Cartesian Infinity and Certainty

From Descartes’ fourth Meditation:

But once I turn my attention back on myself, I nevertheless experience that I am subject to countless errors. As I seek a cause of these errors, I notice that passing before me is not only a real and positive idea of God (that is, of a supremely perfect being), but also, as it were, a certain negative idea of nothingness (that is, of what is at the greatest possible distance from any perfection), and that I have been so constituted as a kind of middle ground between God and nothingness, or between the supreme being and non-being. (Meditation Four, 54, emphasis added).

Descartes, in his confrontation with nihilism, gives us a picture of the human condition as stretched between two versions of infinity. On the one hand is the idea of God as the idea of perfection and the infinite. On the other is nothingness and non-being as an abyss of utter emptiness. Here we have one of the clearest expressions of how Modernity will require a regular and recurring confrontation with nihilism that will feel like riding on a pendulum. We will swing from the desire for perfection on the one side to a distrust in any source of perfection as it fails to live up to certainty. In other words, as we orient ourselves to perfection, we will always have one eye on the possibility that the only thing we can be truly certain of is the complete hollowness of our existence. A bias toward logical demonstration as the method for attaining certainty will always favor nothingness as far easier to prove than the existence of something more perfect than ourselves.

In addition to being the champion of certainty, Descartes is warning us throughout the Meditations of the dangers of tying the idea of God’s perfection to certainty, which would mean reducing perfection to a finite thing. All that he wants us to be certain of is twofold: 1) that an I exists because it has experiences and a free will to act, and 2) that God exists as something superior to this I that thinks. #2 provides meaning and purpose to #1, which would otherwise be an empty cogito made up of meaningless internal mental events firing seemingly at random. This is as far as we should take Cartesian certainty when it comes to perfection: I exist, and something more perfect than me exists that I should keep me turned away from nothingness as our existential condition. Thus the modern experience of the self is not only stretched out between two kinds of infinity, it must orient itself away from the infinity of nothingness and toward the infinity of perfection to avoid nihilism.

Yet we must be careful not to equate nihilism with only the infinity of nothingness. Orientation to perfection can yield its own brand of nihilism. How? If we conceive of perfection as something that can be known and attained with certainty, we make the idea of perfection into something finite and thus imperfect. This opens the possibility of believing that we can be certain about what perfection is. This alignment of certainty and perfection is always a recipe for violence — inquisitions, heresies, gulags, gas chambers, et cetera. This alignment tempts one to say, “I know what perfection is, and it is the same for you as it is for me. If you do not pursue it with me, you are against me.” This is the heart of the Nietzsche’s ascetic ideal as the denigration of this world in favor of another. That other world is founded up on the combination of certainty and perfection.

For Descartes, perfection has no definitive (i.e., finite) content. It is not and cannot be expressed in a doctrine, which is the very embodiment of the finite. This is the historical situation for religion and theology that he occupied. The Thirty Years War encompassed nearly all of his adult life; Galileo was under house arrest for scientifically demonstrating heliocentrism; Protestantism was undergoing its own paradoxical embrace of intolerance amid a plurality of Christian belief systems of its own making. We do ourselves and Descartes a disservice if we treat his notion of the self as an oppressive effect of power relations or as the historically inevitable expression of a European bourgeoisie coming into its own. For those who see Modernity negatively as the rise of instrumental reason and/or the Protestant work ethic, Descartes is an easy whipping boy. It is easy to read his work as the birth of a dehumanizing and sterile embrace of procedural rationality, and to read his Third and Fourth Meditations as unconvincing arguments for the existence of God.

But if we read the whole of his Meditations and take seriously that the human being is “constituted as a kind of middle ground between God and nothingness,” do we not find a way of thinking about ourselves that acknowledges nihilism as our modern reality while giving us the tools to negotiate its inevitable pendulum swings? Do we not find a way of being in the world where certainty is only intermittent and very difficult to achieve, yet we must act? Do we not find in this self an orientation to perfection as infinite possibility?

In this meditation, I want to look closely at how Descartes weaves together the demand for certainty, the freedom of the will, and his idea of infinity. We do him and ourselves a disservice if we untether these three imperatives from each other. I say “imperatives” because these aren’t just concepts: they are part of a spiritual practice — “meditations” have a long history as spiritual practice — that shows us how central nihilism will be to a world where theology and philosophy are not on speaking terms. We find ourselves clinging to a pendulum swinging between being and non-being. This pendulum swing is not simply an effect of relations of power, the rise of the bourgeoisie, or an abstract psychological thought experiment. It is a necessary disposition to ourselves that emerges from, and allows us to cope with, a world turned upside down.

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I’m going to start with the idea of inifinity. We must try to understand how important this idea is for Descartes. The idea of infinity prevents certainty from settling into the idea of perfection and therefore truncating and reifying our notion of God into something we imagine to be concrete and therefore finite. In other words, the idea of infinity prevents perfection and certainty from collapsing into each other. This is the work that it must do and is therefore not just an inert idea but a practical and ethical one.

