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Harv,
I wasn't playing kindergarten games with you, I did realize something about your way of thinking which explains much of your inability to understand where I'm coming from.
First of all, I'm convinced one of the problems is my refusal to use sophisticated jargon. This might turn out to be a minor issue, but it's my experience that people who express themselves in a certain "sophisticated" style usually tend to dismiss people who adopt a more "layman" approach, so to speak. I always hoped you wouldn't mind my vocabulary choices and would rather concentrate on the argument being presented. At this point, I'm not sure you're capable of that (of overlooking erudition issues, that is). In any case...
I'd like to explain to you what I think is wrong with a statement you made recently:
Is that what you mean to say, that "LNC" is an axiom of formal logic? If so, then I agree. The issue with Alan is that he is treating the axiom as needfully true, but that would be demonstrate a proof of an axiom (which there is none).
The issue here is a subtle one. Were it not subtle we probably wouldn't have to discuss it anyway. What I perceive here is some confusion between logic and semantics. Sometimes it can be extremely difficult to understand when a problem is one of logic or one of semantics, I myself have enormous difficulty with it sometimes. In fact, I think most conversations on this forum center around semantic issues, not logical ones. Let me try and explain what I think causes the problem:
Think of a computer. Unless it's broken, it's a perfectly logical machine. Because computers perfectly embody the rules of logic, they can be used to test the logical validity of a proposition simply by expressing it in terms that can be handled by the machine - be those voltage levels, bits, or statements in a programming language. Now what happens here? The computer becomes a tool for "automatic thinking". Instead of having to mentally follow chains of logic, which often get too large or complex for our conscious minds to handle, we can simply express the problem in computer language and let the machine do the job. It works all the time.
Of issue here is that abstract thought, if it's logical, can be expressed in multiple ways, and as long as no errors are made, a valid logical chain expressed in one form can be translated into any other form without losing its validity. That is, probably, the very fact that makes logic our most powerful intellectual tool.
One of the best ways to express logical thought is mathematics. If a proposition is mathematically valid, it is almost certainly logically valid as well. However, math has many limitations and cannot be used to express certain types of problems (eg, problems involving singularities). Next to math, the best thing we have is semantics. As much as math can be said to be "logic applied to numbers", we can probably describe semantics as "logic applied to words". However, there is a problem that is seldom taken into account: while the rules of semantics are clear, the definitions of words are not.
Let me now go back to your sentence:
the axiom as needfully true, but that would be demonstrate a proof of an axiom (which there is none).
While the sentence is semantically valid, I maintain that it's not logical. The crux of the problem lies in the meaning of the word "proof", which in my opinion you are failing to fully take into account. It's my contention that, whatever it is that "proof" means, the word can only have meaning if the basic axioms of logic are accepted. That is, without logic there is no proof of anything!
So it's not that you can't demonstrate a proof of an axiom of logic, it's rather than any such exercise would be completely futile and meaningless. The axiom is not needfully true, it's needed for the concept of truth to have any meaning.
For instance, I said the statement A = A is valid in any conceivable universe. Notice, I didn't say "any universe", which is quite a different thing. There might in fact be universes in which A = A is false. There is one problem with those universes, though - they can't be conceived! Most important of all, since we can conceive the universe in which we exist, we can say with all certainty that A = A must necessarily be true in our universe. Taking it a bit further, the fact that we think logically is proof that logic is a valid means of thinking, and no other proof is required. But of course there are other means of thinking.
I'm not sure this can be easily understood. Probably not. The subject is full of subtleties and unfortunately I have no time to further elaborate. That's all I can offer, I hope it helps explain my position. And if it doesn't, that's OK too.
Warm regards,
Aurino
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