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      CommentAuthorpcstru
    • CommentTimeOct 13th 2021 edited
     
    Posted By: AngusI didn't say that mathematics exists in the material world. I said it has some sort of existence in addition to the material world.

    "in addition to", I suspect you are arguing that it has an existence essentially independent of either the material or metaphysical world. I might say it is weakly coupled to the material world but it is fundamentally a product of metaphysics - it simply doesn't exist outside of a mind. It is an idea created and communicated by our minds.

    The problem with an independent existence (which you may deny you are arguing for) is, essentially every communicable idea could be said to have an independent existence. So it's not special or surprising in that respect either.


    Both mathematics and the material world are there to explore but are not created by us.


    I disagree that mathematics is a construct. Though sure you can build bathematical constructs just as you can build material ones.

    Surely at least the process of building mathematical constructs is a process of creation? "I made this thing". Is a child building with lego creating, or just mapping out one of the finite inevitable paths available to them given the constraints of lego and the pieces they have available? Was the inventor of Lego discovering Legomatics or creating it?


    [strike]The parallel between mathematics and language is false. Language lacks a consistency requirement. You can say anything and there is no way within language to evaluate its validity. Hence unicorns.[/strike]

    Hmmm. That is not correct. I left it in so you can see what I've gone away to think about.


    There is no way to communicate Mathematics as an idea without the intermediary of 'ordinary' language. How would you know something was "mathematical" without a word for it?
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      CommentAuthorAngus
    • CommentTimeOct 13th 2021
     
    It is obviously true that one can find in the mathematical world items that have no correspondence in the material world just as you can make statements in languages that do not refer to real things - i.e. unicorns. Therefore I struck out that sentence and continued looking for a way to distinguish language from mathematics.

    There are many languages. Each language has rules for making understandable statements. The scope of a language can be extended, mostly by metaphor. There is no requirement for consistency in languages - they evolve and eventually become incomprehensible to the original speakers.

    As far as I am aware there is just one mathematics. The only requirement for new mathematics is that it fit with the old mathematics. The mathematical world does not evolve, but our knowledge of it expands - the expansion is creative of course, but it is understanding that is being created, not mathematics.

    it simply doesn't exist outside of a mind
    - the nub of the discussion. I asked earlier if there would be three of anything if there were no people. Was there three of anything before apes learned to speak? For me “threeness” is a primordial part of the extended universe that contains the material and the mathematical worlds. I draw support from the infinite elaboration that the idea of counting can unveil if a creature has developed enough mind to appreciate the mathematical world.

    To say that any communicable idea has the same kind of existence as the mathematical world misses the elaboration of that world. Mathematical ideas offer windows into it. Just any old idea won’t. The inventor of Lego probably wasn’t discovering anything in the mathematical world. The creator of the General Theory of Stacking Plastic Blocks may have been. The line between invention and discovery may be blurry, but that doesn’t invalidate the distinction.

    Of course we can’t communicate without some form of language. I don’t see what that has to do with the concept of a mathematical world independent of the material world.
    • CommentAuthorAsterix
    • CommentTimeOct 13th 2021
     
    Would it be a stretch to say that mathematics started out as a way to conduct business? As in, "I will give you three clams for that fish."
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    I think it began as a tally strategy used in trading, as you say.
    • CommentAuthorloreman
    • CommentTimeOct 13th 2021
     
    Mathematics exists in the “material world”. The distinction between the “material world” and some esoteric mental world is a false one. It’s like saying that tv programs don’t exist.
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      CommentAuthorAngus
    • CommentTimeOct 14th 2021
     
    Posted By: AsterixWould it be a stretch to say that mathematics started out as a way to conduct business? As in, "I will give you three clams for that fish."


    Not a stretch. Just wrong, depending on what you mean by mathematics. If you mean "the human discovery of mathematical relationships" then I'll accept it. If you mean "mathematical relationships", then I won't.

    But I'm preaching atheism to the choir, so it's time to give up.
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      CommentAuthoroak
    • CommentTimeOct 14th 2021
     
    At least your position is the correct one.
    Take some satisfaction in that.
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      CommentAuthorpcstru
    • CommentTimeOct 14th 2021
     
    Posted By: loremanMathematics exists in the “material world”. The distinction between the “material world” and some esoteric mental world is a false one. It’s like saying that tv programs don’t exist.


    TV programmes have physical manifestation; in the performance, recording, transmission, reception, display etc. Where exactly in the physical world is the + particle/field to be found? Are the axioms of set theory hanging out in a cave on Mars? What equipment do we need to detect them?

    I'm not aware anyone is saying things in the mind don't exist; just that they are products of the mind. Sure you can't have a mind without the physical universe, so the material world is the basis of all existence, even things that don't exist. But then you can't have ideas without a mind and ideas do not have to relate to the material world, so it seems in some sense decoupled from it and it is meaningful to consider it distinct.
    • CommentAuthorloreman
    • CommentTimeOct 14th 2021
     
    What is a “product of the mind”? Maths, when being performed - or discovered, is a series of electro-chemical impulses (and that’s at a gross level, further down the turtles it’s a series of spins and probabilities) with the irony being that the physical expression of thinking about mathematics conforms with the relationships and rules which mathematics is used to describe.
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      CommentAuthorpcstru
    • CommentTimeOct 14th 2021
     
    Posted By: loremanWhat is a “product of the mind”? Maths, when being performed - or discovered, is a series of electro-chemical impulses (and that’s at a gross level, further down the turtles it’s a series of spins and probabilities) with the irony being that the physical expression of thinking about mathematics conforms with the relationships and rules which mathematics is used to describe.

