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Universal logic

  1. Sep 7, 2010 #1
    Hi again, everybody. I have been mulling over lately some important assumptions we made when thinking, but suddenly I realize I cannot justify them all. Here is one of them:

    Supposing there exists parallel universes, would their physics laws obey our logical rules?

    Or rephrasing it: Could exist something illogical in this one or another universe? Is that possible?

    Or another rephrase: Are mathematics nonsensical in other universes?

    I feel much more comfortable thinking that the Universe (including parallel universes) always behaves respecting the rules of logic (and thus mathematical rules), but I cannot find any reason to justify that. So, can I conclude this assumption is just kind of a religious act of faith, or a personal preference?

    Logic is an entire philosophical branch. Is it right to say that it is based on an unjustifiable hypothesis? We suppose logical rules are universal, but why? Can we be sure about that? Based upon what?

    Thanks for any hints about it.
     
    Last edited: Sep 7, 2010
  2. jcsd
  3. Sep 7, 2010 #2
  4. Sep 7, 2010 #3
    I know about them, but the problem here is the link between them. To get a theorem from an axiom you need to apply logical reasoning. And nobody uses to deny logic, because it is quite obvious. Nevertheless, I cannot explain how can we be so sure about logic. There is no logic to yield logic.

    Is it absurd to ask about the origin of logic?

    How can rational people explain where logic comes from?

    Can we be absolutely sure about the reliability of logic in this universe and any other? I am, but not in a rational way but in a faithful or dogmatic way. I just see it quite obvious but I cannot explain why. Can you?
     
  5. Sep 7, 2010 #4
    my intuition says that it all boils down in the end to definitions and tautologies.

    someone else might tell you something different though.
     
  6. Sep 7, 2010 #5
    So, logic is true by definition. It sounds to me like dogma, isn't it?

    If someone, for example, says that in a parallel universe logical rules could be defied ... which would be your reply? Acceptance, reluctancy or rejection. Based upon what arguments?

    Mine would be rejection, but by no arguments. Is that faith?
     
  7. Sep 7, 2010 #6

    apeiron

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    What you are asking about is the basis of logic. Many have thought about this and I like the Peircean approach best.

    You can start with the idea that absolutely anything is possible. So logical or illogical, the distinction does not inherently exist.

    But then what comes to be, what does come to persist, must obey the constraint of being self-consistent. It would have to cohere and work synergistically as a system - otherwise there would be no "system". ie: something that seems lawful, regular...logical.

    To be illogical, a world would have to lack global consistency. But a world in interaction would eventually knock against itself in every manner possible to arrive at some kind of global equilbrium or state of consistency. It would self-organise to arrive at some prevailing state of order (and even chaos is an exact form of order - disorder expressed evenly across all possible scales of a system). So worlds must become logical, even if they don't have to start out that way.

    Now this might not be what you have in mind as "logical". But what do you have in mind as a fundamental logical fact?

    You could make the standard response of 1+1=2. Now that is true as a mathematical fact based on axioms. It would also seem true as a physical fact in all worlds organised enough, globally coherent enough, so that there are stable, persistent, examples of bounded one-ness and simple constructive, additive, actions.

    So what seems a strong truth given mathematical axioms, becomes rapidly more qualified when we talk about facts as a physical necessity. We can begin to see the need for deeper facts such as the fact that things can develop, that things can persist. Which is where we then get to the importance of a global constraint of self-consistency as being a very primary fact that answers the question of "what is logical?".
     
  8. Sep 7, 2010 #7

    Hurkyl

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    All praise the holy lexicon!

    But seriously, logic defines what it means to be "true", so it would be pretty silly if that definition was incompatible with logic!
     
  9. Sep 8, 2010 #8
    That is new for me. Thanks a lot for mentioning it. Nevertheless I feel quite uncomfortable about this idea, because I cannot render an illogical world connected with a logical one, through time, or evolution. An illogical world, as I understand it, should be a meaningless, nonsensical and indescribable world due to its lack of coherence.

