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Atomism, Wittgenstein and God

October 17, 2013

I was recently reading Robert Fogelin’s assessment of atomism in the Tractatus Logico-Philosophicus and (strangely enough) it prompted a few ideas about the concept of God. I thought they might be worth sharing.

First of all, what do we mean by “atomism”? Fogelin sets out the basics with admirable clarity:

  1. Change (in a wide sense) is a matter of the combination and separation of constituent entities.

  2. Not everything is subject to change, for there must be an unchanging basis for change. Atoms, entities that are not the result of combination nor subject to division, constitute this unchanging basis.

  3. Combination and separation are possible because atoms exist in a void (in a space) that provides a field of possible combinations.

(Fogelin, Wittgenstein, Second Edition, p5)

A few things to note. “Atoms” here are not to be confused with atoms in physics. The atoms of physics are, of course, divisible and subject to change. But for the atomist philosopher, “atom” is the name of whatever it is that cannot be divided into parts or changed in any way. To avoid confusion (ha!) they’re often called “simples”, and I’m going to follow that convention. Anyway, the idea is that such things must exist or else how is the whole business of reality (matter, complex objects and so on) going to get off the ground?

That sounds reasonable enough, but a bit of reflection suggests that these “simples” are likely to be very strange things indeed. One oddity is that although they must exist (since they are a necessary condition of reality) it makes no sense to say either that they do exist or that they don’t. Allow me to explain.

Complex objects are made up of simples. So object “X” might be made up of two simples: a and b. It certainly makes sense to say that X exists since it’s possible that it might not have existed (ie, the simples a and b might not have been combined in the requisite way). Therefore “existence” and “non-existence” are the combination or non-combination of simples. That’s what (according to the theory) those terms mean. But if that’s true then we cannot predicate either existence nor non-existence to simples themselves. They are prior to existence and non-existence; they are what you must have in order for existence and non-existence to be possible.

Pretty weird, eh? But things can get even weirder if you decide, like a vicar in an Alan Bennett sketch, that “God’s a bit like that, isn’t he?” What I’m getting at is this: it is often claimed that God’s existence is necessary. He didn’t just turn up via a happy accident; he is a necessary pre-condition of the world itself. Indeed, the “ontological argument” infamously tries to prove this claim. There are many versions, but, roughly, it goes like this:

  1. We have the idea of a completely perfect being, ie, God.

  2. A being that exists is more perfect than one that doesn’t exist, therefore:

  3. God must exist.

Oceans of ink have been spilt trying to decide if this makes sense and, if it doesn’t (which is most people’s position), setting out exactly what’s wrong with it. Kant, for example, thought the problem was that it treats existence as a predicate – a quality that objects have or lack, in the same way that my jeans have the quality of being blue but lack the quality of being clean. But existence, he declared, is not a predicate. Frankly, no-one’s sure if Kant was right about that, but it’s probably fair to say that existence is at best a strange type of quality. (There’s no dining table in this room – does that mean that there’s a dining table here which lacks the quality of existence?)

But here’s the thing: if we assume that God is a necessary precondition of reality then, as with the atomists’ simples, it cannot make sense to say either that he exists or that he doesn’t. My chair exists, and so does Scotland and the Fibonacci number – but it only makes sense to say that because those things might not have existed. They have what we might call an “ontological status”. But God is in an altogether different category. The word “God” doesn’t refer to any type of thing; God has no ontological status and therefore the statements “God exists” and “God doesn’t exist” are both nonsense. To put it another way: if the opposite of your claim is nonsense then your claim itself is nonsense. So if God’s existence is necessary then it’s nonsense to say that he doesn’t exist and – therefore – it’s nonsense to claim that he does. Or to put it yet another way: whatever can exist can be destroyed. God cannot be destroyed therefore God cannot exist.

