Science Forums 2

[CraigD]

Let me first address a simple question Don asked about formal logic.

Originally Posted by Qfwfq

The implication is also formally a true one, what can you deduce from it?

Originally Posted by Don Blazys

I also can't see how you can possibly claim that the implication:

51/3=2 (implies) N*0=0

is "formally true". The equation 51/3=2 is false, while the equation N*0=0 is true. How can something false imply, "formally" or otherwise, something true?

Qfwfq is correct, because, in formal logic, “something false can imply something true”.

Like all formalism, formal logic is simply a collection of rules exactly defining the meaning of the symbols - operators and term - used in it. Unlike more well-known formalisms such as arithmetic, statements in ordinary formal logic evaluate to one of only two values: True and False.

The implication operator, , is defined as follows:


So the statement evaluates to True.

It's common to mix arithmetic statements with logical ones. Such a statement,

while intuitively silly-looking, is formally true.

On the less simple question of the Don's claim to have proven Beal's conjecture, I can offer only vague comment and advice.

I don't believe Don's proof is correct

Proofs are considered correct , categorizing roughly, for either formally or “sociologically”.

A formal proof is correct when each statement of a proof is “mechanically” produced according to a formal operation postulated to be correct for the formal system in question.

A “sociological” proof is “correct” when the intended audience of the proof believe it to be so. The importance of a sociological proof depends strongly on its audience. For example, for mathematical proofs, the acceptance as true by many professional academic mathematicians is more important than the acceptance, of, say, a gathering of friends.

By neither of these standards are Don's proofs correct.

My advice to Don is to take the various unusual phrases he's used in his proofs, and give them exact, formal definitions. “Cohesive term”, I believe, would be the best one to start with. State precisely the rule for transforming one expression into another given by the phrase. Don't attempt to prove anything, and avoid vague statements such as “cohesive terms are a consequence of the properties of logarithms”, and simply define the concept.

A final bit of advice: When people don't agree with you, don't simply state that you know you're right. Quoting from the site rules

Do not endlessly show us that *your* theory is the *only* truth. And don't follow this up by making people look stupid for pointing out that there are other answers, especially if they provide links and resources. It will get you banned!

In short, when encountering disagreement, back up steps in your argument until you encounter agreement, then, at the first step at which you encounter disagreement, support your claim with links and references to accepted texts, and discuss, being prepared to acknowledge that you may be wrong.