Descartes now has his foundation. He spent the First Meditation emptying his thought out, using his methodological doubt to render anything dubious and set it aside. From that process, he has arrived at three bulletproof, doubt-proof beliefs: his existence (that he does exist), his essence (that he is a thinking thing), and the fact that he has ideas, even though every single one of them might be wrong.
It is very little to go on, but it is from this foundation that he will reinstate the world, bring God back, and create science.
At this point, Descartes' only method is methodological doubt, and it is a very crude tool. It eliminates so much that he now needs to refine his approach in order to build things back up. He moves from methodological doubt into a new epistemological tool by examining the beliefs he has already established, the three that have proven doubt-proof, and asking what they have in common. What is it about them that has enabled them to withstand the doubt?
What he decides is that, for all three of them, he is able to have what he calls a clear and distinct perception of them. This is his phrase, and it has become a technical term. It is precisely because he can have a clear and distinct perception of these beliefs that he can be certain they are true and that they can withstand the doubt he is using to filter so many others out. It is worth remembering that the beliefs he filters out are not thereby declared false or defective; the scenarios he invents, that he might be dreaming, that there might be an evil demon, are not ones he actually believes. The doubt is a tool for sorting beliefs by strength and type, and he has already sorted them into empirical and a priori varieties, with more distinctions still to come.
To have a clear and distinct perception of something means being able to see everything there is to know about it. He can take it apart, examine every single component, and reassemble it, confident that nothing has been missed. There is no shadowed corner where error might be hiding; he has shone a light over every aspect and seen it whole, and so he knows it must be true. Once he has done that, he feels he can trust it. This principle has come to be called the truth rule: if you can have a clear and distinct perception of something, then it must be true.
We will work through one example together, just to show what a clear and distinct perception actually feels like, since that phrase remains quite vague and indistinct on its own. Mathematics is, of course, a very good example of clear and distinct perception, and we can take a very simple case: can we know that two plus two equals four? We believe it, but can we really, truly know it? Can we be absolutely certain it is true?
How do you know it is true? Simply because a first-grade teacher told you? That is not adequate evidence; she said some things that were probably a little dubious. Because you have taken two objects and two objects and put them together? That is not perfect evidence either, as we will see when we return to Hume. For Descartes, however, the evidence here is a priori: we look directly at the idea, take it apart, and see its truth from within.
So let us examine the ideas themselves. What is two? Two is nothing more than a duality of entities; there is nothing else to the idea. We take apart these ideas and see that this is the only thing two means. We look at addition, and all addition means is bringing things together. There is no underside, no hidden corners, no backside to it. That is the whole of it.
Two plus two is just this: two dots and two dots brought together. We are not looking at words or symbols, but at the actual meanings. And the only meaning of four is four dots. The equals sign means that what is on one side is the same as what is on the other, which it is. When you focus entirely on this, it is very simple. We can only do this with small ideas, because you must absorb everything about the idea at once and hold every piece of it in your mind simultaneously.
If you work through this carefully and truly see all there is to see, then you can know for the first time that two plus two really does equal four. You believed it before, but now you know it in a completely different way. Descartes would say you have proved it for yourself. Rather than accepting it on faith or on the authority of someone else, you have seen its truth directly. The truth is laid fully open, and there is no way to doubt it at this point.
There is nothing else to it. There is no other meaning lurking somewhere, no surprise waiting to emerge, no relevant factor you might later realize you had overlooked. You are entertaining every single factor that could possibly be relevant. You have it all, and you see the truth of it. This is what a clear and distinct perception is. For Descartes, it represents the highest level of epistemological evidence possible.
Clear and distinct perception can only be had a priori. You cannot have a clear and distinct perception of anything empirical. For one thing, as Descartes notes, you can only ever see one side of something at a time. While looking at the front of an object, you cannot see the back, and the moment you turn it around, the front is blocked. This is, incidentally, a topic that the twentieth-century German philosopher Husserl would later explore at great length.
There is simply no way to use sensory data to take in all aspects of something at once. Every sensory perception is partial by its very nature, always from one perspective, always incomplete. An idea, by contrast, if it is simple enough and you can familiarize yourself with it sufficiently, can be turned over in the mind from every angle and grasped all at once. You can absorb it in its entirety simultaneously and know that every part of it is correct.
