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Mathematical and logical truths exist before we have discovered them, so

  1. Nov 29, 2008 #1
    So does that mean that a world can exist through purely a system of numbers, values and rules?

    This system can exist without any physical matter, as it is only a mathematical pattern/system, and not an object.

    The system can include such things as "time" and "dimensions", but only the mathematical interpretations behind them. As this system of rules and patterns evolves to deeper and deeper complexities, things resembling 'life' and 'objects' can exist. (It is still only the values and properties of these things that exist, and not the objects themselves).

    I propose that humans and the universe are nothing more than one part of a mathematical system that can and always has existed without necessary "existing" any more than the number 4 'exists'.

    This explains why there is no real analogy or familiarity to explain the phenomena in the quantum world, the particles and fields really are nothing more than values and numerical properties that follow rules.

    This also means that every other possible (stable) system of values and rules does exist just as much as ours does (which links in with the multiple universes idea), which explains how life originated despite the improbabilities.

    Furthermore, I think that if something is possible, then it has to 'exist', just because we are nothing but a set of values following a set of rules.

    Tell me your thoughts, I haven't had too long to think about it, I just wanted to here someone else's view.
     
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  3. Nov 29, 2008 #2

    epenguin

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    "Mathematical and logical truths exist before we have discovered them"

    :confused: Where?
     
  4. Nov 29, 2008 #3
    We're assuming that if two independent civilisations were to develop mathematics, even on opposite sides of the universe, the mathematical rules they deduced would be identical. For example, prime numbers are always only divisible by one and themselves, regardless of your location in time and space.

    A problem arises when you try to explain how an individual conscious entity can exist simply as a set of mathematical rules. If this were possible, if I wrote the algorithm for George on a piece of paper (presumably a very large piece of paper), it too would be conscious just as George is himself. Call it a hunch, but that can't be right, can it?
     
  5. Nov 29, 2008 #4
    Wouldn't that mean our conscious has limits/boundaries?...it seems logical...after all, we can't really imagine anything beyond our conscious.
     
  6. Nov 29, 2008 #5

    epenguin

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    That is not a very good example as that is just a definition (of prime numbers).
    But I agree there are theorems about prime numbers that someone could independently discover elsewhere. They might have a handful of 20 stones and discover they could arrange them in a rectangular pattern

    .....
    .....
    .....
    .....

    but that they could not make any rectangular pattern with one less stone.

    Only in my view, and I think there is a philosophy that says this (constructivism?) until there are beings collecting stones, counting and arranging, "19 is prime" does not exist. Only the stones exist.

    I think things exist independent of us, but not "truths". I am challenging your introductory premise.

    However maybe this is not mainly what interests you, your ideas formulated a bit differently can perhaps be pursed independently of this quibble. :smile:
     
    Last edited: Nov 29, 2008
  7. Nov 29, 2008 #6

    turbo

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    The "truths" don't exist as entities. They gain that authority as we try to make sense of the world, and come to realize that there are some rules that we can apply under a range of circumstances (perhaps even most or all circumstances) and obtain reliable and testable results. Many, many times we have discovered and promulgated "truths" that turned out not to be true at all, and there is absolutely no reason to believe that many cherished ideas in modern science will be shown to be inaccurate, incomplete, or "not even wrong".
     
  8. Nov 29, 2008 #7
    I feel like the exasperated parent whom a child has just played the "Why?" game with, except that you, George, have gone about 100 "Why?"s beyond the usual point of conclusion of the game! I find all that has been said so far interesting, but I won't lose any sleep thinking about it. The reason is that, to questions such as "What is Existence?", there is simply no answer which is simultaneously both rational and satisfactory. You can step outside of science and resort to supernatural explanations, thus feeling satisfied. Or you can deduce that the idea of an "answer" to the question of existence is meaningless, thus being rational. But you can't have both at the same time.
    There's a thought. I'm sure you don't really mean paper, of course. When you represent a mathematical truth on paper, you have made marks on paper, you have not Created a Truth. Can I assume that you refer to "paper" as an analogy for something else? And if so, the question becomes: what? Is the paper "Existence". If so, what is the ink -- and how do you define "Existence", for that matter? See how these questions quickly become utterly meaningless. Almost as quickly, it becomes impossible to even formulate the next question.

    George, I think that you have posed a fascinating, if unanswerable, question; but it is my advice that you not spend too much time or effort in looking for an answer anyway. You might become rather depressed.

