Infinite Regress is a Slippery Slope

A friend of mine, who blogs sporadically as Squelchtoad, had a great response to the NYT review of Krauss’s book A Universe from Nothing that I mentioned in the recent neuroscience post.  I’m excerpting Squelchtoad’s commentary, but you should hop over and read the brief piece yourself:

But it occurs to me that the Albert riposte to Lawrence Krauss might also work at least for the more naïve versions of that theological argument. What does it mean for God to be a “necessary being”? Well, some old school theologians would have said it meant He was logically necessary. That is, the proposition “God does not exist” is actually logically impossible. But there’s an Albert Problem: Why are there laws of logic? Aren’t they themselves “something rather than nothing?”

If showing that “God exists” is a necessary proposition within a given logic is enough to prove that God actually exists, the logic itself, it seems to me, must actually exist in some sense akin to the way that the laws of quantum physics exist. This brings us back into Albert territory. The logic is a “something” that really exists rather than “nothing.” Why is there that logic rather than nothing?

…At this point the theologian, I think, is forced to throw up his hands and point out that I can’t ask a “why?” question about things like logic and/or metaphysics, the existence of which are a precondition for causation. Fair enough. But then “Why is there something rather than nothing?” suddenly seems a whole lot less coherent a question overall, so long as the logic and metaphysics are taken to be part of the something.

“Uncaused first cause” is starting to sound like a much better answer than “necessary being.” The theologian may just have to accept that he can’t explain why God exists (uncaused), just that He does. Frankly, I think that ought to be enough. That said, it’s also why I don’t find the “Why is there anything?” argument to be convincing argument for theism. I fail to see how answering “Why is there anything at all?” with “(My specific) God is a brute fact” should be any more persuasive than answering it with “the universe and its laws are brute facts.”

I endorse pretty much all of Squelchtoad’s piece (that’s why I couldn’t resist grabbing such a long pull-quote.  Whether theist or atheist, everyone has to bite the bullet at a certain point and accept something without proof or cause.  We seem to (mostly) have consensus on some of these things (causality, the existence of matter, the existence of other minds) and diverge radically on others.

Acknowledging this fact doesn’t compel us to throw up our hands and let everyone assert whatever First Cause and knock-on effects that suits them.  If you assert a brute fact that isn’t meant as a solution to a problem like the origin of matter or the existence of moral law, there’s no way to contradict you, but your assertion is almost too boring to merit response.

People have proposed a number of different First Cause problem, so we can compare them and try and see if some seem better constructed that others or if (fingers crossed) a couple actually pay rent beyond the problem they were constructed to solve.

If none of them seem better than any other, then you may try just naming the thing you don’t know “First Cause.”  But if that seems like cowardice disguised as epistemological modesty, then you have to decide if and when it’s better to choose a solution instead of holding your beliefs in abeyance.

About Leah Libresco

Leah Anthony Libresco graduated from Yale in 2011. She works as a statistician for a school in Washington D.C. by day, and by night writes for Patheos about theology, philosophy, and math at www.patheos.com/blogs/unequallyyoked. She was received into the Catholic Church in November 2012."

  • Patrick

    I’m not sure that works. There seem to be plausible (in my opinion, compelling) accounts of how “laws of logic” (I hate that phrase, but what can ya do, you know?) can be logically necessary. Specifically, laws of logic are a system of statements that refer to each other and to the relationships between themselves. Because they do not refer to things outside of themselves, the universe can be however it happens to be, and the truth of these “laws of logic” would not change.

    I don’t know if that’s relevant to Krauss. I kind of doubt it. But its relevant to the quoted material.

    • Ray

      I’m not sure I buy this. I’m not sure what you mean exactly by the “laws of logic” being logically necessary, but most versions seem circular at best and in contradiction to things like Godel’s theorem at worst. Now you may say that logical axioms are true by definition, but this is really just referring back to a convention that says “definitions don’t need to be justified.” Which is certainly a fine convention in most cases, but it still seems to be asserting the brute fact that you in fact defined the term in that way. Also, if you start with no defined terms, what are you supposed to define things in terms of?

      Long story short, I don’t see a way out of the Munchhausen trilemma: http://en.wikipedia.org/wiki/M%C3%BCnchhausen_Trilemma

      • Patrick

        “Now you may say that logical axioms are true by definition, but this is really just referring back to a convention that says “definitions don’t need to be justified.””

        When the definitions refer only to the relationships between a series of concepts, no, they don’t need justified in the sense that I think you’re requesting. Justifying a definition is demonstrating that it applies to the thing you say it applies to. Logical axioms do not contain references to factual matters.

