Relative identity
Peter Geach's proposal that “the same” always means “the same something” — so two things could be the same being without being the same person. It is often reached for as a way of stating the Trinity without contradiction.
Ordinary identity is absolute: if x is y, then x and y share everything, full stop. Peter Geach proposed instead that identity is always relative to a kind — x is the same F as y, and the question "but is it the *same*?" with no kind supplied is incomplete.
Applied to the Trinity, this promises a way to say that the Father is the same God as the Son but not the same person as the Son, without contradiction. Whether it delivers is contested: critics argue that it either changes the subject or requires giving up principles about identity that are doing work elsewhere. It is a way of *stating* the doctrine consistently, which is not the same as an argument for how many persons there are.
Where this comes up
Sources
- Peter Geach, Reference and Generality (1962); Debby research packet OTC-002