Tuesday, June 17, 2008

Did God create all things?

Vlastimil Vohanka has drawn my attention to an article by the American theologian William Lane Craig, which deserves a separate post. Craig, despite the fact he tends to include rather creepy-looking pictures of himself in his published work, is an admirable writer, who generally manages the trick that is essential to good philosophy, of being both clear and difficult at the same time. Here, he raises the question of whether numbers could have been created by God. He says that Christian theology requires us to say that everything that exists apart from God was created by God (John 1:3). But numbers, if they exist, are necessary beings. They thus would seem to exist independently of God. And (simplifying his point somewhat) the number 3 must have existed prior to God’s creating the number 3, which is impossible! "I remember the sense of panic that I felt in my breast when I first heard this objection raised at a philosophy conference in Milwaukee. It seemed to be an absolutely decisive refutation of theism. I didn’t see any way out."

First of all, I'm not sure this raises any genuinely theological issues. Craig should have read Augustine, who says (On the Literal Exposition of Genesis IV, c. 7) 'Six is a perfect number, not because God completed all things in six days, but rather, conversely, the reason God completed things in six days, was because that number is perfect, which would be perfect even if those things did not exist'. Moreover the second part of the verse from John which Craig quotes ("Through him all things were made; without him nothing was made that has been made") leaves open the possibility that there are some things which weren't made or created at all.

In any case, the solution that Craig comes up with does not do the trick. His solution is to propose some half-way house between being a thing of any sort whatever, and being a thing to which we are 'ontologically committed' (a favourite expression of his). Thus he agrees that we can 'quantify over' numbers, i.e. admit that there are such things as numbers, but not admit that numbers 'really exist', or that we are 'ontologically committed' to them.

There is a lot I could say about this, including how this is a good example of how pretensions to formal logic completely obscure something that should be quite simple. Here, I will briefly note that this manoeuvre does not resolve the difficulty at all. The first part of John's verse says nothing about real existence, or about 'ontological commitment'. It simply says 'God created all things'. Whether we are ontologically committed to numbers or not, whether they 'really exist' or not, Craig agrees that numbers are things, i.e. that some things (perhaps things that are fictional, or which don't really exist in any strong sense) are numbers. In which case, it logically follows that God created numbers.

Ironically, he says that "The existential quantifier simply serves to facilitate logical inferences." Quite. But then logical inference is what guarantees the move from 'God created all things, and some things are numbers' to 'God created numbers', and that is precisely the inference that creates his problem.

Note that Craig mentions a book by Jody Azzouni, Deflating Existential Consequence: A Case for Nominalism which I mean to read one day, and which will deserve a post or two when I have.

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12 Comments:

Blogger David Brightly said...

I don't follow entirely. I can accept your point that some things may not be made at all, but then you say that Craig agrees that numbers are things. I'm not sure that he does. Most of the article seems to be a rejection of Quine's argument that we are somehow obliged to accept the existence of (some) mathematical objects. In particular, he comes round to favouring a Fictionalist understanding of mathematics, whereby the number 3, just like Sherlock Holmes, is no thing at all. Or, as you yourself put it: As for 'Sherlock Holmes', it refers to nothing.

3:30 pm  
Blogger Ocham said...

I wondered at the time whether this might be a confusion, which was why I added the brief qualification/explanation just after. Craig agrees that some things are numbers in the 'quantifier sense'.

But why can't we read John 1:3 in the quantifier sense also?

If you argue that John 1:3 is to be read in the sense of 'things' meaning 'physical things' (and there is such a sense, surely), then there is no problem to begin with, and Craig's convoluted argument is unnecessary.

If, on the other hand, John 1:3 is to be read in the quantifier sense then we have

(x) God made x

and if we agree with Craig that we can quantify over numbers:

(E x) number(x)

which means there is still a problem. Either Craig's solution is unnecessary, or it doesn't work.

5:41 pm  
Blogger Ocham said...

Sorry, as usual I miss your second point. Sure, Craig also argues for a 'Fictionalist' understanding of mathematics, but this still misses the point. He either agrees that

(A) for some x, x is a number

is true or not. And he maintains that no number is created, i.e.

