I brought up meaning because you said: "Actually, the term 'true' has a very specific meaning in math." An undefined term can acquire meaning, it just can't be reduced (in mathematics) any further. This is why my response was in regards to how 'true' can have meaning in math and still remain an undefined term.

I think I missed your point, sorry about that. In any case, the term "true" has very specific meaning and definition in math. The definition is given by the symbol '='. The meaning of 'true' in math is the same as the meaning of math itself. Truth, and the equal sign, are meta-concepts in math, as they refer to math itself.

Notice how the '=' sign embodies the notion of truth: to say "it is true that 2 + 2 = 4" is exactly equivalent to saying "2 + 2 = 4". "It is true that..." is redundant, as the concept of truth is already expressed by the '=' sign. That is why it makes no sense to question whether "it is true that 2 + 2 = 4", as it is exactly equivalent to asking "given that X is a true assertion, is it true that assertion X is true?".

Right. But, what I said is that the term 'true' is never defined in mathematics. The conditions of truth are defined, and this is done in formal systems with axioms, rules of inference, etc. This is why I said that the term true "is simply an undefined term that is used under certain conditions".

I think you are confusing the mathematical notion of truth, as expressed by the '=' sign, with the philosophical notion of truth, which concerns statements about reality. People tend to get confused by that; I suppose it's hard to understand that mathematics is not concerned with reality at all. People learn at a very young age that "you're not supposed to add apples and oranges", when in fact you're not even supposed to add apples and apples. The only thing you can add is numbers. By the time one is old enough to assimilate that, the notion that numbers refer to "things" is too deeply ingrained in one's consciousness.

• 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