    P.S. Incidentally, I can't believe that the thread has made it even this far without a Douglas Adams reference. Do you feel cheated?

    - m.e.t.a.
     
  9. Nov 29, 2008 #8
    But in mathematics and logic, though? Certainly that's happened in science but there aren't any civilizations that have concluded that 2 + 2 = 5 that I know of. Mathematical and logical principles, however they have been expressed between different cultures (like the Mayans using a base 5 number system or the Egyptians only being able to conceive of fractions with "1" in the denominator) have always turned out to be reconcilable.
     
  10. Nov 29, 2008 #9

    turbo

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    You're right, of course. Mathematics is the most provable, testable science that there is, and it is simple in that we are dealing with concepts, not real-world observations with experimental errors. For the macroscopic world, it is a wonderful system. Once we get to the quantum scale, difficulties arise. It seems that our mathematics cannot be used to construct reasonable models of the quantum world. A fault of quantum theory or a limitation of mathematics? I lean toward the former, but the latter is not out of the question.

     
  11. Nov 29, 2008 #10
    What do you mean that mathematics cannot be used to construct reasonable models of the quantum world? What else is used to construct those models?

    I don't understand why you appear to be suggesting that mathematics stops working at the quantum level. To my knowledge it does not, in fact it's so reliable that we pretty much explore the quantum world exclusively with mathematical modeling.

    Nothing we have discovered relative to quantum phenomena has rendered invalid one iota of mathematics. Mathematics doesn't have some preference for the macroscopic over the quantum world any more than science deciding that the heavens were heliocentric rather than geocentric revealed any problems in mathematics.

    IMO you are confusing mathematics with physics. The science of physics is what explodes due to paradigm shift every few centuries and has to be put back together from scratch... mathematics continues working through it all with at most some new notation being desirable.

    P.S. I also do not regard mathematics to be some sort of science. They're completely different things. Mathematics isn't established or expanded by the scientific method nor are its conclusions tested by experimentation as those of science are.
     
    Last edited: Nov 29, 2008
  12. Nov 29, 2008 #11
    A true philosopher's way of putting it.
     
  13. Nov 29, 2008 #12

    turbo

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    Mathematics has been used to model and test quantum theories, and the accordance with theory has been impressive. One need only audit a few of Roger Penrose's popular lectures to get a feel for this.

    Mathematics started with simple enumeration, and advanced from there. Once we get to quantum scales, we have to start casting out infinities in order to get these great results. I don't think that it's a fault of our understanding of mathematics, but we cannot reject it out hand either.

    One glaring problem is the 120 OOM too-small (is that a big enough disagreement?) prediction of the expansive force expected to arise from the energy of the quantum vacuum. It's not infinity, but we currently throw it away because it is convenient to do so. (Refer to Dirac) Do we have a fundamental defect in quantum theory (vs classical physics) or is there some defect in our application of mathematics to this field. Epistemology might help here, but it's honored more in the breach these days, it seems.
     
  14. Nov 29, 2008 #13
    Oh, sure. But physicists erroneously applying mathematics to a problem of science isn't the same thing as a flaw or limitation in mathematics itself.

    In essence I'm pretty skeptical of assertions that mathematics is something that has no independent existence. Yeah, science is proven to be erroneous or the product of a fixated point of view over and over again down the centuries but mathematics has had an entirely different history. Yet it seems to me that scientists often try to surreptitiously gather mathematics into the failures of science, misery loves company don'cha know...
     
  15. Nov 29, 2008 #14

    Pythagorean

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    I'm detecting a bias....

    Mathematics is sometimes necessary but always insufficient for accurately describing anything in the universe. 2+4 = 6 tells me nothing in the context of my experience in the universe. 2 apples + 4 tomatoes could be equivalent to 2 fruits or 6 fruits depending on who you talk to and how they define a fruit. These shortcomings are inherent to describing reality. Of course mathematics in its purest form is free of them... because mathematics in its purest form has nothing to do with reality (which itself is much less stable than the concept of mathematics)

    An alien race might come up with an alternate method for manipulating their world that doesn't require mathematics. It seems anthrocentric to claim the human method of observation and manipulation is the only one.

    Also, every human race has come up with theology independently too. If aliens were to be religious would we have to start considering the validity of religion as a universal truth as well?
     
