Concept

Identity of indiscernibles

Overview

The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities x and y are identical if every predicate possessed by x is also possessed by y and vice versa. It states that no two distinct things (such as snowflakes) can be exactly alike, but this is intended as a metaphysical principle rather than one of natural science. A related principle is the indiscernibility of identicals, discussed below.

A form of the principle is attributed to the German philosopher Gottfried Wilhelm Leibniz. While some think that Leibniz's version of the principle is meant to be only the indiscernibility of identicals, others have interpreted it as the conjunction of the identity of indiscernibles and the indiscernibility of identicals (the converse principle). Because of its association with Leibniz, the indiscernibility of identicals is sometimes known as Leibniz's law. It is considered to be one of his great metaphysical principles, the other being the principle of noncontradiction and the principle of sufficient reason (famously used in his disputes with Newton and Clarke in the Leibniz–Clarke correspondence).

Some philosophers have decided, however, that it is important to exclude certain predicates (or purported predicates) from the principle in order to avoid either triviality or contradiction. An example (detailed below) is the predicate that denotes whether an object is equal to x (often considered a valid predicate). As a consequence, there are a few different versions of the principle in the philosophical literature, of varying logical strength—and some of them are termed "the strong principle" or "the weak principle" by particular authors, in order to distinguish between them.

The identity of indiscernibles has been used to motivate notions of noncontextuality within quantum mechanics.

Associated with this principle is also the question as to whether it is a logical principle, or merely an empirical principle.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

In the original texts

Passages from public-domain books where Identity of indiscernibles is discussed.

This is, of course, a further objection to the dogma of internal relations, since I think it is obvious that the principle of Identity of Indiscernibles is not true. Indeed, so far as I can see, the dogma of internal relations essentially consists in the joint assertion of two indefensible propositions: (1) the proposition that in the case of no relational property is it true of…
G. E. Moore, Philosophical Studies
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That gives rise to these eternal, and usually mistaken, contentions on necessity and contingency, on the possible and the impossible. But provided that it is understood that necessity and possibility, taken metaphysically and strictly, depend solely upon this question, whether the object in itself or that which is opposed to it implies contradiction or not; and that one takes into account that contingency is…
Gottfried Wilhelm Leibniz, Theodicy Essays on the Goodness of God, the Freedom of Man and the Origin of Evil
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XLIX. That the eternal truths cannot be thus enumerated, but that this is not necessary. What I have already enumerated we are to regard as things, or the qualities or modes of things. We now come to speak of eternal truths. When we apprehend that it is impossible a thing can arise from nothing, this proposition, EX NIHILO NIHIL FIT, is not considered as somewhat existing, or as the mode of a thing, but as an…
René Descartes, Selections from the Principles of Philosophy
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To certain facts, certain facts always do, and, as we believe, will continue to, succeed. The invariable antecedent is termed the cause; the invariable consequent, the effect. And the universality of the law of causation consists in this, that every consequent is connected in this manner with some particular antecedent, or set of antecedents. Let the fact be what it may, if it has begun to exist, it was preceded by…
John Stuart Mill, A System of Logic
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3). Secondly, the indivisible is so called in relation to species, as man's reason is something indivisible. This way, also, the indivisible is understood before its division into logical parts, as we have said above (De Anima iii, 6); and again before the intellect disposes and divides by affirmation and negation. The reason of this is that both these kinds of indivisible are understood by the intellect of itself…
Aquinas Thomas, Summa Theologica, Part I
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Identity of indiscernibles

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Philosophers who discussed Identity of indiscernibles

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