    So, this approach accepts the possibility of existence of illogical things. Right? Nevertheless my intuition, or call it faith, tells me that an illogical thing cannot exist. And that is the point I am trying to expose and ask here: Being a rational person (meaning that my conclusions are derived from logical rules), can I accept the existence of certain illogical things (even disconnected to our world, in some kind of parallel universe)?

    Accepting them wouldn't it imply my logic is wrong, or at least non-universal?

    Doing philosophy and science it is a prior condition to be rational, to respect logical thinking. It is not right to say then, that an illogical world is unacceptable under a scientific and philosophical point of view?

    Philosophy and Science are based upon rationalism, the same I try to be myself, trusting in logic. But I cannot explain why. I can only feel my rejection to considering an illogical thing or world. The only similar thing to an explanation I find is an anthropic point of view: the world must be entirely logical for me (or human being) to be able to understand it.

    I think it was Einstein who said: "The most incomprehensible thing about the world is that it is at all comprehensible.". It is a way of saying that we have not any reason to explain why logic always rules. So, if we cannot explain it, we must accept it as an hypothesis, axiom, starting point, dogma or act of faith. Right?
     
  10. Sep 8, 2010 #9

    Hurkyl

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    Science is based upon a mix of empiricism and rationalism -- pure reason is not science!



    One thing to keep in mind is that "logical" tends to be used more as a synonym for "intuitive" or "can be rationalized (in an 'acceptable')" way, rather than the literal meaning "of or pertaining to logic".
     
  11. Sep 8, 2010 #10

    apeiron

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    I see what you mean but this other realm, this set of initial conditions, would actually be taken as neither logical nor illogical in itself. It is just a raw potential (a vagueness in Peircean logic). Or indeterminate as QM might put it.

    So the story would go that in the beginning there is just a potential that could produce anything. Fluctuations in all sorts of directions. And to start with, everything would be as logical as it was illogical. There would be nothing, no wider established context, to decide the matter either way. But as some prevailing state coalesced, it would define what is logical (that which hangs together as a global self-organised state) and then also what was illogical (any continuing fluctuations, these would be squeezed out of the picture as a matter of global constraint).

    Take as an analogy an ideal gas, a collection of particles in a box that has arrived at a global equilibrium temperature. There is an average prevailing kinetic energy. This is the "logical" state of particles. They will be constrained to some gaussian average motion. Then insert into the box a much colder or hotter particle. The kinetics of this particle would be "illogical" - counter to the natural motion of the system. However because all particles are in free interaction, the new particle will quickly be tamed. It will be a fluctuation constrained to the prevailing ambience.

    Or another analogy is a sum over histories approach to QM. Anything is possible, but most of the possibilities are self-cancelling if there is the global constraint as represented by the familiar principle of least action.

    http://en.wikipedia.org/wiki/Path_integral_formulation

    Many people indeed say about QM that indeterminancy is "illogical". But I am saying what is logical, what is illogical, comes only after a potential has become constrained to state. And these kinds of states are in fact self-organising. The observer is created by the act of observing, effectively.
     
  12. Sep 8, 2010 #11
    I accept the correction, although at least I find one exception to it, the "top-bottom" approach, or High-Road to do physics (S.L. Glashow) seems to me like pure reason at science scope.

    But the important thing yet is the question: Is an illogical world unacceptable under a scientific and philosophical point of view?
     
  13. Sep 8, 2010 #12
    If I understand it correctly, this means logic is a by-product/epiphenomenon/result of certain physical process at certain time "in the beginning". So, you need physics laws plus time to get logic. But physics laws are based on logic. So logic is created upon logic. Is that logical?

    P.S.: Do we really need logic to be created?
     
  14. Sep 8, 2010 #13
    It is true, but I find a common meaning for both: logical meaning there is no conflict between two truths. Considering that, it is right to say something is logical (rational, acceptable) when it is not in conflict with what we assume to be true, that including the Aristotelian syllogistic logic (pertaining to logic).