All this, of course, has serious implications for the ontological argument. As its very title suggests, it doesn’t hesitate to allot God an ontological status: he exists. But the argument tries to prove that he exists necessarily and so according to its own assumptions its conclusion must be nonsense. That’s not good. But might it be amended to avoid this problem? The only alternative candidate I can think of runs like this:

  1. We have the idea of a completely perfect being, ie, God.

  2. A being that exists is more perfect than one that doesn’t exist, therefore:

  3. Shut up.

That works, I think. But now let’s complicate matters by returning to Wittgenstein. In the Tractatus he adhered to a form of atomism and agreed that it was nonsense to talk of simples existing or not existing (actually, he thought it was nonsense to talk of most things – including his own philosophical theories). In his later years, however, he developed a very different approach to philosophy and had some intriguing things to say about simples. His thoughts on the matter are pretty difficult, but here’s a rough outline:

When we say “existence and non-existence involves the combination and dis-combination of simples” it seems as though we are describing a feature of the world. But in fact what we are doing is laying down a rule that defines what we mean by “existence” and “non-existence”. (I’ll leave it to you to decide if the atomist’s definition matches our everyday one regarding those words.) Now, rules are intrinsically categorical; they say things must go like this, not that. So if we mistake a rule for a description of the world then it can seem as if what we are “describing” is not just true but necessarily true. Existence must be the combination of simples, and those simples must exist. But all that really means is that we must posit the existence of simples or else we cannot have the rule. In effect, the atomist creates a strange game with language (a “language-game”, Wittgenstein would’ve called it), then presents this game as a description of the world and, in the process, makes it seem as if he’s discovered these weird entities – simples – which exist necessarily. What’s more, the rules of the game are so constituted that they create a paradox concerning existential claims about simples – they say both that simples must exist and that it’s nonsense to say they exist. (A fuller account of all this is here for anyone interested).

Now let’s try to apply these insights to God. People describe God in various ways: he’s omnipotent, omnibenevolent, exists necessarily, and so on. But are these really descriptions or are they actually rules by which we define the concept “God”? Don’t they constitute a kind of language-game which is tied in to the wider “game” of religious practices? (When I say “game” here I don’t mean to imply that the practices are trivial; I’m pointing out that they’re analogous to games insofar as they’re rule-governed. For Wittgenstein the term “language-game” covers pretty much all types of activity involving language.) Moreover, don’t the rules of the language-game concerning God generate the same kind of paradox as the one concerning the existence of simples? Following through the rules of the concept we seem to arrive at a position where God’s existence is both necessary and nonsense (as is, don’t forget, his non-existence).

Here it’s tempting to say that if the rules generate a paradox then that proves they must be wrong. But that, I think, groundlessly extrapolates the status of paradoxes from areas such as mathematics. In a mathematical language-game a paradox is usually pretty deadly, but need that be the case here? (And even in mathematics they’re not always so deadly. We’re taught at school that there’s no such thing as the square root of minus one. But in some areas of mathematics there most certainly is such a thing.) The point here is that rules are neither true nor false; they’re either established or they’re not. We either play by them or we don’t. And sometimes, it seems to me, we can accept rules even though they occasionally generate difficulties. For the ultimate “justification” of a language-game is not that all its rules operate smoothly, but that the game is played. This is linked to a comment Wittgenstein made right at the end of his life:

You must bear in mind that the language-game is so to say something unpredictable. I mean: it is not based on grounds. It is not reasonable (or unreasonable). It is there – like our life.

On Certainty, §559

Still, you might think, if the concept of God simply comes down to the rules people have established about him, doesn’t that show that it’s simply something we’ve made up? After all, the rules of the language-game are our rules. And this last point is correct. But it doesn’t just apply to language-games such as religion or chess or rugby league. It also applies to mathematics, logic and the concept of measuring length. Now, have we “just made up” mathematics?

This is not to claim that religion is as deeply woven into our lives or as ubiquitously accepted as mathematics. Atheists and Christians alike learn the multiplication tables. But the point is that just because the rules of language-games are our rules that doesn’t mean they’re all a simple matter of caprice. Some are, some aren’t. And nor does it mean that they’re all somehow “unreal”. Is the language-game of measuring things unreal? The question is: what status do we want to give to religion? Deciding that is not a matter of deciding whether it’s true or false, for a language-game is neither. It’s a matter of deciding whether or not we want to play the game.

