Do we need identity?
A propos of a discussion going on at the Maverick Philosopher’s place, I revisited ‘Do we need Identity’, chapter 6 of The Logic of Natural Language, a work by the late Fred Sommers that should be on everyone’s bookshelf. As the title suggests, Sommers questions the doctrine of ‘relationism’, i.e. the view that identity is a relation, and that the verb ‘is’ functions both to connect subject and predicate, as in ‘Venus is a planet’, and to relate objects, as in ‘Hesperus is Venus’.
I summarise his argument as follows. First, the distinction between the ‘is’ of predication and the ‘is’ of identity is not obvious, otherwise philosophers would have spotted it earlier. It is sometimes attributed to Leibniz, but Sommers questions whether it is to be found in that philosopher’s writings. Second, it only seems obvious after we have accepted the category distinction made by modern logic between object words and concept words. If we agree that ‘Venus’ and ‘Hesperus’ must be represented in the syntax of modern logic by lower-case letters, we must represent them as ‘a’ and ‘b’. But then ‘a is b’ is ill-formed if we read the ‘is’ as the ‘is’ of predication. In the aptly named ‘predicate logic’, the verb ‘to be’ is swallowed up into the predicate: we must represent ‘Venus is a planet’ as ‘Fa’, where ‘F’ stands for ‘is a planet’. As Sommers ironically comments
It is therefore obvious that ‘a is b’ has the form F(a,b,) where F is the grammatical predicate which represents ‘is identical with’ or ‘is no other than’. Clearly, it is only after one has adopted the syntax that prohibits the predication of proper names that one is forced to read ‘a is b’ dyadically and to see in it a sign of identity.
It may still be objected that identity really is a relation, and that the modern syntax makes explicit what was there all along, but more of that later.