Concerning this passage from Phaedo:
I mean, for instance, the number three, and there are many other examples. Take the case of three; do you not think it may always be called by its own name and also be called odd, which is not the same as three? Yet the number three and the number five and half of numbers in general are so constituted, that each of them is odd though not identified with the idea of odd. And in the same way two and four and all the other series of numbers are even, each of them, though not identical with evenness. (104a-b)
In a math.stackexchange question Jon Ericson suggested:
The philosophical point is that there exists an Idea (or Form) called Odd and odd numbers are merely specific instances of Odd. The [numbers] are not, themselves, identical to the concept of Oddness.
I made a remark on this statement:
More to my point, I don't fully understand the point of [the quote].
Why is there a distinction made between odd, in the context of numbers, and some other esoteric and undefined sense of odd? I'm not saying it's not valid, I'm just saying I don't see the use.
I realize that not all philosophers are mathematicians, but I do not believe this is an exclusive question. So, can anyone enlighten me on why Plato made this distinction?
This particular discussion begins (I think) on [103e] and spans on until [105c].