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Another way to think of it is that all numbers are imaginary. Numbers aren't real. Platonism is wrong. Imaginary numbers aren't "out there" somewhere. The whol

• hansbo 5y ago
  But even if you deep dive enough, there are discrete values, like in Quantum Mechanics. And as long as you have discrete values, you have integers, no? So integers do not seem only like human models, they seem to me as something innate in the universe.
  • dTal 5y ago
    "Discrete values" are also a human metaphor. You say there are two apples on your desk? I say there is a fuzzy quantum mess of probability distribution functions on your desk. "Two apples" is in your mind.
    • shusaku 5y ago
      I’m baffled that you’re invoking QUANTum mechanics to ascertain that discrete values don’t exist. At any rate, nominalism has a rich history, so I doubt these hacker news comments will solve the issue…
    • nh23423fefe 5y ago
      and spin?
  • igorkraw 5y ago
    are atoms discrete? we used to think so. we might never get a better model than quantum physics and it might still be wrong and fail to explain things. So there is a human idea of "discrete element" that we used to apply to everything - and as we look closer, it always breaks down. that doesn't mean it's a useless abstraction, but it is am abstraction - a tool for thought, a map, not the territory
  • helen___keller 5y ago
    Quantum mechanics is a mathematical description of the behavior of the universe, so wouldn’t invoking this to prove mathematical objects exist be begging the question? Not to say I agree with GP, but I don’t think it will be so easy to prove GP wrong either
• mannykannot 5y ago
  > But it is the only scientifically supported one. Really? What is the empirical evidence for it?
• throwaway17_17 5y ago
  I agree that this view it is not popular, but I also do not think that supporters often articulate their view/support well. I am a hard materialist and the amount of platonic-leaning discourse around the fundamentals of mathematics confuses me. I do not know how so many people (typical those outside philosophy and mathematical foundations) just assume a platonic style view.
  • dTal 5y ago
    I am currently reading "Where Mathematics Comes From" by George Lakoff and Rafael E. Núñez - the same Lakoff who authored the seminal "Metaphors We Live By", so I have a lot of time for him. At first it seems like they're just going to explore the pedagogical psychology of mathematics - how interesting! But then right at the end of the preface they hit you with "and by the way this is all there is to it, mathematical Platonism is a lie", which struck me immediately as straying out of their lane. But it seems their investigation into the titular question overwhelmingly led them to this conclusion. The argument is pretty simple - if there is a "platonic mathematics", we cannot have any direct experience of it. All mathematical thought, like all thought in general, is metaphorical. The predictive power of mathematics in the real world is unsurprising because we throw away the metaphors that don't work well. I do not like this conclusion. Mathematics has always been something of a religion for me. But I can find no flaw with the argument. From a scientific perspective, mathematics bottoms out at "what goes on in human noggins".
    • imbnwa 5y ago
      >The argument is pretty simple - if there is a "platonic mathematics", we cannot have any direct experience of it. Aside, but this is also Aristotle's exact argument against Platonism in general, though when he makes it in the Nichomachean Ethics he is specifically talking about ethical Good (if the definition/actual taking place of the Good lies in some other plane, we can't participate in it so no one is or can be good), but the idea is the same even when he's talking about what a soul is in De Anima. Aristotle doesn't believe in 'souls' in the way we think of them as religio-spiritual entities that exceed the capacity of the body; a 'soul' for Aristotle is the body but in a way that radically challenges the idea of a body as mere shell or vessel - soul is what any form of life repeats doing, as a body, in order to continue being itself. It should be noted that a lot of time at Aristotle's Academy was spent in Zoology, studying animals and their anatomy.
• mjburgess 5y ago
  This view isnt "scientifically supported" because science is neutral on (indeed, even presupposes) the existence of abstract objects. No one believes abstracta have a physical location -- they lack physical properties. The claim "2 + 2 = 4" is true -- and clearly not true invirute of anything anyone thinks... if we kill that person (/people), it is no less true. Indeed, if numbers don't exist (for example), do we suppose that we can't communicate issues of quantity with other species (, & possible alien life, etc. etc.) ? (If we can, what shared things are we talking about when we quantify?) It seems deeply implausible to say that our use of number is circumstantially psychological -- any description of reality is going to be indispensably quantitative --- quantity is what we are talkng about. We are not talking about ourselves.
