### Single Idea 18897

#### [catalogued under 5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic]

Full Idea

Because predicate logic contrues identities dyadically, its account of inferences involving identity propositions needs laws or axioms of identity, explicitly asserting that the dyadic realtion in 'x=y' possesses symmetry, reflexivity and transitivity.

Clarification

'Dyadic' means two-place

Gist of Idea

Predicate logic has to spell out that its identity relation '=' is an equivalent relation

Source

Fred Sommers (Intellectual Autobiography [2005], 'Syllogistic')

Book Reference

'The Old New Logic', ed/tr. Oderberg,David S. [MIT 2005], p.14