Logic has empirical foundations, sort of.

Propositional logic

Propositional logic (Photo credit: Wikipedia)

Massimo Pigliucci has an interesting post at Scientia Salon on philosophical zombies.  Massimo looks at David Chalmers’s argument for philosophical zombie arguments and, I think, does an excellent job at showing the problems with them.  But in the discussion, a distinction is made that I find interesting.

Apparently, Chalmers admits that zombies are probably not naturally possible, but sees them as logically or metaphysically possible, and sees that as grounds for moving forward.  Massimo spends some time looking at whether or not metaphysically possible and logically possible are the same thing.  I’m not going to get into that, but if you find it interesting I definitely recommend his full post.

My interest is in the distinction between something being logically possible and it being possible given the natural laws of our universe.  When I first read this distinction, I composed a long comment raising objections that such a distinction wasn’t, well, logical, then realized I was utterly wrong, and instead commented on the limitations of logic.  Here’s the main portion of my comment as Scientia Salon:

I’m always a bit suspicious when people start talking about things being logically possible but not possible with our current natural laws, and yet proceed to try to make meaningful conclusions based on that logical possibility. Many things are logically possible given inaccurate premises. It’s logically possible for water to not be H2O, but only if my premises are wrong or incomplete or if I’m using an uncommon definition of “water”.

It’s not clear to me that even invoking the multiverse rescues this endeavor. We have no guarantee that logic as we understand it would have any traction outside of our universe. An assertion that logic necessarily transcends our universe strikes me as a statement of faith.

But this raises an interesting question.  What exactly is logic?  It turns out that logic is not one of those things that are easily definable.  Per Wikipedia, here are some attempts at a definition:

Arranged in approximate chronological order.

  • The tool for distinguishing between the true and the false (Averroes).

  • The science of reasoning, teaching the way of investigating unknown truth in connection with a thesis (Robert Kilwardby).

  • The art whose function is to direct the reason lest it err in the manner of inferring or knowing (John Poinsot).

  • The art of conducting reason well in knowing things (Antoine Arnauld).

  • The right use of reason in the inquiry after truth (Isaac Watts).

  • The Science, as well as the Art, of reasoning (Richard Whately).

  • The science of the operations of the understanding which are subservient to the estimation of evidence (John Stuart Mill).

  • The science of the laws of discursive thought (James McCosh).

  • The science of the most general laws of truth (Gottlob Frege).

  • The science which directs the operations of the mind in the attainment of truth (George Hayward Joyce).

  • The analysis and appraisal of arguments (Harry J. Gensler).

  • The branch of philosophy concerned with analysing the patterns of reasoning by which a conclusion is drawn from a set of premisses (Collins English Dictionary)

  • The formal systematic study of the principles of valid inference and correct reasoning (Penguin Encyclopedia).

I’m not sure which of these I’d prefer.  A distressing number refer to “reason” with most definitions of “reason” referring back to logic.  But Gottlob Frege’s definition seems closest to my own current personal intuition about it, namely that logic represents the most fundamental relationships in our universe.  These relationships are so fundamental, that we can take them and extrapolate truths using them, and often we’ll be right.  (We won’t always be right.  More on that in a bit.)

Does this mean that I think that, as Hilary Putnam discussed, logic is empirical?  Yes and no.  I think logic rests on foundations that are empirically observable.  But it extends into realms that are not observable and often not physical.  We extend it the same way we extend mathematics.  (Indeed, everything I’m saying here can also be extended to include mathematics, which has often been called quantitative logic.)  All logical reasoning could be called tautologies, although that is misleading because many tautologies are not intuitively obvious and many of them are important to understand.

But logic, even in its foundations, doesn’t feel empirical.  I think the reason it doesn’t is because we didn’t learn it empirically.  Remember that humans are not born blank slates.  We come with cognitive machinery pre-wired to some degree.  That pre-wiring includes an innate capacity for logical reasoning.  (We don’t always use it, but we have the capacity.)  Why do we have that capacity?  Like anything else, we evolved it, almost certainly because it provided a survival advantage.

But that capacity evolved to deal with the working of the universe at the level at which we operate, on the scales well above quantum physics but much smaller than astronomical phenomena.  Logic seems to work well at this in between scale, but there’s no guarantee that it will work at other scales.  Although the results of astronomy and cosmology seem to show that it does seem to scale well to much larger scopes.

But when we go down to particle physics, logic takes a hit.  Many things about how we logically expect the world to work start to be wrong.  Of course, there are many interpretations that attempt to salvage some logic from observed quantum phenomena, but they are still forced to posit a world that would be considered illogical if experimental results didn’t force the issue.  Indeed, some philosophers have even proposed an alternate system of logic based on quantum mechanics.

