Wednesday, October 8, 2014

Another argument from Mersenne

In The Impiety of Deists, etc., Mersenne also gives this theistic argument:

And if there is no God, no independent being, it would be impossible that one exist, and thus our imagination would exceed all the beings of the word: and the being of our thoughts and our fantasies [phantasies] would infinitely exceed all real beings, and what would be imaginary would surpass the true, which cannot be. (p. 75)

There are a couple of interesting things. First, often Leibniz gets credited with noticing that if God possibly exists, then God actually exists. But here we see Mersenne claiming the contrapositive, almost two decades before Descartes' Meditations (in an objection to Descartes' Meditations, Mersenne also makes the point in the Leibniz form).

Second, we get an interesting argument:

  1. If God doesn't exist, our imagination exceeds reality.
  2. Our imagination does not exceed reality.
  3. So, God exists.
We can also replace "exceed(s)" with "infinitely exceed(s)", which makes (2) even more plausible and (1) is still true. There are obvious connections between this and Descartes' infinity argument in the Meditations.

When thinking about this argument, I was initially puzzled why Mersenne starts the argument by arguing that if there is no God then the existence of God is impossible. After all, (1)-(3) doesn't seem to require the impossibility of God, just the non-actuality of God. My tentative interpretation is that Mersenne has in mind a fairly strong notion of "exceeds". Possibility has a certain foot in reality, and so for imagination to fully exceed reality, one would have to not only imagine something greater than what actually exists, but greater than what is possible. Now, God is greater than all non-divine possibilities. So if God is impossible, then the content of our thoughts outruns not just actuality but possibility, and that's what makes that content strongly outrun reality.

If this is right, then we can expand the argument as follows:

  1. If God doesn't exist, it is impossible for God to exist. (Premise)
  2. God is greater than all possibilities and actualities other than God. (Premise)
  3. We can think of God. (Premise)
  4. We cannot think of anything that exceeds all actualities and possibilities.
  5. God doesn't exist. (Supposition for reductio)
  6. God is not a possibility or actuality. (4 and 8)
  7. We can think of something that exceeds all actualities and possibilities. (5, 6 and 9)
  8. Contradiction! (7 and 10)
  9. So, God exists. (By reductio)

Finally, it is rather interesting how Mersenne argues for the thesis if God doesn't exist, he can't exist. In the context of another argument, he says:

He isn't a being, as we supposed, he can't exist: since who would make him, and who would give him being [qui luy donneroit estre]? (p. 119)
My first thought on this was that Mersenne subscribes to the causal theory of possibility that I've defended. My second thought, however, was that his argument may be broader. The "who would give him being?" rhetorical question may work on any view on which possibility is grounded in actuality given the plausibility that God's possibility couldn't be grounded in anything other than himself, or else he wouldn't truly be an independent being (and notice the focus on independence in the first Mersenne quote).

By the way, while I am relying on my own translations in the above (partly for fun), professional translations can be found here.


Heath White said...

I have no idea what Mersenne was thinking but my first guess was that he had read his Anselm. There, he learned that the idea of God is the idea of a being that exists both in reality and in the understanding ("imagination"). So if God does not exist in reality, then in fact we cannot even have the idea of God, since that is the idea of a really existing being. And if what we can have an idea of is a good guide to what is possible (as your typical French rationalist will hold) then if God is not actual, he is not even possible.

But it may (and probably more likely) be the "independence" line of reasoning you mention. God is by definition uncaused and eternal. If there is no such being to start with, so to speak, then there is no way to produce him later.

Alexander R Pruss said...

By the way, both my independence-based suggestion and the Anselm-based suggestion run need to explain why he doesn't doesn't give any argument when he first makes the claim on page 75 that "if there is no God, no independent being, it would be impossible that one exist". He does have Anselm's argument as a wholly separate argument quite some distance later (p. 114), and then a couple of pages even later, in the context of yet another argument, he gives the causal argument I cited.


I just read his discussion of Anselm's argument. He doesn't connect it with his remark that if God doesn't exist, he can't exist.

By the way, all in all, this is interesting when connected with Mersenne's later criticism of Descartes' ontological argument. There Mersenne will say that Descartes only proved that if God is possible, God exists. But in this earlier book, Mersenne is quite willing to endorse Anselm's argument. Either he changed his mind, or his criticism of Descartes is only meant to prompt Descartes to strengthen the argument rather than being a dissent from it.

Mike Almeida said...

I don't understand either (2) or (7). Why is it supposed to be true that we cannot imagine anything that is greater than any possible thing? And even supposing we cannot (maybe because we lack the faculty), how could that cognitive limitation figure in a proof that God exists?

I incidentally had the same thought as Heath here. It looks like he had Anselm in mind.

Alexander R Pruss said...

My best guess as to the justification of (2) and (7) is implicitly something like the idea we get in the Meditations that all the objective reality in our ideas must come from things that have at least as much formal reality, actually or eminently.

In fact, I think Mersenne can do slightly better than Descartes. Whereas Descartes needs the principle:
(*) For every idea J, there is a cause C such that C formally has at least as much reality as J has objectively,
Mersenne's argument may only need:
(**) For every idea J, there is a cause C such that J does not have infinitely more reality than C.

Descartes' argument presupposes the scholastic principle that the amount of reality cannot rise between cause and effect. A lot of people find this hard to reconcile with evolution. Mersenne's version only presupposes that the amount of reality cannot rise infinitely, which is fully compatible with finite rises like one gets in evolution.

Alexander R Pruss said...

Eventually, Mersenne will criticize Descartes' argument, specifically citing spontaneous generation as a possible counterexample.

I am now inclining to think that Mersenne's later criticisms of Descartes are meant to provoke his friend to strengthen the argument rather than to refute the argument conclusively. They are more like criticisms we write on a paper that we basically agree with.

It could also, however, be that the causal noninferiority principle that Descartes uses is false, but Mersenne's implicit infinitely weaker version is true.

Ale Mor said...
This comment has been removed by the author.
Ale Mor said...

Yeah, if I was an atheist, I´d argue (6) is false. I am wondering what Pruss means by imagine, though.
Going back and forth on it. I was wondering why (4),(8),(9) were necessary for the argument. Seems to me that the correct (10') is : we can think of something that exceeds all possibilities and actualities other than the concept of God, and of the concept of God which is not actual nor possible. If I am right the last bit is not a concept that exceeds all actualities and possibilities , it is just a concept that is not actual nor possible , just like an square circle.

(10') we can think of something that exceeds all possibilities and actualities other than the concept of God, and of the concept of God which is not actual nor possible does not seem to be equialent to (10) We can think of something that exceeds all actualities and possibilities. (5, 6, and 9)

Alexander R Pruss said...

If I'm an atheist, then I believe that there is no God. In doing so, I had better be thinking of God (namely, that he doesn't exist). So maybe an agnostic could deny 6, but an atheist can't.