Picking up a post by Phil Windley, he says he likes dictionary.com's definition of identity, which expresses "being the same as". I very much agree.

Accordingly, in mathematical terms, identity defined this way is a function, returning either a Yes or a No, on two arguments that are being compared. Now that's a really simple and useful definition, isn't it?

Coincidentally the exact point I was trying to make with my This and That presentation at OSCON this year: my This object really wanted to know whether That1 and That2 were the same, and bad things happened because it couldn't be sure. Identity doesn't have to be that complicated as some people seem to want to make it, does it?

[I recognize there are (many) higher levels — but why not start with something very simple that is clear and can be built upon? Which coincidentally is exactly the approach we've been taking with LID and now with YADIS.]