As I commented above, we also have no guarantee that logic would have any meaning outside of our universe.  If there are indeed other universes in a multiverse with different natural laws, logic as we understand has a good chance of not working.  (This incidentally is one reason why you have to treat logical arguments about the beginning of the universe with a large grain of salt.  Extrapolating about the beginning of the universe based on how it works from within isn’t guaranteed to show anything.)

And, of course, even in settings where logic applies, logical reasoning is only as good as its premises.  If our premises are wrong or incomplete, it doesn’t matter how good our logic is; we may still be completely wrong.  (As an old programmer, I’m reminded of situations where I got the program logic perfect, but misunderstood some of the business requirements for the program I was writing; perfect logic but still wrong results.)

None of this is to say that logic isn’t tremendously useful.  Reaching conclusions with logic (or mathematics) is far more likely to be correct than reaching them with intuition and emotion, at least on matters outside of everyday life.  But we should be mindful of the limitations of reaching conclusions with logic alone.  The history of science is one where logical extrapolation often pays off, but just as often doesn’t.

Think I’m wrong about this?  If so, I’d love to read your…logic in the comments 🙂

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42 Responses to Logic has empirical foundations, sort of.

  1. Hariod Brawn says:

    I think I side largely with you on this SAP. Logic and reason work efficiently within the matrix of our means of understanding – meaning what is known by means of how our brain represents the world to human subjectivity. Still, it’s only an ape brain; so let’s not get carried away and abandon humility as a result of our faith in what we apes call ‘reason’. We may, after all, be as dumb as we look.

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  2. s7hummel says:

    it’s very embarrassing that i have to constantly hide behind my poor knowledge of english. and this in spite of the great texts that appear here… but my poor mind is not gifted in understanding! so i still remain in the humiliation of my intellectual development. so i can only express my gratitude to all for your patience. unfortunately, it seems that i’m in the early stages of my ineptitude than its end. but sometimes i have to deal with really difficult text. at least difficult for me! here is one of those texts where it is not possible for me alone understood it. can anyone have any idea how to figure it out… (Dream or nightmare, we have to live our experience as it is, and we have to live it awake. We live in a world which is penetrated through and through by science and which is both whole and real. We cannot turn it into a game simply by taking sides.)

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    • As I said on the other thread, no worries at all on the language barrier. I can definitely detect a sharp mind on the other end and fully understand the difficulty. I’m very happy to have your commentary and discussion here!

      Based on the remarks at the end of your comment, I think you got my main point. Logic is useful, but if you start with non-real premises, you are definitely playing a game. The game might have value, but any conclusions from it should be applied with caution to reality.

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      • s7hummel says:

        “no worries at all on the language barrier” know you’re trying to be nice! but as a man little complain and repent over itself right away a better mood has. this is at least the nature of the Poles! i know that i have to fight these weaknesses but maybe a little later…

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  3. s7hummel says:

    more’s the pity! but we’ll be back to Amir Aczel (Pseudophysics) + additional text. of course if you felt like it and if you’ll allow… i also have a very interesting text for thought (of the highest importance), but a little later.

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  4. Hi SAP,

    I have to say I completely disagree with you on this stuff. Logic is, as you say, a set of tautologies. All the logical rules follow from the definition of the terms. There is no possibility that there could exist another universe where this would not be so, because it is independent of anything in this universe.

    Quantum mechanics does not defy logic. It is unintuitive. That is not the same thing. If what we observe disagrees with our a priori conclusions, it is because we are reasoning from incorrect premises and not not because there is anything wrong with reason itself.

    My feeling on logic is that it is universal. More than one kind of logic may exist, but I suspect that any coherent well-defined logic can be modelled and worked with in the context of the familiar logic, perhaps making modifications such as substituting TRUTH and FALSE for predicate functions etc. This implies that any sensible well-defined logical system can be implemented as a computer program, for instance, a claim which I feel is true.

    I also disagree that Massimo’s argument against Chalmers was any good. In the back and forth it became clear to me that he had made a basic mistake. He argued against Chalmers by showing that metaphysical possibility collapses to logical possibility, thinking that this invalidated Chalmers argument by showing it was based upon a redundant or nonsensical concept.

    But he doesn’t seem to realise that metaphysical possibility is just about what can exist. If it collapses to logical possibility, then that means that anything that is logically consistent can exist (in some possible world). This helps rather than hinders Chalmers’ argument, because now all he has to show is that p-zombies entail no contradictions, which would prove that they are possible, which would mean that consciousness is not entailed by the laws of physics, which would mean that physicalism is false.

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    • Hi DM,

      “There is no possibility that there could exist another universe where this would not be so, because it is independent of anything in this universe.”

