Identity and Individuation
Two articles have now ended with the same unfinished business. Admit events, and the question arrives of when two descriptions describe one event. Admit properties, and the question arrives of when the property this thing has is the one that thing has. Putting an entity on the list is not enough. An ontology that cannot say when it has one of something rather than two has not really said what it accepted.
Identity
Definition
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.
English uses "same" for two quite different things, and the whole subject depends on keeping them apart. Two mugs off the same production line are the same in the sense of being exactly alike. There are two of them. Hesperus and Phosphorus are the same in the sense that concerns us here. There is one of them, and the ancient astronomers took there to be two. The metaphysics ladder gives these two senses their standard names; here it is enough that they are different, and that only the second is identity in the strict sense.
The strict relation is governed by a principle that almost nobody rejects: if a is identical with b, then everything true of a is true of b. It has to be so, since there is only one thing there, and one thing cannot both have and lack a property.
The principle is what makes identity claims informative. Finding a difference is finding two things, and every argument for distinctness in metaphysics runs through this. The Ship of Theseus, the statue and the clay, and the mind and the brain are all cases where the argument takes the same form: here is something true of the one and not the other, so they are two.
Check your understanding
Telling one from another
Knowing what identity is does not tell you how to determine, in a given case, whether you have one thing or two.
Definition
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.
Definition
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.
The set case is the model because it is clean. Any question about whether these are one set or two reduces to a question about membership, and membership questions are settled independently. That is what a criterion is supposed to deliver: a route from a question you cannot answer directly to one you can.
Most kinds do not oblige so neatly. Ask for the criterion for events and the two answers from the previous article are in competition. Ask for the criterion for properties and the same fork appears. Ask for the criterion for persons and the question turns into one of the largest debates in philosophy. Failure to supply a criterion is not proof that a kind of entity does not exist, but it is a debt, and the demand for payment has been used to considerable effect. Willard Van Orman Quine made the demand a central tool of his ontology, and the intermediate tier follows that thread.
Counting
Definition
Countability
The feature a kind has when it makes sense to ask how many of them there are, and there is a determinate answer.
Some questions of the form "how many?" have answers and some do not, and the difference is not about difficulty. Ask how many chairs are in the room. Ask how many pieces of furniture. Both have answers. Now ask how many things are in the room, with no restriction at all. The chair is a thing. So is each of its legs, so is the top half of the chair, and so is the aggregate of the chair and the lamp. Nothing about the room fixes a number, because nothing in the question says what to count.
That is the observation the next definition is built on. Counting requires a kind, and different kinds carve the same material differently. There is one deck and there are fifty-two cards, and the two counts are both correct because they are counts of different things.
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Sortals
Definition
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.
Terms like "red" and "heavy" do not do this. They apply to things, but they supply no way of counting: "how many reds are in the room" has no answer until a kind is supplied. The contrast is why sortals matter. They are what makes counting possible at all.
Peter Strawson brought the notion into contemporary use, and David Wiggins built the most developed account of what it is to be a thing of a kind around it. The Stanford Encyclopedia entry on sortals notes that the notion resists sharp definition and that counting and identity can come apart, so what is offered here is the working version rather than the settled one.
The connection to the rest of the article is direct. A criterion of identity is always a criterion for things of some kind, never for things as such. This is why the question "is that the same one?" cannot be answered until you know what "one" is being asked about, and why the Ship of Theseus is a hard case: the material and the vessel are two kinds, and they give different answers about the same stuff.
Objection
If identity questions cannot be answered without a sortal, then identity is not one relation. It is a family of relations, one for each kind. The ship and the wood are the same wood and not the same ship, and there is nothing further to say about whether they are the same simply.
Reply
This is Peter Geach's doctrine of relative identity, and it is a serious position rather than a confusion. Geach argued that absolute identity is not expressible at all, and that every genuine identity claim is a claim of sameness under some kind.
The standard response accepts the role of sortals in answering identity questions and denies that it follows that identity is relative. On this view the sortal tells you what you are asking about, and once that is fixed the relation asked about is the ordinary absolute one. The ship and the wood are two things sharing their matter, not one thing that is self-identical under one sortal and not another. That reply preserves the indiscernibility principle, which relative identity has to qualify, and preserving it is a substantial advantage. The dispute is not closed, and the intermediate tier returns to it.
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What this buys
Three demands can now be made of any ontological proposal. Say what kind of thing is being admitted. Say when you have one of them and when two. Say whether the counting question has an answer.
Proposals that cannot meet these are not thereby refuted, but they are incomplete in a way that is easy to overlook when the entities sound familiar. Applying the demands to the cases from the previous articles is a useful exercise, and the results are uneven: sets pass easily, events are contested, properties depend entirely on which theory of them is adopted.
The next article turns the machinery on existence itself, and asks whether existence is a property in the sense the last two articles have been using.
Further reading
- P. F. Strawson, Individuals: An Essay in Descriptive Metaphysics, Methuen (1959).
- Peter Geach, Reference and Generality, Cornell University Press (1962).
- David Wiggins, Sameness and Substance Renewed, Cambridge University Press (2001).
- Stanford Encyclopedia of Philosophy, "Identity", by Harold Noonan and Ben Curtis.
- Stanford Encyclopedia of Philosophy, "Sortals", by Max A. Freund and Richard E. Grandy.
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