• Banno
    14.5k
    Here.

    So, could the liar paradox cause a bridge to collapse?

    It seems not.

    It is a mistake to think that because a line can be drawn between two point, that the line is there even if undrawn. It is a mistake to think Chess was discovered.

    And it seems Sokal needed to pretend that "metatheorems" are not part of the game of mathematics to protect mathematics proper from what he thought of as monsters. Seems overkill.

    Playing with contradictions leads to the new game of paraconsistent logic.

    Maths is made up.
  • Wayfarer
    13.8k
    The meta question is, what unwanted implications of the converse do you avoid by believing that?
  • Banno
    14.5k
    So tell me the answer. After all, that's what you are for.
  • Wayfarer
    13.8k
    I can't tell you what the motivations are for wanting to believe that maths is made up. You need to answer that yourself. (Anyway, I'm not going to be around to discuss it, I've just scored a work assignment and have to give it my sole attention for the next while.)
  • Banno
    14.5k
    That your mind is elsewhere doubtless explains the paucity of your reply.
  • Tom Storm
    2.2k
    Enter idealism discussion.
  • TheMadFool
    12.6k
    Let's look at something else that's made up - religion - and compare that with math and check how they stack up in re their power to provide an explanatory basis for reality as we know it.

    Made up gives me the distinct feeling that we're in subjectivity territory and when was the last time, any two people agreed on that score. Math is, whatever it is, at least not all up here, in our heads.
  • T Clark
    6.6k


    This is an interesting article. I also followed some of the links. To be honest, it starts about level with the bottom of my nose and quickly goes over my head. It has always confused me when people talk about paradoxes as if they undermine the validity of mathematics. In particular, I've always found the reactions to Russell's paradox and Godel's theorem hard to understand. Godel's proof of his theorem has always seemed goofy to me. I don't understand how the claim that one odd, trivial contradiction proves that math is incoherent in any meaningful way makes sense.

    I've been meaning to bring this up as a subject, but I'm not a good enough logician to even figure out a way to formulate the question. This article has been helpful, even only by showing me that I'm not alone in my skepticism.

    Thanks for the link.
  • Banno
    14.5k
    Made up gives me the distinct feeling that we're in subjectivity territory and when was the last time, any two people agreed on that score. Math is, whatever it is, at least not all up here, in our heads.TheMadFool

    There's that subjective/objective confusion again. it's not all either subjective or objective, and never the twain. Is Chess "in your head"?
  • TheMadFool
    12.6k
    There's that subjective/objective confusion again. it's not all either subjective or objective, and never the twain. Is Chess "in your head"?Banno

    What means this :point:
    Maths is made up.Banno
    ? Try to think in terms of collective subjectivity, perhaps inter-subjectivity or mass hallucination if you like.

    Is the mathematical universe like religion's heaven?
  • Banno
    14.5k
    collective subjectivityTheMadFool

    inter-subjectivityTheMadFool

    hallucinationTheMadFool

    But if it is subjective, it's private, and hence not part of our conversation.

    Further, what sense is one to make of inter-subjective? Something is both private and public? Bioth subjective and yet objective? Looks like a splint - an attempt to fix something that is broken.

    No, if it's part of the conversation then it is not subjective.

    Unless what is meant is something like that my preference for vanilla is subjective. In which case is the argument that maths is mere preference?
  • TheMadFool
    12.6k
    But if it is subjective, it's privateBanno

    That is precisely what made up means.

    No, if it's part of the conversation then it is not subjectiveBanno

    I just had icecream yesterday and it was delicious.

    vanillaBanno

    :grin:
  • Banno
    14.5k
    But if it is subjective, it's private
    — Banno

    That is precisely what made up means.
    TheMadFool

    Really? I don't think so.
  • Srap Tasmaner
    3.1k
    And it seems Sokal needed to pretend that "metatheorems" are not part of the game of mathematics to protect mathematics proper from what he thought of as monsters. Seems overkill.Banno

    I think you misread that. Sokal is only saying, what I thought was widely known, that the overwhelming majority of working mathematicians have nothing to do with foundations at all. It is functionally a sub-field of the discipline, just as much as complex analysis or differential topology.
  • TheMadFool
    12.6k
    Really? I don't think so.Banno

    I'll make a statement and then ask a question. J. R. R. Tolkien's universe is made up. You claim math too is made up. Is there a difference between Tolkien's world and the math world? The floor is yours.
  • Srap Tasmaner
    3.1k
    So, could the liar paradox cause a bridge to collapse?Banno

    On balance, I think the answer might be yes.

    The real harm will not come in unless there is an application, in which a bridge may fall down or something of that sort [] You cannot be confident about applying your calculus until you know that there are no hidden contradictions in it. — Turing

    And it's yes in part because of Turing. Nowadays engineers will to some degree rely on software to design bridges. It is fact that software complexity has created enormous challenges, and that it is not nearly so simple to verify correctness as one might wish. (In some fields like aircraft design there are strict, explicit standards for the provable correctness of programs, and still ... 737.)

