May 28, 2009

Mathematical Intuitionism and the project

I don't really know what im talking about, but ...

It occurred to me that my project does not use negation as failure, and also doesn't use the law of excluded middle. Its not like Im purposely trying to go against what would be normal, I only did what I thought made sense when writing. This just goes to show how much creatively there is in ignorance.

Im not trying to view this projects as something mathematically concrete. I don't really refer to anything as a "Model". My reasoning for the ternary model was that any proposition exists in one of THREE states with respect to a body of knowledge, that it either is confirmed, denied, or bears no relation. It looks like ive somehow stumbled into being a mathematical intuitionist though.

Funny how the wikipedia article, which is my only source of info on this area, doesn't mention anything about ternary logic, or modal logic (my ternary logic is really just a cheap substitute for modal logic after all).

At any rate this intuitionism appeals to me on some really sort of zen level. Maybe God can separate out all logical statements into True, and False. We however can't and it leads me to be very unsettled. I don't think ive ever written a nonconstructive proof in college. Now I don't feel safe in saying that anything thats not false is true.