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Well I Agrre With That....

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Posted by Mark on September 5, 2001 04:14:10 UTC

But I don't agree with it when applied to mathematics.......

Once defined.......the logic takes on a "set in stone" sort of character. In other words, once you define death as the absence of life......then it follows that you are either alive or dead. There is no grey area. This is what you said above.......so what you're saying is that once our definitions are taken into consideration, all truths follow as a consequence. That's how I believe it to be also, if that really is what you meant.....

But in mathematics logic is in the proof. Therefore, although all truth is defined the moment you construct definitions.......the actual logic lies in the derivition of this truth. Its like reading an instruction manual written in code and sequences. We must use logic to determine what the pages say and mean, although the overall message exists in full, unchanging, regardless of whether or not we understand it. If we don't decode it....it still says what it says...

So if a prime number is a number divisible by one and its self....then it logically follows that 2 is the only even prime number as a consequence of our definition. But how do we know this? The answer lies in the proof. We can't argue the truth....it is set in stone....with no grey area.
If such wasn't the case.......then why do we have mathematicians at all.......? Any layperson could come along and say, "well since such & such is the definition, then it follows that...." When asked to back up their claim........rather than a logical proof they could proclaim, "Well that's just the consequence of your definitions." That in itself is circular reasoning.

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