The problem with intensional idioms is that they do not support substitutivity of identicals salva veritate.

To some, this body of research has been taken to progressively undermine the very foundations of Cognitive Science, which takes rationality and substitutivity as axiomatic.

The third schema is known as Leibniz's law, "the principle of substitutivity", "the indiscernibility of identicals", or "the replacement property".

The concepts that are used to explain this concept are extensionality, definiteness, substitutivity of identity, unfoldability, and referential transparency.

W.V.O. Quine takes substitutivity salva veritate to be the same as the "indiscernibility of identicals".

The latter, while providing a crucial guide for the understanding of the way terms are used in different contexts, does not allow for a simple explanation based on substitutivity.

Many other propositions have also been mentioned as laws of thought, including the dictum de omni et nullo attributed to Aristotle, the substitutivity of identicals (or equals) attributed to Euclid, the so-called identity of indiscernibles attributed to Gottfried Wilhelm Leibniz, and other "logical truths".