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

        You can even invent necessarily true nonsense statements. “Ablech is more Zoog than Dree” is a necessarily true statement if you define “Dree” to mean “that which is less Zoog than Ablech.” We can know that without even having actual definitions of Ablech, Zoog, or Dree.

      • Ray

        ok, but how do you define your concepts without reference to terms you already know the definition of and/or physical objects?

      • Ray

        e.g. your nonsense definitions made use of “is” “more” and “less.”

        • Patrick

          So? We have definitions for those words

          I think you’re confusing the question of whether a statement is necessarily true with the question of whether a statement usefully reflects the real world. The point of the nonsense statement was to give an example of a necessarily true statement that is not, in fact, a useful description of the world.

          • Ray

            I sincerely doubt that you learned words like “is” by having them defined for you in terms of other words, I suspect you learned them by imitating your parents. But more importantly, it has to be this way. If you can only use words you already know in your definitions, the first word you learn must have a zero word definition.

            The problem with learning by experience, though, is the classic problem of induction: You are imposing order on your observations without any guarantee that such order exists.

          • Ray

            Which is not to say that the axioms of a system (e.g. logic) are not logically necessary within that system, they are, but this is only saying that the axioms are true if the axioms are true, which is circular.

          • Ray

            Also, this distinction is somewhat of a moot point. By asserting the existence of God (who while supposedly outside the world can still be the cause of miracles within the world) the theist is already committed to a certain system of axioms describing the world (in particular one constructed to make the existence of God a theorem.)

          • Anonymous

            Given axiom x, the statement, “x->x” is circular. Given no axioms and no particular universe, the statement, “All statements (not necessarily axioms) ‘x->x’ must be true,” seems to hold (and at least not be blatantly circular). Of course, just because I cannot imagine any pathologies doesn’t necessarily mean they don’t exist… but that’s still a better argument than the empiricist has given for the non-existence of god (most people can imagine a universe in which god doesn’t exist).

          • Ray

            anon

            Yeah, but how do you know the -> symbol means what you think it does? You’re still assuming some axioms (in particular the axioms of propositional calculus.)

          • Patrick

            “I sincerely doubt that you learned words like “is” by having them defined for you in terms of other words, I suspect you learned them by imitating your parents.”

            You’re confusing how human beings learn thing with the separate question of why things are true.

            “Yeah, but how do you know the -> symbol means what you think it does? You’re still assuming some axioms (in particular the axioms of propositional calculus.)”

            You’re confusing the connection of meaning to a symbol with the usefulness of the concept expressed by the symbol.

            “Which is not to say that the axioms of a system (e.g. logic) are not logically necessary within that system, they are, but this is only saying that the axioms are true if the axioms are true, which is circular.”

            Now you’re confused about circular reasoning.

            P: “Blorg, therefore blorg.”

            P is true. It is also circular. The fact that it is circular is a problem IF AND ONLY IF you are offering P in order to demonstrate the truth of “blorg.” The whole reason that circular logic is a bad thing is because it sneaks in one kind of truth (tautological truth) while pretending to offer another (empirical, deductive, etc).

            “Also, this distinction is somewhat of a moot point. By asserting the existence of God (who while supposedly outside the world can still be the cause of miracles within the world) the theist is already committed to a certain system of axioms describing the world (in particular one constructed to make the existence of God a theorem.)”

            I’m not posting right now to address arguments about the necessity of God. I’m posting to counter the assertion that “laws of logic” need “justification.”

            Ontological arguments for the existence of God have their own problems. The biggest is that they tend to rely on the truth of non necessary propositions in order to demonstrate the logical necessity of God. But anything you prove from contingent premises is just going to be contingent.

            For example, Anselm’s ontological argument relies on a concept of “greatness.” But nothing in his argument, or anywhere else anywhere in philosophy or theology, demonstrates that “greatness” as he uses it is a logically necessary concept that must, for logically necessary reasons, be applicable to the universe. This transforms his argument from an ontological one to an empirical one, defeating it on evidential grounds.

          • Anonymous

            I never thought I’d end up in a situation where the symbols to content ratio is much too low. In the classroom, it’s almost always the other way around. (i.e., I agree with Patrick… you don’t need the symbol. The content is true in any system or any universe.)

  • @b

    >>Whether theist or atheist, everyone has to bite the bullet at a certain point and accept something without proof or cause. We seem to (mostly) have consensus on some of these things (causality, the existence of matter, the existence of other minds) and diverge radically on others.

    Unfortunately our instinct is to use our instinct to bite the bullet.

    Rather than to differ to respected physicists like Krauss, who are at this point in history are the most trustworthy experts to answer how our universe’s initial nothingness led to its first material something.

    • @b

      Note, most are comfortable differing to contemporary academic concensus if and only if those modern teachings don’t clash loudly against the beliefs they’ve already formed or absorbed.