I’ll end with a quote from Wittgenstein’s Philosophical Investigations and leave you to decide its relevance.

But mathematical truth is independent of whether human beings know it or not!” – Certainly, the propositions “Human beings believe that 2×2=4” and “2×2=4” do not have the same sense. The latter is a mathematical proposition; the other, if it makes sense at all, may perhaps mean: human beings have arrived at the mathematical proposition. […] (Is a coronation wrong? To beings different from ourselves it might look extremely odd.)

Philosophical Investigations, Part II, §348

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13 Comments
  1. Great stuff.

    “Now, have we “just made up” mathematics?”

    Of course, in RotFoM, Wittgenstein said exactly that. I can’t recall the *exact* quote, but in one of the middle parts he says not to make any mistake: mathematicians are *inventors*, not discoverers.

    • Indeed. Not every language-game is a mere matter of caprice. Sorry – I misread your comment! Glad you enjoyed the post. 🙂 And you’re right: Wittgenstein did say maths was invention not discovery. I say a bit more on that in my replies to Paul below.

  2. I love the contrast between your two blogs – one is careful and tightly argued and the other is this one 🙂 I think atomism is a pretty crazy view; it is not absolutely clear how you plausibly get it going. How do you make the jump: simples must exist “or else the whole business of reality” does not get off the ground? I am not a Tractatus expert but as far as I understand it, the initial (and not unreasonably!) assumption is that meaning must be possible and this is then taken to justify the claim that simples exist (since what anchors a meaningful proposition to reality is its reference to the simples). There are probably analogous arguments for simples that don’t arrive at them via mistaken or misleading theories of meaning, but in my view they will always be fallacious arguments. I don’t think there is anything that must exist and certainly not simples.
    On a different topic I think mathematics is as invented as man-made measurement systems or money – the fact that we use mathematics all the time does not prove that it is in some sense out there, any more than the fact that we measure lots of things and put prices on many of them proves that these things are also out there. Of course, there is a sense in which all these systems are out there – for it is hard to imagine how any group of beings could successfully function in the world we live in if they did not have something that at least vaguely looked like our systems of mathematics, measurement and money. Is pi a deep feature of reality? I suppose if we came across a highly advanced civilisation who lacked the concept of pi (or anything like it), we would be astonished, but is it literally inconceivable? And if it is conceivable, would we be right to snigger at them and say they were missing something really basic?

    • Yes, the Tractatus seems to argue from the possibility of language to the existence of simples, even though it starts with a description of its ontology. I was thinking more of Leibniz’s atomism in The Monadology. There he argues that reality is complex, it can be broken down into finer and finer elements, but the buck has to stop somewhere or else how can anything exist? Of course, he then goes on to say that the ultimate constituents of reality are souls (or monads) and that each soul contains an infinity of other souls. That’s a strange place to wind up given that he starts by wanting to defend our everyday notion of reality! I think it’s a case of “crazy name, crazy guy”.

      As for maths, I agree with you – it is an invention, not a discovery. It’s a system of rules we have developed and refined into an astonishingly complex edifice. My caveats about that were intended to ward off the suggestion that wholesale changes to the rules would be as easy as, say, changing the offside law in football. Maths is ultimately grounded in practices that are extremely important to us: sharing things out equally (or in a certain proportion), seeing who has more of something, making sure you have the right amount, and so on. Fundamentally changing mathematics (or abandoning it) would mean a profound change in the way we live.

      But, as you say, there are tribes with very little mathematics – in fact I read recently of one that apparently has no numbers whatsoever. Are they stupid? I don’t think it’s a matter of intelligence (they’re human beings, after all); it’s about how they live.

