John Page

Please excuse my lack of rigor here. What I was trying to say was that it was possible that B and ~B.

In the context fo my example, I believe that in reality ~A (non-determinsitic universe) and ~B (a system of representing the universe is not incoherent) are mutually exclusive.

Ah!

Clutch

Nope, doesn't follow either.

Unless you just mean: PossA & Poss~A

That's fine; it just says that A is contingent.

But Poss(A&~A) is very different, an absurdity, and certainly is not derivable from anything Scorpion or ex-xian have said.

John Page

Agreed, its a logical absurdity since it violates LNC axiom.

But this brings us to the absurdity of logic as A and ~A can't coexist. It therefore follows that logic must operate in a causal environment (reality as we know it) in order to compare things for A'ness hence it being PossA & Poss~A. Unless A is considered axiomatic, it must always be contingent - consequence of LOI - and if A is contingent how can we ever know what it is?

IMO, for the OP proposition to be anything other than false requires equivocation (such as a redefinition of the moon or cheese).

Cheers, John

Clutch

John, if you say "It therefore follows that...", it's a good idea to have the next bit actually follow from what you've said!

In this case, the bit you say follows (whatever it means) isn't even vaguely suggested by the fact that A&~A is a contradiction.

You've got this idea that logic is causal. Your arguments have all been of the form:

[ill-formed formal gobbledegook]; therefore, logic is causal.

I can't stick around to pursue this, but I do recommend just looking at a logic text. Bergmann et al's The Logic Book, or even Stephen Read's Thinking about Logic. Good luck.

John Page

Clutch:

Then let me try and explain my leap of intuition (which, naturally, seems totally obvious to me, but which I'm happy to expurgate to see if it makes sense to anyone else). Here's the whole paragraph:

I guess I had hoped that anyone reading the above would see the explanation of why it follows in the third sentence - the result was a consequence of the LOI and that the underlying assumptions/axioms within the system of logic cause the results/conclusions.

To restate the case: Logic operates in a causal environment because a proposition's truth value (A v ~A, but not both at the same time) is contingent and determined by the system of logic in question. If the environment was not causal, we would not be able to resolve the proposition's truth value.

My view is that logic is a formal system implemented within the mind/brain and, this being the case, logic is necessarily causal. This contrasts with a rock, for example, which is not causal (although the mind imputes that it may have been caused by something).

Here's some more reasoning based on posts earlier in the thread:

"If it is raining then the street will be wet"
A B A=>B
-----------------
T T T
F T T
F F T
T F F

From the first and last entries, there are some A for which B and some A for which ~B. This means the truth value of B is conditional. For something to be conditional means that something must determine what it is - and if logic is a closed system it is the logic system that is the deterministic cause.

As a BTW, it struck me as odd that material implication is not equivalent to any single Boolean logic operation. i.e. In lines 2 and 4 when assuming that there is no precedence so (A&B) ~=(B&A). Boole proposed his logic operations as non-procedural (i.e. with precedence of processing).

Anyway, as you seem to understand much more about logic than I, I'd be interested to know if you consider logic causal, non-causal or acausal.

Cheers, John

Scorpion

I'm sorry to say I don't have the slightest idea what you're talking about John - I'm so lost I'm not even sure what question I should ask to get anywhere with this. I'll shoot in the dark and see if I hit anything:


Uh, conditional on what? I don't see any conditionality attached to B in this example?

-S-