Tuesday, September 17, 2013

The "Fallacy" of Infinite Regress

There is a preacher on our campus Diag:
(h/t to Monica Harmsen, our former President and current Historian.  Sign reads "It's easy to be an atheist when you don't think about where everything (including God) came from.")

that I just had a discussion with regarding an argument that he tried to use to support the existence of a deity.  I had to go turn homework in for a class so I had to cut off our conversation, and we only got as far as arguing over whether or not infinite regression of causes is a fallacy.  I wanted to talk a bit on this before I went about my day again.

The pamphlet that I was handed has, amongst its 40 (40!) footnotes, an explanation of the fallacy of infinite regress that I will quote (stretched across 2 footnotes):
"Positing (infinite) prior dependencies to account for subsequent ones is not the solution: it is the problem. Fn. 11 [so, going off of footnote 11, which reads...] E.g. no matter how many dominos you add to a line or group, they will never "fall" by themselves because every faller is completely dependent upon its prior.  That's why dominos only fall when some outside force makes it happen.  All the more so with domino existence.  See also Tyson & Goldsmith Origins pg. 44 [link], Vilenkin pg. 204 [no link to page, but some discussion and Amazon has notes for p. 204], Scientific American pg. 50 (inset) [link], F. Collins The Language of God 2006 pg. 54-67 [no suitable link].  Plus, using various interpretations of quantum mechanics and/or special/general relativity and/or singularity theories (no mass = no thing) to ignore that and/or negate the fallacy of infinite dependent regress and the necessities of source/production is a composition fallacy, category mistake, and a red herring. (Craig pgs 150-156)."
I don't know why the Scientific American article is referenced.  Best guess is that the inset says "Expansion probably accelerated early in cosmic history as well, erasing almost all traces of the preexisting universe, including whatever transpired at the big bang itself," and thus that's just like arguing that the universe had an infinite prior universes.  It's not clear that was the intent behind the statement though.  The reference to Tyson and Goldsmith is just for a quote of them off-handedly positing that there might be multiverses or that the universe popped into existence from nothing we could see.

The important thing here is that it's being claimed that asserting there is an infinite number of explanatory events is inherently fallacious – in particular this preacher asserted that it's a "vicious infinite regress," which I can only satisfactorily define as a regression that posits new explanations to account for a cause, explanations that themselves require explanations.  There are two main points to be made here:

Self-referential sequences

Let's say that I know a mathematical rule is true for the number 1; I can also show that if it is true for some natural number n, then it is true for the successor n + 1.  Thus, since 1 satisfies the rule, so does 2 (n + 1 when n = 1), and then 3, and then 4, so on.  Each number suffices the next.  This is mathematical induction, and is in a sense a form of infinite regress.

This analogy isn't quite complete; it's more like infinite progress, not infinite regress.  Each satisfactory number implies the next, but what we're actually trying to better understand is a cause/effect chain in reality, where it is not knowing the cause that allows us to presume the effect, but rather that knowing the effect allows us to presume the cause.

Induction is a form of self-referential thinking, and we can use that type of thinking to come up with a much better analogy: take for example the Fibonacci sequence, which goes 0, 1, 1, 2, 3, 5, 8, 13, so on, with each number being the sum of the two prior.  We are often satisfied with starting with zero, but if I was to ask "what are the first 3 numbers in the sequence that satisfies N = M + L, where M and L are the immediate and secondary predecessors, and we know 5, 8, 13 are in order in that sequence?"

Why would you say (0, 1, 1), aside from an a priori assumption that the Fibonacci sequence is the only sequence that satisfies that condition?  In fact, that the sequence even has a beginning?  We know we can count forward – we can count backward too: 13, 8, 5, 3, 2, 1, 1, 0, 1, -1, 2, -3, 5, -8, 13, -21, etc.  Negative numbers are not part of the Fibonacci sequence, BUT they do satisfy the sequence's element predictor.  So I can say that the sequence isn't started by (0, 1, 1), but by (-21, 13, -8).  I would be completely correct.  I would be completely correct too to say that it has no beginning.

