.Defined in Religious Language · Theism · Advanced
Virtue epistemology
The approach on which the primary objects of epistemic evaluation are the believer's stable cognitive qualities, and a belief is justified or knowledgeable in virtue of issuing from a good quality of the believer rather than from a process considered impersonally.Defined in Reliabilism and Virtue Epistemology · Epistemology · Intermediate
Virtue ethics
The family of theories on which the primary subject of moral assessment is character rather than action, and right action is understood by reference to what a person of good character would do.Defined in Consequences, Rules, and Character · Ethics · Beginner

W

Weak atheism
The condition of a person who does not believe that God exists, without thereby believing that God does not exist. Also called negative atheism.Defined in Theism, Atheism, and Agnosticism · Theism · Beginner
Weak König's lemma
The statement that every infinite subtree of the binary tree has an infinite path. The full lemma, for finitely branching trees, is stronger; the restriction to binary branching is what yields the system called WKL-zero when the statement is added to the base theory.Defined in Reverse Mathematics · Logic · Advanced
Weakening
The structural rule permitting a sequent to be extended with an additional formula that plays no part in the derivation: from $\Gamma \vdash \varphi$ infer $\Gamma, \psi \vdash \varphi$. It expresses the assumption that unused premises are harmless, and with it comes the theorem $\varphi \rightarrow (\psi \rightarrow \varphi)$ and the derivation of a conclusion from an irrelevant premise.Defined in Substructural Logics · Logic · Advanced
Well-formed formula
A string of the language of propositional logic built according to the following three clauses. First, every sentence letter is a well-formed formula. Second, if $\varphi$ is a well-formed formula then $\neg \varphi$ is one, and if $\varphi$ and $\psi$ are well-formed formulas then $(\varphi \land \psi)$, $(\varphi \lor \psi)$, $(\varphi \rightarrow \psi)$, and $(\varphi \leftrightarrow \psi)$ are each one. Third, nothing else is a well-formed formula. The abbreviation wff is standard and is pronounced as it looks.Defined in Propositional Logic and Well-Formed Formulas · Logic · Intermediate
What it is like
Thomas Nagel's formulation of the subjective character of experience: an organism is conscious in this sense if there is something it is like to be that organism, some way the world seems from its point of view.Defined in Consciousness Versus Cognition · Philosophy of Mind · Beginner
Will to believe
William James's thesis that when an option cannot be settled on intellectual grounds and is living, forced, and momentous, it is legitimate to let considerations other than evidence decide it.Defined in Pragmatic Arguments for Belief · Theism · Intermediate

Z

Zero confirmation of universal laws
The result that on every member of Carnap's continuum, in a language with infinitely many individuals, the probability of a universal generalisation is zero and remains zero after any finite body of confirming evidence. The generalisation is the conjunction of infinitely many instances each with probability less than one, and the product tends to zero.Defined in Inductive Logic and the Carnap Programme · Logic · Advanced