(B) (x) x is a number implies x is uncreated.

and John 1:3 says

(C) (x) God created x

Contradiction.

5:47 pm  
Blogger Vlastimil Vohánka said...

O,

Neither I follow.

Concerning Yablo's position, Craig wites,
"When a speaker uses figurative language, the literal content is not what the speaker is asserting. There is what Yablo calls a “real content” to figurative statements which may well be true. This is not to say that figurative statements can always be successfully paraphrased into expressions of their real content. Numbers may be indispensable as representational aids for the expression of the real content of mathematical language."

Consider:
There are over five Es | the number of Es

To slightly paraphrase Craig, according to Yablo, we simulate belief, perhaps quite unconsciously, that the number of Es exists, but it is a mere figure of speech which is a vehicle of the real content.

So, it seems to me, according to Craig it is not clear that "(E x) number(x)", even if true, implies "some number is a thing".

10:43 am  
Blogger David Brightly said...

Again, I'm not convinced that Craig does agree that some things are numbers in the 'quantifier sense'. Couldn't a Fictionalist reasonably claim that

(E x) number(x) & ...x....

could be rephrased (Craig says 'nominalised') to remove the apparent quantification over number objects?

In my comment I rather ignored your qualification on Craig agrees that numbers are things, as this confused rather than clarified the issue for me. Isn't this using 'thing' in a very loose way indeed, as when we might say that Sherlock Holmes is a fictional thing but that 'Sherlock Holmes' does not refer? And doesn't it drive a wedge between thing-hood and existence, which I took you to see as equivalent?

3:46 pm  
Blogger Ocham said...

It was a clear mistake to use the English word 'thing', as this has two distinct senses: a 'quantifier' sense in which we speak of 'anything you like', for which Latin has the word 'aliquid' or 'quodlibet', and a more heavy-duty sense in which we mean usually a physical or material or real thing, for which Latin uses the word 'res', from which we get the word 'reality' and 'real'.

To be clear, I meant that Craig agrees (at least in much of his argument) that numbers are things in the 'quantifier' sense, i.e. he would agree that

Ex x = 4, i.e. some x is a number

But he hopes to deflect this by not treating the word thing in 'God created all things' in the same sense. This seems arbitrary. How do we know that John meant just physical or real things, and not absolutely anything you like? If we are allowed to choose what John was quantifying over, there is no problem at all, and Craig's convoluted explanation is unnecessary. But if we can't, then the problem remains.

5:09 pm  
Blogger Vlastimil Vohánka said...

O,

As I understand Craig, according to him: It is not true that some number is a physical thing. It is not true that some number is a material thing. It is not true that some number is a real thing.

But it seems to me that according to Craig it is not clear that some number is a thing (i.e., something, a genuine object, though not necessarily a physical, material or real object) in any sense. Craigs does not explicitly rule out the option that numbers are NOT even intentional objects. But, of course, according to Craig it IS clear that we use figures of speech like "(E x) number(x)", "(E x) number(x) & ... x ..." , "the number of Es is n", etc.


David,

I don't think Craig asserts that it is reasonable that

(E x) number(x) & ...x....

could be rephrased to remove the apparent quantification over number objects. He seems to me to be agnostic about that. He also does not prefer Fictionalism over Yablo's Figuralism. To quote the already cited passage again: "When a speaker uses figurative language, the literal content is not what the speaker is asserting. There is what Yablo calls a “real content” to figurative statements which may well be true. This is not to say that figurative statements can always be successfully paraphrased into expressions of their real content. Numbers may be indispensable as representational aids for the expression of the real content of mathematical language."

11:36 am  
Blogger Ocham said...

>>But, of course, according to Craig it IS clear that we use figures of speech like "(E x) number(x)", "(E x) number(x) & ... x ..." , "the number of Es is n", etc.

Correct. And my point is simply that

A. (E x) number(x)

B. (x) number(x) implies not created(x)

C. (x) God created x

is inconsistent. All the stuff about whether or not numbers are material or immaterial, intentional or non-intentional, real or not, is completely irrelevant.

I take your point (in reply to David) that Craig may not hold that (A) is true, and that it is 'figurative' in some sense. But that is very vague, and it is entirely unclear what the real 'literal content' is.

