Metalogic

The difference between reasoning inside a logic and reasoning about one

8 min

Necessity, form, and topic neutrality as three candidate marks of a logical truth

10 min

Lewis Carroll's regress and why a rule of inference cannot be one more premise

9 min

Whether logic describes how we think, and Frege's case that it cannot

9 min

The liar and Russell's paradox as arguments that look valid and end in contradiction

10 min

Rival logics, the quantum logic episode, and what it would take to give up a law of logic

10 min

Intuition, convention, and inference as candidate sources of logical knowledge

9 min

Reading soundness and completeness as claims about the fit between proof and truth

14 min

Substitutional, modal, and model-based accounts of what it is for a conclusion to follow

16 min

How an English argument gets a form, and whether there is one correct way to formalise it

14 min

Sentences, statements, or propositions: what logic's validities are about

12 min

Carnap's principle of tolerance and Quine's regress argument against truth by convention

15 min

Quine's charge that a rival logician has only changed the subject, and how the rival replies

15 min

Prior's rogue connective, Belnap's conservativeness reply, and Dummett's demand for harmony

16 min

Van Heijenoort's contrast between Frege's universalism and the model-theoretic view, and what each makes of metalogic

22 min

The charge that model-theoretic consequence gets the extension of validity right only by luck

26 min

How completeness lets a formal notion be proved coextensive with intuitive validity

22 min

Logical constants as the isomorphism-invariant operations, McGee's theorem, and Feferman's objections

25 min

Why no logic stronger than first-order logic keeps both compactness and Löwenheim-Skolem, and what that is supposed to prove

25 min

Non-normal valuations that respect every classical rule, and the bilateral and open-ended repairs

24 min

Prawitz validity, canonical proofs, and Dummett's fundamental assumption as a theory of what connectives mean

26 min

Whether classical negation can be harmonious: stability, general elimination rules, and multiple conclusions

25 min

Dummett on the justification of deduction, rule-circularity, and Boghossian's blind reasoning

24 min

Harman's challenge that logic says nothing about reasoning, and MacFarlane's bridge principles

25 min

Williamson and Priest on choosing a logic the way one chooses a scientific theory

24 min

Kripke's argument, developed by Padró, that some logical rules cannot be adopted by anyone who lacks them

22 min

Beall and Restall's generalised Tarski thesis, the collapse argument against pluralism, and Russell's logical nihilism

24 min

Shapiro and Cook on formal systems as models of natural-language consequence rather than descriptions of it

20 min

Securing infinitary mathematics by finitary consistency proofs, Tait's analysis of finitism, and partial realisations

24 min

Gentzen's consistency proof for arithmetic by transfinite induction up to epsilon-naught, and what it secures

26 min

Gupta and Belnap on truth as a circular concept defined by revision sequences

25 min

Why every consistent theory of the liar seems to generate a new liar in its own vocabulary

24 min

Strict-tolerant logic, validity Curry, and keeping classical logic by giving up cut or contraction

26 min