    I don't know enough about this stuff to point to examples, but Turing's general point that allowing contradictions can be dangerous is almost certainly correct, precisely because of the emergence of computers.
  • Richard B
    67
    I believe Wittgenstein was trying to convince Turing of the following:

    1. If you arrive at a contradiction the result would be inaction

    2. If a bridge collapsed, an engineer is not wondering if the foundations of math is problematic, but if the calculation was wrong, it was not put together as per plan, or materials used were inferior

    As for the Liar paradox, “I am a Liar” has a clear use is ordinary circumstances of life. Take it out of that and put it in the philosophical world, and one gets deep into confusion.
  • Banno
    14.5k
    But you said that what is made up is subjective. Is Lord of the Rings subjective? What does that mean?

    I think it pretty clear that equating made up and subjective is a long stretch.

    But moreover, it is this sort of contortion that leads me to ignore the subjective/objective distinction - it causes far more issues than it solves.
  • Banno
    14.5k
    If that is all he is claiming, then that'd be cool. But
    Metatheorems in mathematical logic, such as Gödel's theorem or independence theorems in set theory, have a logical status that is slightly different from that of conventional mathematical theorems.”

    ...seems to imply more; a difference in logical status.

    I'm somewhat ill-disposed to Sokal, finding his criticism of philosophy a bit too clever. Btu that would be an interesting topic in itself.
  • TheMadFool
    12.6k
    But you said that what is made up is subjective. Is Lord of the Rings subjective? What does that mean?

    I think it pretty clear that equating made up and subjective is a long stretch.

    But moreover, it is this sort of contortion that leads me to ignore the subjective/objective distinction - it causes far more issues than it solves.
    Banno

    What do you mean by "made up" then? As is obvious, our conversation has stalled, fallen at the first hurdle as it were.

    Denying mathematics any form of realism implies that it's got a subjective side to it, a collective kind i.e. it's a world that can be shared between individuals just like a work of fiction but lacking any form of real world relevance. Is this true? I think not. You've flown, me too.
  • Banno
    14.5k
    Witti's thinking might be along the lines that if the Liar's paradox is something we make up, then it is a game to one side of the mathematics of bridges. I gather that's why the article mentions Sokal's difference in logical status. In that regard I agree with
  • Caldwell
    604
    It is a mistake to think that because a line can be drawn between two point, that the line is there even if undrawn.Banno
    W is missing the point. A line is a distance. Two points apart entails a distance, therefore a line.
  • Banno
    14.5k
    As is obvious, our conversation has stalled, fallen at the first hurdle as it were.TheMadFool

    Yep.
  • Caldwell
    604
    But I agree with W regarding the bridge and contradiction.
  • Banno
    14.5k
    Good comeback.

    Is the line something distinct from the two points? I think it must be, since it includes all the points in between. If it is, is it there even when undrawn?

    And Chess was there to be discovered?
  • Caldwell
    604
    And Chess was there to be discovered?Banno
    No.
  • Caldwell
    604
    If it is, is it there even when undrawn?Banno

    Correct.

    Drawing the line is just a physical representation of the line. And saying it this way is even incorrect. But you get my point.
  • TheMadFool
    12.6k
    YepBanno

    Too bad. I was just getting into the groove but it looks like I misread the situation. Typical MadFoolery. Carry on.
  • SophistiCat
    1.7k
    W is missing the point. A line is a distance. Two points apart entails a distance, therefore a line.Caldwell

    A line is not usually defined as a distance, if it is defined at all: in some systems it is a primitive element, which is not defined, but merely constrained by the axioms of that system.

    I think what you are getting at is that for us to be able to define or describe a line, the world must already be such as to allow for such an object. And if that is so, then all the elements and constraints that are needed to make up a line (points, distances, etc.) are already in place. So what is there left to be invented?

    I think a Wittgensteinian answer would be to say that the world (or rather, the "world" of our thoughts and conversations), its objects, and the way we put them together to construct other objects are all part of a language game.
  • baker
    2.9k
    I think it pretty clear that equating made up and subjective is a long stretch.Banno

    Pffft. I'd venture to say that most people believe that "made up" and "subjective" are one and the same thing.* There surely is some reason why people believe that. How can you so readily dismiss it with an idle hand gesture?


    *Ever had a health problem and went to see a doctor? You list your symptoms, but the doctor doesn't believe you. He believes only those that he can see or otherwise assess by himself, with whatever resources he has available or willing to use. You could be having a bad headache for weeks, but if the doctor isn't willing to do any tests, isn't willing to send you to an MRI test -- then, for him, you don't have a headache. And since he's the one calling the shots, there's nothing you can do.
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