Descartes and Having Infinite Ideas

In Descartes we encounter an interesting argument, the so-called Causal Argument (CA) from the Third Meditation. It is the first of two arguments Descartes provides for the existence of God, and in my opinion it has the more interesting implications (the other is, of course, the more famous ontological argument).

The CA goes something like this:

P1. I have an idea of an infinite being, God.

P2. An effect cannot have more reality than its cause; it must have just as much or less reality.

1. My idea of God could not have come from:

         A. anything finite

         B. nothing

2. My idea of God came from an infinite being.

3. God exists.

Step 1 follows from the premisses by P2, where we define infinite things to have more reality than finite things (Descartes is a rationalist, after all), and finite things in all likelihood more than nothing. Step 2 follows by a process of elimination: If my idea didn't come from a finite thing or from nothing, all that's left is an infinite thing. Step 3 just names that infinite being as God as says that if my idea came from an infinite being, that being must therefore exist.

So here's an objection to Descartes' argument (expanded from Gassendi's objection): An idea of something infinite has just as much reality as the idea of something finite, because both those ideas are finite. The idea of the infinite being is just a finite idea. It's content, that it is an idea of an infinite being, does not affect this. The content of the idea was created by a process of adding or amplifying various perfections one has experienced in the world. In other words, it is a spurious infinity; one cannot experience or even intellectually apprehend infinity, even though it is possible to trick oneself into thinking such a thing is possible.

In other words, there are two major objections: Step 1 is illegitimate because something finite can indeed come from something finite; and P1 is false because the content of the idea is not a truly infinite God, but a spurious infinity. This first objection is the most interesting, so I will begin with it.

To make sense of Descartes' argument, we can make the following (initially strange) assertion: the idea of an infinite thing is itself infinite. In other words, in the context of the CA, step 1 is justified because the idea of God is infinite and thus by P2 it could not have come from a finite source. I believe this is what Descartes is trying to say, and that this is not a simple confusion of form and content.

But what does it mean to say that an idea itself is infinite? How can an idea held by a finite being be infinite? How could the mind grasp an infinite thing not only in the content of an idea but in its very form? As Descartes notes in his reply to Gassendi, one cannot “grasp” the infinite, and that is the whole point. It is not something possible through the senses or through the imagination, but only through the intellect. The intellect is the only way to access infinity. But, as noted, this is not a simple question of content, of having an idea of infinity, but of having an infinite idea.

An interesting implication: God is inseparable from the idea of God, or rather, the idea of God is God. But it is not our understanding of our idea of God, because this is fuzzy and, as Descartes notes, similar to a student's idea of a triangle—the student knows a triangle has three sides, but he is ignorant of the many more advances properties possessed by the triangle. This is a refutation of Gassendi's objection that we only know a part of God, because we cannot apprehend him as a whole. Rather, our imperfect idea of God is not the idea of a part of him, but akin to the student's idea of a triangle.

In any case, the idea of God is God also because his essence is existence. Here we have an interesting bridging of thought and being, which corresponds perfectly with the above idea that an idea of an infinite being is itself infinite.

So we have three terms: God, the idea of God, and our idea of God. The first two, strictly speaking, are one and the same. But our idea of God is still infinite—it is not exactly limited by anything, as a part would be limited by another part. Rather, there are no parts in its content, and therefore nothing to limit the form either, due to the weird coincidence of form and content.

This has only been a brief exposition of what I think is a very interesting thread in Descartes. In the future I hope to better explore what having an infinite idea means, as well as move a bit away from Descartes' dogmatism. In any case, I found the account of the role of the intellect to be quite lacking in Meillassoux (in his terms, he did not explain how it is that mathematics/science/whatever can do what it does, etc. etc.).