This is how Descartes intends to move forward. Clear and distinct perceptions are what he believes we can trust. With the three foundational ideas now established, we also have a new tool, one that does not merely tear down, as methodological doubt did, but that can actively build. Clear and distinct perception is the constructive instrument that will allow him to reconstruct knowledge on secure foundations.
Our next task is to defeat the evil demon. The evil demon was the third skeptical argument from the first meditation, the most powerful one, the one that threw everything into doubt, both empirical beliefs and a priori beliefs. We have recovered some a priori beliefs: the simple ones we can perceive clearly and distinctly. We have those back, but there are very few of them, and we can only hold one at a time. We need to start beating back the skeptical arguments from the first meditation and get out of the matrix.
For Descartes, the only way to defeat the evil demon is to prove that God exists. Only a God can take down the evil demon. Only if we know that God exists can we trust our senses enough to know that there is a world outside of us. Until we establish that, we cannot trust any of our ideas. They could all be dreams, they could all be the matrix, they could all be a simulation. We need God to bridge what is inside our skulls and what is outside, to look at the ideas in our heads and at the world outside and confirm that yes, these match.
This correspondence is what we need in order to do science. When you look at a chair, there must be something out there causing you to have that idea. Remember, that is the whole goal we are aiming at: the ability to control the world, to have medicine, to build machines. All of that requires an external world. So our next step is to defeat the evil demon by proving that God exists, which I will do right now. Nothing up my sleeves, no props.
Proving God's existence has been a very common pursuit among philosophers for a very long time. The Meditations actually contains two such proofs. One of them is quite poor; it relies on a great many medieval assumptions you have to accept before it gets off the ground, and we will not be examining that one. The other is a proof that Descartes essentially plagiarized. It is known as the ontological proof, and it was created by a twelfth-century monk named St. Anselm.
The ontological proof is entirely a priori. There are empirical proofs of God's existence, but Descartes cannot use them, because he does not yet know there is a world outside of him. He needs God to establish that very point. The only resources available to him at this stage are the three things in his foundation: his existence, his essence as a thinking thing, and his ideas, every one of which could be wrong. From those three things, and really from just one of them, his ideas, he is going to construct a proof of God.
The proof begins from the fact that Descartes has ideas in his head. He has an idea that he is seeing a wall. He does not know if there really is a wall, does not know if walls exist, does not know if the world exists, but he does know that he has an idea of a wall. The first thing Descartes points out is that ideas have essences, even when we do not know whether the things they are about have existence.
When we examine these ideas, we cannot know whether they are true in the sense that anything outside the mind corresponds to them, nor whether anything outside us is causing them. It could be a dream, it could be the Matrix, it could be a demon. But we do know that even if an idea lacks existence, it still has essence.
Consider unicorns. Unicorns do not exist, but they do have an essence: a horse with a horn. If the idea of a unicorn had no essence, we could not even deny their existence, because there would be nothing determinate whose existence we were denying. If neither speaker nor listener knew what was meant by "unicorn," the statement "unicorns don't exist" would be meaningless, no different from saying "flabbleblas don't exist," which means nothing precisely because "flabbleblas" has no essence.
Because we know what unicorns are, we know what it means to say they do not exist. We can only deny the existence of something because it already has an essence. There is a meaning, a definition, a set of necessary properties belonging to the idea, and this remains true even if the idea corresponds to nothing beyond itself. The idea still has an essence.
An essence is something I cannot control. I cannot change the meaning of unicorn, that is simply what the word means. Whether unicorns exist or not, their essence is fixed in the mind. And these essences can have implications; they can entail other properties. Because a thing has one property, that may mean it necessarily has others as well.
Descartes' favorite examples are always geometrical. Consider the idea of a triangle. The idea of a triangle is, very simply, a shape with three sides: that is the definition. He does not know whether any triangles exist in the world; all he knows is that he has the idea of one, and yet that idea has necessary properties. It has an essence. It must have three sides, or it is not a triangle. If someone says, "I just saw the rarest thing, I saw a four-sided triangle," you would say, "No, you didn't. That is not a triangle." You cannot see one, because three sides is a condition of being a triangle at all.
But the essence does not stop at three sides. Once you have that essence, further properties can be derived from it. Any closed shape with three sides must have internal angles that add up to 180 degrees; that is a law of geometry. It does not matter whether there is a single triangle in the universe, whether there has ever been one, or whether there ever will be one. The idea itself has necessary properties regardless of whether anything in the world corresponds to it.
