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I have never understood the relativism about math fundamentals. What does it matter what we "agree to" or not? Either it is true or not. There is like no room f

I have never understood the relativism about math fundamentals. What does it matter what we "agree to" or not? Either it is true or not. There is like no room for "kinda true but really it ..." in '1 + 1 = 2'. And I am not talking about notation semantics here.

lcnPylGDnU4H9OF 4y ago
> kinda true but really it ... This isn't what I'm talking about. The agreement means it's not "universal". It's only true because we agree it's true. Can you prove that 1 = 1 or do we have to agree that 1 = 1? If you can't prove it, is it a "universal truth"? I'm asserting that a truth which requires an agreed context[0] is not "universal". [0] https://en.wikipedia.org/wiki/Axiom https://en.wikipedia.org/wiki/Axiom
- Retric 4y ago
  The universal nature of mathematical truth isn’t dependent on agreement. Instead it’s only universally true when you include all those seemingly unspoken “agreements.”
  - lcnPylGDnU4H9OF 4y ago
    > isn’t dependent on agreement It is by definition. If you disagree, go write a mathematical proof that 1 = 1. There are many in the world who would love to see it.
    - Retric 4y ago
      Hardly, there are sets of axioms where 1 = 1 which already show this in exquisite detail.
      - lcnPylGDnU4H9OF 4y ago
        I'm not sure what you mean by this, particularly this phrasing: "sets of axioms where 1 = 1". 1 = 1 is an axiom, not something that's proven by any set of axioms. But I'm willing to believe I'm simply naive here. You say there is some set of axioms which prove that 1 = 1. Are those axioms not agreements? Since you seem to be familiar, what are those axioms?
        Retric 4y ago
        What you are missing is 1 = 1 isn’t inherently true on it’s own. There are sets of axioms where 1 = 1 is false, different sets where it’s undefined, and finally sets of axioms where 1 = 1 is true. However, for a given set of axioms there is no choice and nothing to agree upon. That’s what makes math universally true.

lcnPylGDnU4H9OF 4y ago

> kinda true but really it ... This isn't what I'm talking about. The agreement means it's not "universal". It's only true because we agree it's true. Can you prove that 1 = 1 or do we have to agree that 1 = 1? If you can't prove it, is it a "universal truth"? I'm asserting that a truth which requires an agreed context[0] is not "universal". [0] https://en.wikipedia.org/wiki/Axiom https://en.wikipedia.org/wiki/Axiom

Retric 4y ago
The universal nature of mathematical truth isn’t dependent on agreement. Instead it’s only universally true when you include all those seemingly unspoken “agreements.”
- lcnPylGDnU4H9OF 4y ago
  > isn’t dependent on agreement It is by definition. If you disagree, go write a mathematical proof that 1 = 1. There are many in the world who would love to see it.
  - Retric 4y ago
    Hardly, there are sets of axioms where 1 = 1 which already show this in exquisite detail.
    - lcnPylGDnU4H9OF 4y ago
      I'm not sure what you mean by this, particularly this phrasing: "sets of axioms where 1 = 1". 1 = 1 is an axiom, not something that's proven by any set of axioms. But I'm willing to believe I'm simply naive here. You say there is some set of axioms which prove that 1 = 1. Are those axioms not agreements? Since you seem to be familiar, what are those axioms?
      - Retric 4y ago
        What you are missing is 1 = 1 isn’t inherently true on it’s own. There are sets of axioms where 1 = 1 is false, different sets where it’s undefined, and finally sets of axioms where 1 = 1 is true. However, for a given set of axioms there is no choice and nothing to agree upon. That’s what makes math universally true.