The Existence of God

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The proof of the existence of God is an interactive proof just like the Cogito. In fact it is a kissing cousin to Anselm’s ontological proof. Descartes just recasts things a bit. He talks about the causes of my ideas and of my idea of a perfect entity whereas Anselm just challenges us to conceive of a greatest something.

This proof is best laid out in an interactive form. Spinoza stumbled into a nearly incoherent morass when he tried to recast this interactive proof in deductive form beginning with definitions and axioms and moving step by step from one proposition to another. It just won’t work that way and Spinoza ended up wavering between a stipulative definition of something whose essence is to exist and a reversion to the interactive proof in his Notes and Additional Proofs.

These are the steps of Descartes’ proof of the existence of God in the Third Meditation:

1)      Something must cause the existence of anything that exists.

2)      A cause must have greater reality or perfection than its effect. Even my ideas must be caused by something that has greater reality than they do. If my ideas have objective reality then they must be caused by something outside these ideas than has formal or actual reality.

3)      I cannot be the cause of my idea of an infinite substance since I am a finite substance and have less perfection than an infinite substance.

4)      The cause of my idea of an infinite substance must also be an infinite substance, namely God.

Between (2) and (3) we need to conjure in our minds the idea of an infinite substance.

Objection 1: Let us for the moment accept all this gobbledygook about objective and formal reality and infinite substances. Now, even though an infinite substance would be infinite, my idea of an infinite substance is itself a finite substance and could be “caused” by myself, another finite substance, alone without external help. In that case my idea would not have objective reality (assuming “objective reality” means corresponding to something of which it is the idea). There would be no formal or actual reality that my idea stands for. My idea would be caused by my combining other ideas. (This seems, by the way, to be the objection of Caterus which Descartes for his part seems to misrepresent. For Descartes rephrases Caterus' assertion that some ideas may not be caused by something outside the mind, i.e. they might not correspond to something that has "formal" or "actual" reality, as a belief that other ideas might actually exist outside the mind in some sense.)

Descartes argues that the concept of an infinite substance cannot be the product of my own mental activity by simply negating “finite” because “infinite” is in fact a more basic concept than “finite.” “Finite” must be defined as the negation of “infinite.” But his analysis of “infinite” is not the only one possible. Let a₁, a₂, a₃… stand for lengths of string of varying lengths as measured, say, in meters. a₁ is one meter long; a₂ is two meters long etc. where the values of x in a_x are defined recursively by means of a recursive definition of the sequence of integers. Then we will say that for any integers m and n that are values of x, a_n is greater than a_m if n>m.  It follows that a_∞ is an a_p such that p>x for any value of x. Assuming for the purposes of this illustration that "long" and "large" are interchangeable and that lengths of string are objects, then this definition of “infinitely large object” is not based on a negation of “finite.” Yet it has been constructed out of other concepts like “long” and “more” just as the concept “unicorn” combines the concept “horse” and “horn.”

In his First Replies (Pléiade pp.352-353. He may be reiterating this point in the Second Replies, p. 373, where he distinguishes between ideas which are "formally" in the mind and those which are merely "eminently" in the mind.) Descartes excludes extended imaginary spaces, among which he presumably includes infinitely long bits of string, from his grouping of really infinite things. They are he says, not infinite, just indefinite. The indefinite is unlimited in just one way whereas the infinite is unlimited in every way. Most infinite sequences presumably are indefinite while only God is infinite. I pass. This is infinitely incoherent. By the way, is the number of ways that the infinite is unlimited itself infinite or just indefinite? In the same passage Descartes distinguishes between an infinite thing and its infinity (the formal reason of the infinite thing). We know, he says, the infinite thing positively but not in its complete extension (étendue). As regards the infintity of the infinite thing, we can conceive of it positively but we only know it negatively. Anselm would have been proud. This sounds like John Kerry saying he voted to invade Iraq but he didn't vote to invade Iraq. I cannot resist quoting the immortal sentence from this paragraph: "...the infinite, as infinite, is not in truth understood, but it is understood..." I hope the infinite is easier to understand than that sentence. (To be fair he uses two different words in French, comprendre and entendre. However, the only other possible translation of entendre produces: "...the infinite, as infinite, is not in truth understood, but it is heard..." This sounds more like Messiaen.)

In his Second Replies (Pléiade pp. 374-375) Descartes address (without the benefit of recursive definition) the infinite sequence of integers, but merely states mysteriously that I that the idea of an infinite sequence cannot come from myself.