The idea of infinity is also what keeps the Meditations — and all of Descartes work — from becoming yet another attempt to assert a new Christian doctrine. What do I mean by this? Christianity had become battles over which group could claim accurate knowledge of God and Jesus. Christianity after Paul had always struggled with itself as a practice or as a belief system. The Reformation doubled down on the belief-system bias. Salvation depended on which version of the truth you embraced. Descartes did not go down this path. He doubled down on his method rather than form a new Christian belief system. For me, this is the admirable and innovative move he makes in the face of his historical circumstances, and it is what makes him a towering intellect in Western history. Of course, his method is not without significant problems, but by choosing to read Descartes as pointing out a new brand of nihilism, I feel like I’m paying due respect to what he was actually trying to achieve as a thinker in his own time trying to find a way out of a major impasse in intellectual, spiritual, and political history.

Thus the idea of inifinity must be a practical principle that we use to keep perfection and certainty from inhabiting each other. (This is my take away from Levinas’ reading of Descartes in Infinity and Exteriority.) In fact, when we imagine God, “we should keep in view not simply some one creature in isolation from the rest, but the universe as a whole” (Meditation Four, 55). God is not a finite thing; he is “the universe as a whole” and his works, which include humanity, are imperfect and finite parts of the infinite whole. We will always be tempted to contain this whole within a finite concept because that is how thought works. We must avoid this temptation. Perfection, God and the infinite represent, within our thought process, the authentic belief in the existence of an infinity that maintains our sense of purpose and meaningfulness without letting all of this become yet another way to separate orthodoxies from heresies.

Thus the idea of the infinite must be seen as an open-ended orientation to always seeking to be better without letting that orientation become a dogmatic attachment to an end point. Cartesian certainty should never seek dogmatic end points that force all of history to conform to those end points. To do this would be to make the infinite into the finite — to cut it off and thus to seek it as something that can be attained permanently. This is particularly true of the pursuit of knowledge, which can never be complete:

Moreover, although my knowledge may always increase more and more, nevertheless, I understand that this knowledge will never by this means be actually infinite, because it will never reach a point where it is incapable of greater increase. On the contrary, I judge God to be actually infinite, so that nothing can be added to his perfection. (Meditation Three, 47, emphasis added)

The double use of “actually infinite” is essential to understand. To insist on the word “actually” enforces our commitment to a thought process that always tries to keep the experience of the infinite from being contained within the finite. It also indicates how easy it will be for the infinite to be contained by the finite because that is how our cogito’s work. In seeking perfection, we are tempted to seek the certainty of an end point for ourselves and for history. To prevent this, we must adopt the idea of infinity not as a concrete image, but as a mental technique.

The idea of infinity is what guarantees that the “middle ground” that we occupy between perfection and nothingness is experienced as a lack of perfection:

for error is not a pure negation, but rather a privation or a lack of some knowledge that somehow out to be in me. And when I attend to the nature of God, it seems impossible that he would have placed in me a faculty that is not perfect in its kind or that is lacking some perfection it ought to have. (Meditation Four, 55).

This is not an easy passage to unpack, but I shall try because I think it is important as a statement about how to deal with modern nihilism. It comes on the heals of the passage I cited earlier about the “middle ground.” Here Descartes is telling us how we should orient ourselves to our errors in judgment. We can’t always have perfect clarity as we act, but this shouldn’t tempt us to attribute our errors to the nothingness side of the equation. Rather, our errors of judgment are our own errors that come about because we misuse the perfect capacity for methodical reasoning that God gave us. Perfection always remains a possibility as long as we “attend to the nature of God,” but this perfection is never complete because perfection is not finite. To “attend to the nature of God” is to remain oriented to an infinite openness of possibility. Because this orientation cannot be an orientation to a finite perfection, we can never have a clear understanding of what it is ahead of time.

This cannot be undersold. To envision perfection as an end point is to cut off infinity as an open-ended orientation to possibility. This is not trivial, as I’ve tried to make clear to myself in these meditations; nor is it abstract and inconsequential. Modernity is littered with the debris of human life in its long march toward many different forms of perfection as the finite end of history. Rather, our orientation to infinite perfection is an orientation to history that cannot and should not be obsessed with end points. At those moments where we think we’ve achieved an end point, we need to immediately “attend to the nature of God” and start looking for the infinite within the finite we’ve just created.

Descartes is not unaware of the inherent problems of an open-ended notion of perfection. Can our free will just run amok doing whatever it wants because it is pursuing its own idea of perfection? Doesn’t this perfection need some content in order for it to avoid becoming the nihilistic free-for-all that the nothingness side of the equation would license? Is there no real difference between infinity as nothingness and infinity as perfection? This is the nihilistic underpinning of Modernity that Descartes is dealing with, and it is why the alliance between free will and the intellect takes center stage in the Fourth Meditation.

