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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.
From these hypotheses, it is also possible to prove that there is only one God in each world by Leibniz's law, the identity of indiscernibles: two or more objects are identical (the same) if they have all their properties in common, and so, there would only be one object in each world that possesses property G. Gödel did not attempt to do so ...
In metaphysics, identity (from Latin: identitas, "sameness") is the relation each thing bears only to itself. [1] [2] The notion of identity gives rise to many philosophical problems, including the identity of indiscernibles (if x and y share all their properties, are they one and the same thing?), and questions about change and personal identity over time (what has to be the case for a person ...
Gottfried Leibniz's Principle of the identity of indiscernibles states that two things are identical if and only if they share the same and only the same properties. This is a principle which defines identity rather than difference, although it established the tradition in logic and analytical philosophy of conceiving of identity and difference as oppositional.
In some contexts one considers the more general notion of order-indiscernibles, and the term sequence of indiscernibles often refers implicitly to this weaker notion. In our example of binary formulas, to say that the triple ( a , b , c ) of distinct elements is a sequence of indiscernibles implies
The indiscernibles argument then asserts that the identity of indiscernibles is violated, for example, by identical sheets of paper. All of their qualitative properties are the same (e.g. white, rectangular, 9 x 11 inches...) and thus, the argument claims, bundle theory and metaphysical realism cannot both be correct.
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The "identity of indiscernibles" is frequently invoked in modern logic and philosophy. It has attracted the most controversy and criticism, especially from corpuscular philosophy and quantum mechanics. The converse of this is often called Leibniz's law, or the indiscernibility of identicals, which is mostly uncontroversial. Sufficient reason ...