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.

• Getting to the truth - harvey1 - July 17, 2003 - 15:32 UTC
  • math = truth - mikelev - July 17, 2003 - 15:58 UTC
    • more on T - harvey1 - July 17, 2003 - 18:37 UTC
      • or, in other words... - sillyuniverse - July 17, 2003 - 19:02 UTC
      • Definitions and axioms... - smartguy - July 17, 2003 - 19:05 UTC
      • Too complicated - mikelev - July 17, 2003 - 19:36 UTC
        • Anonymous "Mike" writes... - smartguy - July 17, 2003 - 19:44 UTC
          • ??? - mikelev - July 17, 2003 - 19:56 UTC
            • You weren't supposed to... - smartguy - July 18, 2003 - 01:36 UTC
              • Sorry, Mark; your insult only labels yourself as a quack! - carefuluniverse - July 18, 2003 - 02:53 UTC
                • I'm a savage to be taught by "white man"? - smartguy - July 18, 2003 - 04:16 UTC
                  • Wow that post was confusing.... - carefuluniverse - July 18, 2003 - 04:49 UTC
              • Who are the Brain Police? - sillyuniverse - July 18, 2003 - 03:14 UTC
                • Mike I like you... - smartguy - July 18, 2003 - 04:56 UTC
                  • I think consensus opinion should not be cited - carefuluniverse - July 18, 2003 - 05:07 UTC
                    • I'm a contributory component of said consensus... - smartguy - July 18, 2003 - 05:16 UTC
                      • arf arf ....arf arf ....arf arf arf.....hee haw..hee haw.... - kantolfir2 - July 18, 2003 - 06:29 UTC
        • Simple sentence - harvey1 - July 17, 2003 - 20:18 UTC
          • Your sentence is un-moo - mikelev - July 18, 2003 - 13:22 UTC
            • Correction...(?) - smartguy - July 18, 2003 - 19:11 UTC
              • I concur - harvey1 - July 18, 2003 - 21:16 UTC
            • Un-moo? - harvey1 - July 18, 2003 - 21:00 UTC
              • A definition of mathematical truth - harvey1 - July 19, 2003 - 14:32 UTC
                • eternal life - dolphin - July 20, 2003 - 12:13 UTC
                  • Good grief - harvey1 - July 20, 2003 - 14:50 UTC
                    • Alan, he'll do it! He can also remove posts! - quiet - July 20, 2003 - 15:20 UTC
                    • explanation - dolphin - July 20, 2003 - 16:34 UTC
                      • Another explanation - harvey1 - July 21, 2003 - 02:42 UTC
                        • I can explain - dolphin - July 21, 2003 - 05:31 UTC
                          • Not an answer - harvey1 - July 21, 2003 - 11:41 UTC
                            • A car at an intersection - dolphin - July 23, 2003 - 07:55 UTC
                • math-world - dolphin - July 20, 2003 - 17:10 UTC
                  • Let's not get carried away - harvey1 - July 21, 2003 - 04:02 UTC
                    • Recognized names in the field of philosophy - quiet - July 21, 2003 - 04:43 UTC
                      • definition and meeting - dolphin - July 21, 2003 - 05:21 UTC
                    • Why no reply? - harvey1 - July 21, 2003 - 11:47 UTC
                    • reply part one - dolphin - July 22, 2003 - 08:52 UTC
                    • reply part two - dolphin - July 22, 2003 - 09:41 UTC
                    • reply part three - dolphin - July 23, 2003 - 07:04 UTC