Difference between a theorem and a tautology?

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Reply Wed 25 Feb, 2009 02:41 pm
I have to write a 3 page paper within the hour and I just don't have enough for 3 pages... some ideas would be MUCH appreciated, thanks! Surprised
 
kennethamy
 
Reply Wed 25 Feb, 2009 07:48 pm
@whiskyblanket,
whiskyblanket wrote:
I have to write a 3 page paper within the hour and I just don't have enough for 3 pages... some ideas would be MUCH appreciated, thanks! Surprised


Is this for logic? A tautology is a logical truth. It is true for all substitutions of its variables. A theorem is a statement deduced from the axioms of the system, and from other theorems and tautologies.
 
hammersklavier
 
Reply Tue 3 Mar, 2009 04:10 pm
@whiskyblanket,
Tautology: a = a
Theorem: a + b = b + a (= c)

Thinking of Godel, the tautology is the inherently unprovable statement that allows completeness, that is, it's an axiom. To Kant (if I'm reading the Prolegomena right), a theorem can be presented in two ways: a + b = b + a (analysis or restatement of subject in predicate) or a + b = c (synthesis or the predicate being a wholly different concept derived from the subject). For example, the statement A line is the shortest possible distance connecting two points is a tautology (Euclidean axiom) whereas the statement A line is a sequence of points extended in one direction is a theorem based on said tautology (note lines can be either finite or infinite).
 
 

 
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