Objection 2: Descartes uses “cause” in two different senses when he talks about something outside the idea causing that idea and my being the cause of that idea. In the first case (If any sense is to be made at all of the notion of “cause” in this usage) Descartes appears to understand the cause of an idea as something the idea stands for. In this sense my dog Bill is the cause of the idea of my dog Bill because I really have a dog named Bill and my idea is of that particular dog. However, that cannot be Descartes’ meaning when he asserts that I cannot be the cause of my idea of something infinite because I am finite (Unclear but let it pass). For example, I am the cause of my idea of my unicorn Bill in a different sense than Bill is the cause of my idea of my dog Bill. I am the cause of my idea of my unicorn Bill because I have combined various ideas including horse, horn and personal possession. I do not have to have hooves and a horn to be the cause of my idea in this sense.  In fact there is no cause of my idea of my unicorn Bill in the same way that Bill is the cause of my idea of my dog Bill. Likewise I very well could be the cause of my idea of an infinite thing by combining several ideas including "really big" and "most" even though I personally am finite (In some moods I won’t even concede that). And just as there may be no cause of my idea of my unicorn Bill in the same way that Bill is the cause of my idea of my dog Bill, there may be no cause of my idea of something infinite in the same way that Bill is the cause of my idea of my dog Bill.

Note 1: In one curious paragraph (Pléiade p. 314) Descartes begins by stating that he will give reasons why the idea of a perfect entity is not an invention of my thought but rather the image of a true and immutable nature. But his reasons don’t show anything of the sort. At most they would show that this perfect entity couldn’t be anything except God (and really they don’t even show that). The first reason is that I cannot conceive of anything else but God that exists necessarily. The second is that I cannot conceive of more than one such God.  The third is that, if there is such a God, it must exist eternally. The final reason is that I know an infinite number of other things in God that cannot be diminished or changed. Descartes seems disinclined to try to prove any of these assertions, and even if he did it is unclear how any of them would prove that there is an entity that exists necessarily.

Note 2: It is important not to mistake how Descartes uses geometrical properties in his proof of the existence of God because this casts some light on how he understood the application of geometrical reasoning to first philosophy and also what he thought about the vexing issue of the ontological status of mathematical entities. Geometrical figures play a role in a type of reasoning where a property of something can be discovered that cannot be deduced by logic alone. We can discover that the sum of the angles of all triangles equals two right angles without the use of syllogistic logic. His point is that we can form a clear and distinct idea that the properties of triangularity and the-sum-of-angles-equals-two-right-angles belong together necessarily in the figure of a triangle. Similarly, he argues, we should be able to see clearly and distinctly that perfection, existence and really-does-exist all belong together. It would be wrong to think that Descartes is arguing that because geometrical figures exist God exists also. Some passages in the Fifth Meditation are more interesting for the subject of the ontological status of mathematical objects than for theology. Geometrical figures are not material objects for Descartes and they are certainly not minds. In fact he is willing to accept the notion that they may not exist. In speaking of triangles (Pléiade p. 311) he concedes that they may be in “aucun lieu du monde hors de ma pensée,” but even so, and this is his real argument, they must necessarily have certain properties. The most, he says, is that triangles are “something.” We should remember that, despite a certain amount of propaganda to the contrary, not all mathematicians are Platonists about mathematical objects.

Note 3: Veitch mistranslates "vallée" as "valley" in Meditation V producing one of the great philosophical howlers of all time since plains deserve some consideration too. For the record, in French "vallée" (Lat. vallis) means any land formation surrounding a mountain that is lower than the peak. The French word word for "valley" is "vallon."

Note 4: In his Replies to various Objections Descartes lets down his guard a bit and begins to babble incoherently or else he relies more heavily on the arguments of the schoolmen (It’s always hard to tell the difference).

Tucked away in the First Reply (Pléiade p. 351) is an alternative proof of the existence of God. To wit: There are two senses in which a thing can exist by itself (par soi): (1) No cause can be found for its existence (This is the negative sense). (2) It exists solely through the superabundance of its own power (puissance) (This is the positive sense). God exists by itself in the second or positive sense. I recognize in myself that I do not exist by myself in the second sense. So I must exist by another and this other must have enough power so that it exists by itself. This other is God. Descartes insists that he is not speaking of existence here in the sense of “bringing into existence” but rather in the sense of “maintaining in existence.” So a historical chain of causes (whose existence has not been proved anyway) as in the Thomistic proof is irrelevant. God is what maintains me in existence now at this moment.  Once again, I pass. The only thing I recognize to have a superabundance of power is my own penis. It is worth noting that the first set of Objections and Replies contains the clearest juxtaposition of the Thomistic causal proof of the existence of God and the Anselm-Descartes ontological proof. In either case the objector carries the day. In each case the core of the proof is the subject of attack. Aquinas expresses serious doubts about the existence of anything whose concept involves existence and Descartes undermines the very concept of a cause. [ Next ]

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