  • echopurity 5y ago
  • jhedwards 5y ago
    I've thought about this problem quite a bit and, while my initial position was the same as above (math is not "real" per se) I had to concede that integers are real, because quantity is self-evidently real. If you have four oranges, the quantity "four" is right there. If you take away one of those oranges you know that the result cannot be split evenly without a remaining orange because of the properties of odd numbers. If you cut the remaining orange in half then you get a rational number, but is that self-evidently real? The halves of the orange are only "halves" because we consider them in relation to their origin, which we consider to be "one" orange. So rational numbers necessarily involve the human action of relating some quantity to a reference quantity, therefore they are a higher-level abstraction built on top of the fundamental physical property of quantity. In the end I decided that math is based on a foundation of quantity (and maybe "space" as well?) and everything else was a derived abstraction. I am very curious if anyone else has a good argument for other parts of math being fundamental.
    • dagw 5y ago
      integers are real, because quantity is self-evidently real. But the there are more integers than there are quantifiable 'things'[1]. Are integers that are a lot larger than, say the size of the power set of all fundamental particles in the universe still "self-evidently real". [1] Assuming a finite universe (or a finite number of finite universes) and a few other things.
• andreareina 5y ago
  Science has nothing to do with it, rather it's a question of philosophy and what we define as being real.
  • dTal 5y ago
    Science is "what we have evidence for". Is there evidence for some abstract mathematics that we didn't invent?
• dandanua 5y ago
  > there's no god "behind the curtain" have you looked there already? :)
• tasha0663 5y ago
  You can boil down pretty much everything to "an accumulated edifice of metaphors designed by human brains, for human brains". In the game Hearts, if you take most of the spades you lose. However, if you manage to take all the spades you win, and they call it "shooting the moon". In a similar fashion, when you reject everything as an unreal system of metaphors, Platonism "shoots the moon" by having us reexamine what we thought we meant by "real" in the first place.
• voldacar 5y ago
  This is one particular point of view, and it's extremely sloppy reasoning to say that it's "scientifically supported", given that mathematics is not a form of science. There are plenty of very smart people, not just mathematicians but also physicists & scientists who are mathematical platonists.
  • dTal 5y ago
    There are plenty of smart people - scientists even - who believe in all kinds of deities. Mathematics is indeed not a form of science. But the existence and shape of mathematics is an observable phenomenon, and so metamathematics - the study of what it is and where it comes from - can be studied scientifically. How do you know mathematics exists? Well, there's a textbook right there. Who wrote the textbook and why? A human, expressing metaphors inside their heads. How did those metaphors get inside that human's head? Ah, well, that's the interesting bit - the answer of course transpires to be "a combination of innate ideas imprinted by genetic evolution by natural selection, and sociology". And you don't have to stop there, you can explore in glorious detail exactly where each idea comes from, what innate monkey-ish tendency is being deployed, how exactly ideas like "infinity" fit in a mind designed for finding fruit and chasing things. We can similarly bring all manner of religious beliefs under the anthropological knife. It's not a pretty process though, to the people who believe in them.
    • carapace 5y ago
      > metaphors inside their heads. You're begging the question presupposing the non-Platonic viewpoint here. How do we know that metaphors are "inside the head"?