Let's put this in terms of cause and effect: given an event and given that an event implies a specific cause, that cause also being an event, there follows an infinite series of causes.  The only way this statement is false or void is if there is a conceptual change in how cause and effect work anywhere along the chain (take, for instance, the beginning of the universe and thus the beginning of time), or if an event does not at all predict a specific cause.  If I cannot say for certain that there was a particular cause for an event, then the universe is ultimately non-deterministic and we would, so it seems to me, inadvertently solve our question of whether or not there's a specific deity; and if the chain is broken because we can't demonstrate a possible way of knowing how cause extends past a certain point in time, we run into my second point:

Limits on observation: we can guess but we cannot know

In the case of the universe we have a very fundamental problem: we cannot actually observe to the point of the Big Bang, nor model before it nor arbitrarily close to it.  There is a horizon past which we have no way to determine whether or not there could be an infinite regress; regress is a proposition, but not demonstrated.

Take our lovely domino analogy.  We can see back 100 dominos – what was before then?  Well maybe it's God; maybe it's another domino, maybe it's a billion dominos, maybe it's a volcano that knocked one over and a domino that initiated the volcano before that, or maybe it's just turtles all the way down or dominos all the way back.

Back to Fibonacci: if I had no conception of negative numbers (this was, in fact, something that persisted for some time until they were invented by the Chinese maybe some ~2200 years ago), I would not be able to conceive past zero, and thus would not be able to tell you that a possible start to the sequence I talked about before is (-21, 13, -8).  My conceptual horizon, hopefully easily understood as analogous to an observational horizon, does NOT imply that the sequence is bounded on the lower end.

If the elements in a sequence can be deterministically and mechanistically tied to each other, then not only does our lack of ability to observe a definitive start compel us to have infinite regression as an open possibility, it makes it a logically self-consistent one, and a rather appealing one in that it doesn't require an outside explanation.

And you simply won't find people who say that there is definitively a multiverse, or that there are definitively an infinite vacua in which universes form (this seems to be what Vilenkin talks about), or that the universe for sure arose out of nothing.  I would be gravely mistaken to call myself even an amateur on these subjects, but if I may: these ideas are hypotheses that mechanistically describe how one universe leads to another, or more, and are internally consistent with concepts we understand in cosmology.  They are still being explored; most will probably never be experimentally verified.  But the infinite regress some of them rely on is nothing more than self-referntial.  We do not require some new unexplained mechanism, which would cause the regress to be "vicious" and thus unsatisfactory.


I would tentatively say, right now writing this on my own without other people to bounce ideas off of, that a general deity is not any more or less out of the question than the above-listed hypotheses.  Again, we have limits on our observation, so we cannot actually say if there was a "first cause" and what that might be if there even was one.  We must say we do not know (at least, I'll say that as a non expert).


  1. An infinite regress of events is not itself a logical contradiction, and so you are right in saying that such a construction can form a self-consistent hypothesis. However, I'm dubious that an infinite regression best explains the universe. From what I can find on google, the Borde-Guth-Vilenkin theorem shows that in most models of an inflationary universe, there is necessarily a finite past (although, interestingly enough, the first several pages of google results only contain references to this theorem as cited by Christian apologists, or in atheistic responses to apologists. The theorem itself doesn't even have a wikipedia page). I would rather say that an absolute beginning to the universe justifies God no more than any other hypothesis. We need to look at additional evidence to decide whether or not God exists.

  2. In the quote by Craig:

    "Plus, using various interpretations of quantum mechanics and/or special/general relativity and/or singularity theories (no mass = no thing) to ignore that and/or negate the fallacy of infinite dependent regress and the necessities of source/production is a composition fallacy, category mistake, and a red herring. (Craig pgs 150-156)."

    An explanation of God as a "mind" or a "person" is also a category mistake: minds and persons are complex, worldy things that cannot be ripped out of their evolutionary context and taken as metaphysical primitives.

  3. If you ever talked to a theologian like William Lane Craig, I'm sure he would insist that infinite regression is not a logical contradiction, but instead a metaphysical absurdity.