    Sounds like hard determinism, the universe is just playing itself out, the events of today absolutely inevitable from the moment of creation; even these thoughts typed now were baked in from that moment, including all of the lovely unicorns. Our perception of freewill, free thought, is just a delusion.

    Sure, with such a worldview, there are no products of anything but the material world. The problem with such a view seems to be the never ending supply of turtles needed to support it.
    • CommentAuthorloreman
    • CommentTimeOct 14th 2021
     
    No, it’s not hard determinism, because my understanding is that QM won’t allow for that. The Universe is probabilistic but not pre-determined.

    However, everything that happens within it, including “thought” has a physical component, involving interactions between different bits of space-time. It would be really interesting to know whether, in a group of people thinking about a particular mathematical process at the same time, their brains light up in similar ways.
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      CommentAuthorpcstru
    • CommentTimeOct 14th 2021
     
    Posted By: loremanNo, it’s not hard determinism, because my understanding is that QM won’t allow for that. The Universe is probabilistic but not pre-determined.

    I'm not at all clear about that; it looks like another turtle - quite squashed by all the turtles above and squashing the turtles below.

    If your 'freewill' is just a product that rises up from 'random' collapses of waveforms, then you have no control over that. Your free will is just as illusory; you have no way to effect any control over that collapse.


    However, everything that happens within it, including “thought” has a physical component, involving interactions between different bits of space-time. It would be really interesting to know whether, in a group of people thinking about a particular mathematical process at the same time, their brains light up in similar ways.


    Sure, everything is predicated on the material world as a substrate. The central question then is whether there is such a thing as strong emergence - processes that are essentially identity independent of the substrate from which things emerge that cannot be predicted in principle by the physical models of that substrate. You can't have unicorns without a substrate that supports a mind and the operational mind, but you won't find or predict the existence of unicorns by looking at our models of the material world.
    • CommentAuthorAsterix
    • CommentTimeOct 14th 2021 edited
     
    Posted By: Angus
    Posted By: AsterixWould it be a stretch to say that mathematics started out as a way to conduct business? As in, "I will give you three clams for that fish."


    Not a stretch. Just wrong, depending on what you mean by mathematics. If you mean "the human discovery of mathematical relationships" then I'll accept it. If you mean "mathematical relationships", then I won't.


    Oh, I take your point. As in "Did hydrogen exist before Cavendish put a name to it?" Of course it did.
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      CommentAuthorAngus
    • CommentTimeOct 14th 2021
     
    That fairly.well summarises the whole argument.
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      CommentAuthorpcstru
    • CommentTimeOct 14th 2021
     
    'hydrogen' (assuming we can agree what it is) exists as a material thing, you can go out an grab a bag of it. Mathematics does not - go catch me a bag of wild integers or show me a material mediator of addition. Did Unicorns exist before someone put a name to them? Do they exist after that?
    • CommentAuthorAsterix
    • CommentTimeOct 14th 2021
     
    You may as well ask "Did thought exist before humans put a name to it?"
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      CommentAuthorAngus
    • CommentTimeOct 14th 2021
     
    I think we are at the point where we have to decide what "exist" means. Bill Clinton came to a similar dilemma, I seem to reacall.
    • CommentAuthorAsterix
    • CommentTimeOct 14th 2021 edited
     
    Pardon me, but I'm not going to crawl down the "what is existence" rabbit hole. Was there thought before humans?

    "Thought is not a saffron-robed monk pissing in the snow"
    --Severn Darden

    From this.
    • CommentAuthorloreman
    • CommentTimeOct 14th 2021
     
    Posted By: pcstru
    Posted By: loremanNo, it’s not hard determinism, because my understanding is that QM won’t allow for that. The Universe is probabilistic but not pre-determined.

    I'm not at all clear about that; it looks like another turtle - quite squashed by all the turtles above and squashing the turtles below.

    If your 'freewill' is just a product that rises up from 'random' collapses of waveforms, then you have no control over that. Your free will is just as illusory; you have no way to effect any control over that collapse.


    However, everything that happens within it, including “thought” has a physical component, involving interactions between different bits of space-time. It would be really interesting to know whether, in a group of people thinking about a particular mathematical process at the same time, their brains light up in similar ways.


    Sure, everything is predicated on the material world as a substrate. The central question then is whether there is such a thing as strong emergence - processes that are essentially identity independent of the substrate from which things emerge that cannot be predicted in principle by the physical models of that substrate. You can't have unicorns without a substrate that supports a mind and the operational mind, but you won't find or predict the existence of unicorns by looking at our models of the material world.


    Who said anything about “free will”? “Strong Emergence” is predicated on the existence of an observer with a particular set of values. “Unicorns” exist-they are a cipher useful to those who wish to ridicule an opposing argument.
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      CommentAuthoroak
    • CommentTimeOct 15th 2021
     
    Would 4 plus 5 equal 9 if there were no language-speakers to express the idea? Yes.