    Sorry if I said something wrong, because I am a noob in logic.

    So the question again, would be:

    Is an illogical (irrational or non-syllogistic) world unacceptable under a scientific and philosophical point of view? and why?
     
  15. Sep 8, 2010 #14

    apeiron

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    I tried earlier to distinguish two senses of logic. One is a mathematical idea, a particular established model of causality. If this, then that.

    The other is our feeling that the world operates in a globally regular fashion.

    So we have a model of causality (and why not many such models?), and an assumption from observation that the world we are modelling is causally regular. The same "logic" must apply everywhere - even in alternate or parallel universes.

    You have to make this basic distinction between the modeller and the modelled to see that the modeller just might have got his facts wrong in what he has been assuming. And also that the model does not itself have to exist for the modelled to exist.

    So I was saying forget about the modeller for the moment. Let reality start in a way that is pre-logical. Then whatever emerges as a self-consistent world - one with a regular global self-constraining structure - would quite naturally define what is "logical". And equally, what is then "illogical".

    Now we as modellers are the result of a world having come into being. Can we look back and say that it was "logical" that the world is the way it is. Was there only one possible outcome from a sum over histories of all possible self-consistent developments from states of pure potential, pure and unbounded indeterminancy?

    A variety of views could be argued from here.

    But it would help if you knew more of the history of the development of the idea of logic itself perhaps.

    For instance, Aristotle took a systems approach based on the four causes. And your question could be answered by saying that "to be logical" is the final cause of reality. Logic does not have to be there in the initiating conditons (the substantial and efficient causes in Aristotle's book). Instead it is the teleological goal towards which the whole process of development was tending (the formal and final causes).

    You are thinking of logic in terms of syllogisms and boolean algebra probably. Particular mathematical algorithms that are used to "do logic" in computational fashion. But this is just a subset of logic as a subject.

    Reality clearly has its emergent, self-organised, regularities or its "logical rules". Do you think that our formal models of logic have captured all those rules, or captured their full richness?

    We know from people's bafflement with QM that this cannot be. We know from metaphysics and systems science that there are larger models of logic that have yet to be formalised (in a way they can be implemented simply as a "machine").

    So getting back to the Peircean approach (which is also that of Aristotle, Anaximander, etc). Logic, laws, habits, regularities - these are all stuff that emerges as reality develops into crisp and persistent being. They begin tentative, and grow strong and hard with time. Vague constraint becomes very firm constraint.

    Looking back, we may get the feeling that things always had to turn out the way they did, at least in the broad or fundamental sense. We can say logic was reality's guiding purpose. In the beginning, it looked as though anything might have happened (the illogical was a possible outcome). But by the end, only the logical could make sense.

    Your way of looking at it insists that only crisp beginnings can lead to crisp outcomes. There has to be something definite at the start. Logic and laws and even time and space can't just simply coalesce into being in a developmental fashion.

    But that is just a particular model of how things happen. Peirce and others have worked with a different mental model of how logic arises into being. This is why Peirce, for example, said abduction is prior to induction or deduction.

    Human technology of course is completely based on the machine model of logic, not a holistic, organic, systems model. We live surrounded by cars, computers and the other fruits of a particular way of thinking. And it must be this that continues to blind people to the broader models that have always existed in philosophy.
     
  16. Sep 8, 2010 #15
    Yes, I think I understand this approach. Thanks for the explanation. It is well explained and very interesting. But I still find a problem here. You are describing an evolution along time, from an illogical state to a final logical state. If this evolution is a process based on rules, and these rules are fulfilling some kind of logic, then you are starting from logic to end up again in logic. This approach uses logic to create logic. Is not that absurd?


    Yes, I agree with you. There are at least two points of view here:

    1.- Mine: logic is universal and do not evolve in time.

    2.- Yours and Peirce's: logic is not universal and creates/evolves along time.

