Fundamental Reality III: Chains, Parsimony, and Magic

Some optimistic folks hope that Science will eventually explain everything about the world.  But this hope seems absurd in light of the fact that explanations always involve presuppositions.  The structure of explanation is always that we explain one thing A in terms of some set of other things B, C, D... which exist, or which have happened.  (Let's not be too particular about what we mean by “things” here, whether “objects”, “events” or what...)  One could then ask what is the explanation of B or C or D, and these things will in turn typically have explanations in terms of other things.  This gives us various types of explanatory series, and we can ask whether these terminate in some type of ultimate explanation.

So it seems that the best we could possibly do is to have one thing or principle whose existence is unexplained, and then use that to explain everything else.  That one thing would then have no other explanation outside of itself.  However, we can still evaluate how plausible it is that it should exist, based on various considerations of parsimony.  We can ask:

  1. Is this entity the type of thing where it would make sense for it to just exist on its own?  Or is it the sort of thing that would more naturally be explained by reference to something else?
  2. Is this the simplest conception of fundamental reality, or can we get away with a simpler one? (Here I am using simple in the sense of Occam's razor, although if there were really just one unexplained entity, not composed of parts, it would also be simple in the Medieval Scholastic sense of being non-composite.)

You might notice that the people of a scientific bent tend to focus exclusively on the second question, while traditional metaphysics focuses more on the first question.  In my view both questions are relevant.

I said that explaining everything in terms of one thing is the best we can do.  We might have to settle for less, such as a plurality (hopefully small) of unexplained fundamental principles.  However, that would not only be more complicated, it would also raise questions about what is it that joins these (supposedly separate) principles together.  We might therefore reasonably hope that the principles in question would at least have some type of internal unity, without being too dogmatic at this stage about what kind of unity we are looking for.

Some people might propose that the chain of explanations extends backwards forever in an infinite chain.  Thus nothing has any ultimate explanation, but rather each one is explained by the thing before it, and so on.  Alternatively one could have the explanations arranged in a circle, which is similar to the infinite regress for what I am about to say.

The chain of explanations wouldn't necessarily have to be embedded in any kind of temporal sequence, but if it were, one would have to have a universe which is eternal to the past.  Now there are physics problems with trying to make a compelling physical model along these lines, with neither a geometrical nor a thermodynamic type of beginning.  But here I'm trying to explore more general metaphysical considerations, of the sort that are accessible from the nearest armchair, so I'll try to appeal to intuition instead of esoteric quantum cosmology considerations, for which the evidence of a beginning is mixed.

Personally, I find an infinite regress, with nothing more behind it, rather unsatisfactory.  It is not that I think there is any logical inconsistency in a universe which extends backwards in time forever.  There isn't.  The universe might well work that way.  But I feel like such a chain of explanations wouldn't actually explain anything in the chain properly.  For example, in the “ekpyrotic” scenario where the universe involves an eternal bouncing back and forth of two membranes, it wouldn't tell us why there are two membranes rather than one or four.  It would just boil down to saying that: things just are the way they are because they are the way they are.  Of course, if there were some additional extra explanation outside of time which somehow determined that there had to be two membranes, that would be different, and would make me much more satisfied with a time that goes back forever.

Somebody might retort that explaining everything in terms of one unexplained thing is just as bad in that it also has something which “just is the way it is”.  But at least in that case it there's only one thing like that, not a whole chain of things.  I find in myself an intellectual preference for building explanations on a foundation.  Axiomatic reasoning is usually regarded as more intellectually respectable than circular reasoning.  If we deduce things from axioms, those axioms can be appreciated and evaluated.  Whereas if we deduce things from a chain going back to infinity, I feel that the entire system is unsupported in a vicious way.  So I'm fine with time going back to infinity, but only if there is something which transcends time which makes time do that.  Of course, Nature does not necessarily have to correspond to my intuitions, but I don't think it's irrational to believe that at least some of our intuitions give us rational guidance about how the universe should work.  Without some rational intuitions leading us to seek explanations, Science couldn't even get off the ground.