      • http://whatloveteaches.blogspot.com/ Slow Learner

        Most typos, I let it go. But having ‘differ’ for ‘defer’ – changes the sense of your sentence completely.
        Differ – be different from/disagree.
        Defer – accept superior expertise.

  • http://www.smidoz.wordpress.com Smidoz

    I am a fan of the “laws of logic,” but what struck me is the logical necessity for something to exist. It’s fair to say that it would be logical for something to be the case, but not fair to say that this is proof. A priory statements are often very logical, but are essentially meaningless, since they express something about the definitions of words. So in order for statements to be useful, they need to be logical statements originating in empirical data. The data alone isn’t necessarily enough to make claims about what it may mean, so one needs to check that ones claims are logical. If ones claims are not logical, it doesn’t disprove anything, but it does rule out that line of thinking as a valid proof. If one uses the data logically, then the conclusions are seen as valid. This doesn’t prevent someone coming along with a different logical interpretation of the data, which may seem equally valid, then the discourse gets going in such a way, that we can hopefully arrive at a better model of reality.

  • Daniel

    these are deep murky philosophical waters but I find it hard to see how logic is a brute fact. Suppose there was nothing, would there be logic or numbers then? I have trouble seeing how could they could exist. I mean nothing means nothing, right? it seems that if God exists then numbers and logic must depend on God for their existence.

    But Squelchtoad equivocates when he says that a necessary being is identical to logical necessity. What most people have in mind by necessary being is something that is metaphysically necessary or causally necessary.

    • http://squelchtoad.wordpress.com Squelchtoad

      Daniel,

      I agree completely with you about logic, but not all theologians do. If you read my whole post, I talk about metaphysical necessity as well.

    • Anonymous

      Actually, fundamental logic is more easily satisfiable if your set of things is the empty set. In that case, the statement, “All statements ‘x->x’ must be true,” is still true. It’s just vacuously true… because you have no statements to plug into it. Many theorems are vacuously true when you take the empty set at some point.

      • http://squelchtoad.wordpress.com Squelchtoad

        Without getting into too much philosophy of math (FWIW, I have vaguely formalist leanings), I think you’re presupposing a notion of logical truth (not to mention notions of “statement” and “the empty set”) that wouldn’t exist if formal logic didn’t exist, let alone if nothing existed in the profound sense that David Albert means.

        You may claim that that formal logic is a formalization of something conceptual that is more fundamentally true within our universe. Yet hard as it may be to imagine that conceptual truth being otherwise (ie. “the laws of logic not existing” or “being different”) it is, in fact, possible. Hard as it may be to picture what a universe in which the law of the excluded middle doesn’t hold, we can still ask why the law of the excluded middle *does* apparently hold. Yet when we do, we reach the point in my post that begins:

        At this point the theologian, I think, is forced to throw up his hands and point out that I can’t ask a “why?” question about things like logic and/or metaphysics…

        • Anonymous

          I’m reasonably adept with pathological cases, so I don’t really need to picture anything. I would actually claim that the law of the excluded middle is subject to pathological cases (probably even some non-pathological exceptions), while the law of identity is not… even if logic is not Aristotelian.

          Furthermore, the notion of empty set is an attempt to describe the profound pathology of David Albert… the situation in which nothing exists. This notion doesn’t have to exist inside that world, it is simply our way of describing it. Otherwise, one could not speak of that pathology in any way, since that description would involve things necessarily not present within the pathology itself (i.e., we couldn’t talk about how profound the nothingness is, because in that universe the idea of profoundness doesn’t exist… not to mention the idea of nothingness).

          In that pathology, where nothing can be said about nothing, all statements ‘x->x’ are true. In fact, in that universe, the above is vacuously true… too bad no one’s around to say it.

          • http://squelchtoad.wordpress.com Squelchtoad

            Warning: silly math stuff follows

            In that strict sense, I agree. The notion of vacuous truth can be understood to formalize what it means to make statements—within this existing universe—about Albert-style nonexistence[1]. Albert-style nonexistence can be expressed formally—within this existing universe—as the empty set.

            ([1] Or, perhaps more precisely, how vacuous any meaning conveyed is.)

            But I think formalizing statements about Albert-style nonexistence in the way you propose doing so actually proves Daniel’s point. If the set of that which exists = {}, then {logic} cannot be a subset of that which exists. If logic exists, then “the set of that which exists” cannot strictly be equivalent to the empty set.

            It seems weird to say “logic does not exist,”
            given that we’re using formal logic do it, but, as you’ve shown, there’s actually nothing wrong with that. In our universe, where such formalism is possible, we can formally describe a universe in which such neither such formal logic nor any Platonically “real” logic it may formalize actually exist.

