Ahhh - Aristotelian Logic

So, I'm going to update twice in one day - well, technically it's now Thursday, but I'm still awake.

Aristotle has what is referred to as the square of opposition

A (all p is q) E (no p is q)


I (some p is q) O (some p is not q)

It's called the square of opposition due to the way the axioms are set up. If E is true, the I is false, and vice versa. If A is true, then O is false, and vice versa. If A is true, the E is false, and vice versa, but both A and E can be false. If A is true, then I is true. If E is true, then O is true. It's possible for both I and O to be true. This is the basis of Aristotelian logic.

I'm writing my paper on modal logic, which then adds a 'necessary' or 'possible' before the logic axioms. So, necessarily all p is q, and so forth. Anyway, when I learn more and think more about it, I'll write more =)