Back to Home

God & Science Forum Message

Forums: Atm · Astrophotography · Blackholes · Blackholes2 · CCD · Celestron · Domes · Education
Eyepieces · Meade · Misc. · God and Science · SETI · Software · UFO · XEphem
RSS Button

Home | Discussion Forums | God and Science | Post
Login

Be the first pioneers to continue the Astronomy Discussions at our new Astronomy meeting place...
The Space and Astronomy Agora
Sure

Forum List | Follow Ups | Post Message | Back to Thread Topics | In Response To
Posted by Michael Levine on July 17, 2003 14:59:52 UTC

Hi Harvey,

Thanks for the reply.

I didn't say that the term 'true' had no mathematical meaning. Meaning is possible by distinguishing true results from false results (i.e., in two-value logic), by following rules of inference that lead to only true results, etc. This is not a definition per se. A definition is a reduction, but you cannot reduce the word 'true' in mathematics. The reason is that any reduction would entail use of axioms (etc) that are considered 'true'.

I'm sorry but I have no idea what you are talking about there. Can you be less elusive and more specific? For one thing, truth has nothing to do with meaning, I don't know why you brought meaning up. A statement can be true even if you don't know what it means. For instance, this statement:

"if A includes B, and B includes C, then A includes C"

The truth of that statement is far clearer than its meaning. Which is the whole point of mathematics, to discover what is true regardless of meaning.

Axioms are statements that tell you under which certain conditions a mathematical statement is to be considered 'true'.

But that's the whole point. You can't have truths without axioms, but the truths of math are no less true just because the axioms can't be proven true. Whether explicitly or not, all mathematical truths are expressed in the form "if A then B". Math never says "things are such and such", all it says is "if things are such and such, then such and such necessarily follow".

With that in mind, it doesn't even make sense to talk about the truth of an axiom.

Follow Ups:

Login to Post
Additional Information
Google
 
Web www.astronomy.net
DayNightLine
About Astronomy Net | Advertise on Astronomy Net | Contact & Comments | Privacy Policy
Unless otherwise specified, web site content Copyright 1994-2024 John Huggins All Rights Reserved
Forum posts are Copyright their authors as specified in the heading above the post.
"dbHTML," "AstroGuide," "ASTRONOMY.NET" & "VA.NET"
are trademarks of John Huggins