Criterion of identity

The principle of individuation is a criterion that individuates or numerically distinguishes the members of the kind for which it is given, that is by which we can supposedly determine, regarding any kind of thing, when we have more than one of them or not. It is also known as a 'criterion of identity' or 'indiscernibility principle'. The history of the consideration of such a principle begins with Aristotle. It was much discussed by the medieval philosopher Duns Scotus (c. 1266–1308) with his "haecceity" and later, during Renaissance, by Francisco Suárez (1548–1617), Bonaventure Baron (1610–1696) and Leibniz (1646–1716).

Taking issue with the view expressed in certain Platonic dialogues that universal Forms (such as the Good, the Just, the Triangular and so on) constitute reality, Aristotle (384–322 BC) regarded an individual as something real in itself. An individual therefore has two kinds of unity: specific and numerical. Specific unity (that is unity of the species to which an individual belongs) is a unity of nature which the individual shares with other individuals. For example, twin daughters are both human females, and share a unity of nature. This specific unity, according to Aristotle, is derived from Form, for it is form (which the medieval philosophers called quiddity) which makes an individual substance the kind of thing it is. But two individuals (such as the twins) can share exactly the same form, yet not be one in number. What is the principle by which two individuals differ in number alone? This cannot be a common property. As Bonaventure later argued, there is no form of which we cannot imagine a similar one, thus there can be 'identical' twins, triplets, quadruplets and so on. For any such form would then be common to several things, and therefore not an individual at all. What is the criterion for a thing being an individual?

In a passage much-quoted by the medievals, Aristotle attributes the cause of individuation to matter:

The whole thing, such and such a form in this flesh and these bones, is Callias or Socrates; and they are different owing to their matter (for this is different), but the same in species, for the species is indivisible.

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