The idea of a triangle has an essence, three sides, and that essence entails necessary properties, such as internal angles summing to 180 degrees. This is purely a priori, purely a matter of the idea itself, and yet we are still constrained by it. You cannot choose to have a triangle whose internal angles add up to 179 degrees, because then it simply would not be a triangle. It must have this property.
The third step is this: among my ideas is an idea of God. What is the essence of that idea? The essence of the idea of God, according to this proof, is to be a supremely perfect being. A supremely perfect being is not merely perfect in one way or another, but is a being that is perfect in all ways, completely and absolutely perfect, possessing all possible perfections.
Now that essence, just like the essence of three sides, has implications. It entails other properties. Just as three sides entails 180 degrees, the definition of all possible perfections means that any perfection one can conceive of, God must have. To flesh out the definition of what God is, all you have to do is identify possible perfections. If you identify a possible perfection, God has it, because the idea of God is precisely to have all possible perfections. If you are thinking of a god that lacks some possible perfection, you are no longer thinking of God, any more than a four-sided triangle is a triangle.
So what are some possible perfections? Omniscience: perfect knowledge. God is the being with all possible perfections, and perfect knowledge is a perfection, therefore God is omniscient. Omnipotence: perfect power. Perfect power is a perfection, therefore God is omnipotent. Omnibenevolence: perfect goodness. That too is a possible perfection, so God has it.
Now consider perfect existence: existing from all time and for all time, self-caused. That is a possible perfection, and God has all possible perfections, therefore God has perfect existence. Therefore God exists. The idea of God is the idea of a being that has all possible perfections; existence is a perfection; therefore God has it.
If you are thinking of a non-existent God, if you are an atheist, then you are not actually thinking of God. You are like the geometrician thinking of a four-sided triangle: that is simply not a triangle. You cannot deny the existence of God according to this proof, because whatever you are denying is not God. If you deny existence to that being, it is no longer God, since it lacks a perfection. You are saying that the being which has all possible perfections does not have a possible perfection, and that is a contradiction. The only way to be consistent, the only way to even be speaking coherently about this idea, is to attribute existence to it. Therefore, you cannot logically deny that God exists.
This proof has never convinced anyone in history. No one has ever become religious because of it. But the question is: if you think it is wrong, as most people do, where exactly is the mistake? Philosophy is wonderful because you can argue against anything. There are no authorities. It does not matter that Plato said something; you can say he was wrong. But you have to have a reason.
You cannot simply say, "It's wrong — obviously it's wrong, it can't be right." That is not a legitimate reason to reject a belief. You cannot just say, "It must be wrong because I don't believe the conclusion." You have to see why it is wrong. Descartes is not saying, "God exists because I believe in God." He is not appealing to faith, and he is not saying, "The Bible says God exists, therefore God must exist." Descartes is giving us reasons.
He is laying out the tool that all philosophers use: an argument. He is assembling premises — ideas that lead to a conclusion. You can attack the premises, reject a premise, or argue that the premises do not lead to the conclusion. But you cannot simply say, "I don't like the conclusion, therefore I reject it." You have to find a flaw.
You are welcome — indeed, encouraged — to look for one. But you have to actually find it; you cannot merely reject the argument out of hand. You have to be open to the possibility of being wrong, open to changing your mind. I am not trying to convince you of any theological position — only that we should all be reasoning carefully. With that in mind, let us look at some possible objections.
One objection runs as follows: all you are doing is thinking. You cannot think something into existence. You cannot simply put a collection of words and ideas together and expect that, as a result, something exists. That is true — but it is not what the argument claims. The argument does not cause God to come into existence; it recognizes that God has a certain property.
Consider triangles. The fact that we perceive triangles as having interior angles summing to 180 degrees does not make that true. If it did, we could change it — we could all agree to have 179-degree triangles. But we cannot, because we have no control over it. We are not making that property happen; we are recognizing that it is there. We are seeing it, not creating it. In the same way, the ontological argument does not create God. It recognizes, it perceives. It shows us a property that God already has rather than conferring that property upon him.
