Re:Claude Shannon: How a Genius Thinks, Works, and Lives
by pmarreck on Monday July 24, 2017 @10:28AM
(#14838714)
"A and A" is not a meaningful statement, though; it's a tautology, no? if you exclude those, what do you have?
Re:Claude Shannon: How a Genius Thinks, Works, and Lives
by jacksnipe on Monday July 24, 2017 @10:44AM
(#14838813)
It's not a tautology, because its truth relies on the truth of A. A true tautology would be something like "A or not A".
However, I address your concerns in the second part of my comment, as "A and A" is derivable from "A", and so is excluded.
If we assume that rational means "true", then it is clearly false:
If statements A and B are true, then the statement "A and B" is true. In fact, if the statement A is true, then "A and A" is true, so if there is at least one true statement, there are infinitely many.
If by "rational" you mean "true and meaningful", well, then we have to define meaningful.
The strongest definition of meaningful that I can muster is "contains information that cannot be logically deduced from previously known rational statements". But then by Godel incompleteness (assuming that we accept arithmetic as rational), there will always be a (true) statement we can make that is independent of our previous statements.
So while I think the discovery was more or less inevitable, there's certainly a flaw in your proof!