So, what we call math is a logic of ANY existence. It does not have to be an object, it may be a rule, or a concept, or a time, for example. ANYTHING which can exist may immediately be labeled as "1" versus absence (non-existence) labeled as "0".

So, there is only ONE axiom required to make math valid:

1. Something exists.

Everything else follows by labeling existence of this something by 1 and non-existence by 0.

Actually even less than one axiom. Nothing has to exist at all (just use one number: 0). So, math can handle stuff even "before it comes to existence".

So, your set of axioms is far too redunant - if something exist, it is already described by math/logic as the number 1 (or "yes" in logic notation). Even if something does NOT exist yet, it is still described by math (0, or "no").

• '0' requires comparison with '1' to have meaning - dolphin - October 1, 2001 - 23:35 UTC
  • Nope. Not required.It is just another sybmol for "non existence" - alexander - October 1, 2001 - 23:49 UTC
    • Your concept relies on "existence" reference - dolphin - October 3, 2001 - 07:22 UTC
• Let's rehash some more - harvey1 - October 2, 2001 - 00:27 UTC
  • Explaining once more time (in little hope you will get it). - alexander - October 2, 2001 - 00:59 UTC
    • Here's the problem - harvey1 - October 2, 2001 - 03:17 UTC
      • I found the problem. - alexander - October 2, 2001 - 20:02 UTC
        • Good insight - harvey1 - October 2, 2001 - 20:21 UTC
          • Yes, physical and mathematical existence is the same thing. - alexander - October 2, 2001 - 23:54 UTC
            • So then... - harvey1 - October 3, 2001 - 00:44 UTC
              • Conceptually - yes. - alexander - October 3, 2001 - 03:33 UTC
                • I think you should know my answer - harvey1 - October 3, 2001 - 04:37 UTC
                  • I did not know philosophy already has a name for it. - alexander - October 3, 2001 - 17:45 UTC
                    • Clarification - harvey1 - October 3, 2001 - 18:17 UTC
                      • Correction - harvey1 - October 3, 2001 - 18:18 UTC
                      • But what do you think about lack of "physical" objects/concepts? - alexander - October 3, 2001 - 19:14 UTC
                        • You don't want to know - harvey1 - October 3, 2001 - 19:39 UTC
                          • I'd rather call it materialism. - alexander - October 3, 2001 - 20:07 UTC
                        • I knew you weren't gonna like it - harvey1 - October 3, 2001 - 20:52 UTC
                    • Mathematical idealism - harvey1 - October 3, 2001 - 21:28 UTC
                      • Clarification - harvey1 - October 4, 2001 - 02:19 UTC
                        • Harvey, what is your opinion about philosophy in general and - alexander - October 4, 2001 - 21:23 UTC
                      • Philosophy - harvey1 - October 4, 2001 - 22:57 UTC
        • I'm thinking of it in another way - free_willy - October 2, 2001 - 21:04 UTC
        • You have to analyse what '1' actually means - dolphin - October 3, 2001 - 07:24 UTC