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.