    Metaphysics is hard to define. It at least has something to do with categories of being and causation. A tentative distinction that we can make is that metaphysics is known through experience, whereas logic is a priori. Craig would insist that certain things are "metaphysically impossible," even if they are not logically impossible. If you are wondering what that is supposed to mean, that's a very good question. I would guess that Craig would define a metaphysical impossibility as "something which contradicts what we know from our most fundamental experiences of the world." Craig considers the statement "everything which has a beginning has a cause" to be such fundamental metaphysical truth. He also thinks that an infinite regression of causation falls into the category of intuitive nonsense (he tries to give various explanations for this, some of which I covered in my post about the Kalam Cosmological Argument). Unfortunately for Craig, theories like quantum physics and relativity also contradict our fundamental experiences. Quantum physics shows that our notion of a billiard-ball-like "particle" is not in fact actualized in matter. Relativity shows that time itself depends on the observer, contrary to our deepest intuitions from everyday experience.

    It is worth noting that Craig assumes the A-theory of time when he argues that infinite regress of time is absurd. The A-theory states that the present moment is uniquely real, and that the future "does not exist" in some strong sense ontological sense. He uses the A-theory to derive what he deems to be absurdities. (For example, his "actual vs potential" infinite arguments). Although as we discussed in my Philosophy of Religion class, his arguments are dubious at best. And I am of the opinion that the A-theory is hopelessly flawed.

  4. I'm attempting to talk like a philosophy major, although it is worth noting that my understanding of the above subjects is mostly limited to internet searches and personal deductions.

  5. It's not clear to me that causality even makes sense when you start to approach the Big Bang. The concept of the line of dominos is quite inadequate to explain a more fundamental issue with the idea of infinite regress of causality: the question of "what came before the Big Bang" or "what caused the Big Bang" may not be unanswerable, but simply nonsensical; the idea of time before time should at least make us do a double take.

  6. Hi, I am the guy with the sign. Thank you for taking the time to read it/my handout and respond to it. It seems, however that the main point may have been overlooked - dependency (not causality). I posit that any and all events within a series of dependent material events are dependent upon their priors. As such, no series of dependent material events can produce itself, even if you appeal to infinity (a material one (since that is what we are attempting to account for), not a numerical one) because the problem of dependency is never overcome by the addition of priors within that system. Instead, every added prior simply extends rather than solves this dependency problem. That's why no matter how many dominos you have they never fall (not to mention exist) unless some outside force makes it happen. So, given that the cosmos, from sub atomic to multiverse, is a series of dependent material events, the cosmos could not have produced itself. Here some divert focus to 'time' (e.g., Hawking ) "Asking what was before the Big Bang is like asking what is south of the South Pole." An intriguing word picture, but it artificially ducks the production issue. Details about that and God on my web page: Proof-of-God.org.


    1. Hi Doug, thanks for the comment! I rarely check through the comments on our posts because we get so few viewers, but let me see if I can briefly respond to yours (several months after the fact):

      Dependency does not itself seem to be a problem, as my self-referential example should at least illustrate. That there is another event that "caused" the next doesn't solicit a never-ending "an what caused that?" chain, unless each new explanation is ad-hoc itself. We could view a system as a closed Markov chain, and that would not require a "first event" even though each state determines the next probabilistically.

      I'll have to read up more on cosmological models that do not follow single-direction entropy flow, I do believe some exist. This is something that another author here (Jon White) is more familiar with, so pardon another wait for a follow-up!

  7. Yesterday I talked with Douglas for about 4 hours outside the San Diego Pride Festival, so I think I have a fair idea where he’s coming from. Douglas has been spending his retirement years visiting college campuses and promoting his 13- (or more) step proof for the existence of God. The problem of “infinite regress” came up in the context of his idea that material events are “dependent” on “priors”, which is how I came across this blog via Google. (Go Blue!)

    If you are willing to be patient with Douglas, you can eventually get a handle on the nature of his proof, which is his own variant of the cosmological argument - a type of proof by induction (he dislikes the comparison). On closer examination, he concedes that his framework is merely a set of propositions *consistent with his Christian beliefs, but is not an actual proof. I asked him several times to explain his “dependency of material events on priors” and we traded examples, but he conceded that it is a fuzzy step in his argument, being similar to Aristotle’s material cause or formal cause - take your pick. Proofs by induction are very clever things in math, but are seldom extendible to the natural world, to cosmology, or to quantum physics.