      And of course my wider point was that religion also ties into some pretty fundamental aspects of our lives. So, in a sense, it is “just” a language-game, but changing or abandoning the game might not be as easy as some people seem to think.

  3. Actually, in the spirit of this blog I am tempted to take my argument even further 🙂 As far as I know, native American Indians do not have anything like our system of mathematics, nor did they have anything like our system of classical music, but is it right to see the latter as an understandable cultural difference and the former as a failure by them to arrive at a more sophisticated understanding of reality? Who are we to tell the North American Indians that they were insufficiently in touch with reality? Aren’t we really saying that if they had wanted to do all the things we have done (sent people to the moon, caused climate change etc), then they would have needed to develop something like mathematics? But isn’t that much the same as saying that if they had wanted to produce something as wonderful as Bach’s cantatas, they would have had to develop something like our system of classical music? What we seem to be saying is: Mathematics is a fundamental feature of how we understand and interact with reality therefore anyone who does not have our system of mathematics is failing to properly get to grips with reality. Surely we are projecting our concepts/systems into reality and then saying that anyone who does it differently is either unsophisticated (polite abuse) or stupid/wrong (less polite abuse) 🙂

    • Glad you enjoy the blog, by the way – and you’re right: it’s not exactly a bastion of intellectual rigor :). The starting-point of this post was that I was struck by the similarity between the atomist’s claim that certain things exist necessarily and claims to the same effect concerning God. Moreover, they both reach the same conclusion: if something must exist then (paradoxically) it makes no sense to say it does exist. (And, no, that’s not exactly a standard, modern-day theological position – but if you go back 600 years a lot of theologians made exactly that point.) It comes to this: if you trace through the implications of the concept of God then everything you say about him must be nonsense. And that, it seems to me, means that at its heart religion (or, at least, monotheism) is not propositional. It is about how you live.

  4. Perhaps this should be our slogan: “if you don’t have a good grasp of maths, you are not in touch with reality” 🙂

  5. “But existence, he declared, is not a predicate. Frankly, no-one’s sure if Kant was right about that, […]”

    That existence is not a predicate can be seen from the simple fact that there are many languages where existence is not grammatically a predicate. That is, the verbs in the equivalents of the English “X is ” and “X is (= exists)” are two different words that are not even cognates; or being is shown by syntax, by an adverb, or whatnot, without there being any verb for it at all.

    One such language is Chinese, and the eminent British sinologist Angus Graham has a series of very interesting articles where he discusses this. In one of them he quotes the Chinese translation of the passage from Kant where he demolishes the ontological argument, and then re-translates it into English. It’s completely hilarious, because in Chinese grammar one cannot even fall into the mistake that Kant diagnoses as a mistake. Kant criticises the ontological argument for confusing three different senses of the verb “to be”, where the translation has three completely different verbs. And that there is a verb at all in the translation of the “key” sense of the three is a desperate expedient by the Chinese translator, because in colloquial Chinese there would be none.

    That the ontological argument was able to emerge at all is merely an accident of the grammatical structure of certain European languages. But it took 700 years to progress from St. Anselm (the originator of the classic form of the argument) to Kant, and another 200 years from Kant to Graham. This is truly a testament to the parochial nature of Western philosophy until very recently.

    • “X is ” above should have been “X is [adjective]”, using chevrons, but WordPress ate them and what was between them.

    • Hi Tommi – how interesting! I wasn’t being particularly serious about the ontological argument because, frankly, I don’t think it deserves it. It was never much more than a charming piece of theological propaganda. But it’s always fascinating to see how different languages can completely alter the force of an argument.

    • I recall an early first year philosophy seminar by Larry Chase at Univ Kent at Cant in early ’70’s. He wrote on the board in the style of a maths equation,
      God=Perfect being
      Perfect=Whole
      Whole=not lacking anything
      Not lacking anything=Not lacking existence
      THEREFORE God=Exists

      I think this was an intro to linguistics. It got us thinking. Later, Larry admitted most of his linguistics tricks were courtesy of Frederick Waismann, his tutor at Oxford.

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