    But this is my question:

    * Choosing between approach #1 or #2 is just a matter of faith?

    Or rephrasing it:

    * Is an illogical world unacceptable under a scientific and philosophical point of view? Is there any scientific or philosophical argument against/in favor of approaches #1 or #2?
     
    Last edited: Sep 8, 2010
  17. Sep 8, 2010 #16

    apeiron

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    No, it is about an evolution from a pre-logic state to a state where there is logic becomes defined by what can exist (and so what is illogical is also now clearly defined as what cannot exist).

    This is a crucially different view. So we could say that in the first moments of reality, it may have been going in many directions, some which in retrospect were "illogical". But rapidly - as in a phase transition - all these other tentative directions got wiped up as a prevailing state coalesced.

    Following this approach, you might ask could the universe, or multiverse, have the condensed matter physics equivalent of frustrated domains - bounded patches where a different logic froze out locally?

    So even following this different view of how reality comes to be, there are a variety of sub-scenarios to explore.

    But it is not about a developmental gradient from illogical to logical, instead it is about a separation of a pre-logic potential into a reality that crisply exist because it was found to be logical - globally coherent - and another part of reality that does not exist with equal definiteness, because it is illogical and so cannot hang together,


    If they are different models, then we would decide on the basis of which seemed the most useful. And there is no reason not to use both.

    If I wanted to build a machine, I would use the logic of machines. If I wanted to build an organism, I would have to use the logic of organisms. But then organisms develop, they don't get built. Which is why I would talk instead about developing an organism.

    It is horses for courses. But when it comes to the cosmic-scale questions, we know machine analogies fail. Developmental approaches look far more promising to me as a modelling language.
     
  18. Sep 8, 2010 #17
    Ok. Understood. If I say pre-logic instead of illogical and discontinuous instead of gradient, I still find the same problem here:

    You are describing a discontinuous evolution along time, from a pre-logic state to a final logical state. If this discontinuous evolution is a process based on rules, and these rules are fulfilling some kind of logic, then you are starting from logic to end up again in logic. This approach uses logic to create logic. Is not that absurd?

    Are you meaning it is right to say that:
    - #1 logic is eternal and at the same time #2 logic was created at the beginning
    - #1 logic is universal and at the same time #2 logic is local, at least in time

    Is not that also absurd?
     
    Last edited: Sep 8, 2010
  19. Sep 8, 2010 #18

    apeiron

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    I see you think it is absurd, but I simply don't.

    I have no problem thinking of rules gradually emerging and so gradually organisation taking hold.

    Ever heard of genetic algorithms or neural networks? Even computer science has explored self-organisation and evolution as a way to grow a "logic".
     
  20. Sep 8, 2010 #19
    I can understand neural networks and genetic algorithms are systems capable of finding or approaching a desired algorithm, but never as a way to grow a logic.

    Neural networks and genetic algorithms are systems that are built upon logical rules, the same as Peirce's approach, if I am not wrong. So, logic is there before they begin to run.

    The logic that for example something that it is true cannot be false at the same time cannot be created without falling in the absurd. Just thinking about a pre-logic status where this rule fails is absurd, because this very rule fails and fulfills at the same time, so we cannot describe the status in a meaningful way.

    So, if we try to avoid the absurd, we cannot explain neither render the process of logic being created. Do you agree with it?

    By the way, do you avoid the absurd?
     
  21. Sep 8, 2010 #20

    apeiron

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    You say this, but Peirce indeed said that vagueness (what I am describing here as pre-logic, a state of indeterminancy) is exactly something to which the principle of contradiction does not appy.

    http://www.digitalpeirce.fee.unicamp.br/peichi.htm
    http://www.digitalpeirce.fee.unicamp.br/lane/p-prilan.htm

    Aristotle too made the point with his example of the battle of salamis. The middle has to be excluded for it to be divided into the true vs the not true.

    http://books.google.co.nz/books?id=...=persian fleet excluded middle battle&f=false
     
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