Re: OT: Solipsism

In article <20060112113801.FB8.0.NOFFLE@xxxxxxxxxxxxxxxxxxxxxxxx>,
Dirk Thierbach <dthierbach@xxxxxxxxxxxxxxxxxxx> wrote:
>R. Dan Henry <danhenry@xxxxxxxxxxx> wrote:
>> On Tue, 10 Jan 2006 09:48:37 +0100, Dirk Thierbach
>> <dthierbach@xxxxxxxxxxxxxxxxxxx> wrote:

>>>But without the tautologies of algebra and differential calculus they
>>>are quite useless.

>> Where did you ever get the idea that mathematics is a system of
>> tautologies?

>>From studying at university :-) In this case, having learned logic.
>By definition, in mathematics a tautology is a statement that is
>true under all possible assignments of values to the variables.
>All theorems, lemmas etc. in mathematics are tautologies. A mathematical
>proof consists in convincing the reader that it is indeed a tautology.
>
>I know that this is not the way the word is used outside mathematical
>logic... for example, it almost always has a connotation of "trivial".
>(But all proofs are trivial, once you have understood them...)

Mathematics is built from axioms and rules of inference (logic).

The logic part may be considered to be tautological (how else would
one even define a tautology other than by appealing to the rules
of logic), but the axioms are not tautologies, they are bald
assertions that we accept because they appear to us to be self-evidently
true. So mathematics cannot be considered to be purely tautological.
--
John Brock
jbrock@xxxxxxxxx

.

Relevant Pages

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  • Re: OT: Solipsism
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    (rec.arts.books.tolkien)
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