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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 Ref
'The Old New Logic', ed/tr. Oderberg,David S. [MIT 2005], p.14
| 18904 | 'Predicable' terms come in charged pairs, with one the negation of the other [Sommers, by Engelbretsen] |
| 18903 | Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen] |
| 18893 | Translating into quantificational idiom offers no clues as to how ordinary thinkers reason [Sommers] |
| 18894 | Predicates form a hierarchy, from the most general, down to names at the bottom [Sommers] |
| 18901 | Truthmakers are facts 'of' a domain, not something 'in' the domain [Sommers] |
| 18895 | Logic which maps ordinary reasoning must be transparent, and free of variables [Sommers] |
| 18900 | Unfortunately for realists, modern logic cannot say that some fact exists [Sommers] |
| 18898 | In standard logic, names are the only way to refer [Sommers] |
| 18897 | Predicate logic has to spell out that its identity relation '=' is an equivalent relation [Sommers] |