      My question is, if logic is completely independent of anything in our universe, then how do we know about it? It seems to me that either it must relate to some aspect of the universe for our brain to process it, or the universe must relate to some aspect of it? Given your platonism, I suspect you would assert the latter, but then my question would be, how can we know that? How can we know whether the universe emerges from logic, or logic emerges from the universe?

      My main point was that if logic emerges from the universe, then it may be contingent on the universe.

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      • It does relate to some aspect of the universe, because nothing can exist that is not logically consistent, including the universe, meaning that the universe is necessarily logical. We evolved with the ability to do logic because it is useful, for navigating this universe but also for considering others.

        Logic is not dependent on the universe because logic is just the study of what follows from some axioms. Every logical law is a consequence of those axioms, and follows (and has to follow from) from the definition of those axioms. You can pick whatever axioms you like. The ones we have settled on are not chosen because they are the only ones possible in this universe but because they are simple and more complicated rules can be built from them.

        I think this is related to the fact that all you need to do any computation, no matter how advanced, from rendering the latest Pixar movie to a simulation of a whole universe is a universal Turing machine with a few very basic computational operations. The details of what those particular operations are don’t matter so much because it is often possible to emulate the classic Turing operations in the context of other formal systems — that is numerous systems have been shown to be Turing complete: http://en.wikipedia.org/wiki/Turing_completeness#Examples

        Logic doesn’t emerge from the universe, but the universe has to be logical.

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        • DM,
          I appreciate your thoughts on this. I hope I don’t sound too much like a broken record.

          “Logic is not dependent on the universe because logic is just the study of what follows from some axioms.”

          But what is an axiom but something we have previously observed (in this universe), have an intuition about (rightly or wrongly from instincts or experiences acquired in this universe), or calculated or reasoned to be true based on other axioms?

          And what determines whether or not something follows from an axiom? That it matched or avoids contradicting previously successful follows? What determined that those things actually followed? Ultimately, what is the measure of logical correctness?

          Whatever the answers, how can we conclude that they transcend our universe? That we can logically extrapolate to non-physical entities? What tells us that these entities are anything but mistaken or incomplete conceptions of reality?

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          • Hi SAP,

            “But what is an axiom but something we have previously observed (in this universe), have an intuition about (rightly or wrongly from instincts or experiences acquired in this universe), or calculated or reasoned to be true based on other axioms?”

            I don’t think an axiom has to be true. An axiom is just part of a definition. When you choose your axioms, you define the system you’re talking about. The axioms of logic are not true in and of themselves, but if we take them to be true, we have defined logic. I’m sure other axioms are possible, but any system which is useful and flexible enough to rival logic is likely to be just the same old logic in disguise. Try it, Make up an arbitrary system of logic-like axioms and/or operators that actually do something non-trivial and see if they don’t turn out to be just the same old logic but with different symbols or something.

            Euclid’s geometrical axioms are the standard examples. The parallel postulate in particular is not true of itself, but if you assume it is true then you have defined Euclidean space, whereas assuming it to be false can lead to hyperbolic or elliptic geometry.

            “And what determines whether or not something follows from an axiom?”

            The axiom itself. As a definition, the axiom defines what follows from it. It’s like asking what determines whether or not it is true that an unmarried man is a bachelor. Or whether it follows that a bachelor who marries is no longer a bachelor. These truths are entailed by definition. There is nothing particularly strange or mysterious going on.

            “Whatever the answers, how can we conclude that they transcend our universe?”

            Because logical contradictions, by definition, cannot be true. There is no possibility that there exists a universe where a logical contradiction is true. That would itself be a contradiction, and if you assume a contradiction is true you are throwing reason out the window.

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          • Hi DM,
            I said this to Robin over at Scientia Salon, but it seems like we’re communicating across a conceptual boundary where one of us may be missing a crucial realization. (I’m open that it may be me, but of course if I thought it was, I wouldn’t be arguing my points.)

            “I don’t think an axiom has to be true.”
            I totally agree with this. It’s one of the limitations of logic that we have to be mindful of.

            “Try it, Make up an arbitrary system of logic-like axioms and/or operators that actually do something non-trivial and see if they don’t turn out to be just the same old logic but with different symbols or something.”
            So useful logic is constrained, but what constrains it? As a pattern in this universe, as a substructure of it, I can’t just create any arbitrary but workable logic. But I can’t see where my inability to do so has any relevance to how things might or might not work outside of our universe. My mind is constrained by how things work in this universe. I understand that, and I think its implications include what I discussed in this post.

            What is a definition but a designation that a piece of language refers to a particular pattern or structure? What is a contradiction but two exclusive patterns? But what makes some of them contradictory and others consistent? Again, whatever the answer is, what about it implies that it transcends our universe?

