Dispute with LPL and the Dept of Philosophy

This is outrageous!! "Boole" refuses to do things correctly, and there's a chance that the Dept of Philosophy will back LPL instead of one of their own students in his lone struggle against the perversion of logic by these dangerous programs.

Once you've read what I have to say below, and have agreed completely 100% and unqualified with me, sign up for the protest march later in the season, and we'll toyi-toyi outside the Muckleneuk campus, necklace a few innocent passers by, and overturn a few cars. That'll make 'em sit up and listen!

Right, so here goes:
As I understand it, the idea of a "Truth Table" is to set out all possible combinations of truth values for atomic sentences on the left, and then check the implications on the right, using the rules for the various connectives. Do any of you disagree with that proposition (and the tacit additional information I've edited out)? No. Obviously not, because then you'd be dead wrong, wouldn't you? So we agree that the left hand side sets out possible combinations, then.

Now what that means is that we manually apply some counting rules to the left side. We do some crude combinatorics, parrot fashion. I know that's very roughly put, but you know what I mean, and you obviously agree wholeheartedly with what I mean, rather than what I say, don't you? Good.

Now are there hard and fast rules for combinatorics that cover all situations? For instance, "you must have 2ⁿ possibilities if you have n objects". Of course not! Nonsense, rubbish, and poppycock! What if you're actually counting the properties of objects, and one of your objects lacks some properties that the others have?

Seeing as it'll be more exciting for you, my comrades in this struggle to overcome logic, I won't fill in the rest of the dots from that last paragraph, and will leave you to see it for yourself.

Look at it this way. Let A be a logical falsehood. By virtue of that fact it is never true. In other words it's not possible for it to be true. In other words when you're counting the possibilities for its truth values on its own, you would count only those that are ... er ... possible, surely? Or when we count possibilities must we also count impossibilities - as a kind of honorary "possibility"?

So starting with just A alone, we count its possible truth values: There's, F ...
and that's it, isn't it? So I count "one". Anyone disagree that this is the correct number of possibilities?

Now if we count just one possible truth value for A seen in isolation, how on earth do we suddenly get "four" of them when you start assessing combined probabilities? Surely you should only have "two"?

I know you didn't ask what the hell the quotation marks round "four" and "two" are for, but just bear with me while I explain to the others: You don't suddenly get four possibilities. A "Truth Table" is a tree with redundant trunks. We repeat ourselves when counting the leftmost possibilities.

So the tree for A || B, where B is possible should surely then read as follows:
A B | some sentence we don't care about
F T
F F ...

And that's it.

Hah! Try telling "Boole" that. "Boole" rejects this correct truth table, and insists that there are "not enough rows". "Boole" wants me to fill in rows for the non-existent possibilities too.

I'm so angry I could go and burn down the library right now, and I know you all feel the same way, so all we need to decide on then is the date, right?

Ammendment of Pleadings.

Having now gone and submitted grudgingly to doing Truth Tables the Boole way, I think I begin to see that perhaps I'm not as perfectly correct in all things as I usually am. Consequently I'm less angry now, and the Protest Committee (once the secretary, treasurer, master of proceedings, chair/person have been chosen) should obviously downtone their anger in accordance - if that's their whim, of course. I'd suggest that instead of burning UNISA to the ground, we should do this to C-Max, Pretoria.

This would appear to be how it works: Boole is a model for reasoning that would be convincing to something less intelligent than the average insect (Robert Mugabe, for instance). This means that Boole knows absolutely nothing about logical truths like the fact that nothing can be larger than itself (for otherwise it wouldn't be able to be of equal size to itself). Boole simply knows that "all things are possible" - or not. Those of you who are au fait and so on, might like to attack me vehemently, using this as a basis, so I'll just leave things at that for now.

I'm still trying to figure out how this is not a contradiction:

Premise: !A || !B (So, either A or B is false)

I proved: A && B (So, A and B are true)

And somehow fitch doesn't think this is a contradiction. Breaks my heart.

It would only be a contradiction if you used "exclusive or". i.e. either A or B but not Both.

I like to see your proof if possible, unless you meant !(A&&B )