Some people think that the identity notion is captured by the second proposal above. I think we need two notions of identity. I will not discuss that now. Strict identity For all things, for all things, for all predicates, that x and y are strictly identical logically implies that that x has predicate F is logically equivalent with that that y has predicate F. (∀x)(∀y)(∀F)(x=Sy⇔(Fx⇔Fy)) [with obvious interpretation and =S meaning strict identity] This is called Liebniz's law.
Identity and personal identity
Identity and personal identity
Identity and personal identity
Some people think that the identity notion is captured by the second proposal above. I think we need two notions of identity. I will not discuss that now. Strict identity For all things, for all things, for all predicates, that x and y are strictly identical logically implies that that x has predicate F is logically equivalent with that that y has predicate F. (∀x)(∀y)(∀F)(x=Sy⇔(Fx⇔Fy)) [with obvious interpretation and =S meaning strict identity] This is called Liebniz's law.