Existence and arbitrary parameters

Suppose vague existence and vague identity are impossible. Consider cases where a seemingly insignificant difference makes a difference as to existence. For instance, imagine that a tomato plant is slowly crushed. At some point, what is there is no longer identical with the original plant. (One can run the story diachronically or modify it and run at across worlds.)

There will thus be facts that determine when exactly the tomato plant ceased to exist. Moreover, these facts seem to call out for an explanation: Why should this precise degree of crushing make the plant not exist any more?

This degree of crushing seems to be an arbitrary parameter, either a contingent or a necessary one. One reaction to such an arbitrary parameter is to reject the assumption that there is no vagueness in existence or identity. But a theist has another option: The parameter is there, but it is wisely chosen by God.

Note 1: It may seem that an Aristotelian has an answer: The plant ceases to exist when its form departs. But that only pushes the question back to: Why does this precise degree of crushing make the form depart?

Note 2: There could be an indeterministic law of nature that says that given a degree of crushing there is a chance of the tomato plant ceasing to exist. But such a law would have seemingly arbitrary parameters, too.

Not a finetuning argument

In The Impiety... (1624), as part of the 6th argument for the existence of God, Mersenne writes:

The proportion found between all the bodies of the world also shows that there is a God who has made all the universe in weight, in number and in measure: for the earth has no other ratio with the sun than 1:140, with the moon than 40:1, ... (pp. 98-99)

(I don't know off hand what the ratios are exactly meant to be; if they are ratios of volume, the moon is within 25% of the truth but the sun is off several orders of magnitude; if they are ratios of diameter, the sun is within an order of magnitude of the truth but the moon is an order of magnitude off.)

Mersenne's argument is full of such numerical (claimed) facts (the sun goes around the earth in 365.241 days, the moon traverses the Zodiac in 27 days, etc., etc.) and claims that God is needed to explain these facts. Now, I'm right now teaching on the fine-tuning argument, so I am sensitized to seeing such numbers in an argument for the existence of God. But it's striking that nowhere can I see Mersenne saying why these numbers are at all better than others, especially since surely some tuning facts seem very close at hand--surely, for instance, if the sun were much bigger or much smaller than it is, it would be too hot or too cold for life.

Mersenne explicitly insists that the numbers aren't explained by the essential natures of the objects, just before the above quote:

For the sun wouldn't be any the less the sun if it were closer or further from the earth, just as the stars could still be stars if they absented themselves from us by more than 14,000 earth radii.

Mersenne's argument seems to be a pure application of the idea that all contingent facts need explanation, and the arbitrariness of the numbers in the numerical statements seems to be cited precisely in order to show the contingency of the numerical statements. The argument suggests a strikingly strong commitment to a Principle of Sufficient Reason for contingent facts: all he needs to argue for a cosmic cause is to argue that there are contingent cosmic facts. Mersenne is confident that God has "many reasons" (as he says in the case of one of the numerical claims) for making the numbers be what they are, but these are reasons "which we aren't going to know except in Paradise" (101-102).

Mersenne's argument isn't a design argument--it doesn't advert to value-laden features that a God would have good reason to actualize. I think it's a kind of cosmological argument, but an eccentric one. Rather than arguing from generic features like motion or causation as Aquinas did, it focuses on very particular features.

The focus on these very particular features seems to have two benefits. The first is that it makes any appeal to necessity as the explanation implausible. Maybe it's necessary that there is motion, but it is incredible that it be necessary that the ratio of the diameter of the earth to that of the moon have to be 3.665:1 (to use modern numbers). So we get contingency very easily. The second feature is one I didn't notice right away. The astronomical features cited by Mersenne are ones that would reasonably be thought to be permanent features. They are thus prime candidates to be dismissed by it is so, as it has always been so. Mersenne's focus on the seeming arbitrariness of these features makes it very clear that would be no explanation. Thus Mersenne's cosmological argument works whether or not the past is finite. It is not disturbed by an infinite regress but does not need one either.

Of course, we no longer think that these particular features are permanent in the same way--the earth and sun changed in size in the formation of the solar system. But impermanent features are no better explained by an infinite regress than permanent ones--the permanence of the features in Mersenne's argument is only heuristic (and I don't see him explicitly drawing the reader's attention to the permanence). Plus we could run the argument on the basis of the apparently permanent but seemingly arbitrary elements in the laws of nature, such as precise values of constants.

The downside of Mersenne's argument, however, is that unless it is explained why the features are desirable, it is difficult to show that the cause of these features of the universe must be intelligent.

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:

4. If God doesn't exist, it is impossible for God to exist. (Premise)
5. God is greater than all possibilities and actualities other than God. (Premise)
6. We can think of God. (Premise)
7. We cannot think of anything that exceeds all actualities and possibilities.
8. God doesn't exist. (Supposition for reductio)
9. God is not a possibility or actuality. (4 and 8)
10. We can think of something that exceeds all actualities and possibilities. (5, 6 and 9)
11. Contradiction! (7 and 10)
12. 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.

Mersenne's supreme bad vs. supreme good argument

In his 1624 The Impiety of Deists, Atheists and Libertines of This Time... (dedicated to Cardinal Richelieu, by the way), Mersenne gives this fascinating little argument:

Nobody fails to acknowledge that if there is a supremely good being [un estre souverainement bon], it merits the name of God, since we don't mean anything by that name other than that which has all [the] sorts of perfections, and which lacks nothing. Now I will show that this supreme good exists. If it didn't exist, its privation would exist, which would be a supreme bad [mal], and consequently the supreme non-being, since the bad and the non-being are the same thing: but it doesn't in the least seem that the privation exists more than its actuality, which must necessary precede it. Thus one must confess that there is a supreme goodness, and then that there cannot be a supreme badness. So we have a supreme being, since we deny a supreme non-being, it being necessary that the one or the other exist....

There is actually more than one argument here. There is an interesting and deeply metaphysical argument based on evil as the privation of a good. But there is also the kernel of a rather interesting and simple argument:

1. It would be supremely bad if God doesn't exist.
2. The world doesn't exemplify a supreme bad.
3. So, God exists.

My son suggests using the goodness in the world to argue for (2). That would be an interesting hybrid design argument.