Before taking up the alignment between free will and the intellect, it is worth comparing Descartes’ confrontation with nihilism from those of Plato and the Stoics. Charles Taylor has spent a great deal of time making a similar case, and I want to put my own spin on it here through the lens of nihilism. I’ll start with a key passage from the Fourth Meditation on the nature of error and how to deal with it. On the face of it, it sounds a lot like Stoicism with its emphasis on training, preparation and the formation of good habits:

Furthermore, even if I cannot abstain from errors in the first way mentioned above, which depends on a clear perception of everything about which I must deliberate, nevertheless I can avoid error in the other way, which depends solely on my remembering to abstain from making judgments whenever the truth of a given matter is not apparent. For although I experience a certain infirmity in myself, namely, that I am unable to keep my attention constantly focused on one and the same item of knowledge, nevertheless, by attentive and often repeated meditation, I can bring it about that I call this rule to mind whenever the situation calls for it, and thus I would acquire a certain habit of not erring. (61-62, emphasis added)

For Plato and the Stoics, the nature of error had to do with not being in tune with nature conceived of as the providentially organized cosmos. Plato’s belief in “the good” as the organizing principle of reality (The Republic, Book 6) and Stoicism’s resolute belief in providentia, provided the moral guarantee of an outside of ourselves. The possibility of being in harmony with the good and with providential nature is made possible by the soul as an animating force of the self that is part and parcel of this providential cosmos. For Plato and the Stoics, the cosmos is alive. Seneca is clear on this in On Nature, and he is a canonical Stoic when he argues that pneuma is the same animating force that runs through our souls and the cosmos. This is a long-standing vision of pneuma, which we can easily see in the second rendition of God creating mankind in Genesis.

Descartes does not have a providential universe, nor is it alive. He has a mechanical universe. This is well understood, it is why his concept of God as infinite perfection becomes a bit problematic and loses its moral grip. All that God has guaranteed to humanity in Descartes’ world is the capacity to act through our free will and to attain certain knowledge. Moral development is to align these two capacities, which has nothing to do with being in tune with the universe. Yet one does have to be in tune with something if any purpose or meaning is possible for human life. Descartes finds that we must be in tune with ourselves, particularly with our intellect and its “natural light” that shows us when we have attained certain knowledge. Humanity is set free of the cosmos to find its own meaning. Taylor puts this quite clearly: “What moves us now is no longer a sense of being in tune with nature, our own and/or that in the cosmos. It is something more like the sense of our own intrinsic worth; clearly something self-referential” (A Secular Age, 134).

This is made abundantly clear as Descartes wraps up the Fourth Meditation. This citation is a direct continuation of my previous citation:

Since herein lies the greatest and chief perfection of man, I think today’s meditation, in which I investigated the cause of error and falsity, was quite profitable.

I’ll pause here to dwell for just a moment on how Descartes has shifted his discussion of perfection from God to man. This was always the goal, and he has attained it at this point. We must be clear, however, that this perfection is not the attainment of an end point but is the ability to align our actions with the certainty of our knowledge. This is a procedural perfection and not the Stoic and Platonic perfection of being in tune with something greater than ourselves. We are dealing specifically with “the greatest and chief perfection of man” as an entity cut off from a providential cosmos.

Nor can this cause be anything other than the one I have described; for as often as I restrain my will when I make judgments, so that it extends only to those matters that the intellect clearly and distinctly discloses to it, it plainly cannot happen that I err.

This is the chief perfection of man: the ability to engage the intellect to drive our actions. Again, this is Platonic and Stoic, but it is self-referential in a way that was not the case for the earlier philosophers. Humanity is now self-sufficient in its ability to know. The soul as the connection to a good and providential cosmos is no longer required. It is a self-contained entity bottled up within the subject that possess it. In fact, it is equated with “mind.” God is a bit player in all of this. All that God has provided is a promise that the “natural light” is not a deception:

For every clear and distinct perception is surely something, and hence it cannot come from nothing. On the contrary, it must necessarily have God for its author: God, I say, that supremely perfect being to whom it is repugnant to be a deceiver. Therefore the perception is most assuredly true.

We have lost the notion of infinity to get back to what was really at stake: that God does not deceive us. He is not a demon trifling with our attention. At this point, with this guarantee in place, God no longer needs to be present. Self-referentiality is fully established:

Today I have learned not merely what I must avoid so as never to make a mistake, but at the same time what I must do to attain the truth. For I will indeed attain it, if only I pay enough attention to all the things that I perfectly understand, and separate them off from the rest, which I apprehend more confusedly and more obscurely. I will be conscientious about this in the future. (Meditation Four, 62)

Here we have the definitive moment where the Enlightenment is born. Not because reason is coming into its own and not because its own strength is throwing off the shackles of religion. It is the alignment of certainty with action and the making of that alignment into a completely internal operation of the human mind. This mind has the ability to “separate” errors from certainties. Any thought that is confused or obscure must be subject to scrutiny and the demands of certainty. What then will happen to the idea of infinity? It cannot survive this Cartesian move to certainty. We cannot believe authentically in this idea of infinity because it necessarily escapes our ability to be certain about it. At the end of the day, Descartes sides with certainty over infinity, and we lose any notion of an encounter with infinity as part of our moral development.