            My point with all of this is that, if we start talking about outside of our universe, with different laws of nature, then everything we expect about how reality works may be up for grabs.

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          • Perhaps I can illustrate why logic has to hold with a simple example.

            Let’s suppose we have some kind of formal system consisting of a syntax with various symbols and rules about how those symbols can be manipulated.

            Let’s take as an axiom that the symbol $ in our system can always be replaced by the symbol €. By looking at the axioms of our system, we can conclude that the statement “[$8.00]” can be replaced by the statement “[€8.00]”. Your argument that logic could work differently in other universes is like saying that maybe the latter statement cannot replace the former in some other universe. But this is patently false because, by definition, this replacement is legal. If ever that replacement is not legal, then we are simply no longer discussing the same system. In the same way, logic has to work everywhere,

            What you might want to argue is that our logic will work — the same statements are contradictions or tautologies — but it will not be useful for anything in other universes. That is perhaps a better argument, but I don’t buy it. The scenario you seem to suggest is quite literally inconceivable. The flexibility of logic is such that it can be applied to any conceivable situation.

            Perhaps this inconceivability is because the physics of this universe constrain us somehow, but I think Occam’s razor suggests that if illogical worlds are impossible to imagine and there is no evidence or reason to believe that they can exist then it is reasonable to assume that they can’t. For some reason I find it stranger to imagine that there is something built into the laws of the universe that arbitrarily constrains the ways that we can think than to think that logic is universal.

            I don’t pretend that I can prove the point, but I find the viewpoint you are advocating to be very dubious indeed.

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          • I guess this depends on our respective reactions to the idea of the inconceivable. This is going to sound strange, but I can conceive of things that my mind can’t conceive, or that could only be partially conceived. I’m open to the possibility that there may be things in reality that fall into this category. Things we may simply have to work around. Some things we may have limited ability to understand in terms of the layer of reality that our minds work at.

            Now, I’m not advocating that as a general principle. As a matter of motivation, it pays to operationally assume that we will eventually understand all phenomena, since if we can understand something, it is less likely to be achieved by those who have decided we can’t.

            But we also need to remember the reaction of Einstein to quantum mechanics. It didn’t behave according to how he understood the universe to work and, seemingly, his contributions in later life were limited by his dogged adherence to this stance. I know your position is that QM is logical, but you have to admit that no one logically predicted what was found.

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          • Let’s see if we can agree on a few key points.

            1) It seems that there are many more ways the universe could be than the way it is.
            2) In particular, there are many logically possible universes (basically an infinite number)
            3) If there are many logically possible universes (where our logic applies), then in some sense logic transcends this particular universes
            4) Universes where logic does not work are at best ineffable and at worst incoherent or nonexistant, so there’s not much we can say about them other than to acknowledge the extreme skeptical viewpoint that we may be constrained from imagining them by physics, which does not mean that we can be sure they don’t exist.

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          • Hi DM. I enjoy our discussions immensely. Just wanted to mention that before I annoy you 🙂

            I’m not necessarily convinced of 1). A lot depends on what is meant by “could” in this context. Logically with premises different than currently observed reality, it can be true, but that’s an important clarification.

            It seems to me that 2) has an implied premise that logic extends beyond our universe. Of course, that’s the conclusion to 3), which makes the two feel somewhat circular to me.

            On 4), I’m not prepared to say that we could never discover or be aware of a non-logical universe or domain. This reminds me of Massimo’s analogy of a spot on a map that we could know nothing about, but that we could still observe the outlines of, and perhaps see what happens when things enter or leave it. I know you strongly disagree, but I’ve wondered if quantum physics isn’t such a hole.

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          • Hi SAP,

            I enjoy our conversations too. No worries there.

            1) If you doubt this point then you are entertaining the idea that this is the only possible universe. Not only is there not a multiverse, but there cannot be, and even given a one universe reality then it was fated, somehow, to be this one. If other universes are not ruled out by logic, then what is it you think rules them out? If this is the only possible universe, does this mean we should, in principle, be able to deduce how it works from the armchair?
            2) I guess if the first claim is controversial then this one is equally so. But you seem to see an additional problem. If we accept point (1) for now, I can’t see how point (2) is controversial. Using the logic of this universe, we can see how other universes are logically possible, and that our logic would work in them. So our logic is compatible not only with this universe but with a vast array of other logically possible universes. The point is that the laws of physics could be radically different but logic would still work. If the laws of physics are essentially the definition of the universe (as I think they are) then logic is not especially coupled to this universe. That’s not to say that there are not other families of universes which are not compatible with our logic (although I have a hard time accepting that idea, personally).
            3) Follows from (2), we seem to agree.
            4) I don’t see how QM can be such a hole. Being unintuitive is not the same as being illogical. It is something of a meme that we can’t understand QM, but I don’t think this is really true. We can’t understand QM in the same way that we can’t understand a four-dimensional hypercube — we can’t picture it intuitively. It doesn’t mesh with how we feel the world ought to work. But we can do mathematics with it and manipulate the symbols in logical ways so that we do, manifestly, have a logical model of it which works. This is understanding of a kind and this is the kind that matters for discussions about whether it is logical or not.

