Fundamental Reality V: Some Candidates, and a Math Test

What are the possible candidates for the most fundamental principle of reality, which is to explain everything else?  Well, what do we know about the reality which it is supposed to explain?  One thing we know from the study of Physics, is that the world can be described (at least most of the time, to a high degree of precision) by a mathematical system of equations.

So the world is made of math!  (However, we should bear in mind here Bertrand Russell's observation that the fact that the constituents of the world are ordered in a particular pattern does not actually tell us what is the internal nature of those constituent parts...this will come back to bite us later.)  Here I am speaking loosely, in the same rough sense that I said earlier that things happen due to magic.

Well, what should we conclude from the mathematical nature of physics?  I can think of two obvious hypotheses.  Either (1) the fundamental reality is something a bit like an mathematical equation (yet not a mere abstraction, but something which actually makes the world go around), or (2) the fundamental reality is something a bit like a mathematician, i.e. a mind capable of appreciating mathematical relations.  (I don't mean either of these descriptions to be taken too literally here, obviously the fundamental entity cannot be exactly like a set of symbols on the blackboard, or a human mind, but the choice of analogy makes the difference to what effects seem likely to follow.)

If the former hypothesis is true, we would have Naturalism, a worldview which takes the universe as revealed by the Natural Sciences to be the ultimate reality, so that everything else must depend on that.  If the latter is true, we would have a Supernatural or Theistic view of reality.

I don't mean to suggest that (1) and (2) are the only possible candidates for the fundamental entity, just the ones I find most plausible.  Some naturalists might instead propose that the ultimate thing that explains everything else is A) the entire Universe “taken as a whole”, B) the first moment of time, C) the most elementary constituents of matter (whatever they are), or D) some vague principle or force, not structured like an equation, “out of which” the Laws of Physics emerge for some unknown reason.  But I don't think these are quite as plausible as compared to (1).

I only have time to do a drive-by shooting of these proposals: (A) seems problematic as the unexplained source of everything, if we take the term “Universe” literally.  For the Universe (as defined by Naturalists) is just the collection of all the things which exist (e.g. my cat).  So if we say that the Universe as a whole just exists and has no explanation, that would imply that my cat, being one of the parts of the Universe, just exists and has no explanation.  We could try to clarify this hypothesis by saying that actually only certain necessary, eternal, basic features of the Universe that have no explanation.  But then it is no longer the world taken as a whole which is fundamental, but only some aspect thereof.  We are then obliged to give a more specific account of what we mean by that aspect, and this is tantamount to adopting one of the other hypotheses.

If we say (B)—which obviously only works if there is a first moment of time—it seems problematic that the fundamental nature of reality should pass out of existence, and odder still why it should result in consistent laws of physics at later moments of time.  (C) means that there are rather a lot of fundamental realities, and raises difficult questions about what makes them capable of interacting with each other, and how they can be limited to particular places or times.  Without more details (D) is too vague to really be criticized, but in any case it is starting to verge on a (rather murky) Supernaturalism.

Now let's do a survey of Supernaturalistic views, in which there's one or more divinities, conceived as capable of having some degree of understanding, power, and purpose, although it or they might not be very much like a human mind.  One could accept Pantheism and identify God with the Universe.  Or one could embrace Polytheism and believe in multiple gods who are collectively responsible for the Universe as we know it.  Finally, one could invest all of the responsibility in a single Deity who is the source of everything else, which is Monotheism.

Pantheism seems to be open to much the same types of objections as (A) above. (Many forms of Pantheism say that the universe of our senses is an illusion and all that really exists is God, but I have difficulties making logical sense of this position, so I won't consider it seriously.)  Also it is not entirely clear, if God is identified with the Universe, how this viewpoint can distinguish itself from Naturalism, although some Pantheists might have answers to this question.

Polytheism seems to me susceptible to fatal objections, at least if the gods are regarded as metaphysically fundamental.  It seems rather strange that a bunch of fundamental entities should coexist without there being any higher principle which determines why the Pantheon is related to each other in the way that they are.  What decides which god gets its way in the case of a disagreement?  (Or if they always agree, that would seem to suggest something deeper than any of them which causes them to agree.)

Indeed the actual historical Pagans, despite worshiping multiple gods, very seldom conceived of the vast panoply of gods as being fundamental aspects of reality.  Instead they usually invented elaborate theogenies explaining how the gods themselves came into being (by a variety of scandalous sexual or asexual means of reproduction) from pre-existing matter or divinities.  Often one has a henotheistic setup: worshipping one chief God who is regarded as the primary Creator, together with many lesser gods valued as mediators to the heavenly court.  Or else the different deities are regarded as modes or manifestations of a single one.  Thus, even in polytheistic cultures, the philosophers tend towards Naturalism, Pantheism, or Monotheism in their fundamental philosophy.  This is a tell-tale sign that a religious belief is philosophically untenable: if even the philosophers raised in a tradition cannot accept it.

Notwithstanding the platypus, it seems rather unlikely that Nature was designed by committee.  It has too much internal coherence for that.  Atheists are frequently heard saying that Modern Science is in conflict with Religion, and they are quite right, always assuming that by “Religion” they mean Paganism.  It is quite untenable in a Scientific Age to believe that there is one divinity responsible for lightning, another one responsible for erotic love, another for birds and so on.  The natural world isn't really divided along those lines.

As far as I know there are no polytheists who worship the actual forces of nature as four different gods.  The best I can do along these lines is to suggest that Thor = electromagnetism (obviously!), Odin = gravitation (he's the most subtle), Freyja = strong force (she who binds with ties of love), and Loki = weak force (too busy wreaking mischief to bother holding anything together).  But I think this new cult is unlikely to take off among any demographic group I can think of!

Next: Comparison of the Finalists

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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10 Responses to Fundamental Reality V: Some Candidates, and a Math Test

  1. Andrew says:


    I don't know if my comment is appropriate on this post. But I was wondering if you would ever make a post about the topics of the other speakers in the Carroll-Craig debate? Esp. The fine tuning, I think Robin Collins have an epic anyalsis of it:

    By the way, I see why you equate Freyja with the string force, but I definitely think it should be Kratos. He pulls them in with his strong muscled arm, but he can only reach so far, so the strong force has a limited length in which it is signifficant.

  2. Aron Wall says:

    Welcome, Andrew.
    The whole point of this project is to explain what we see in as simple and elegant a way as possible. So if 3 of the forces are Norse, the fourth must be as well! Besides, it's not politically correct to have an all-male line up.

    I definitely intend to address Fine Tuning in detail at a later point. As for the other speakers in the debate, is there an online written transcript yet?

  3. TY says:

    Dr Wall,
    I’m puzzled by “the fundamental reality is something a bit like a mathematical equation (yet not a mere abstraction, but something which actually makes the world go around).” Maybe you want to make a clear distinction between the equation, e.g., a law of physics or chemistry that describes the system, and the effective fundamental reality -- who makes the equation work, which is hypothesis #2, the mind behind the maths. If this fundamental reality governs the maths, all the finely tuned parameters, and more, then surely this reality is is what we know as the Creator

  4. Andrew says:


    I could only find Collins' (this is only the paper he presented, not a word-for-word transcript) well worth a read anyway:

    Thx for taking my question.

  5. Aron Wall says:

    Dear TY,
    When you call the fundamental reality a "who", it seems that you are already making some Theistic presuppositions. And when you mention Fine Tuning, you are bringing in Design considerations, whereas at this point in the argument I am trying to stick with Cosmological considerations.

    I am trying to be fair to the Naturalism by constructing the most plausible Naturalist metaphysics that I can. Using the mathematically precise nature of physics as a clue concerning the fundamental reality (as Naturalists themselves would bid us do), I suggest that this would be adopting the so-called "Laws of Nature" as the fundamental reality. We express these laws as e.g. equations on a blackboard, but obviously this is merely a metaphor for the true reality, which is (in Naturalism) some impersonal force or constraint which makes the Universe conform to this certain pattern.

    Now, this view could certainly be criticized for describing the fundamental nature of reality using a metaphor (using the laws as discovered by human scientists as an image of the ultimate reality) which cannot be quite literally true. Equations written with symbols in ink on paper cannot cause stars to go supernova. But I cannot see that this is a decisive refutation of Naturalism, since I think Theism is in the same boat. We theists also conceive of God metaphorically (by analogy to a mind, where our only other experience of minds comes from humans and animals).

    I think that any view of the ultimate reality must ultimately resort to metaphors. This is one reason why I don't think the Cosmological Argument can decisively prove Theism, because there is too much leeway in possible metaphorical descriptions of the ultimate reality---metaphors don't have to make sense in every respect, since they are pictures, not literal truths. But that doesn't change the fact that some pictures are more accurate than others.

  6. TY says:

    Dr Wall,
    Fair respons, and I am sympathetic to the view that the Cosmological Argument are not decisively proofs, but I think, still credible arguments that give atheists reason to pause.

  7. David D. says:

    Would the objection to B) the first moment of time: it seems problematic that the fundamental nature of reality should pass out of existence, still be valid if we think about it along the B-theory?

  8. Aron Wall says:

    David D.
    That is a good question.

    It seems to me that even on the B theory, the first moment of time does not sustain the present moment directly (the way God is proposed to do on Theism), but rather causes it to exist by means of the intermediate moments of time. Let us pretend for simplicity that time is discrete, so that moment 0 produces moment 1, which produces moment 2, which prodcues moment 3, and so on. Now we observe moment 1,000,000 producing moment 1,000,001, and ask why did it have the power to do so? The is what I meant by MAGIC in part III of the series. If we say, "because of the laws of physics" or "God", then we are appealing to something which, by stipulation, applies to or is present at the moment 1,000,000 and the next moment. But if we say, none of those apply, rather it is because of moment 0, then even on the B-theory we are appealing to something which is not actually present at moment 1,000,000. It seems better to attribute it to some power existing at moment 1,000,000. (I think a similar argument could be made if time is continuous, but we'd have to work harder to phrase it correctly.)

    Another consideration is that if we call moment 0 a moment of time at all, then we are implicity saying it has the same sort of metaphysical status as any other moment of time, except that it happens to be the first. But it seems odd for the most fundamental reality to be equal in status to all the other moments, which DO have an explanation. It seems like something rather different is happening at moment 0; not only that it arises without any explanation, but also that it somehow explains not just the existence of subsequent moments, but the precise laws which they obey at those later times. And this is something which (at least at first sight) goes way beyond just specifying the configuration of matter at time 0.

    So it seems to me, anyway. As I said in the Introduction, I am only trying to give plausibility arguments, not perfectly watertight deductions. It would be interesting to try to see if there are any Naturalists who actually believe this sub-hypothesis, and check what notion of causality they think makes it work.

  9. I think your analysis unfairly privileges the hypothesis that the fundamental principle is like a mind. This seems like a fairly arbitrary hypothesis, akin to "The criminal's name starts with the letter N.", which should not be favored unless there's specific evidence for it, rather than right away placing it among the two favored hypotheses. Minds are fairly complicated stuff, and the main reason why they seem natural to us is that we have years of experience with our own and other minds. The general shape of this hypothesis is that the fundamental principle is somehow similar to some complex object, and we only know of this complex object through its appearance in the world (and this appearance itself must be derived from the fundamental principle). Perhaps the fundamental principle is similar to some entities we are familiar that are derived from it, but why favor the hypothesis that it is similar to a mind? Why is it any less appropriate to suppose that the fundamental principle is something like a bunch of particles connected with springs? This is not the same as saying that the fundamental principle is something like an equation, and is more like your hypothesis (C). You dismiss (C) because it appears to make fundamental reality composite, but minds are also composite: People have different mental states at different times, and even at a single time if a person makes a mental distinction between two things, the mental concept of the first thing and the mental concept of the second thing are separate entities within the mind.

  10. Aron Wall says:

    Thanks for your thoughtful comment.

    1. This post needs to be read in conjunction with the entire series, particularly (for dealing with your objection here) number VII: Does God Need a Brain?.

    The short answer is that I concede that our own minds are composite, but that is because we are not the fundamental reality. The question is whether it is logically consistent to conceive of a mind that is completely simple (i.e. noncomposite), and I think it is. Such a mind is possible if its subjective experience is completely identical to the objective nature of reality (which I am sure you will concede, is not the case for our own minds).

    Such a simple mind would, by definition, be omniscient. Here we need to make a distinction. Of course the contents of such a mind (the things in the world that it knows exists) would be plural, but its ability to know would be singular and therefore simple, in the sense that, because there is no gap to cross between its knowledge and reality, it has no need of complex perceptual faculties (e.g. eyes) or complex information processing hardware (i.e. a brain). As I argue in that post, this is consistent if we drop the assumption of "representationalism" about God's mind.

    This addresses your objection #2 in your last sentence, that "the mental concept of the first thing and the mental concept of the second thing are separate entities within the mind." As for objection #1, "People have different mental states at different times", this is also inapplicable to God because God is eternal, and therefore timelessly knows the whole of history (past, present, and future).

    (An equation is also a complex object if we write it on a blackboard in the form of chalk-symbols, but of course the chalk-symbols are different from the idea expressed by them.)


    Why is it any less appropriate to suppose that the fundamental principle is something like a bunch of particles connected with springs? This is not the same as saying that the fundamental principle is something like an equation, and is more like your hypothesis (C).

    Suppose we concede that the fundamental reality is simple, but can be understood as analogous to a complex object. Then when I say "the fundamental principle is like a bunch of particles connected with strings, but with the caveat that it is not made of parts" then once I make the caveat, I'm not sure what if anything from the first part of the sentence even survives the qualification, since the first half of the sentence is basically a list of parts. (Note that this is actually quite different from my hypothesis (C), since I took (C) to mean not that the FR is in some way analogous to a collection of elementary particles, but that each actual elementary particle in Nature (e.g. an electron) actually is fundamentally real, with no deeper explanation for its existence.)

    On the other hand, if I say that "the fundamental reality is like a mind, but with the caveat that it is not made of parts", then it seems to me (if my arguments in my first point made sense) that I do have some dim understanding of what the first half of the sentence means, even after I give the caveat. For example I can make deductions from my proposal like "God knows that cars exist". I don't know what, if any, propositions I could deduce starting from your proposal.


    The general shape of this hypothesis is that the fundamental principle is somehow similar to some complex object, and we only know of this complex object through its appearance in the world (and this appearance itself must be derived from the fundamental principle). Perhaps the fundamental principle is similar to some entities we are familiar that are derived from it, but why favor the hypothesis that it is similar to a mind? Why is it any less appropriate to suppose that the fundamental principle is something like a bunch of particles connected with springs?

    From this quotation, you seem to think I am arguing: "Our minds are derived from the fundamental principle, and this by itself gives reason to believe that the fundamental principle is something like a mind".

    But that is not the argument I am making. I agree that it would be a very weak argument if I had made it, since I could replace "Minds" in the quoted sentence with "Trees" or "Rocks", and it would be equally valid. (Actually, the Bible describes God as both "living" and like a "rock", so I needn't claim these analogies to creation have no validity, but in a certain sense they are far less informative than comparing God to a mind.)

    What we need is an argument that gives a non-arbitrary way to pick out "minds" as being a better choice of analogy than any other complex structure in the universe. The argument that I was making started instead with the observation of "the mathematical nature of physics" (something not mentioned in your comment, but a critical part of my argument). I asked how we are to account for this.

    At this point we have a non-arbitrary reason to select "human minds" as a unique object in the universe; namely that among all the entities we know about (apart from supernatural beings whose existence is disputed) we humans have a unique relationship to mathematical structures, seen in our ability to understand and appreciate the patterns in Nature, and indeed to invent new mathematical patterns which are not found in Nature. If John Horton Conway (a human) is capable of inventing the Game of Life, and if the Game of Life is similar in a certain respect to our universe (as a system governed by mathematical rules), then this gives a non-arbitrary reason to think that the creator of our universe can be understood as more similar (in a certain respect) to Conway than to the rock or tree. Only, he would have to be even more intelligent and powerful than Conway in order to create a universe like ours.

    Of course, our ability to create worlds is not limited to mathematical structures. St. Tolkien also created imaginary worlds, and his authorship of the Lord of the Rings might also be taken as a somewhat different (but compatible) model of God's relationship to historical events. He saw human beings as contributing to creation by being "Sub-Creators", made by God in the image of God, and therefore capable of acting like gods on a more limited scale.

    4. "the main reason why they seem natural to us is that we have years of experience with our own and other minds."

    I agree that humans have a certain anthropomorphic bias, due to our social and genetic context, where we sometimes treat things as being more similar to human minds than is justifed by the facts. This is something that must be taken into consideration and carefully corrected for, in order to avoid an excessively anthropomorphic notion of Deity (as for example, found in typical examples of pagan mythology).

    However, it is also possible to overcorrect for this bias, in ways that beg the question against Supernatural worldviews. In particular, Natutralists often make the assumption that it is possible to fully account for human mentality using purely physical properties, so that human minds could be derived from a purely non-mental description of the world. From this, they argue that any comparison of reality to a mind is arbitrary, since it is only our own minds that pick out minds as special.

    However, as I go on to argue in this series (and many philosophers agree with me), Naturalism is unable to give a coherent account of the origin of either normative ethics, or conscious experience. So if we made a list of concepts which we don't know how to reduce to simpler concepts, apparently some mental properties would be on this list. This makes it far more plausible that the fundamental principle would need to be, in a certain sense, mental.

    At the very least, I don't think there is any good reason for consciousness to emerge on any of the Naturalistic scenarios I mention, and in Naturalist scenario (1) (i.e. nothing exists except that which is described by an equation) I think it can be shown to be logically impossible.

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