    • voldacar 5y ago
      You are just assuming the point you're trying to prove > There are plenty of smart people - scientists even - who believe in all kinds of deities. Okay? This is supposed to make me feel - how exactly? I'm not inherently disdainful towards theism or theists, but if I were, I guess your remark would make me like science less, or something? > We can similarly bring all manner of religious beliefs under the anthropological knife I'm not really sure we can, actually. At least not in some kind of non-contentious, "objective" sense. I don't really trust individual humans to give an accurate account of why they believe their beliefs, but I trust "anthropology" and "sociology" even less. My distrust for this on an individual scale comes from the fact that many beliefs & memes exist for purposes of social signalling, group identification, etc, and it might not actually be in your interest to know exactly why you believe what you do. But these auxiliary functions of beliefs, such as signalling etc, seem to me to scale up as you introduce groups and larger-scale activities such as "anthropology" and "sociology". Without some feedback loop keeping them honest, why would I expect anthropologists or sociologists to tell me a true story about why someone believes what they do, any more than that person or anyone else? In aerospace engineering, the feedback loop is that if your design is bad, your jet engine won't work. As a result, I generally trust aerospace engineers about jet engines. But what is there to stop sociologists, anthropologists, etc from just settling on some bullshit that agrees with their preconceived beliefs or flatters their group status and promoting it forever? But back to math. The history of mathematical ideas is complicated and interesting, but it isn't really that relevant to the question of whether the things those ideas are about are "real", which is equivalent to asking whether mathematical platonism is true or not. The question of platonism comes down to the definition of words like "real" and "exist". It is very easy to equivocate using these words, which is why most discussions about mathematical platonism are so low quality. I think the overall question isn't that meaningful so I'm not really a platonist or an anti-platonist. In most parts of human life, when I say "x exists", I mean that I can reach out and touch x, that it has a mass, temperature, surface texture, etc. In math, when I say "x exists" I just mean that I can talk about x without creating any logical contradictions. The square root of -1 may not exist in the same sense as my laptop here, but it exists in the sense that I can do things with it, such as add, multiply, raise to powers, etc, without reaching a contradiction in my formal system. So the whole "out there" thing doesn't really matter. There doesn't need to be an "out there" in order for me to meaningfully say that the square root of -1 exists. I think that a lot of philosophy is like this too, when you mentally zoom in really closely on a problem, it often reduces to some kind of equivocation or inconsistent language usage. Btw I don't really consider anthropology or sociology to be real intellectual disciplines, and I'm pretty on the fence about psychology and economics. I realize that is an unpopular opinion but I've thought about it a lot and I'm pretty certain that it's correct. Aerospace engineering is real because it attaches to some fundamental reality, namely that of the spinning fan blades, the combusting fuel, etc. If you get your engineering wrong, the fan blades won't spin. Likewise, math is attached to systems of axioms. When your do your math wrong, you get a contradiction. Sociology and anthropology don't attach to anything, they're like a closed loop, like theology. If you get your anthropology wrong, nothing really happens.
• canjobear 5y ago
  Reality is that which, when you stop believing in it, doesn’t go away. -Philip K Dick Even if you stop “believing in” math, your proofs are still either correct or incorrect.
  • dagw 5y ago
    The proofs are only correct in as far as you believe in the Axioms of mathematics that those proofs are built on. Stop "believing in" the axioms and the proofs are no longer true or even meaningful.
    • canjobear 5y ago
      But it is still the case that IF the axioms hold, THEN the proofs are either valid or not.
      • marcosdumay 5y ago
        So it's conditional reality. Now make that fit within your usual realistic philosophy...
        • canjobear 5y ago
          Easy. There exist contingency relationships between axioms and theorems provable from those axioms.
          • marcosdumay 5y ago
            Oh, yeas, your proof is quite real. And it's completely meaningless, being all about imaginary things. It can only have any meaning if you adhere to some scientific model. At this point you've deviated so much from the OP discussion that you could as well talk about angels dancing in pinheads. Any quantification of them is as real as your proof.
• tim333 5y ago
  >all numbers are imaginary.... mathematics is an accumulated edifice of metaphors designed by human brains Or you can say they exist but in a different way to physical reality. I mean pi probably still was 3.14159... before humans evolved so it's not our fault really. Personally I think maths not only exists but physical reality is a subset. I mean why else is there something rather than nothing? Scientifically it's the only hypothesis that works for that really.
• nathias 5y ago
  No it isn't scientifically supported because science does not include ontology and episemology as its domain. I'm not a platonist, but the reasons for not being platonists are philosophical.
• garmain 5y ago
  1) I might be missing something, but as far as I can tell "scientific support" in this context seems ill defined. To the extent that it seems rather meaningless term (in this context) 2) While the vast majority of the discourse on the interpretation of mathematics oscillates (fruitlessly) between Platonism and Nominalism, I tend towards a more Aristotelian view. See for example - Franklin: An Aristotelian Realist Philosophy of Mathematics - Keith Hossack: Knowledge and the Philosophy of Number. Note that these two authors do not converge on exactly the same interpretation. Apropos: North (2021): Physics, Structure, and Reality explores the relationship between "mathematical structure" reality and theoretical physics.