While listening to what Wittgenstein has to say about necessity as it pertains to mathematics, I noted that he is not denying that we encounter constraint or necessity when doing mathematics: he is denying that this constraint comes from something outside the game. Rather, it is from the game itself. But what if mathematics is a game we can play with rational beings very different from ourselves? Can we intuit that all would be constrained as we are? Even if they are incredibly smarter? And what about God? Is math a game we play with God rather than being a kind of activity the we aim at God (or at God's Mind) as a kind of ideal object?
How about defining it as an instance of functional complexity? And treating the list of properties as following necessarily from this definition? Okay, this is very diamond-in-the-rough (or perhaps zirconium...) but here goes my thoughts on the matter: (Complexity) Many diverse parts (functional) acting for the sake of the whole I think I need to add something like "not as the instrument of another" or something like that. Given that they act together as one whole and given entropy, etc., the organism will need to posses more order than its surroundings (homeostasis). It will therefore need to take in energy (nutrition), which it will use to sustain its readiness to interact with its environment so as to preserve its own being (homeostasis again?), but which will eventually break down (death), so that in order for that life form to continue it will need to duplicate itself (reproduction), which, upon occurring, will involve both development (growth) to maturity and...
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