    Some quibbles. There is no such thing as “a quanta”, and *it does not have a location, which seems to be a necessary step to the scope of his argument. A word used in one discipline may have a different meaning when used in another. You may believe that quoting the bible strengthens your proof, but it will not take the listener far unless you already believe the bible is a literally true and unimpeachable source of evidence. If your audience becomes “emotional" or “hostile” as your proof eventually arrives to coincide with your Christian beliefs, it may not be because they are fearful and resisting Repentance of Sin, but may quite possibly be for other reasons you have not considered thus far. Perhaps if he had finished his graduate program, he would have been mentored that the number of footnotes does not by itself strengthen an argument - and the quality of sources matters, as does their thoughtful application. Nor does the number of campuses he has visited, or the number of physics professors he has accosted outside classrooms. If you sincerely want to pressure-test your argument, then ask (politely) for feedback from scholars in the field who are familiar with the ins and outs of the cosmological argument, not from the low-hanging fruit of passers-by and visiting prospective students.

    Something I found fascinating was Douglas’s lack of curiosity of any emotional dimension of what he was saying, and this will be familiar to those who know people who are good with abstract propositions but not with reading faces or detecting irony. It may be that his puzzlement over reactions to his driven line of argument is genuine, but I think if you spend your days traveling to college campuses, standing with provocative signs, then it would be disingenuous to act surprised that some people will react negatively or with indifference. If you stand in front of a gay pride festival with an admittedly half-baked argument that requires several minutes to explain, you are indeed drawing the foul, and it does no good to pretend to be a victim, or to demand equal time to respond. Festival-goers were heckling because they are getting in line to celebrate, not because the “gays aren’t interested in having a serious discussion” with you. If you are genuinely believe that two women posing and kissing will lead to a physical assault on your person, then perhaps you need a more non-confrontational way to fill your retirement years.

    Nevertheless, negative attention is still attention, and it was visually apparent that initiating shouting matches was something that filled a deep need in his soul for validation. He was, for a moment, grinning.

  8. http://www.advocate.com/pride/2015/07/21/photos-san-diego-pride#slide-1

  9. https://www.reddit.com/r/atheism/comments/2mwoma/need_help_on_a_physicsphilosophy_question/

  10. http://reasontogether.org/Past_Topics_11.html

  11. Attention seeking. https://www.youtube.com/watch?v=avep_1vbUOA

  12. Contrary to what some claim, thousands of people in many of the best universities in the US have told me that the infinite dependent material regress argument presented in my handout is sound. When some want more explanation (beyond dialogue) I refer them to my website "proof-of-god.org", especially to the end notes in the "science and logic" section. These seem to satisfy virtually all comers. If anyone on this page wants to look at that, and respond to it I will be happy to reply. It may be, however, that such will never satisfy certain agendized trolls, would be psychoanalysts, and false accusing ad hominists. I'll take a pass on that.

    Have a nice day. :) Doug

    1. Doug:

      First, to follow up on my previous comment, there are some infinite models that comport with a low-entropy "start" to our universe, like Carroll and Chen's model:

      But to your points:

      "Contrary to what some claim, thousands of people in many of the best universities in the US have told me"

      I am very skeptical of the claim that you have spoken to "thousands" of people on this issue. I have no doubt for instance that you have spoken to thousands of people in your preaching, but when it comes to professors of philosophy for instance, I think everyone here (myself is included in that) would appreciate if you could name one for me, and maybe I will send along an email to this person to interview them myself.

      "I refer them to my website "proof-of-god.org""

      Your endnote X, which deals with the infinite regress fallacy, does not really present any new information that your pamphlet didn't already include, from what I can tell anyway. The dominoes analogy illustrates dependency of events, but it doesn't actually demonstrate a problem with infinite time. I think that you've not responded to what I said about closed Markov chain systems, neither here nor in your page. Nor do I think are we being helped here by an insistence that we stick to this very classical idea of causality.

  13. Alexander,
    Thank you for your 8/25/15 post. I hope to be able to respond to it sometime this weekend.

  14. Alexander,
    Sorry, but it looks like I won't be able to respond to your 8/25 until next weekend.

    1. Hey Doug, no problem. Thanks for the heads up!