2 ms·

Can you give an example?

by lcnPylGDnU4H9OF 4y ago

Retric 4y ago
Math
- lcnPylGDnU4H9OF 4y ago
  1 + 1 = 2 What does that even mean? What's "true" about that? It's agreed that it's true, therefore it's true.
  - rightbyte 4y ago
    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.
  - Retric 4y ago
    The foundations of mathematics are deeper than that basic assumption. I can for example say 1 + 1 = 10 in base 2, but people imply the base when when saying 1 + 1 = 2 as well as a great deal of other details few people actually care about.
    - lcnPylGDnU4H9OF 4y ago
      > foundations of mathematics This is the agreement that happens and why it's not universal. We have to agree that "1 = 1" for any statements like "1 + 1 = 2" to even make sense, let alone be true. Per your point, we have to agree that we're talking about something other than base 2 in order for "1 + 1 = 2" to be true, despite my intentions for it to be a potential example of a universal truth. Even "math" isn't universally true.
      - Retric 4y ago
        The above is false, math isn’t independent of axioms so there is nothing to agree upon beyond conventions where Math is simply the result of axiom choices. I have a longer answer here: https://news.ycombinator.com/item?id=35659676 https://news.ycombinator.com/item?id=35659676 = 2 @ + 1 1 is a different notation, but the underlying math is unchanged. So if you explain the notation difference an alien that might use = 2 @ + 1 1 they would also agree that in an our notation 1 + 1 = 2. The same relationship is true of the choice of axioms.
        lcnPylGDnU4H9OF 4y ago
        > math isn’t independent of axioms so there is nothing to agree upon beyond conventions where Math is simply the result of axiom choices. > 1 = 1 isn’t inherently true on it’s own This sounds a whole lot like "math isn't a universal truth". I guess we need to take a step back, since it seems this is where the disagreement lies: what does it mean for something to be a universal truth? My position is that a truth is universal if it is self-evident; that is, it does not require an agreement between observers. These axioms are that agreement and therefore Mathematics, which stems from such axioms, is not universal truth.

Can you give an example?

Retric 4y ago

Math

lcnPylGDnU4H9OF 4y ago
1 + 1 = 2 What does that even mean? What's "true" about that? It's agreed that it's true, therefore it's true.
- rightbyte 4y ago
  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.
- Retric 4y ago
  The foundations of mathematics are deeper than that basic assumption. I can for example say 1 + 1 = 10 in base 2, but people imply the base when when saying 1 + 1 = 2 as well as a great deal of other details few people actually care about.
  - lcnPylGDnU4H9OF 4y ago
    > foundations of mathematics This is the agreement that happens and why it's not universal. We have to agree that "1 = 1" for any statements like "1 + 1 = 2" to even make sense, let alone be true. Per your point, we have to agree that we're talking about something other than base 2 in order for "1 + 1 = 2" to be true, despite my intentions for it to be a potential example of a universal truth. Even "math" isn't universally true.
    - Retric 4y ago
      The above is false, math isn’t independent of axioms so there is nothing to agree upon beyond conventions where Math is simply the result of axiom choices. I have a longer answer here: https://news.ycombinator.com/item?id=35659676 https://news.ycombinator.com/item?id=35659676 = 2 @ + 1 1 is a different notation, but the underlying math is unchanged. So if you explain the notation difference an alien that might use = 2 @ + 1 1 they would also agree that in an our notation 1 + 1 = 2. The same relationship is true of the choice of axioms.
      - lcnPylGDnU4H9OF 4y ago
        > math isn’t independent of axioms so there is nothing to agree upon beyond conventions where Math is simply the result of axiom choices. > 1 = 1 isn’t inherently true on it’s own This sounds a whole lot like "math isn't a universal truth". I guess we need to take a step back, since it seems this is where the disagreement lies: what does it mean for something to be a universal truth? My position is that a truth is universal if it is self-evident; that is, it does not require an agreement between observers. These axioms are that agreement and therefore Mathematics, which stems from such axioms, is not universal truth.