Talk:Boolean algebra

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Is it useful in theorem proving? I learned symbolic logic as a teenager, using a game created by a Yale law professor. Ever hear of WFF_'N_PROOF? --Ed Poor Talk 09:17, 1 December 2008 (EST)

Wff 'n proof? YUKK! I'd forgotten about that. I was given that as a child (math and science whiz, relatives buy what they consider appropriate presents, you know the drill.) It was the most boring "game" I had ever seen. It made no sense to me. I guess I was way more interested in stuff like calculus. I now have a decent understanding of formal logic at the college level, and the game might make sense, though I still doubt that I would find it fun.

The game came in a dark blue case, and had an "egg timer" and some cubes with propositional calculus quantifier symbols on them, right?

Getting to the topic at hand, yes, the topic that we call boolean algebra plays a central role in formal logic. But it goes beyond that. Boolean algebra underlies just about everything, such as when we say "It isn't true that 2+2=5." This means that, in the articles relating to this, we have to give short shrift to Boole, De Morgan, Venn, Shannon, etc. It's too bad, but I think that's the way it has to be. There really isn't much that this article should say other than what it says now. If we were to go into applications (formal logic or otherwise), the article would never end.

On a related topic, I think that formal logic (that is, the formal study of theorem proving) is just too complicated for CP. There are a lot of ambitious topics that we are trying to make accessible at the level of the target audience. We can succeed at this if we make sure that there are no unfilled gaps in the pedagogy, that is, we create a complete pedagogical path to the goal. That's what we should be working on. If we can't create the path, we shouldn't try to get to the goal. I've been trying to do that (and probably just barely succeeding) in my work on complex analytic functions. There's a lot we can say if we are very careful about the definition of derivative, and what it really means to extend that definition to complex numbers, and so on.

Speaking of which, there's another guiding principle, that was brought up by ElizabethK, giving the example of Kepler's laws: We sometimes have to make the distinction between that which we tantalize the kids with, and that which we can actually make them understand. So, to take the example of complex analytic functions, I explain the derivative; there's a good chance that an ambitious reader will actually understand that. But then I state, without proof, various wonderful consequences, like the radius of convergence, Liouville's theorem, and analytic continuation. Actually proving those is totally beyond the scope of Conservapedia.

I believe that the same can be said about formal logic. It's an advanced college-level subject. But, of course, this is coming from someone who hated Wff 'n proof :-) If you can do it, I'd be very interested in seeing your results.

SamHB 18:16, 2 December 2008 (EST)