Lukecash12
Registered User

If you can, go have a look in "Member Contributed News" at my Kevin Smith's "Red State" thread... I addressed the last part of my OP to you.

I will try to prepare a definition list from my side for your approval.

In addition, I will give you my OP privately first for the purpose of making sure it is the idea you wanted to debate and feel comfortable with.

If you are happy with my definitions and OP, I will then post with you on the FD board that we are ready to start. Then , if the judges are ready, I will post that OP and we will go.

Sound good? It will probably take me a few days. Shalom, DAK

My two cents:

I personally only consider the set of possible worlds where the Laws of Logic hold (identity, LEM, and non-contradiction), and reject Heyting logic (which rejects LEM), as something which is not logic but something else entirely. Though this is just discussing definitions at some level. You could construct a new version of Kripke semantics where Heyting logic and not Boolean logic applies, although you'd need to fashion new (or extra) axioms, I think, because the ones given in S5 (the symbolic logical language of Kripke semantics) would be invalid under Heyting algebras.

Heh, I'm no philosopher. I'm a mere dabbler.

The problem, I think, is figuring out what is meant by "possible." The usual meaning is "entailing no contradiction." But the definition of contradiction depends on what logic you take; in order to construct a set of possible worlds, you have to stipulate a logic that defines "possible." And what is possible in the sense of logic A may not be possible in the sense of logic B.

So I guess you could talk about the "set of all possible worlds" being "a world W is possible if there exists an algebra under which W entails no contradiction." I'm not sure if this is a fruitful path of inquiry or not...