Furthermore, there are chains of explanation which do not go further and further back into the past, and these chains cannot be accounted for simply by postulating an infinite past.  We might also try to explain why the present-day dynamical processes of nature occur in the way that they do.  For example, suppose I want to know why a balloon attracts hair.  So I say it is because they have opposite electrical charges, which are attracted to each other with an inverse square law.  Well, why is that?  Well, because each charge has electric field lines coming out of it.  Why is that?  Because Gauss's equation said it had to happen that way.  Why is that?  It seems the answer must eventually be: it happens by MAGIC.

Some would say that this is obscurantism and that things happen because of the Laws of Nature.  But we have to remember that the phrase “Laws of Nature” is really a stand-in for whatever mysterious aspect of reality causes things to obey these Laws of Nature. When the phrase was first coined, the word “law” was a metaphor which was taken to imply the presence of a Legislator.  St. Chesterton suggests that the rational agnostic should instead use a different type of terminology, borrowed from fairy tales:

In fairyland we avoid the word "law"; but in the land of science they are singularly fond of it.  Thus they will call some interesting conjecture about how forgotten folks pronounced the alphabet, Grimm's Law.  But Grimm's Law is far less intellectual than Grimm's Fairy Tales.  The tales are, at any rate, certainly tales; while the law is not a law.  A law implies that we know the nature of the generalization and enactment; not merely that we have noticed some of the effects.  If there is a law that pick-pockets shall go to prison, it implies that there is an imaginable mental connection between the idea of prison and the idea of picking pockets.  And we know what the idea is.  We can say why we take liberty from a man who takes liberties.  But we cannot say why an egg can turn into a chicken any more than we can say why a bear could turn into a fairy prince.  As ideas, the egg and the chicken are further off from each other than the bear and the prince; for no egg in itself suggests a chicken, whereas some princes do suggest bears.  Granted, then, that certain transformations do happen, it is essential that we should regard them in the philosophic manner of fairy tales, not in the unphilosophic manner of science and the "Laws of Nature."  When we are asked why eggs turn to birds or fruits fall in autumn, we must answer exactly as the fairy godmother would answer if Cinderella asked her why mice turned to horses or her clothes fell from her at twelve o'clock.  We must answer that it is magic.  It is not a "law," for we do not understand its general formula.  It is not a necessity, for though we can count on it happening practically, we have no right to say that it must always happen.  It is no argument for unalterable law (as Huxley fancied) that we count on the ordinary course of things.  We do not count on it; we bet on it.  We risk the remote possibility of a miracle as we do that of a poisoned pancake or a world-destroying comet.  We leave it out of account, not because it is a miracle, and therefore an impossibility, but because it is a miracle, and therefore an exception.  All the terms used in the science books, "law," "necessity," "order," "tendency," and so on, are really unintellectual, because they assume an inner synthesis, which we do not possess.  The only words that ever satisfied me as describing Nature are the terms used in the fairy books, "charm," "spell," "enchantment."  They express the arbitrariness of the fact and its mystery. A tree grows fruit because it is a magic tree.  Water runs downhill because it is bewitched.  The sun shines because it is bewitched.

I deny altogether that this is fantastic or even mystical.  We may have some mysticism later on; but this fairy-tale language about things is simply rational and agnostic.  It is the only way I can express in words my clear and definite perception that one thing is quite distinct from another; that there is no logical connection between flying and laying eggs.  It is the man who talks about "a law" that he has never seen who is the mystic.
(Orthodoxy, "The Ethics of Elfland").

Let no one think that St. Chesterton said this only because he did not understand the particular explanations given by Modern Science.  He didn't, but it doesn't make any difference, since you come to the same place in the end no matter what.  No matter how many mediators we put in between the hair and the balloon—even if there is a continuum of mediating entities—at some point we need to postulate some sort of fundamental interaction not explained through intermediaries.

If we ask why these direct interactions occur, we either have to say for no reason at all (in which case it is a puzzle why things happen so consistently, since every single instance of an interaction would be a quite separate unexplained occurrence) or else to say that there is some common force or principle: either God or else some other term more acceptable to atheists.  We can call the underlying principle a “Law” if we want to (for lack of better language) but we should be aware that the word doesn't really explain why things had to be this way.

So in what follows, let's suppose that the explanations terminate on one or more unexplained entities, whether laws of physics, divinities or something else.  Because of the uncertainty about what these things actually are, I am not going to impose a rigid grammar on them, but will freely alternative between different terms.  I don't mean to sneak in any substantive assumptions by calling them “things”, “entities”, “principles”, “rules”, “beings”, or whatever.

Still, they must in some sense exist, or they couldn't do any work explaining anything else.  They are not merely logical abstractions, since logical abstractions can't do anything, they can only describe things.  Some people would say that it's a category error to say that laws can do anything, that laws merely describe regularities in Nature, but don't cause them to exist.  Well, if that happens to be true, then (contra Hume) something else must cause those regularities to keep occurring, otherwise it would just be a mighty coincidence that the regularities keep on happening.

In the following reflections I will try to say more about what this “something” might be.  I'm not trying to force a prematurely theological conclusion here.  I'm reasonably confident that any rational, complete worldview must have some set of fundamental entities or explanations which play the explanatory role that God does in Theism, but it is a quite separate question whether the thing(s) that fill that role have to be at all like the traditional conception of God.  This is a question which we will eventually need to face square-on, but first let's try to figure out some properties that any fundamental entities would have to have, no matter whether they are conceived of along Naturalist or Supernaturalist lines.

Next: Necessity, Eternity, and Power

About Aron Wall

I am a Lecturer in Theoretical Physics at the University of Cambridge. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my postdocs at UC Santa Barbara, the Institute for Advanced Study in Princeton, and Stanford. The views expressed on this blog are my own, and should not be attributed to any of these fine institutions.
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8 Responses to Fundamental Reality III: Chains, Parsimony, and Magic

  1. TY says:

    Dr Wall,
    It seems this “something” is a deus ex machina, introduced just to avoid the infinite regress, or get around the explaining B, C, and D in the ultimate sense. Viewed in this light, the something seems contrived. Further, if the something is axiomatic, what is the logical or metaphysical foundation? I guess these questions will be answered in the next post.
    Interesting stuff.

  2. Aron Wall says:

    I'm not sure I understand your point. Given the assumption that there is no infinite regress (or vicious circles), it would seem to logically follow that the chain of explanations must instead terminate at some finite ultimate "something". I don't see any alternatives, do you? Avoiding a logical contradiction would seem to be the least contrived reason possible to postulate something, so I'm not sure why you call it a deus ex machina.

    Perhaps you mean that we shouldn't just stop the chain of explanations in some arbitrary random place, but instead with some type of entity where it seems reasonable that it shouldn't have a further explanation. If so I agree, but that was the point I was making with my criteria 1 & 2 in the post above.

    Or are you saying you don't buy my argument against infinite regresses? I don't claim that this step of the argument is logically compulsory (especially since I don't believe actual infinities are self-contradictory) but I do think it is reasonable, and once one accepts it, the existence of a fundamental entity is required. The rest is just arguing about what that fundamental entity is like.

  3. TY says:

    Dr Wall,
    Thanks for the reply. You surely answered my concern: "Perhaps you mean that we shouldn't just stop the chain of explanations in some arbitrary random place, but instead with some type of entity where it seems reasonable that it shouldn't have a further explanation. If so I agree, but that was the point I was making with my criteria 1 & 2 in the post above."

    As you know, the atheist's famous counter-punch to the "First Cause" is the question: Justify the argument that God is an exception to the infinite regress? Once that hole is plugged, I think it places the axiomatic approach on a solid footing. One of the challenges the theist faces is justifying the First Cause doctrine, the uncasued "something", in language that any reasonable person -- atheists or theist -- would find convincing on its own merits. I believe that’s where you’re headed.. That’s the heavy lifting, which will make lighter work for the theological argument.

  4. Aron Wall says:

    All right, I think we're on the same page. While the rest of my essay will focus more on determining the nature of the fundamental entity, rather than further arguments against an infinite regress, hopefully the greater specificity of detail will make the reasons for stopping at a divine being more clear.

    By the way, in my comment that "Axiomatic reasoning usually regarded as more intellectually respectable than circular reasoning", I should perhaps clarify that I am using the term axiomatic in a way analogous but not identical to the usual meaning---we are not talking about things which are necessarily true from the perspective of limited human reason, but the thing which is the fundamental principle of existence if we understood everything fully. St. Thomas distinguishes between that which is "self-evident in itself" versus that which is "self-evident to us". We are looking for a metaphysical foundation rather than an epistemic one.

  5. James says:


    Thank you for this series :) I've read several of the later 'chapters' and the conclusion but have started over at the beginning. As someone who is confused I wanted to be able to share my perspectives and hopefully enhancing the conversation.

    It seems that many atheist perspectives come back to that's "just the way it is". That is the explanation as to why these laws exist and it seems they may exist outside of time (maybe even that these laws are eternal). However that doesn't offer a satisfying answer as to why these things exist.

    You also raise an interesting point, if these laws only describe nature that doesn't cause nature to exist. (still why are these laws in existence and what is the cause - of everything)

    I find the thought of God being a first cause comforting while also providing a reason why there are 'natural laws' and everything else in existence. At this point my thinking becomes very confused.

    We have "natural laws" that work well up until a point. At a certain point though it seems that the advocates of these laws just give up and say thats "just the way it is" or come back later and we'll have a better fundamental answer. The alternative is to look for what is fundamental outside of the natural realm and accept the supernatural.

    As I mentioned earlier, I am confused :p Hopefully, my comment wasn't to confusing and maybe it (and or a response) will help someone.

  6. I've responded to other posts in this series accepting for the sake of discussion that there's a fundamental cause, but I thought I'd take some time to lay out my qualms with this claim. Here you argue that the chain of explanations must end at a set of unexplanable phenomena that explain everything else. This builds up on your previous post where you clarify what you mean by an explanation. However, your previous post did not define "explanation" precisely but relied on our pre-existing understanding of this notion and then discussed particular ways that other people may understand this concept differently how you handle those cases. Such an explication may be good enough for some purposes, but I don't think it suffices for giving an unambiguous pointer to a set of fundamental explanations. This because the process of seeking out more and more fundamental explanations naturally brings you to the sort of entities where it is most ambiguous whether these entities exist and what qualifies as a cause or not. This is analogous to the sorites paradox, where removing a grain at a time from a heap of sand naturally leads you to situation where it is ambiguous whether this thing is a heap or not.

    In certain specialized circumstances it is possible to give a precise definition for what things cause what other things. Such a framework is clearly unsatisfactory for the purpose of this discussion since the "first causes" within such a framework tend to be artifacts of what things are excluded from the framework. It is conceivable that someday people will design a framework along similar lines whose domain is much vaster and include everything you discuss in your series of posts. Even then the first causes within this framework may be unsatisfying, either because they make us aware of some entity outside this framework that intuitively exists or because the first causes seem to be contrivances that exist with this framework but don't seem to have any broader reality. It is also possible some conceptual analysis will clarify the idea of a cause well enough to unambiguously point to a set of fundamental explanations without being perfectly precise. However, even if such a conceptual analysis exists it need not be unique; there could be another conceptual analysis that equally well matches our intuitive notion of explanations but points to a different set of fundamental explanations.

  7. Aron Wall says:


    Thanks for your comment. But as I think I said pretty clearly in my first post, I'm not trying to give demonstrative, watertight arguments for a fundamental reality (as many philosophers have tried to do in the past). Instead I'm trying to show the mere plausibility of such a worldview.

    As I wrote in the Prologue:

    If at any point you think I am handling things badly and going beyond my evidence, I ask only to be judged by fair standards. It's easy enough to just take a negative point of view, and criticize unwarranted assumptions in other people's arguments. But suppose that someone asked you to stand up and defend your own metaphysical beliefs (say, materialism) with arguments capable of persuading others. Not just something offhand like “This makes sense to me, and I've never seen any good reason to believe otherwise”, but some robust intellectual argument for certain types of existence or nonexistence claims. You'll quickly find that it's a hard thing to do. Yet some particular specific set of metaphysical statements must in fact be true, even if it is hard to see which ones.

    So if you disagree, please do not just say, “There's a hole in your reasoning at line 278, therefore you are being illogical and religion is irrational.” Instead tell me what metaphysical view you find more plausible and why.

    You are raising doubts about whether the concept of "explanation" really applies in a unique way to everything in the universe. You suggest it is like the sorites paradox where having an explanation is like being a "big" heap. But this may be more of a problem with the English language word "big" than with the concept of largeness per se. There is no problem with saying that a heap has a certain size (e.g. 350 grams of sugar), other than the question of error bars I guess. But "big" specifies that something is a large amount without actually stating, except in a vague context-dependent way, just how large it is.

    It is not clear to me how a similar objection with the word "explanation" would work, since explanation is not a term of quantity. The trouble is that your worries that the concept is vague, are themselves rather vague. Perhaps your point would be more clearly made if, instead of simply worrying that the concept is ill-defined, you instead tell me a specific story of how the universe might work (i.e. provide me with a model of a proposed actual ontology of the world), and show me how your objections would be correct if that story is true.

    I don't insist that you actually believe your story, since you are probably agnostic between multiple possibilities, but I think your objections would be much clearer if you could give at least one specific example of what you mean by them.

  8. I agree that the concept of "explanations" is not vague in the same way that "heap" is, which is implicitly involving a quantitative judgement with a vague cutoff. A closer analog is truth in mathematical logic, which according to Tarski's undefinability theorem cannot be defined in a universal way. Rather, the truth of statements in one language can only be perfectly defined in another, in some sense stronger, language. One difficulty in defining truth is that any vagueness or ill-posed whatsoever in language can be inherited to a vagueness in the meaning of "true", by asking whether a statement that involves that vagueness or ill-posedness is true. While not as broad the notion of explanation pertains to every object in world and so has a similar potential to inherit difficulties. While the Liar's Paradox decisively refutes a naive notion of truth I don't think there's a similarly strong argument against explanation, but I can list some individual difficulties.

    First, two examples of artificial frameworks as I mentioned earlier: One consists of the points in spacetime and events occurring in those points, and saying that one event causes another event if there is a future-directed timelike path from the first to the second. Another framework is that a philosopher can posit an entity they call "the One" that causes all other phenomena and has absolutely no properties besides that. The first framework, as you've argued previously, does not encompass everything that has or requires an explanation, and the second framework contains an artificial object that seems to have no relation to the real world.

    Now, general objections: First, it's not clear whether these explanations should encompass explanations for logical facts, for example, "The prime number theorem is true because the Riemann zeta function has no zeros with real part equal to one." This example is not just a logical implication but is also in some sense an explanation, and mathematicians certainly sometimes think about their work in terms of searching for explanations for known and logically necessary facts. On the other hand its unclear whether this is entirely coherent and the subclass of purely world-pertaining phenomena might be more coherent or be equally coherent and worthy of studying in isolation.

    Second, it's unclear whether "indexical facts" such as "I am Itai" and "This is 2019" should be part of the range of phenomena included. These indexical facts are an important part of any person's worldview, because they mediate the relationship between knowledge of the physical world and knowledge of sensory experience. However, if they are included we must conclude that the first cause is subjective and not eternal.

    I had two more issues in mind, but I got interrupted while writing this comment and now I'm having trouble writing them out.

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