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What does it mean in mathematics for two things to be equal, or for two things to have the same "identity"? For example, because anything divided by zero is "undefined", can we say that 1/0 = 2/0? What about the relational database concept of "null" which is supposed to stand for "unknown"? In relational algebra, they say NULL is not equal to NULL, but doesn't that violate the law of identity that everything is equal to itself?

I will begin by acknowledging that neither the philosophy of mathematics nor the metaphysics of identity are my specialties. But if you'll take what I say with a grain of salt, perhaps I might make a helpful observation nonetheless. Keep in mind that "being equal" mathematically is not exactly the same thing as "being identical," mathematically or otherwise. "Being mathematically equal" means, one might say, having the same mathematical value, in the sense of amounting to the same thing. Identity on the other hand means being the same thing, in the sense of having all the same properties. This difference can get confusing because commonly in symbolic logic the equal sign, "=", is used to express identity. But, if you follow me, then "2+2" equals "4" but is not identical to "4." Why? Well, while they both have the same mathematical value, they don't both have the same properties. "2+2", for example, is a formula composed of two Arabic numbers and a symbol for the mathematical relation of addition....