            And indeed the whole point of my post was to highlight the trouble we get into when we try to reason about “nothing,” which exposes, to my mind, the fact that “why?” may not be a meaningful question to ask about the matter of fact that “there is something rather than nothing” provided that our understanding of “something” is broad enough.

          • Patrick

            Squelchtoad- The word “exist” has multiple meanings. So does the word “thing.” You’re mixing them.

            You might as well argue that the empty set can’t exist because if it did then the set of things that exist would include the empty set.

          • http://squelchtoad.wordpress.com Squelchtoad

            Yes, names are slippery, but I don’t think I’ve mixed concepts. The point is simply that you can only describe nonexistence from the POV of existence, for rather obvious reasons. But that doesn’t imply that the formalisms we use to describe nonexistence still exist if nothing exists.

            Your example isn’t quite right, I think. If the empty set were a Platonically real concept, it couldn’t both

            (A) exist
            and
            (B) be equivalent to the set of all things that existed

            because the set of things that existed would have the empty set as an element, and therefore be nonempty.

            But that in no way proves utter nonexistence to be impossible. When we formally describe nonexistence[1], we say that “the set of all things that exist” is equivalent to the empty set. We do not say “the empty set exists.”

            [1] From within this universe.

          • http://squelchtoad.wordpress.com Squelchtoad

            (Nor, for that matter, do we say that the “set of all things that exist” exists).

          • Patrick

            I wasn’t saying that you should actually make that argument. I was saying that it was a bad argument you shouldn’t make, for the same reasons you shouldn’t make the bad argument you are presently making.

            “”But that in no way proves utter nonexistence to be impossible. When we formally describe nonexistence[1], we say that “the set of all things that exist” is equivalent to the empty set. We do not say “the empty set exists.””

            Right. Now just take the next step: for the same reason we don’t say “the empty set exists,” we shouldn’t say “logic exists.”

          • Anonymous

            I think we’re almost there. We’re gotten to this point where something doesn’t necessarily exist, but it is also necessarily true (which sounds strange, but no more strange than a logical proof that logic doesn’t exist).

            Thus, the difficult challenge would be to demonstrate that a statement, “X exists,” is necessarily true. Then, we would have a lower-bound solution to the Albert problem. You could also say that Albert-style nonexistence would be necessarily false.

          • http://squelchtoad.wordpress.com Squelchtoad

            Please don’t patronize me. I understood that you thought it a bad argument (as do I). My point about “not quite right” was that I didn’t think it was apropos. I tried to provide a more apropos argument that revealed what I was actually talking about. But this annoyance on my part isn’t apropos either…

            for the same reason we don’t say “the empty set exists,” we shouldn’t say “logic exists.”

            The empty set can “exist” (at least for a mathematical Platonist–I am not one). It just can’t “exist” if nothing exists. Similarly “logic” can “exist” (for a Platonist), but not if nothing exists.

          • http://squelchtoad.wordpress.com Squelchtoad

            The above was RE: Patrick. RE: Anon: I mean, “X exists for some X” is obviously necessarily true if it can be asserted. ;-) What if it can’t?

            To go less mathy and more literary for a moment, whether we can coherently use the tools of reason (which “exist!”) to reason about the possibility of nonexistence is precisely what I hoped to call into question!

            Basically, I’m unsure that this whole argument hasn’t been a large misunderstanding.

          • Anonymous

            Squelch (can I call you Squelch?)

            The idea is still that we have something that does not necessarily exist, yet is necessarily true. Therefore, even if it cannot be asserted, it is still true. To go more physics, it is not observer-dependent. To go more dynamical systems/controls (my real area), it is not even observability-dependent.

            Pure reason may not be up to the task of getting us this necessary truth, but if it could be shown, it would solve the Albert problem.

  • http://squelchtoad.wordpress.com Squelchtoad

    Better than “toad” ;-)

    And I like this:

    Pure reason may not be up to the task of getting us this necessary truth, but if it could be shown, it would solve the Albert problem.

    I agree that if the the true ontology and the true truth-theory (truth-theory ≠ epistemology in this case, since we want observer and observability-independent truth) are respectively constituted that statements can be necessarily “true” in a meaningful sense even if nothing “exists” in a meaningful sense, then there isn’t an Albert problem.

    I admit that I am skeptical that this is the case; all the truth-theories I’ve encountered and found coherent aren’t even observer-independent.

    • Anonymous

      I think we’re pretty much done with the topic. Thanks for the discussion, Squelch!

      • http://squelchtoad.wordpress.com Squelchtoad

        Ditto. And not a moment too soon; I’ve got work. There’s a reason I only blog “sporadically,” as Leah put it.

        • Anonymous

          ..its the same reason why I don’t blog anymore… and only comment sporadically.


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