            On the general point of (4), earlier you seemed to be arguing both that we cannot conceive of illogical universes and this is because we are constrained to work within the limits of the logic of this universe. However, now you seem to be saying that we may be able to conceive of them at some point, that you are not willing to accept that they are ineffable. Could you clarify this for me?

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          • Thanks DM.

            1) I think it’s possible that the universe is all that is, but it’s also very possible that there is more outside of it. My point is that we should be cautious in using our knowledge of how things work within the universe to draw conclusions about how things might work outside of it, if there is an outside. We have limited or no access to how much or how little of the workings of our universe extend beyond it.

            In my mind, that applies to the physical laws, logic, mathematics, everything. That we might not be able to conceive of all of these things being different outside of the universe doesn’t strike me as a valid reason to have any certitude that it isn’t so, particularly since our ability to conceive is based on the workings of our brain, which must work according to the principles of this universe.

            2) I guess I’m not convinced of the distinction you make between the laws of physics and logic, and again can’t see why logic would be exempt from the things that might vary across universes.

            4) Relativity seems to fit the not intuitive but logical category, but I’m impressed by all the knowledgeable physicists, such as Richard Feynman, who think we don’t understand QM. In general, the more someone seems to know about QM, the more convinced they seem to be that we don’t really understand it. We have empirical observations, and we have mathematics that can relate those observations, but there is far from a consensus among physicists that we understand what is happening between those observations.

            I once read a logical deduction of special relativity from first principles, indicating that it was possible, at least in principle, to have logically worked it out prior to the Michaelson-Morley experiment. I haven’t seen anything like that for QM.

            On the clarification about conceiving and ineffable, there may be domains we can’t understand, but we may be able to understand their boundaries and interactions with phenomena that we do understand. We might even be able to work out mathematics for those boundaries and interactions, without ever being able to understand what was happening inside of the actual domain. Of course, if this situation ever arose, many would insist that we do actually understand the domain because we understood the boundary. This can get into the definition of “understand” which is a rabbit-hole I don’t have the energy to go down right now.

            If the above seems implausible to you, consider that stroke victims with lesions in specific areas of their brain, often can’t perceive one side of their vision. It isn’t that they are simply blind on one side, the idea of the other side becomes inconceivable to them. If we can recognize that there are things that a damaged brain can’t conceive of but that we know exist, why isn’t it possible that there are things that exist that healthy brains can’t conceive of?

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          • Hi Mike,

            1) I think you’re missing the point slightly. I’m not asserting (for now) that there are universes other than this one, or that there is anything at all outside the universe. I’m asserting that the way this universe is not the only possible way for a universe to exist. It may happen that it is the only universe, but this fact is contingent.

            2) Again, you’re missing the point slightly. I didn’t assert that logic could not vary between universes. I’m saying that there is a subset of the possible universes where our logic applies but not our physics. I distinguish between logic and physics because it is not hard to conceive of alternative laws of physics but it is not possible to conceive of logical systems which are completely incompatible with our basic ability to reason. The logically possible (or compatible) universes include all universes we can conceive of in detail.

            4) Many physicists say we can’t understand quantum mechanics. They are referring to how unintuitive it is. I don’t think you would find any who would say that logic does not apply to quantum mechanics. You might find quotes of them saying it defies logic, but unless they are making the same kind of formal point you are trying to make I would interpret them as speaking of common sense and intuition. It doesn’t defy logic. If it did we could not work with it. It would be incoherent, and it isn’t. It’s just very strange.

            I have no opinion on whether QM might be deduced from first principles. I don’t think that question has any bearing on whether it is logical or not.

            I agree that we might identify a border between what is conceivable and what is ineffable. For me, that border lies at the boundary of logic. There is no more to say about it. There may be real things outside this border but we have no reason to believe there are, and if there are there is nothing we can say about them. We may as well ponder the many fascinating properties of square circles or married bachelors or Ysi*345^kk<4$$$$p.

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          • Hi DM,
            1) and 2) I think I understood your initial points, or perhaps I’m continuing to hold the same misunderstandings, since my responses would be the same as the ones I made above.