5:52 pm  
Blogger Dominic Bnonn Tennant said...

Hi Ocham; thanks for this post—it explains what I recently heard Craig say about being a nominalist. I thought that was a very strange position for a Christian to take—at least in terms of the relationship between numbers and created things. I suspect Craig hasn't read very widely on this issue or he wouldn't feel forced into the corner he has taken. Not that I've read widely either, but I have read Greg Welty, 'An Examination of Theistic Conceptual Realism as an Alternative to Theistic Activism' (http://www.proginosko.com/welty/mphil.pdf; Oxford: 2000). I think you'd find it interesting. Basically Welty's proposal, with which I agree (this has always seemed intuitively obvious to me which is why Craig's position surprised me) is that numbers are one kind of God's own thoughts; just like properties and sets and so on. Thus, nominalism obtains at the divine level, but conceptual realism obtains at the created level. This avoids the problem you point out, which I'll reformulate:

1. ∀x God created(x) [John 1:3 etc]
2. ∃x number(x) [assumed]
3. ∀x(number(x) → ¬created(x)) [by necessity]
4. ∴∀x ¬number(x) [mt]

Thus, if a thing is created, it isn't a number; numbers aren't created things. Since I think that the arguments against nominalism are devastating while the arguments for realism are highly persuasive, this leaves only one possibility in terms of numbers' origin: they must in some way be a part of God himself. Sorry if my notation is bad, by the way; I'm not really familiar with first order predicate logic.

Incidentally, I think you legitimately observe that the Bible does not limit in any sense the things which exist which God created. Quite the opposite: the Bible states unequivocally that everything which exists exists by God's creative power; not only initially, but also continually (Hebrews 1:3; Colossians 1:17; Acts 17:28). Ie, everything which exists which is not God is contingent; therefore, existence is not inherent to it (or it would be necessary and already exist), so existence must be continually imposed on it by God. It seems to me this commits us to divine determinism.

Regards,
Bnonn

7:56 pm  
Blogger Ocham said...

Welcome to Beyond Necessity!

Thank you Dominic - some time since I made this post so forgive me if I forget what I was talking about.

You say that there are devastating arguments against nominalism and for realism.

You should know that this blog is the high fortress of nominalism, much to the annoyance of Bill Vallicella who holds the high fortress of realism.

But all visitors are welcome here, sit ye down while I pour you a glass of claret. What then are the arguments against nominalism?

Regards, and welcome again

8:45 pm  
Blogger Dominic Bnonn Tennant said...

Hi Ocham; thanks for the welcome.

You say that there are devastating arguments against nominalism and for realism.

I said I think the arguments against nominalism are devastating (: If you'll forgive me, though, I don't really have the time or personal familiarity with the topic to weigh in on that question. Certainly I'm not qualified to debate you, and I have no particular commitment to persuading you that you're in error here. I tend to choose my battles based on whether I think the error is serious—and, as far as I can see, whether a Christian should hold to nominalism is really not a pressing doctrinal question (; Of course, it occurs to me that I may well be in error in assuming that you're a Christian at all—the fact that you appeared on Triablogue and were quoting Craig here suggested it, but maybe I'm wrong?

What I've personally read on the topic has convinced me that nominalism is untenable, and I think that Christian theism plausibly entails conceptual realism; see Chad McIntosh, 'A Conceptual Argument for the Existence of God' (2008: http://www.doxazotheos.com/?p=66). In particular, I found his citation of Neil Tennant's On the Necessary Existence of Numbers quite persuasive. Anyway, if you have the time, I'd recommend that paper by Welty I linked before—even if you aren't a realist, you will probably find it interesting to see how other Christians are developing ontology in that area. Again, assuming you're a Christian...

Regards,
Bnonn

9:12 pm  
Blogger Ocham said...

Thank you I will follow the links you posted, though it is bed time here.

I'm a bit of a failed Christian. I like the whole magic of it, and I have a big thing about the Church and the Western intellectual tradition. I still go to church. But the more I read the Gospels, the creepier I find them, frankly.

On Christianity and nominalism, I was a student of the late CJF Williams, who was an English Catholic, and very much a nominalist.

10:02 pm  

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