  16. Nov 29, 2008 #15
    I've certainly got a bias, but it's no more of one than when physicists or other scientists try to blame mathematics for things that go wrong in the course of their own discipline! :biggrin:

    That would be anthropocentric if I claimed that, yes... but I didn't. I just said that it has existence separate from human contemplation of it, nothing about mathematics being the only way to do anything.

    And if that's the case, that mathematics or its subject of study has some existence separate from human contemplation of it, it seems odd to say that it has nothing to do with reality. Introducing the problem of defining what a fruit is is again attempting to drag one of the problems of science into mathematics, btw.

    If aliens ended up developing the exact same theology, which hasn't even happened independently between separate cultures on Earth, that would be pretty notable, yes.

    Whereas if aliens developed mathematics reconcilable with human mathematics, many aspects of which have been developed independently in Earth history, no one would be anywhere near as amazed as they would be if we encountered an alien civilization practing, say, Theravada Buddhism.
     
  17. Nov 30, 2008 #16

    Pythagorean

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    (1) I think you have a huge misconception here and you're clumping and stereotyping based on what seems like a personal experience of yours (I also notice not much of your opinion has changed since I last talked to you, further enforcing your bias). I'm pointing this out because it may very well be impossible to have a progressive discussion with you at all.

    (2) Fair enough.

    (3) Actually, if you'd free yourself from your bias of my line of thought you'd see that I outright admitted that science has flaws inherent to it. But the point is that pure mathematics is void of reality. You have to attach qualitative meaning to it for it to describe reality at all. Of course science makes flaws describing reality and mathematics doesn't; mathematics doesn't attempt to describe reality. Science uses mathematics because it's more accurate than language, not because it perfectly describes anything.

    (4) Do you see how you're expecting exact relationships (right down to the name of the religion) for theology, but you'll willing to be much more loose about the relationships between the mathematics of different species?

    Just as cultures in Earth developed different theologies, they developed different mathematical theories and they compared and confirmed some of them, and found others to be erroneous, then they founded better axioms and reformed.

    You will find mathematicians that disagree about math just as you will find theologists who disagree about theological principals. You will find different schools focused on different axioms in both cases.

    Now, I'm not claiming mathematics and religion are the same. Mathematicians designed their axioms in favor of structure and self-consistency. You don't need the rest of the world to confirm mathematics. Religion, on the other hand, based their axioms on observations of reality. It stands more a chance of being wrong since it's actually daring to make a guess about reality.

    Science is somewhere in between religion and mathematics, making guesses about the universe, but using the mathematics (like you'd use a man made wrench) to make sure the observations themselves are consistent enough to make predictions about similar observations.
     
  18. Nov 30, 2008 #17
    On Orion's Belt. :uhh:
     
  19. Nov 30, 2008 #18
    Where? Well, I suppose that question is meaningless after you have presumed that time and dimensions are only mathematical systems. These systems do not exist in a 'place', because a 'place' only has any meaning when dimensions exist.

    But I see what your saying, For something to exist, it needs to exist somewhere, right? Well that is only if it is a physical object. The number four exists, as does the feeling of happiness. But neither of them can be given a position in space or time.

    What I'm saying is that the algorithm for me already exists, and it is me. Of course it can not exist on its own, it needs the 'algorithms' for air, and the world, the universe, time and dimensions. Which if they are all stable and do not involve any mathematical contradictions or paradoxes, then they are mathematical truths and therefore "exist".

    These truths and systems need not even be based on maths, there maybe a world who's fundamental language is not maths or 'logic', but of course it would be entirely impossible for us to imagine or comprehend such a world because our own minds are written fundamentally from mathematics. It's like, if your world does not have space, time, or dimensions, then how could someone from it possibly imagine them? Especially if there fundamental tool for predicting things or explaining things is completely different from maths.
     
  20. Nov 30, 2008 #19
    It is not my aim to answer it, or even argue that it is true. And no, I will not spend much time thinking about it; I am sure it is not an original idea, and as you said it is ultimately unanswerable. However, it is interesting to think about it at least.
     
  21. Nov 30, 2008 #20

    Pythagorean

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    The number four and the feeling of happiness may exist, but the question is is whether they exist outside of the brain. If you say the number four and happiness are descriptions of the state of the system (the system being our physical brain) well that's hard to refute. But saying that the number four existed somehow outside of conscious thought doesn't seem like a falsifiable claim to me.
     
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