            4) I could agree that QM is logical, once we’ve redefined logic to accommodate it (which some have done), but then that only reinforces my point about logic being rooted in how the universe works. I think it’s worth noting that the low opinion many physicists have toward philosophy is rooted in classic logic’s inability to predict QM even as a possibility. (I think Neil deGrasse Tyson stated this explicitly in the interview where he dissed philosophy.) I disagree with their blanket dismissal of philosophy, but I understand where they’re coming from.

            I suspect we’re not going to come to agreement on this. I perceive we’re starting to repeat. We might simply be at the point of needing to agree to disagree.

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  5. Tienzen (Jeh-Tween) Gong says:

    SelfAwarePatterns: “Many things are logically possible given inaccurate premises. … As I commented above, we also have no guarantee that logic would have any meaning outside of our universe.”

    Amen!

    Logic is not a ‘truth machine’, as the validity of its ‘conclusion’ is totally depending upon the validities of its preceding statements. The validity of every logic ‘conclusion’ can be verified independently outside of the logic framework. If this independent verification is in contradiction to the ‘logic conclusion’, that logic conclusion must be wrong.

    The key misconception of this issue is that we think that logic-universe and the metaphysical-possibility-universe are ‘bigger’ than the ‘physics’-universe. There is no evidence and argument to support this misconception. In fact, I have put out my arguments on discrediting this misconception, and there can be reviewed at http://scientiasalon.wordpress.com/2014/08/04/p-zombies-are-inconceivable-with-notes-on-the-idea-of-metaphysical-possibility/comment-page-1/#comment-5704 and http://scientiasalon.wordpress.com/2014/08/08/on-the-philosophy-of-language-part-ii/comment-page-1/#comment-5798 .

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    • Tienzen,
      It sounds like we agree on the limitations of logical conclusions. But it seems clear to me that every logical conclusion is not independently verifiable, although it would be nice if they were. But having some kind of verifiability, or at least falsifiability, definitely gives a conclusion more reliability.

      On logical/metaphysical being broader than physics, I think it’s a matter of definitions. If by “physics”, we mean currently discoverable physics, then I do think metaphysics is “bigger”, but if we mean everything that might ever be discoverable as physics, I’d have some sympathy with your statement, although I’d be nervous about being too certain of it. This itself strikes me as a logical conclusion we should be cautious about.

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      • Tienzen (Jeh-Tween) Gong says:

        SelfAwarePatterns: “If by “physics”, we mean currently discoverable physics, then I do think metaphysics is “bigger”, but if we mean everything that might ever be discoverable as physics, I’d have some sympathy with your statement, …”

        Yes, there are definitely two types of physics: the ‘nature physics’ which rules this universe, and the ‘human physics’ which is discovered by human endeavors thus far. If some part of the nature physics is forever beyond the reach of human effort, it is still an ontological ‘reality’ there, keep ruling this universe.

        My ‘statement’ that logic-space and metaphysical-possibility-universe must be a ‘subset’ of the ‘nature-physics-universe’ is not an opinion statement, but I have showed two pathways of proof.

        One, there is a ‘base’ which gives rise to ‘all’ complex systems (number sets, life-sphere, physical universe, metaphysical-possibilities, etc.), and this is also the base for the nature-physics. This argument was done in the book “Linguistics Manifesto, (ISBN 978-3-8383-9722-1)”. Thus, I will not repeat it here.

        Two, if a ‘base’ is timeless (eternal) and immutable, it will be the ‘base’ for ‘all’. Yet, these two [timeless (eternal) and immutable] must not be the ‘concepts’ of philosophy or theology but must be the physics-processes. That is, they can be grasped step by step and be ‘measured’. Being a process, it must ‘produce’ some products.

        In the ‘human physics’, we have discovered a lot, yet with many open questions. On the other hand, for something to be the ‘base’ of the nature-physics, it not only must ‘reproduce’ all the known ‘human physics’ but also must answer all the open question. I have showed some of those ‘products (product, …, products, …)’ at http://scientiasalon.wordpress.com/2014/06/05/the-multiverse-as-a-scientific-concept-part-ii/comment-page-1/#comment-3158 . There is no point for me to discuss the ‘base’ and the ‘processes’ here before anyone (including you) comments on those ‘products’ first. If those ‘products’ are wrong, no further discussion is needed.

        SelfAwarePatterns: “But it seems clear to me that every logical conclusion is not independently verifiable, although it would be nice if they were. But having some kind of verifiability, or at least falsifiability, definitely gives a conclusion more reliability.”

        For every ‘true-truth’, it cannot be falsifiability by ‘definition’. Yet, ‘every’ true-truth can always be verified. I will not provide the proof on this here, as it can be a good topic for the future discussion. Thus, for any true-truth (logical or else), it can always be verified (within or without a logic framework).

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  6. I think you’re right on a comprehensive level of how we should think about the world, but I also think that Disagreeable Me makes a lot of great points above, particularly about axioms. I’ll take a different track in my response to avoid repetition.

    I do think that the distinctions between logical possibility and material possibility are useful if you understand how they work. Non-applied mathematics is an example of logical possibility in practice. Mathematicians come up with theories that are logically possible, but practically inconclusive – or even just completely useless – until we get some evidence to fill in the variables. I think it can be interesting and helpful to trial balloon ideas through to their logically possible consequences as best we can when we lack empirical evidence (because we’re trying to predict what will happen in the future, or discern between competing reports of an event we haven’t witnessed, etc).

    That being said, logical possibility alone is deeply unsatisfying – even to the most spiritual. St. Augustine’s Soliloquies attempt to engage in a purely rational project (so as to avoid the necessary faults and changes of the unreliable empirical world), and the result leaves Augustine with nothing but empty tautologies and the promise of an immortality devoid of individuation. Despair ensues.

    But I definitely think it’s worse to collapse the distinction completely, because without it we’d bounce back and forth between the two with no real understanding of it. Augustine does this in some of his early attempts to prove the immortality of truth. Trying to be purely logical and accidentally pulling in observations from the world leads him to contradictions and confusions, and it’s only after he learns to disentangle the two that he’s able to put them back together in later work (and I think this point stands even if you don’t like /how/ he puts them together).

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    • Thanks Michelle. I agree with all your points, and found the insights on Augustine interesting.

      I definitely didn’t mean to imply that we shouldn’t do that kind of thinking. The exercise of doing so can lead to insights into the actual workings of reality. My point was that we should be cautious in accepting any conclusions about reality based solely on that thinking.

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  7. Pingback: Logic and the World | Whereof One Can Speak

  8. Why is life full of ups and downs? says:

    But Gottlob Frege’s definition seems closest to my own current personal intuition about it, namely that logic represents the most fundamental relationships in our universe.

    You should read http://www.amazon.com/Where-Mathematics-Come-From-Embodied/dp/0465037712

    to understand that even logic is something that is only human-mind created and is not fundamental to the reality out there.

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    • Thanks for the book recommend.

      It seems to me that a lot depends on what we’re referring to when we say “logic” or “math”. If we mean the notations and techniques, then I think a strong case can be made for them being creations of the human-mind. But if we mean the underlying relationships, then it seems evident to me that they’re not. I think if logic and math were purely human creations with no correlation to anything “out there” in the world, then they wouldn’t have the usefulness that they do. But I fully realize that this is a debate that been going on for a long time, with a lot of bright minds on every side of it.

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  10. Pingback: Is logic and mathematics part of science? | SelfAwarePatterns

  11. Wyrd Smythe says:

    I think I’m squarely in Disagreeable Me’s camp here. Formal logic is a branch of mathematics, and as such it’s as universal as mathematics is. Fundamentally, we’re talking about things such as: If something is true in a given context, then it cannot also be not-true in that context.

    As DM points out, given a formal language, a set of axioms, and a set of legal operations, you have a formal system of logic or mathematics (same thing, really). Denying the universality of logic is to also deny the universality of mathematics.

    Which, of course, you can do, but it’s a fairly extreme claim and demands strong (dare I say “logical” 🙂 ) support.

    “I guess I’m not convinced of the distinction you make between the laws of physics and logic, and again can’t see why logic would be exempt from the things that might vary across universes.”
    Given that the laws of physics are expressed mathematically, the laws of physics are logic. Conversations with a physicist-blogger I know finally resolved a question that’s been bugging me a long time. If the Big Bang “created” physics, what “meta-physics” caused the Big Bang? Physicist Lee Smolin has this theory of “cosmic evolution” where universes are created (possibly in black holes) and evolve towards universes that support more black holes. Literally a Darwinian kind of evolution. Again, my question was about what “meta-physics” enables this evolution.

    Turns out that when physicists talk about different universes with different laws, they usually mean the various parameters which we — so far — take as constants we can’t explain. The masses of particles, the coupling strengths of forces, and so forth.

    But the underlying physics — the idea reality is quantized, for example — is believed to be a universal fact of (all and any) reality. And if there is an underlying physics for all reality, it has a mathematics (logic!) to describe it.

    “I once read a logical deduction of special relativity from first principles, indicating that it was possible, at least in principle, to have logically worked it out prior to the Michaelson-Morley experiment. I haven’t seen anything like that for QM.”
    SR does have a fairly simple mathematics, but would seem to need to be based on two important empirical observations: The isotropy of physics, and the consistency of ‘c’ to all observers. I’d be very interested to know more about what you’re referring to — got a reference handy?

    QM sprang, at least in part, from the burning (ha, ha) question: Why don’t ovens heat up indefinitely until they melt down into white-hot slag? The idea of quantization answers that. (See: “Ultraviolet catastrophe”) I’m not sure if you’d consider that first principles or not.

    “1) It seems that there are many more ways the universe could be than the way it is.”
    In the discussion with DM you challenge this point, and I must be missing something. Isn’t that one of your basic assumptions: that there could be other universes where logic doesn’t work?

    It strikes me that (2) could be reduced to a restatement of (1), and it seems worded as an elaboration of it. How about this for (2): Among those possible universes, at least some are likely to be logical.

    Then (3) follows naturally (and logically). If there are many universes that are logical, logic transcends this universe. The question boils down to what we can say about non-logical universes.

    I agree with (4). It aligns with what I said above about a claim otherwise requiring strong support. To borrow from another part of the conversation, if you claim there is a universe with a square circle (an incoherent concept in ours) or where a fact can be both true and not-true at the same time (also incoherent), that seems to require a strong argument.

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    • Wyrd, I apologize for what is an inadequate response. This is an old thread for me and a bit of a long one and I would probably have to reread all of it to answer each point, but my energy level isn’t up to it right now. Maybe at some point in the future.

      On the special relativity reference, it was long ago. It was something similar to this (although the one I read was longer, more involved, a bit more rigorous).
      http://www.universetoday.com/91733/astronomy-without-a-telescope-special-relativity-from-first-principles/

      On quantum mechanics, I was talking about wave / particle duality, not quanta in particular. I know of no way to have predicted that bizarre set of circumstances prior to experimental observations. (Incidentally, on something being both true and not-true, that’s pretty much what the many worlds interpretations of quantum mechanics predicts, completely throwing counter-factual definiteness under the bus.)

      On the rest, all I’ll ask is how we can say anything with certitude about how things might work outside of our universe? Any attempt would be an extrapolation based on how things work within our universe, which is all we have access to extrapolate from. Saying with certitude that any aspect of the workings of our universe must be true outside of it strikes me as a statement of faith. It seems to me that the very term for that concept, saying that math or logic is “universal”, betrays universe centric thinking. It’s a bit like a character in a video game concluding that the world outside of the video game must operate by the same rules as the game.

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      • Wyrd Smythe says:

        No problem, I can fully appreciate not wanting to re-visit old territory!

        “Incidentally, on something being both true and not-true, that’s pretty much what the many worlds interpretations of quantum mechanics predicts,”

        That’s why I carefully qualified that with “same context.” As far as anything in this universe goes, the result is true or not-true. In the supposed alternate, it’s not-true or true.

        You don’t get off the hook that easily, my friend! 😛

        “On the rest, all I’ll ask is how we can say anything with certitude about how things might work outside of our universe?”

        Well, that’s kind of the meat of the conversation. Essentially you’re denying that logic and mathematics would not be universal, which is an extraordinary claim, so you need to provide something more than your faith that it could be so. My faith in the universality of these things is pretty well-grounded.

        I think the analogy is apt that you believe in a “god” (an idea) you can’t explain or define. Those who find that idea hard to swallow have a fair amount of evidence giving their faith a strong level of confidence.

        Now you know how religious people feel. 😄

        If your video character had theories about the universality of mathematics — based on observations of how his world worked — he’d be right!

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        • “Essentially you’re denying that logic and mathematics would not be universal, which is an extraordinary claim”

          An extraordinary claim I’m not making. I’m only making the epistemically cautious point that we can’t know whether logic (or any aspect of our universe) persists outside of the universe. The extraordinary claim here is that logic must persist outside of the universe, and it’s the position that seriously requires justification.

          If the game character thought that reality outside of the game must proceed in discrete levels, he’d be wrong. If he thought he’d have multiple lives, he’d be wrong. If he thought the game designer was the ultimate designer, he’d be wrong. He might make some lucky guesses, but he’d have no way to know which were which.

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          • Wyrd Smythe says:

            That’s not what we’re talking about though. The mathematics that underpins his world is the same mathematics that underpins the larger world.

            The universality of math is demonstrated. Your claim amounts to the idea that there is some reality where “2+2” does not equal “4” — and that is an extraordinary idea.

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        • Wyrd, I started to respond, but then realized I would be repeating my previous statements, which would in fact be responses to repeats of your previous statements. In other words, I perceive that we’ve started looping. It’s probably time for us to recognize we just disagree on this. It won’t be first time, or I’m sure the last 🙂

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  13. Pingback: SMBC: What if the universe is made of math? | SelfAwarePatterns

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