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[Mathematical truth as a social construct] > Yeah, that is how it feels like nowadays, It's always been that way. (Again, I really recommend the book[1] ).

[Mathematical truth as a social construct] > Yeah, that is how it feels like nowadays, It's always been that way. (Again, I really recommend the book[1] ). And it's hard to see how it could be otherwise. (Also depends a little about what exact mathematical truth we are talking about and whether you are a Platonist or Constructionist) That doesn't imply what either the recent proponents or the critics seem to think. It does not at all imply arbitrariness or that anything goes. > however the truth is bound in a narrow set of assumptions. Yes, it is. Again, something being a social construct does not make it a free-for-all. More the opposite, because the constraints are socially enforced. > And while there is an epistemologic level to reality, you would dismiss reality entirely by calling it a social construct. Mathematics ≠ Reality. Science is about reality, but scientific truth is also a social construct (see Popper), and highly constrained by reality (ibid). [1] https://www.amazon.de/Mathematical-Experience-Phillip-J-Davis/dp/0395929687 https://www.amazon.de/Mathematical-Experience-Phillip-J-Davi...

feanaro 4y ago
Saying Mathematics ≠ Reality fails to capture a large portion of the story, since a subset of mathematics is clearly necessary to be able to encode science, and confirmed by science, and is in that sense a part of reality.
- mpweiher 4y ago
  It's not necessary. It is empirically useful. Mathematics is about describing possible worlds. Given these assumptions (including the rules of the game), what follows? Science is about figuring out the real world. The real world has no obligation to be describable by mathematics. That it is so describable is fortuitous. "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
  - feanaro 4y ago
    > It's not necessary. I didn't mean "necessary" in the sense of modal logic, but in a more colloquial sense. Physical laws as known to us today are described using mathematics. We know of no other viable ways to describe them. In that sense, (a subset of) mathematics is necessary for this purpose. It was just meant as a restatement of the concept of unreasonable effectiveness of mathematics in a more natural language. > The real world has no obligation to be describable by mathematics. There is no obligation, but that it is so in our particular world is undeniable fact.
naasking 4y ago
> Mathematics ≠ Reality Conjecture. A mathematical universe is consistent with everything we know, in which case math is literally the study of reality.
- mpweiher 4y ago
  This is simply false, for at least three reasons. There are probably more. 1. Math can describe lots of universes that differ from observation. For starters, just look at all the different kinds of space-time there could be. 2. On top of that, even the math that we have that describes our current universe is...tricky: the math at the core of our two best physical theories (General Relativity and Quantum Mechanics) is inconsistent, i.e. they both cannot be true at the same time. Lots of our greatest minds have tried to find a mathematical formulation that makes the two compatible, but so far none have succeeded. So there may not actually be a mathematical formulation. 3. And finally, nature is under no obligation to be describable mathematically. That it is so describable is a fortuitous circumstance, and one we might be finding the limits of (see (2)). "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
  - naasking 4y ago
    > Math can describe lots of universes that differ from observation. This has all been hashed out already. Look up the mathematical universe hypothesis and Wolfram's Ruliad for two different but similar approaches. The basic idea is that all consistent mathematical objects exist, and we simply inhabit one of them. The fact that QM and GR are inconsistent with each other is not an issue because they describe different universes in mathematical space that are close but not equal to our own. > And finally, nature is under no obligation to be describable mathematically. That it is so describable is a fortuitous circumstance That too is a conjecture. There is exactly zero evidence that nature is non-mathematical, but people who keep saying this are basically insisting that it's effectiveness at describing reality is simply a continuous chain of grand coincidences. To say this is statistically implausible bordering on impossible is the kindest way to put it.

feanaro 4y ago

Saying Mathematics ≠ Reality fails to capture a large portion of the story, since a subset of mathematics is clearly necessary to be able to encode science, and confirmed by science, and is in that sense a part of reality.

mpweiher 4y ago
It's not necessary. It is empirically useful. Mathematics is about describing possible worlds. Given these assumptions (including the rules of the game), what follows? Science is about figuring out the real world. The real world has no obligation to be describable by mathematics. That it is so describable is fortuitous. "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
- feanaro 4y ago
  > It's not necessary. I didn't mean "necessary" in the sense of modal logic, but in a more colloquial sense. Physical laws as known to us today are described using mathematics. We know of no other viable ways to describe them. In that sense, (a subset of) mathematics is necessary for this purpose. It was just meant as a restatement of the concept of unreasonable effectiveness of mathematics in a more natural language. > The real world has no obligation to be describable by mathematics. There is no obligation, but that it is so in our particular world is undeniable fact.

naasking 4y ago

> Mathematics ≠ Reality Conjecture. A mathematical universe is consistent with everything we know, in which case math is literally the study of reality.

mpweiher 4y ago
This is simply false, for at least three reasons. There are probably more. 1. Math can describe lots of universes that differ from observation. For starters, just look at all the different kinds of space-time there could be. 2. On top of that, even the math that we have that describes our current universe is...tricky: the math at the core of our two best physical theories (General Relativity and Quantum Mechanics) is inconsistent, i.e. they both cannot be true at the same time. Lots of our greatest minds have tried to find a mathematical formulation that makes the two compatible, but so far none have succeeded. So there may not actually be a mathematical formulation. 3. And finally, nature is under no obligation to be describable mathematically. That it is so describable is a fortuitous circumstance, and one we might be finding the limits of (see (2)). "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
- naasking 4y ago
  > Math can describe lots of universes that differ from observation. This has all been hashed out already. Look up the mathematical universe hypothesis and Wolfram's Ruliad for two different but similar approaches. The basic idea is that all consistent mathematical objects exist, and we simply inhabit one of them. The fact that QM and GR are inconsistent with each other is not an issue because they describe different universes in mathematical space that are close but not equal to our own. > And finally, nature is under no obligation to be describable mathematically. That it is so describable is a fortuitous circumstance That too is a conjecture. There is exactly zero evidence that nature is non-mathematical, but people who keep saying this are basically insisting that it's effectiveness at describing reality is simply a continuous chain of grand coincidences. To say this is statistically implausible bordering on impossible is the kindest way to put it.