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.
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 form of the principle is attributed to the German philosopher Gottfried Wilhelm Leibniz.
[1] The identity of indiscernibles has been used to motivate notions of noncontextuality within quantum mechanics.
[10] In a universe of two distinct objects A and B, all predicates F are materially equivalent to one of the following properties: If ∀F applies to all such predicates, then the second principle as formulated above reduces trivially and uncontroversially to a logical tautology.
In that case, the objects are distinguished by IsA, IsB, and all predicates that are materially equivalent to either of these.
This argument can combinatorially be extended to universes containing any number of distinct objects.
[12][13] Another important distinction concerns the difference between intrinsic and extrinsic properties.
Notice that to show that the identity of indiscernibles is false, it is sufficient that one provide a model in which there are two distinct (numerically nonidentical) things that have all the same properties.
Per his argument, two objects are, and will remain, equidistant from the universe's plane of symmetry and each other.
Even bringing in an external observer to label the two spheres distinctly does not solve the problem, because it violates the symmetry of the universe.
However, one famous application of the indiscernibility of identicals was by René Descartes in his Meditations on First Philosophy.
This argument is criticized by some modern philosophers on the grounds that it allegedly derives a conclusion about what is true from a premise about what people know.
[19] Numerous counterexamples are given to debunk Descartes' reasoning via reductio ad absurdum, such as the following argument based on a secret identity: