Grandfather’s time machine; Physical possibility and logical impossibility

I have been tempted in the past to construe the relation of physical possibility to logical possibility as injective (i.e., that all physical possibilities are logical possibilities) but that there are many more logical possibilities than there are physical possibilities (for instance, it is logically possible to go faster than the speed of light even if our best physics were to tell us that this isn’t possible, meaning ‘physically’ possible). However, maybe I’m wrong; maybe there are examples of things which are physically possible and which aren’t logically possible.

Here’s one example. I decide to take a time machine to travel back to when my Grandfather was being born, and kill him. Now, if one accepts the B-theory either on philosophical grounds, or even on the grounds that our best physics is B-theoretic (I’m more skeptical about this, but it could be argued), then this scenario would apparently be physically possible. However, contradictions do not arise in reality – but this is a constraint imposed by logical possibility. Thus, it is not logically possible that one killed one’s Grandfather before the time at which the Grandfather spread his seed. Physically there is no reason why it cannot happen (unless one gratuitously imports explicitly logical assumptions into physics). So, because of the kind of enterprise physics is, a theory of physics may make something which isn’t strictly logically possible physically possible.

Of course, we should say that anything which isn’t logically possible isn’t comprehensible as a hypothesis (a proposal about how the world could or might be) at all, and thereby argue that the suggestion is evacuated of meaning altogether, and so there’s no way for that suggestion to have the property of being physically possible.


About tylerjourneaux

I am an aspiring Catholic theologian and philosopher, and I have a keen interest in apologetics. I am creating this blog both in order to practice and improve my writing and memory retention as I publish my thoughts, and in order to give evidence of my ability to understand and communicate thoughts on topics pertinent to Theology, Philosophy, philosophical theology, Catholic (Christian) Apologetics, philosophy of religion and textual criticism.
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4 Responses to Grandfather’s time machine; Physical possibility and logical impossibility

  1. Larry Myers says:

    Interesting idea, but may I suggest another way of looking at it. As we discover new physical possibilities our logical possibilities change. If you look intl the past this becomes more clear. 2 thousand years ago it wasn’t “logical” for the earth to go around the sun, but now we know it is physically possible and now logically possible. 100 years ago it wasn’t logical to think time slows down and speeds up but Einstein came along and our logic changed. And right now it isn’t logically possible for particals to be forever popping in and out of existence but we are shown through quantum mechanics and experiment that this is physically possible, so we must now change our logic.

    • I have heard this suggestion before, and it seems completely untenable to me. Allow me to explain why. First, two thousand years ago it was logical for the earth to go around the sun, it’s only today that people have said that the sun going around the earth seems ‘logically impossible’ and that’s because of the influence of Einstein’s view of relativity (which makes it impossible for the earth to go around the sun objectively, or for the sun to go around the earth objectively, since motion is always relative and there is no preferred frame of reference from which motion and quiescence can be measured). Even today though, so long as one doesn’t take Einsteinian relativity to be an analytic truth (i.e., if they, for example, allow the logical possibility of things like the Lorentzian view of relativity, or the logical possibility of traveling faster than the speed of light in our space-time, etc.) then one can’t let an Einsteinian model of relativity determine our modal logic.

      Remember that logical possibility is broad. It is logically possible for a whale to transform into a cow, or for an owl to give birth to a toad. These are logical possibilities, even if they aren’t physical possibilities. Physics is about creating models of our experiences of the physical world which exemplify certain explanatory virtues like having explanatory power, explanatory scope, parsimony, elegance, and/or other virtues such as falsifiability. For a model to be comprehensible (literally for it to be sensible) it cannot involve contradiction. If you were to suggest that the best model of some physical phenomena we could create involved a contradiction (like suggesting that we take Schrödinger’s cat not just as a methodological assumption but as a postulate about the physical world) then I would stare you down with incredulity. Physical models are not even comprehensible unless they postulate something which is broadly logically possible.

      Strictly speaking, the only part of modal logic which is purportedly challenged by the Copenhagen interpretation of QM is the Principle of Sufficient Reason. If one accepts the PSR, of course, then God’s existence, being logically entailed by the PSR, will also be something to which one is committed to accept, and that would lead to a much more interesting discussion (since one’s view of logic will not be so plastic if one isn’t a naturalist). However, first, there are empirically equivalent competing interpretations of QM which are physically deterministic, and so logic may help to adjudicate between different physical models, and second even the Copenhagen interpretation, taken merely as our best empirical modelling of phenomena at the Quantum Mechanical level, does not offer a logical counterexample to the PSR since the Copenhagen interpretation can be shown to be compatible with the PSR with certain metaphysical assumptions. Only if one is a very rash realist about the Copenhagen interpretation of QM can a problem arise between physics and logic. However, if physics and logic conflict, logic, and not physics, should be preferred. Logic stands at the foundations of physics, but physics does not stand at the foundations of logic. Logic, like Mathematics, is one of the assumptions of physics, but physics is not an assumption of Logic. To say that Physics should be able to change Logic is like saying that physics should be able to change mathematics. It’s just misconceived.

      Now, suppose I were to take you even more seriously – perhaps you mean that even epistemology should be naturalized (in a Quinean way). That would mean that you would accept that the principle of non-contradiction could literally be falsified by physics. First, then, I should say, there are clearly some things which no model of natural science can falsify, like Putnam’s principle that not every single proposition is both true and false. So, you would have to divide* analytic logical truths, then, into two categories: those which are in principle falsifiable, and those which are in principle not. How would you go about doing this? You can’t just appeal to logic, obviously. You also can’t appeal to physics insofar as physics adopts the presumptions of logic. Maybe you could argue that insofar as some model of physics can be paraconsistent, so long as it were empirically adequate (and more empirically adequate than all competing models), you could argue that if X is a paraconsistent model, and if X is the most empirically adequate model, and if X does not operate with some logical axiom like the principle of non-contradiction or the ex nihilo nihil fit, or any other, then X makes those principles obsolete. However, not only is this a terrible way of doing physics (what can falsification even mean if one abandons principles like these by which consistency is measured), but this is also a terrible way to think of logic. It means that one commits themselves to one of the following two claims: 1) that propositions which are logically necessary are only contingently logically necessary (contingent upon our empirical preferences), or 2) there are no logically necessary propositions (so that Av~A will turn out to be possibly false or possibly meaningless).

      This is all just confused though. Physics is supposed to be about creating intelligible models of reality. That which is not logically possible is strictly not intelligible. Therefore, a physical model which posits the logically impossible is unintelligible and can’t be believed (literally the human mind cannot give it assent, and even if some non-human mind could give it assent that mind would ‘believe’ the proposition in an incommensurable way – we would have no access thereby to justification, which means we could never be justified in believing it even if it were true (and nothing which is logically impossible is possibly true, ergo etc.) ergo etc.).

      Of course, you’ll notice, if you’re sharp, that I’ve just adopted my own presumption to prove my case. I assumed the validity of demonstrating the logical incoherence of your suggestion, when your suggestion was that logical coherence should be changed in light of empirical models of experience. It’s the same as when one argues that philosophy is no good, and a philosopher gives an argument to think it is good – the philosopher has just done philosophy to vindicate philosophy. The person who is staunch enough to reject all critical thinking and logic (which are the proper parts of philosophy, after all) will not take seriously any argument, not matter how good, for philosophy’s worth. So too you may be so stubbornly irrational that you think that my argument tries to proceed by appealing to logical intuitions we all share, but you are trying to bring those very things into question. I don’t expect you to go that far of course, I think that any sane person would be too embarrassed to defend such a radical position (a position which, ultimately, isn’t even intelligible because it itself offends logic).

      So, in the end, I think the proposal that physics can reset the parameters of logic is just unintelligible. Logic already sets the parameters of physics, always has, and always will. If Logic did not set the parameters of physics then physics would literally be beyond human comprehension – it would be in an even worse position than materialists sometimes accuse some Theologies of being in.

      • Larry Myers says:

        Well that was an intense response….. But i think i see the difference in view, I am saying that “people’s” logic changes light of new facts, and I guess you are saying that logic itself doesn’t change?

  2. Well, if by “people’s logic” you mean just the way people are, by intellectual custom, used to thinking about the world, then sure that has changed, and in great part that has changed because of science. However, look back at the post above and you’ll see that I was trying to find an example of something which is physically possible given our best model of physics, and which is not logically possible (strictly and properly speaking). So, when you suggested that maybe Physics could change Logic, I was thinking about that suggestion in the context in which it was issued (this posts comment section). In the post itself, that would have meant that since physics allows for an obvious contradiction to arise in the world, we should just adjust our logic accordingly. That’s why my response was so ‘intense’. That is one of the more irrational trends of scientism today, and I quite honestly abhor it. You don’t seem to be arguing for it anyways though.

    Maybe it’s just a terminological issue. When I say Logic, I think you have something different in mind. Maybe you think ‘reason’ or something like that, which is a bit of a vaguer notion. When I say Logic I mean, first and foremost, modal Logic. However, at the risk of being presumptuous and sounding uncharitable (which the following sincerely isn’t meant to be, so I hope you don’t take it as such), I’d like to suggest that you may be just mixing some closely related categories. I think that you think “people’s logic” is their rational use of reason, and that this just is ‘Logic’. Those are all three (or at least two) different things (I’m still not entirely sure what the first one is). Even by looking at your original examples, I’m left in the dark. Your first example was ” 2 thousand years ago it wasn’t “logical” for the earth to go around the sun, but now we know it is physically possible and now logically possible.” First, as I pointed out, today it’s not physically possible that the earth go around the sun, since, on Einsteinian relativity, everything is just in motion relative to something else, the earth only goes around the sun in the same sense that the sun goes around the earth (i.e., they move relative to each other). However, regardless, it was considered logically possible 2000 years ago, and 4000 years ago (if it weren’t logically possible for the earth to go around the sun then it wouldn’t have been logically possible for the sun to go around the earth). People’s logic didn’t change. People’s theories changed. So, if by “people’s logic” you mean ‘how people use logic’ or ‘how people thought about logic’ or anything like that, then clearly you’d be wrong. If by “people’s logic” you meant something not directly related to Logic, like what people thought was reasonable, then you’d obviously be right, but I fail to see how that would be relevant to the post. I think you kind of meant both at the same time, and that overlap is what made the point seem relevant.

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