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One of the interesting questions (without any satisfactory answers) in Philosophy is “How does language relate to the world?” Perhaps it doesn’t. Perhaps langu

by ukj 6y ago

One of the interesting questions (without any satisfactory answers) in Philosophy is “How does language relate to the world?” Perhaps it doesn’t. Perhaps language is just a tool we, humans, use for thinking and representing our knowledge. Mathematics is a language... Mathematical objects need not exist anywhere else but in the Mathematician’s head.

mhh__ 6y ago
If you read Wigner's famous essay, you can make an argument that if not the mathematics itself, there is some kind of structure which is mathematical if not symbolic.
- ukj 6y ago
  Sure. Any argument for structuralism is countered by non-structuralist/post-structuralist.
  - mhh__ 6y ago
    That's sounds like philosophy, I'm out!
    - ukj 6y ago
      And just one post back you recommended a Philosophical essay ;)
      - mhh__ 6y ago
        It was partly a tongue-in-cheek dogwhistle to the physics crowd, but I do sort of feel that even the essay I cite is useless - interesting, yes. I (and I have tried) really struggle to see what the point is in learning all these philosophy terms when it usually or always ends up being unfalsifiable or a overly proud euphemism for yet another concept. To take a specific example, I'm curious what post-structuralism actually means as applied to the structure I was trying to refer to - there are certain symmetry groups that seem to apply everywhere we look, but the actual structure is itself isn't a symbolic concept in the same way the standard model is.
        ukj 6y ago
        To me, the value of Philosophy isn't in learning any particular jargon/terminology (any more than learning the jargon of "symmetry groups" is a useful activity) - the value is in the general understanding of the process of how to develop jargon/terminology from first principles. From a physicists' perspective: to develop the language needed to describe/express the physics you are experiencing. There is certainly an element of wheel re-invention in first principles thinking, but acquiring maker's knowledge seems like a more rewarding endeavour than acquiring only user's knowledge. This process of creating new languages/jargon has a name in Computer Science: Meta-linguistic abstraction [1], and so the value of Philosophy (to me) is in the first paragraph of the Wikipedia article: >metalinguistic abstraction is the process of solving complex problems by creating a new language or vocabulary to better understand the problem space. And so this I find it fascinating when you say that... >there are certain symmetry groups that seem to apply everywhere we look Because your meta-language for talking about your experiences is the language of symmetry groups. Post-structuralism (and all Philosophy, really) is merely an attempt to escape the reductionist nature of that sort of language-centric thinking - it's an attempt to drag us out of the cave of Logocentrism [2]. Mathematics is only up to isomorphism - there's nothing in the symbolic denotation without the human connotation, so if structuralism is about symmetry (equalities) , post-structuralism is about asymmetry (inequalities). [1] https://en.wikipedia.org/wiki/Metalinguistic_abstraction https://en.wikipedia.org/wiki/Metalinguistic_abstraction [2] https://en.wikipedia.org/wiki/Logocentrism https://en.wikipedia.org/wiki/Logocentrism
seiferteric 6y ago
Mathematics is uniquely weird in that anywhere in the universe, a species can come up with the same things... So to say Mathematics is not real, and yet it is independently discoverable by anyone is just really weird to me.
- eyelidlessness 6y ago
  There are very credible linguists who theorize that there’s a universal human grammar and language foundation. It’s not a stretch to think that if they’re right about humans, the theory may apply to other life with language which we haven’t encountered yet. If that’s the case, the property you’re describing belongs to abstract thought and language generally, of which mathematics is a subset.
  - gizmo686 6y ago
    The idea of universal grammar is that it is the portion of human language that is hardcoded into the genetics of humans. We would not expect other species to have the same universal grammar that humans do.
    - eyelidlessness 6y ago
      The notion is that there’s a commonality, the presupposition is that it’s genetic. But without knowing the mechanics of those genetics I don’t think you could say one way or another whether the expectation would be limited to humans.
- ukj 6y ago
  The line of reasoning is purely speculative. Since we are the only species who have Mathematics, I will continue insisting Maths is invented, till we can compare notes with other life forms.
  - eyelidlessness 6y ago
    We’re the only species with which our species communicates maths. But we observe other species expressing mathematical properties we communicate. Does (for example) a snail “know” or “understand” the “golden ratio”? Who knows! But a snail’s shell expresses it. That’s partly something we can observe (so it can be designated “invented”), but partly something that appears so much it’s either a biological commonality, subject to some unknown universal constant, or an expression that many forms of life find a way to express.

