In the Tractatus Logico-Philosophicus, Wittgenstein makes many sweeping, cryptic claims, sometimes quite philosophically radical, with little to no argument or explanation. These are some of the most frustrating parts of the book, but also the funniest. (“Logic must take care of itself.” “Superstition is the belief in the causal nexus.”) One of these claims is as follows:
That identity is not a relation between objects is self-evident.
For as long as I can remember, that is, for as long as I have been thinking about these sorts of issues, I have always agreed with Wittgenstein on this point. I agreed with him when I first read the Tractatus many years ago, and I agree with him now having just read it again. Identity is not a relation between entities (an entity and itself).
What is going on here may be unclear to the metaphysically uninitiated, so let me explain. It is philosophical commonplace to say that every entity is related to itself by a relation of identity. (I use ‘entity’ in a neutral way to refer to any particular thing, object, property, event etc. of any kind.) Further, it is often thought that this is something that we can be as sure about as anything. This may seem like an odd claim, but may make more sense when you see how it can be written: