The Design Argument. The design argument reasons from the orderliness of our universe to the existence of some designer. The design argument is consistent with the thesis that our universe has a plurality of divine designers. Hume says “A great number of men join in building a house or ship, in rearing a city, in framing a commonwealth: Why may not several deities combine in framing a world?” (1779: 77) So the design argument is consistent with the existence of many Gods.

The Cosmological Argument. The cosmological argument reasons from causal or explanatory sequences in our universe to the existence of a First Cause or First Explainer (or something similar). The cosmological argument is consistent with the thesis that our universe has a plurality of first causes or necessary grounds (Bartel, 1982). And it’s consistent with the notion that other possible universes all have their own First Causes. Here’s how Bartel puts it:

It seems rather rash to affirm without further ado that there must exist one and only one uncaused First Cause. Might there not be several causally-independent beings who are collectively responsible for the existence of all contingent beings? Or, granted that there exists only one First Cause in the actual world, might there not exist two or more First Causes in some other possible world? Or, granted that there cannot be more than one First Cause in each possible world, might not the First Cause in one possible world be distinct from the First Cause in another possible world? (Bartel, 1982: 34)

So the cosmological argument is consistent with the existence of many Gods.

The Ontological Argument. The ontological argument goes roughly like this: (1) God is that than which no greater is possible; (2) if God doesn’t exist, then any existing thing is greater than God; (3) but that contradicts the definition of God; (4) therefore, God exists. If this argument works for God, then it works for another God, call it God-2, who is also that than which no greater is possible. And it works for God-3, God-4, and so on. The ontological argument is consistent with the existence of an infinity of maximally perfect beings (e.g. Grim, 1982; Kane, 1984; Leftow, 1988; Harwood, 1999).

So why do monotheists say there is one God? What’s the argument? If you believe in the traditional arguments for God, then why not accept polytheism?

Swinburne says “Theism is simpler than polytheism” (2010: 40). But why is it simpler? Swinburne seems to think that positing one infinite God is simpler than positing many finite Gods. And that’s just false. One infinitely complex thing is equivalent in its complexity to infinitely many finitely complex things. Positing the one infinite number Aleph-0 is equivalent to positing the entire infinite sequence of finite natural numbers.

I’m not aware of a single philosophical argument for monotheism. Surely this is just a failure of my awareness. But I’ve actually been looking (through academic resources like The Philosophers Index, JSTOR, Google Scholar, and so on). Not one article shows up that aims to defend the uniqueness of God. I’m guessing that there aren’t any good arguments for the uniqueness of God. So here’s a nice closing quote:

Polytheists, who are unduly despised, accept the idea of higher or greater and lower or lesser forms of being. But they often regard the higher forms as coming later, with their arrival marked by the increasing progress and differentiation of the universe, symbolized by the successive generations of the gods. They might well say that the idea of a hierarchy of greatness makes much more sense if we introduce lesser gods from whom the greater can gradually emerge without the inelegant monotheists’ leap straight from humanity to the Most High God. (Hughes, 1990: 349)

It makes far more sense to posit an endless series of ever-greater gods. If you don’t want lots of gods in our universe, just go modal: every possible universe gets exactly one god, its own local deity. Here it’s also interesting to note that many atheistic objections to the existence of God don’t apply to the existence of the finite gods of modal polytheism.

Bartel, T. (1982) Cosmological arguments and the uniqueness of God. International Journal for Philosophy of Religion 13 (1), 23-31.

Grim, P. (1982) In behalf of ‘In behalf of the fool’. International Journal for the Philosophy of Religion 13, 33-42.

Harwood, R. (1999) Polytheism, pantheism, and the ontological argument. Religious Studies 35, 477-491.

Hughes, M. (1990) Creation, creativity, and necessary being. Religious Studies 26 (3), 349-361.

Hume, D. (1779 / 1990) Dialogues Concerning Natural Religion. New York: Penguin.

Kane, R. (1984) The modal ontological argument. Mind 43, 336-350.

Leftow, B. (1988) Anselmian polytheism. International Journal for the Philosophy of Religion 23 (2), 77-104.

Swinburne, R. (2010) Is there a God? Revised Edition. New York: Oxford University Press.

I am not such an agnostic because I do think that it is a matter of knowledge that there are no personal gods.  It is no harder for me to dismiss the existence of Yahwheh or a personal Allah or a divine Jesus as fictional or mythical than it is for all of us 21st Century modern people to dismiss out of hand claims that Thor or Zeus or Spider-Man or Aquaman exist.

But some atheists are reluctant to call themselves atheists because there remain the various god conceptions of the philosophers, some of which are, or may in the future be, plausibly formulated.  Might there be a single source of all being distinguishable from the known universe and fitting a certain, longstanding, traditional philosophical definition of the word “God”?  Perhaps.

This or a number of other concepts one might formulate are, or at least could be, sufficiently conceivable and sufficiently consistent with our best science and metaphysics as to be reasonably plausible.  One might for one reason or another disfavor belief in one or another of the possible metaphysical god concepts and yet still not think of one’s disbelief as raising to the level of knowledge.

I consider someone like this open to deism and agnostic about deist gods.  I myself fit this description.  But then why call myself an atheist if I am philosophically agnostic about whether some single “divine” principle which originates existence exists?  Should I not just call myself an agnostic?

No, I should not just call myself an agnostic.   The reason I am an atheist is because I am the opposite of a theist, not the opposite of a deist.  And I am not agnostic about theism, I am agnostic about deism.  I am gnostic about theism.  I know Yahweh and a divine Jesus and a personally construed Allah, etc. do not exist with the same kind of sufficient evidence and degree of certainty that I know Aphrodite and Green Lantern do not exist.

An impersonal metaphysical principle which somehow accounts for existence or order, etc. is an entirely different thing.   Proving such a thing exists would get you no closer to proving the existence of Yahweh or a divine Jesus than proving numbers are real entities would prove the real existence of The Count from Sesame Street.

Theists are quite fond of arguing for a deistic god and assuming that it is the same thing as providing evidence for a theistic one, when it’s not.  Or, a bit more modestly, other theists think that the inconclusiveness and relative philosophical open endedness of the deist god question translates into a plausibility of the theist god.

But it does not.

I do not feel like participating in the equivocations of theists by granting them that lack of knowledge about whether a deist god may exist translates to lack of knowledge about whether the personal gods upon which religions are actually based exist or not.

The believer in a personal god is a theist.  I do not believe in any personal gods, so I am an atheist.  My considered reasons for disbelief raise to the level of knowledge by our ordinary standards for knowledge claims.  Therefore, I am a gnostic atheist.  That the existence of some deistic, impersonal god may very plausibly be proved to me is irrelevant.  Even were I to come to be a deist by affirming the existence of a “divine” impersonal metaphysical principle of some sort, I would remain a gnostic atheist. The positions are entirely compatible.

Your Thoughts?

The Church of Google website gives nine lovely arguments for the divinity of Google.

The Church of Google website also gives excellent replies to objections against the divinity of Google.

Brilliant!

It sometimes surprises me, although it shouldn’t, how religious devotees feel the need to regularly reinforce their own convictions in groups of like-minded individuals. I suppose this is the purpose of regular Sunday church services, for example, to reinforce the community of belief in between the rest of the week when the real world may show no evidence of God, goodness, fairness, or purpose.

Nevertheless I was not prepared for the self-congratulatory hype that I have seen spouted on the web, and have received in emails, including a typically disingenuous email from Wiliam Lane Craig to his followers regarding a debate I had with him in North Carolina last week. While carrying out the debate in the first place was something that broke my normal rules–as I said during the debate, I far prefer civil conversation and discourse as a way of illuminating knowledge and reality–I will break another rule and write this blog-like note on my own perspectives, in the hope that it may circulate and counter some of the nonsense that has propagated in the fundamentalist and religious blogs of late. Perhaps Craig will post this on his blog and send it out as well.

I believe that if I erred at all, it was in an effort to consider the sensibilities of the 1200 smiling young faces in the audience, who earnestly came out, mostly to hear Craig, and to whom I decided to show undue respect. As I stressed at the time, I did not come to debate the existence of God, but rather to debate about evidence for the existence of God. I also wanted to demonstrate the need for nuance, to explain how these issues are far more complex than Craig, in his simplistic view of the world, makes them out to be. For this reason, as I figured I would change few minds I decided also to try and illustrate for these young minds the nature of science, with the hope that what they saw might cause them to think. Unfortunately any effort I made to show nuance and actually explain facts was systematically distorted in Craig’s continual effort to demonstrate how high school syllogisms apparently demonstrated definitive evidence for God.

Let me now comment, with the gloves off, on the disingenuous distortions, simplifications, and outright lies that I regard Craig as having spouted. I was very disappointed because I had heard that Craig was more of a philosopher than a proselytizer, but that was not evident the other evening.

Craig began with an attempt to demonstrate his scientific and mathematical credentials by writing a rather meaningless equation on this first slide, which he then argued would be the basis for his ‘evidence’. The equation, in words said that if the probability, given the data, gave one a greater than 50% likelihood for God’s existence, then this was evidence. He even presented this as a pseudo- Bayesian
Argument.

The problem is that using mathematical probabilities in this fashion ONLY makes sense if you have a well defined probability measure, and if one can check that the conclusions one draws are not sensitive to one’s priors. He did not explain this at all, nor do I think he understood it when I tried to explain it to him. For the rest of the evening Craig simply proceeded to spout his claimed evidence, and then proceeded to state that each gave him a greater than 50% belief in God. The whole purpose of the mathematical nonsense at the beginning was to give some kind of scientific credibility to a discussion which was anything but. It was disingenuous smoke and mirrors. (Moreover, as I tried to explain, in modern scientific experiments, merely finding an unexpected result, with say only a 20% chance of being wrong, is not sufficient to establish evidence. One needs to go to much higher levels of confidence, especially if the claim being made disagrees with all other evidence. It is hard to think of a grander claim than evidence for a divine being who creates the universe without apparent purpose, dominated by dark matter and dark energy and containing hundreds of billions of galaxies, lets it evolve untouched for billions of years, and then roughly a million years into human evolution decides to intervene at a time before Youtube or any other objective recording and archiving tool was available.)

Next, if one is going to frame the argument scientifically, as I argued is essential when discussing empirical evidence, which Craig later took great pains to disavow, one must point out that in science when one is trying to explain and predict data, one tries to explore all possible physical causes for some effect before resorting to the supernatural. Happily it is precisely this progress in our natural philosophy that ended such religious atrocities as the burning of witches. In each and every case the actual syllogism that one ended up with was:

Craig either doesn’t understand how something could happen, or instead believes that events happened that confirmed his pre-existing belief system.
In the absence of understanding physical causes or exploring alternatives, this implies evidence for the existence of God.
Therefore there is evidence that God exists.

This is what I framed as the “God of the Gaps” argument and I continue to view, upon reflection, most of the claims of Craig as falling in this well-known theological trap.

Let me work backwards through his 5 “arguments”:

The resurrection of Jesus, and that fact that the followers of Jesus were willing to die for their beliefs provides evidence of God: I admit that this claim is so sloppy and fatuous that in an effort to demonstrate some margin of respect for Craig I tried to avoid it for as long as I could. Craig argued that most New Testament scholars believe in the resurrection. Even if this were true, though Craig provided no evidence of this, this of course is simply proof that New Testament scholars have an a priori faith that guides them. It is like claiming that most Islamic scholars may believe that Mohammed actually ascended to heaven on a horse. In the first place, there are no definitive eyewitness accounts of these events, and in the case of the claimed resurrection the scriptures were written decades after the claimed event, and the different accounts are not even consistent. Not only are there serious theologians who doubt the resurrection, there are historians who doubt the historical existence of Jesus himself. Whatever one’s views in this regard, however, one must ask oneself the simple question: Is it more likely that all known physical laws were suspended so God could demonstrate divinity–and moreover demonstrate this in a hackneyed way that recreated previous resurrection myths, down to the number of days before being raised from the dead, of several previous, and now long-gone religious cults—or is it more likely that those who were preaching to convert fabricated a resurrection myth in order to convince those to whom they were preaching of Christ’s divinity? Finally, the remarkable, and completely trite claim that the fact the Christians were willing to die for their beliefs demonstrates the validity of these beliefs would be laughable, if it weren’t so pitiful. Especially, as I indicated during the event, in light of the fact that people were recently willing to fly planes into skyscrapers because of their beliefs in a religious framework that I know Craig has openly disavowed. Throughout history people have been willing to die for their beliefs, and it is often the beliefs one is willing to die for that are most suspect. Did Roman soldiers believe in Romulus and Remus. Did Viking warriers believe in Thor. Did Nazi soldiers believe in the superiority of the Aryan race. I found and still find Craig’s statement not only facile, and not even worthy of a high school debater, but I find the claim offensive.

FineTuning: The appearance of design is one of the most subtle and confusing aspects of our Universe. Charles Darwin, with his Origin of the Species, brilliantly and masterfully explained how the modern world, with its remarkable diversity of life forms may have the appearance of design without any design at all. It was one of the greatest and most striking scientific discoveries of all time, and it is the basis of modern biology and medicine, leading to countless other discoveries that have continued to save countless lives. Craig is aware, from his superficial reading of cosmology, of fine tuning problems in Cosmology, which he then immediately argued requires the existence of intelligent life, implying purpose to the universe. Not only does he fall prey to the same fallacy that those who, before Darwin enlightened us, ascribed design in biology fall prey to, he also continually misrepresented the nature of any apparent fine-tuning of quantities that we currently may not understand from first principles. I tried to explain to him that the current entropy of the universe is not fine tuned, nor need the initial entropy be fine tuned, because Inflation provides a mechanism to wipe out initial conditions and produce huge amounts of entropy, without God. I tried to explain to him that the Cosmological Constant, which is perhaps the most confusing finely tuned parameter we know of in the Universe, is fine tuned in a mathematical sense, compared to the naïve value we might expect on the basis of our current understanding of physical theory. While it is also true that if it were much larger, galaxies would not form, and therefore life forms that survive on solar power would not be likely to form with any significant abundance in the universe, I also explained that if the Cosmological Constant were in fact zero, which is what most theorists had predicted in advance, the conditions for life would be, if anything, more favorable, for the development and persistence of life in the cosmos. Finally, even if some parameters in our currently incomplete model of the universe do appear fine tuned for human life to be possible, (a) we have no idea if other values would allow other non-human-like intelligent life forms to evolve, since we have no understanding of the locus of all possible intelligent life forms. And, beyond this, just as bees are fine tuned to see the colors of flowers which they can pollinate as they go about their business does not indicate design, but rather natural selection, we currently have no idea if the conditions of our universe represent a kind of cosmic natural selection. If there are many universes, for example, as may be the case, and as are predicted in a variety of models, none of which were developed to address God issues, we would certainly expect to find ourselves only in those in which we can live. All of these are subtle and interesting issues worthy of discussion by knowledgeable and honest intellects. I found Craig to be lacking in both of the qualities during his discussion of this issue.

Absolute Morals: Craig argued that the existence of absolute morality gives evidence for God. Once again this is simple minded. Indeed in a meeting we convened at my Origins Project of distinguished philosophers and neuroscientists we debated the subtle issues of morality and human evolution, the possible variants of morality, and a host of other issues, without once ever resorting to God. As I tried to explain to Craig, paraphrasing fro Steven Pinker, if there were a God, either God would have the choice to determine what is right and wrong or not. But in this case, if God determined that raping and murdering 2 year-olds is morally acceptable would it be so? If not, as reason and experience suggests, then God really has to resort to other considerations, kindness, compassion, etc (except for the Old Testament God!), on which to base God’s decisions. But if that is the case, why not just dispense with the middle-man? Lastly, if there is evidence that God provides absolute Morality, it is missing from the world of our experience, where different religious groups, all of whom claim divine inspiration, have incompatible moral views, often leading to horrendous and violent acts against women and children, for example. Indeed, the Old Testament is full of such acts.

Contingency: Frankly the argument that humans or the universe do not have to exist but they do as providing evidence for God is something I find unfounded, so I will not devote any more words here to this subject. Many ‘contingent’ phenomena occur by natural causes, from earthquakes to snowflakes and I do not have to invoke God’s will to explain them. What applies to earthquakes and snowflakes applies to the Universe. Just because I cannot yet explain the origin of the Universe does not imply the existence of God…again God of the Gaps.

Our Universe had a beginning, therefore God must have created it: Actually the issue of the beginning of the Universe is the only truly interesting question worth discussing here. A host of scientific arguments need to be discussed here, and there is no doubt the question of chicken and egg is a vexing one for cosmologists as well as theologians. However, let me make a few points here: (1) All things that begin may have a cause, even if the cause is rather obscure and purposeless. However, what is important to note is that every known physical effect whose cause we understand has a physical cause. There is no reason therefore to assume the same will not be true of our universe itself. (2) There are no arguments that our universe need be unique and not derived from something pre-existing, or even eternal. Indeed, the Ekpyrotic Universe promoted by Turok and Steinhardt, which I don’t find compelling, argues for potentially eternal periods of expansion and contraction. Craig doesn’t understand the physics. (2) I continued to try and explain that quantum gravity may imply that space and time themselves are created at the moment of the big bang. This is a rather remarkable statement if true. But if it is true, in the absence of time itself, how one can ascribe arguments based on causality is unclear at best.

This last point illustrates what I tried hardest to explain. Classical human reason, defined in terms of common sense notions following from our own myopic experience of reality is not sufficient to discern the workings of the Universe. If time begins at the big bang, then we will have to re-explore what we mean by causality, just as the fact that electrons can be in two places at the same time doing two different things at the same time as long as we are not measuring them is completely nonsensical, but true, and has required rethinking what we mean by particles. Similar arguments by the way imply that we often need to rethink what we actually mean by ‘nothing’, from empty space, to the absence of space itself.

What I hoped I could convey to the truly open minded intellects in the audience, of which of course Craig was not one, was that the amazing effort to understand how the universe works reveals wonders far more remarkable than those presented by Bronze age myths, developed before we had any clear understanding of how the universe works. Simply arguing that one doesn’t understand the results, or doesn’t like the results and therefore one has to resort to supernatural explanations, which was the crux of Craig’s rather monotonous repetition of his syllogisms, is indeed intellectually lazy, as I did say at the time.

I have taken great effort to describe our actual understanding of the Universe and its implications for understanding how it might be possible for something to come from nothing, i.e. non-existence, in my new book, which will come out in January of 2012.

Your Thoughts?

According to Leibniz, God selects our universe for actualization because God knows that it is the best of all possible universes. But how does God know that? It’s not sufficient to say that God just knows it. God’s knowledge of the best universe requires an explanation. And Leibniz gives one: God runs a search algorithm. The search algorithm starts with a sorting algorithm. God compares possible universes with respect to goodness:

The infinity of possibles, however great it may be, is no greater than that of the wisdom of God, who knows all possibles. . . . The wisdom of God, not content with embracing all the possibles, penetrates them, compares them, weighs them one against the other, to estimate their degrees of perfection or imperfection, the strong and the weak, the good and the evil. It goes even beyond the finite combinations, it makes of them an infinity of infinities, that is to say, an infinity of possible sequences of the universe, each of which contains an infinity of creatures. By this means the divine Wisdom distributes all the possibles it had already contemplated separately, into so many universal systems which it further compares the one with the other. The result of all these comparisons and deliberations is the choice of the best from among all these possible systems. (Leibniz, Theodicy, sec. 225)

The output of this sorting algorithm is an ordered series of equivalence classes of universes. All universes in the same class are equally good. Leibniz uses an architectural metaphor to illustrate the output of the sorting algorithm. The totality of possible universes is like a library. The library is organized into levels. Each level is an equivalence class of possible universes. Higher levels of the library have better universes. Leibniz refers to the library as the Palace of the Fates. Leibniz describes this Palace in a story in which the goddess Athena takes a priest Theodorus for a tour of the mind of God:

You see here the Palace of the Fates . . . Here are representations not only of that which happens but also of all that which is possible. God, having surveyed them before the beginning of the actual universe, classified the possibilities into universes, and chose the best of all. . . . These possible universes are all here, that is, as ideas [in the mind of God] . . . . They went into other rooms, and always they saw new universes. The halls of the Palace rose in a pyramid, becoming even more beautiful as one mounted towards the apex, and representing more beautiful universes. Finally they reached the highest hall which was the most beautiful universe of all: for the pyramid had a beginning, but one could not see its end; it had an apex, but no base; it went on increasing to infinity. That is because among an endless number of possible universes, there is the best of all . . . but there is not any one which has not also less perfect universes below it: that is why the pyramid goes on descending to infinity. (Leibniz, Theodicy, secs. 414-417).

According to this Leibnizian story, the divine designer runs a search algorithm that involves two steps: first, it sorts the universes; second, it actualizes the universe that comes out on top in the sort. But if that’s all the divine designer does, then it isn’t God. All the design arguments show is that there is some computer running a trivial search algorithm. The computer is not a person; it isn’t conscious; it doesn’t have free will. It isn’t God. It isn’t even any of the Gods of the Philosophers. (Or, if it is, the term “God” is so trivial that it’s not worth arguing about, not worth worshiping, not really worth much of anything.) The designer is simply an abstract mathematical machine. It converges to a solution (to a final or halting state). The solution is the universe.

Design arguments are wonderful! They justify the existence of a platonic computer that is in no way divine. Atheists ought to use design arguments against theists. Why don’t they?

The theistic version of the Fine Tuning Argument goes like this: (1) The Fine Tuning Argument is sound. (2) If the Fine Tuning Argument is sound, then there is a Tuner. (3) Therefore, there is a Tuner. (4) If the Tuner is God, then God exists. (5) The Tuner is God. (6) Consequently, God exists.

The atheistic version of the Fine Tuning Argument goes like this: (1) The Fine Tuning Argument is sound. (2) If the Fine Tuning Argument is sound, then there is a Tuner. (3) Therefore, there is a Tuner. (4) If the Tuner is not God, then God does not exist. (5) The Tuner is not God. (6) Consequently, God does not exist.

The fourth premise in the atheistic version follows from the definition of God. If God is a tuner, then God is essentially a tuner. It’s not possible for God to exist and for God to fail to be a tuner. The theist, on learning that the Tuner is not God, can’t say that God’s busy doing other things or that fine-tuning the universe falls outside of God’s job description. On the contrary, it’s part of what it means to be God.

The fifth premise is what the atheist has to justify. The atheist has to prove that the Tuner is not God. This can’t be done by just blithely saying that the Tuner might not be God. It isn’t enough to just point to some other alternative possibility. Mere possibility is not what is asked for here. The atheist has to demonstrate that the Tuner is not God.

The way to do this is to present an alternative that is clearly a better explanation for the fine tuning than God. The argument goes like this: (1) The Tuner has a feature F if and only if F is required for tuning the universe (say, for life). (2) If the Tuner were God, then the Tuner would have additional features. (3) Therefore, the Tuner is not God.

Finely-tuning universes for life doesn’t seem to be very demanding. The assumption behind all the fine tuning arguments is that tuning involves setting the values of some finite number of numerical parameters. If there are n parameters, then their value ranges are the coordinate axes of an n-dimensional space. Each point in this space has the form (v1, . . . vn). The Fine Tuning Arguments always seem to assume that these values are plugged in to some fixed system of equations E. Thus E(v1, . . . vn) is the form of some possible universe. It’s usually also assumed that the equations apply to some initial conditions. They act as an operator on the initial conditions i. Any initial condition is a member of some set of initial conditions I. So the full form of a universe is (E(v1, . . . vn))(i). This form has to be tested for life. Here’s the algorithm:

    algorithm FineTuneForLife() [
        for every point (v1, . . . vn) in the space (P1, . . . Pn) do [
            for every i in the set of initial conditions I do [
                if (the form (E(v1, . . . vn))(i) permits life),
                    then make a universe with that form;]]]

Either there is some machine (some computer) that can run the algorithm FineTuneForLife, or else there is not. If there is no such machine, then perhaps the Tuner is God. If there is such a machine, then the Tuner is not God. The Tuner is merely a computer. More precisely, the Tuner is the simplest machine that can run the algorithm FineTuneForLife.

I doubt that any finite state machine can run FineTuneForLife. I’m not sure that any Turing machine can run FineTuneForLife. But Turing Machines are not very impressive; there are far more powerful transfinite computers. The outer limits of computation are said by some mathematicians to be equivalent to the constructible hierarchy of sets (also known as L). If there are models of our physics that fall within the constructible hierarchy of sets (also known as L), then there is a machine that can run FineTuneForLife. So the atheist has to defend this claim: there are models of our physics that lie in L. And I think that’s a claim that is very easy to defend.

It’s worth pointing out that FineTuneForLife is a simple brute force search. There are almost certainly very powerful ways to optimize that search. More optimal searches usually require less powerful computers.

It’s also worth pointing out that human beings already know how to finely tune toy universes for artificial life. Small numbers of human beings, working for only a few decades, have already produced impressive software universes that contain life-like structures. So, how hard can it be to run something like FineTuneForLife? Does it really require an intellect whose power transcends that of every logically possible machine? The successes of artificial life suggest that fine tuning isn’t all that hard. If it can be done by a machine, then God does not exist.

The Effectiveness Argument goes like this: (1) Mathematics is effective in science. (2) The best explanation for this effectiveness is that physical reality is grounded in mathematical reality. (3) So, by inference to the best explanation, all physical reality, including our universe, is grounded in mathematical reality – in pure mathematics.

The second premise in the Effectiveness Argument is supported by a variety of writers. Dipert (1997: 332) argues that “the very possibility of a clear understanding of the world requires the possibility that it is a simple mathematical structure”. Steiner (1998: 4 – 5) puts it even more powerfully like this:

The strategy physicists pursued . . . to guess at the laws of nature, was a Pythagorean strategy: they used the relations between the structures and even the notations of mathematics to frame analogies and guess according to those analogies. The strategy succeeded. . . . The success of the Pythagorean strategy might lead the reader to conceptual Pythagoreanism, the view that the ultimate properties or ‘real essences’ of things are none other than the mathematical structures and their relations. More radically, one might adopt metaphysical Pythagoreanism, which simply identifies the Universe or the things in it with mathematical objects or structures. (Some physicists write as though an elementary particle just ‘is’ an irreducible group representation, or even that the entire universe is.)

Steiner (1998: ch. 4) brilliantly discusses many examples in which the pythagorean strategy of identifying physical things with mathematical things is successful. His cases include: Maxwell’s study of electromagnetism; Schroedinger’s study of wave mechanics; Dirac’s study of the positron; Schwarzschild’s solution for the equations of general relativity (i.e. black holes); Heisenberg’s study of the symmetries of nucleons; Kemmer’s study of pions; Gell-Mann’s and Ne’eman’s study of particle systems with unitary spin and the consequent discovery of quarks; Einstein’s inference of the field equations for general relativity; the Heisenberg-Born-Jordan derivation of matrix mechanics; Schroedinger’s derivation of the Klein-Gordon equation; the derivation of the Yang-Mills equation; the study of analytic continuations in crossing symmetries.

As a continuation of Steiner’s reasoning, Tegmark (1998: 44) says: “the usefulness of mathematics for describing the physical world is a natural consequence of the fact that the latter is a mathematical structure.” Accordingly, Tegmark (1998: 46-47) simply collapses the distinction between mathematical and physical existence:

One might say that wherever there is light, there are associated ripples in the electromagnetic field. But the modern view is that light is the ripples. One might say that wherever there is matter, there are associated ripples in the metric known as curvature. But Eddington’s view is that matter is the ripples. One might say that wherever there is physical existence, there is an associated mathematical structure. But according to our TOE [theory of everything], physical existence is mathematical existence. (The italics are Tegmark’s.)

Dipert, R. (1997) The mathematical structure of the world: The world as graph. Journal of Philosophy 94 (7), 329-358.

Steiner, M. (1998) The Applicability of Mathematics as a Philosophical Problem. Cambridge, MA: Harvard University Press.

Tegmark, M. (1998) Is ‘the Theory of Everything’ merely the ultimate ensemble theory? Annals of Physics 270, 1-51.

Wigner, E. (1960) The unreasonable effectiveness of mathematics in the natural sciences. Communications on Pure and Applied Mathematics 13, 1-14.

The ground doesn’t even come close to matching any of the descriptions of any of the gods of mythology or even philosophy. So it’s hard to see why affirming the existence of the ground would be offensive to atheists. And yet, looking at the various responses to my last post, it seems that many atheists object. Why?

The ground is not mysterious. Leibniz has given us a great deal of information about it. First, it exists necessarily. Second, the very fact that the ground is not involved in physical relations is informative. To say that the ground is not involved in physics means that the ground is an abstract object. Abstract objects are objects that don’t participate in any spatial, temporal, or causal relations. Mathematical objects are abstract.

Mathematical objects include things like sets, numbers, vectors, functions, and so forth. If mathematical objects exist, then they aren’t physical. And, just to be clear, they aren’t concepts. Numbers aren’t things in your brain. There are infinitely many numbers; but you don’t have infinitely many things in your brain. If numbers exist, then they have an entirely objective existence that doesn’t depend on you or your thoughts at all. If you think math is all in your head, then you can’t do math.

Mathematical objects obviously play roles in science (especially in basic physics, which is intensely mathematical). The Quine-Putnam Indispensability argument says that since mathematical objects are needed for science, they exist. If you believe in quarks and gravity, you ought to believe in math. If there are no numbers, what sense would it make to use equations to describe the physical world? And, of course, you can’t just say you believe in some mathematical objects and not others. You get the whole system or none of it. And, looking back to Leibniz, mathematical objects exist necessarily.

These ideas about mathematics are known in metaphysics as platonism. Platonists affirm the objective reality of a world of mathematical entities. And, even though we can’t see or touch mathematical objects, we obviously know a lot about them. Indeed, math is the most stable and enduring part of human knowledge. Math involves proof – everything else is uncertain. Of course, platonism, like every part of philosophy, is controversial. But platonism comes with enormous benefits. Why not use them?

You can use platonism to complete Leibniz’s Sufficient Reason Argument. The following logic justifies the thesis that the ground is a mathematical object: our universe is mathematically structured; the best explanation for the mathematical structure of our universe is that it is generated by a mathematical object. It’s reasonable to believe the best explanation. Accordingly, there is some mathematical object that generates our universe. And that object is the ground.

How could the ground be a mathematical object? What does that even mean? To start to answer this question, consider a cellular automaton like the game of life. Such cellular automata can have incredibly rich physical content. Any instantaneous stage of some game of life can be encoded in a bit string – a sequence of 0s and 1s. Another way of putting this is to say that the stage supervenes on the bit string. A game of life is a series of stages; so any game of life supervenes on a series of bit strings. The bit strings aren’t arbitrary. They are generated by the iteration of a function which encodes the causal laws for the game of life. The function is Turing-computable. So every game of life supervenes on a sequence of bit strings generated by the iteration of an abstract Turing machine. The abstract Turing machine is itself just a function from numbers to numbers.

Many writers have thought hard about the possibility that our universe supervenes on the iterations of some abstract Turing machine. This is the computable universe hypothesis. (See, for instance, the work of Ed Fredkin or Jurgen Scmidhuber). I suspect our universe is too complex to supervene on the iterations of a Turing machine. But there are far more complex abstract machines. So the hypothesis that the ground is a kind of mathematical object is perfectly intelligible.

It’s easy to see why a theist might object to the mathematical ground – it directly competes with the theistic god! If the mathematical ground exists, then the theistic god doesn’t exist (or at the very least, that god is cosmologically unemployed).

Should atheists object to the mathematical ground? If so, why? Platonism gives atheists an enormously powerful metaphysics – a world of abstract, eternal, transcendental, necessary objects. But none of them are gods. And that world is knowable by reason (it’s the very peak of rationality). You’d expect atheists to embrace that.

So I’m wondering: can atheists do math?

These first cause arguments are debates about the structure of contingent physical existence. It’s fun to reason backwards in time along causal chains, but that reasoning remains entirely within the system of contingent physical things. The deeper questions are these: Why is there a universe rather than no universe? Why are there any physical things rather than no physical things? Why are there any contingent things rather than no contingent things? No first cause argument (or atheistic reply) even tries to answer those questions.

Aquinas’s Third Way and Leibniz’s Sufficient Reason Argument are much deeper arguments. Theists and atheists both ought to study them carefully. Leibniz’s Sufficient Reason Argument is especially interesting. Here it is:

(1) Neither in any single thing, nor in the total aggregate and series of things, can the sufficient reason for their existence be discovered. (2) Let us suppose a book entitled The Elements of Geometry to have existed eternally, one edition having always been copied from the preceding. (3) Although you can account for the present copy by a reference to the past copy which it reproduces, yet, however far back you go in this series of reproductions, you can never arrive at a complete explanation; (4) You always will have to ask why at all times these books have existed, that is, why there have been any books at all and why this book in particular. (5) What is true concerning these books is equally true concerning the diverse states of the universe, for here too the following state is in some way a copy of the preceding one (although changing according to certain laws). (6) However far you turn back to antecedent states, you will never discover in any or all of these states the full reason why there is a universe rather than no universe, nor why it is such as it is. (7) You may well suppose the universe to be eternal; yet what you thus posit is nothing but the succession of its states, and you will not find the sufficient reason in any one of them, nor will you get any nearer to accounting rationally for the universe by taking any number of them together; (8) The reason must therefore be sought elsewhere. (9) Things eternal may have no cause of existence, yet a reason for their existence must be conceived. . . . (10) Hence it is evident that even by supposing the universe to be eternal, the recourse to an ultimate reason for the universe beyond this universe . . . cannot be avoided. (11) The reasons for the universe are therefore concealed in some entity not in the universe, which is different from the chain or series of things, the aggregate of which constitutes the universe. (Leibniz, 1697)

As it stands, this argument has some well-known problems (it isn’t really even an argument, it’s just a proto-argument). But the argument can be rebuilt in ways that make it incredibly strong. Rebuilding it is mostly tedious logic. There’s no need to do that here. I’m going to assume that some rebuilt version of the argument is sound. What’s most interesting about this argument is what it says about existence.

Leibniz says the universe is the totality of physical things. It’s a spatially, temporally, and causally closed system. The entire universe is contingent – it might exist but it might not exist. Why does it exist? Why is there a universe at all? You can’t answer that question by appealing to anything that is internal to the universe. You can’t answer that question by appealing to any entity that participates in any spatial, temporal, or causal relations. This isn’t an inference back in time to a first cause. If there is a first cause, then it falls within the scope of the question. If there’s a first cause, it’s just another part of the universe – and thus it needs to be explained. And Leibniz is perfectly happy to say that the universe has always existed – no first cause at all. Leibniz says that “the reasons for the universe are concealed in some entity not in the universe”. Call this entity the ground.

Contrary to theists, the ground isn’t any concrete god. It isn’t the god of the Old Testament. It isn’t the creator of Genesis. It isn’t Yahweh or El-Elyon. And it isn’t any of the gods that have appeared in any of the mythologies of old paganisms. It isn’t Zeus or Thor. All those old gods are just concrete physical things – they participate in spatial, temporal, and causal relations. And since creation seems to entail causing an effect at some time, the ground isn’t a creator at all. For the theists, it just gets worse. Since the ground doesn’t participate in spatial, temporal, or causal relations, it can’t be a person. The ground doesn’t have any psychology. The ground doesn’t perceive the universe or intervene in it. The doesn’t have any thoughts, no beliefs, no desires. And the ground isn’t the god of deism. After all, that god is a first cause. The ground is deeper than all those gods.

What about the gods of the philosophers? Well, the ground exists. So it can’t be Plato’s form of the good; it isn’t the One of Plotinus. All those old philosophical gods are somehow beyond existence. And the ground isn’t Tillich’s ground of all being; on the contrary, it’s just the ground of the physicality of our universe. What about Spinoza’s god? I have to confess that I don’t entirely understand what that god is supposed to be – which makes me doubt that it’s Spinoza’s god. Anyway, the argument from evil entails that the ground certainly isn’t all-powerful and all-good and all-knowing. So the ground can’t be the big 3O god of classical theism. Leibniz’s argument doesn’t seem to support theism at all.

Onwards, then, to the atheists. Assuming that the ground isn’t one of those old-fashioned religious or theological entities, what would it be? Well, the ground isn’t any physical thing or structure or event. The ground isn’t the big bang or the cause of the big bang. It isn’t space-time or some quantum field or some black hole or any other exotic physical thing. It isn’t any physical thing at all. It’s important to understand the scope of this assertion.

It may very well be true that our observable cosmos, including everything that we can measure or empirically detect, is a simulation running on some alien super-computer. But if that’s true, then our observable cosmos isn’t the universe – it’s just the part of the universe that we can observe. The whole universe is a much bigger place. If our universe is running on some alien super-computer, then the Leibnizian question applies to that super-computer and to the aliens that made it. Why do those contingent physical things exist? The ground isn’t the super-computer or the alien civilization. The ground explains the aliens and their artifacts. Perhaps our universe contains many smaller cosmic domains (as in inflationary cosmology, or Smolin’s fecund universe hypothesis). If it does, then that entire multiverse is a contingent thing. Why is there a multiverse rather than no multiverse? The multiverse needs to be explained. If our universe is a big foam composed of lots of cosmic bubbles, then the ground explains that foam.

Given all this metaphysics, here’s the test question: Should atheists affirm or deny the existence of the ground?

Leibniz, G. W. (1697) On the Radical Origination of the Universe. In P. Schrecker & A. M. Schrecker (Trans.) (1988) Leibniz: Monadology and Other Philosophical Essays. New York: Macmillan, 84-86. The translation is slightly edited for consistency.

The theists say: (1) If the reasoning in the cosmological argument is correct, then God exists. (2) The reasoning in the cosmological argument is correct. (3) Therefore, the argument proves that God exists.

The atheists say: (1) If the reasoning in the cosmological argument is correct, then God exists. (2) The reasoning in the cosmological argument is not correct. (3) Therefore, the argument fails to prove that God exists.

Atheists and theists both agree on the major premise: if the reasoning in the cosmological argument is correct, then God exists. Why the agreement? Why grant that the cosmological argument is an argument for God? Sometimes atheists do point out that it might not be an argument for God – it might be an argument for something else. But I’ve never seen that possibility seriously explored. And it’s too bad.

On the one hand, atheists can attack theism by showing that the classical arguments for God are logically flawed. On the other hand, atheists can attack theism by showing that those very same arguments are arguments for things that are not God. Which attack is deeper?

I think it’s clear that the second line of attack is much deeper – it’s much, much more threatening. When your enemies attack your arguments, well, you can always deal with that. But when your own arguments turn against you, you’re in big trouble.

So I’m going to encourage atheists to look at the classical arguments to see what else they might be used for. Fix them up, make them all shiny, and use them to drive to some new place. For an illustration, stay tuned . . .