by ukj 6y ago

mhh__ 6y ago

If you read Wigner's famous essay, you can make an argument that if not the mathematics itself, there is some kind of structure which is mathematical if not symbolic.

ukj 6y ago
Sure. Any argument for structuralism is countered by non-structuralist/post-structuralist.
- mhh__ 6y ago
  That's sounds like philosophy, I'm out!
  - ukj 6y ago
    And just one post back you recommended a Philosophical essay ;)
    - mhh__ 6y ago
      It was partly a tongue-in-cheek dogwhistle to the physics crowd, but I do sort of feel that even the essay I cite is useless - interesting, yes. I (and I have tried) really struggle to see what the point is in learning all these philosophy terms when it usually or always ends up being unfalsifiable or a overly proud euphemism for yet another concept. To take a specific example, I'm curious what post-structuralism actually means as applied to the structure I was trying to refer to - there are certain symmetry groups that seem to apply everywhere we look, but the actual structure is itself isn't a symbolic concept in the same way the standard model is.
      - ukj 6y ago
        To me, the value of Philosophy isn't in learning any particular jargon/terminology (any more than learning the jargon of "symmetry groups" is a useful activity) - the value is in the general understanding of the process of how to develop jargon/terminology from first principles. From a physicists' perspective: to develop the language needed to describe/express the physics you are experiencing. There is certainly an element of wheel re-invention in first principles thinking, but acquiring maker's knowledge seems like a more rewarding endeavour than acquiring only user's knowledge. This process of creating new languages/jargon has a name in Computer Science: Meta-linguistic abstraction [1], and so the value of Philosophy (to me) is in the first paragraph of the Wikipedia article: >metalinguistic abstraction is the process of solving complex problems by creating a new language or vocabulary to better understand the problem space. And so this I find it fascinating when you say that... >there are certain symmetry groups that seem to apply everywhere we look Because your meta-language for talking about your experiences is the language of symmetry groups. Post-structuralism (and all Philosophy, really) is merely an attempt to escape the reductionist nature of that sort of language-centric thinking - it's an attempt to drag us out of the cave of Logocentrism [2]. Mathematics is only up to isomorphism - there's nothing in the symbolic denotation without the human connotation, so if structuralism is about symmetry (equalities) , post-structuralism is about asymmetry (inequalities). [1] https://en.wikipedia.org/wiki/Metalinguistic_abstraction https://en.wikipedia.org/wiki/Metalinguistic_abstraction [2] https://en.wikipedia.org/wiki/Logocentrism https://en.wikipedia.org/wiki/Logocentrism

seiferteric 6y ago

Mathematics is uniquely weird in that anywhere in the universe, a species can come up with the same things... So to say Mathematics is not real, and yet it is independently discoverable by anyone is just really weird to me.

eyelidlessness 6y ago
There are very credible linguists who theorize that there’s a universal human grammar and language foundation. It’s not a stretch to think that if they’re right about humans, the theory may apply to other life with language which we haven’t encountered yet. If that’s the case, the property you’re describing belongs to abstract thought and language generally, of which mathematics is a subset.
- gizmo686 6y ago
  The idea of universal grammar is that it is the portion of human language that is hardcoded into the genetics of humans. We would not expect other species to have the same universal grammar that humans do.
  - eyelidlessness 6y ago
    The notion is that there’s a commonality, the presupposition is that it’s genetic. But without knowing the mechanics of those genetics I don’t think you could say one way or another whether the expectation would be limited to humans.
ukj 6y ago
The line of reasoning is purely speculative. Since we are the only species who have Mathematics, I will continue insisting Maths is invented, till we can compare notes with other life forms.
- eyelidlessness 6y ago
  We’re the only species with which our species communicates maths. But we observe other species expressing mathematical properties we communicate. Does (for example) a snail “know” or “understand” the “golden ratio”? Who knows! But a snail’s shell expresses it. That’s partly something we can observe (so it can be designated “invented”), but partly something that appears so much it’s either a biological commonality, subject to some unknown universal constant, or an expression that many forms of life find a way to express.