. . . In Descartes, we find an intuition of the same order regarding the ontological status of truths. We know that Descartes gives the name of ‘substance’ to the general form of being as really existing. ‘What there is’ is substance. Every ‘thing’ is substance: it is figure and movement in extended substance; it is idea in thinking substance. This is why Descartes’s doctrine is commonly identified with dualism: the substantial ‘there is’ is divided into thought and extension, which in man means: soul and body.
Nevertheless, in paragraph 48 of the Principles of Philosophy, we see that substance dualism is subordinated to a more fundamental distinction. This distinction is the one between things (what there is, that is to say substance, either thinking or extended) and truths:
I distinguish everything that falls under our cognition into two genera: the first contains all the things endowed with some existence, and the other all the truths that are nothing outside of our thought.
What a remarkable text! It recognizes the wholly exceptional, ontological and logical status of truths. Truths are without existence. Is that to say they do not exist at all? Far from it. Truths have no substantial existence. That is how we must understand the declaration that they ‘are nothing outside of our thought’. In paragraph 49, Descartes specifies that this criterion designates the formal universality of truths, and therefore their logical existence, which is nothing other than a certain kind of intensity:
For instance, when we think that something cannot be made out of nothing, we do not believe that this proposition is an existing thing or the property of some thing. Rather, we treat it as an eternal truth that has its seat in our thinking, and which is called a common notion or maxim. Likewise, when we are told that it is impossible for something to be and not to be at the same time, that what has been done cannot be undone, that he who thinks cannot stop being or existing whilst he thinks, and numerous other similar statements, we recognise that these are only truths, and not things.
Note that the crux of the cogito (the induction of existence through the act of thought) is a truth in this sense. This means that a truth is what thought goes on presenting even when the regime of the thing is suspended (by doubt). A truth is thus what insists in exception to the forms of the ‘there is’.
Descartes is not a dualist merely in the sense conferred to this term by the opposition it draws between ‘intellectual’ things, that is ‘intelligent substances, or rather properties belonging to these substances’, and ‘corporeal’ things, that is ‘bodies, or rather properties belonging to these bodies’. Descartes is a dualist at a far more essential level, which alone sustains the demonstrative machinery of his philosophy: the level at which things (intellectual and/or corporeal) and truths (whose mode of being is to (in)exist) are distinguished. It is necessary to pay careful attention to the fact that unlike ‘things’, be they souls, truths are immediately universal and in a very precise sense indubitable. Consider the following passage, which also links truths to the infinite of their (in)existence:
There is such a great number of [truths] that it would not be easy to draw up a list of all of them; but it is also unnecessary, since we cannot fail to know them when the occasion for thinking about them arises.
And it is true that a truth is an exception to what there is, if we consider that, when given the ‘occasion’ to encounter it, we immediately recognize it as such. We can see in what sense Descartes thinks the Three (and not only the Two). His own axiom can in fact be stated as follows: ‘There are only (contingent) corporeal and intellectual things, except that there are (eternal) truths’. Like every genuine philosopher, Descartes registers, at the point where ontology and logic rub up against each another, the necessity of what we have chosen to call ‘materialist dialectic’. . .