Another objection concerns the concept of God itself. The argument hinges on the idea of God as a supremely perfect being, but not everyone holds that idea of God — people conceive of God in many different ways. Very well. Let us set the name "God" aside entirely and simply call this being Bob. Bob is a supremely perfect being. Bob possesses all possible perfections: Bob is omniscient, omnipotent, omnibenevolent, and Bob has perfect existence. By the logic of the argument, Bob — as this idea — must have those properties, and therefore Bob must exist. Bob seems an awful lot like God, so we can worship Bob. Even if the traditional idea of God is not your idea, this being with all possible perfections must exist, according to the argument, and that is all the argument requires.
Perhaps you did not previously hold this idea of God — but you do now. You should not have watched. You have been infected with it, and now that you have the idea, you can no longer deny God's existence without contradiction, according to the argument. To deny that God exists, once you possess this concept, is to commit a logical contradiction. There should perhaps have been a warning at the start of this video: "Do not watch if you wish to maintain consistent atheism." But now that you have the idea, the argument holds that you cannot coherently deny God's existence.
Please do come up with further objections — that is what philosophy is for, and anyone can produce one. It simply has to be good: relevant, reasoned, and not merely a reaction along the lines of "I don't like this conclusion and I don't want it to be true."
Why did Descartes bring this up in the first place? Why did he talk about God at all? It was in order to slay the evil demon — to dispose of the third skeptical argument. The way this works is through one of the divine perfections. God exists: that is one perfection. Another is omnibenevolence: God is all-good. An all-good being would not deceive us directly, but neither would such a being allow us to be deceived in a way that we had no resources to resist.
Even if God does not directly deceive us, Descartes argues, if God leaves us in a position where we cannot avoid deception, then God is responsible for it. Consider the analogy: if you drive someone out into the middle of the desert, push them out of the car without water, and drive away, you have not actively murdered them — but you have placed them in a position where they cannot survive, and so you are responsible for their death. Similarly, if we are in the clutches of the evil demon and there is no way for us to find truth, no way to resist the deception, then God is allowing us to be deceived and would bear responsibility for it. But divine benevolence cannot permit that.
God must therefore have placed something in our hands that enables us to find truth even under deception, even in the worst possible epistemological conditions. And what is our best tool for finding truth? Clear and distinct perception. If that — the very best we are capable of — could still be wrong, then God would be responsible for our deception. Descartes concludes, therefore, that we can absolutely rely on clear and distinct perceptions.
When we have gone through the full process of examination — scrutinizing an idea from every angle, every shadow, every side — and we are convinced of its truth in a way that admits of no improvement, it must be true, because God exists and God is not deceptive. We must have some means of attaining knowledge, and clear and distinct perception is the best means we have. The third skeptical argument, therefore, cannot stand.
We cannot be completely at the mercy of a being that can trick us in ways we have no means of overcoming. We do have a means of overcoming it, but it is incumbent upon us to use it. The freedom to use or misuse our minds is up to us. We are the ones who decide whether we rely on clear and distinct perceptions, whether we work at them and examine our ideas with genuine care.
It is a great deal of work. Consider the example of two and two making four — seemingly simple, yet it still took us several minutes to work through it carefully, to truly focus and concentrate. It is not easy. But if we grow lazy and abandon that rigorous route, the fault lies with us, not with God.
At that point, we take on full responsibility for any errors we make, because we have the ability to avoid those errors if we put in the effort — the effort that Descartes calls science.
Looking back at the three groups of beliefs from the First Meditation, we can see that the first two groups are types of empirical beliefs, and the third is a priori. The first two fell to the sensory deception and dream arguments, while the third fell to the evil demon argument. Well, the evil demon has now been refuted — a stake has been driven through its heart — and so we can have a priori beliefs, provided we work at them carefully and make sure they are correct.
But what about empirical beliefs? Descartes argues that if all of our perceptions of the world were caused by something that had nothing to do with how things actually appear — if it were all a dream, if it were all the Matrix and none of this existed — we would have no way of discovering that, and God would therefore be responsible for our deception. Since God is no deceiver, there must be a world out there that is roughly like what we perceive, even if it need not be exactly like it.
Descartes argues that the senses are very poor tools for gaining knowledge. They are subject to deception, they are crude, and they are subjective. If we are in the same room, I might feel that it is quite hot while you feel that it is quite cold. That is not a good basis for science, because the data is not replicable — I will get one response and you will get another.
Sensory data is simply not good data for the sciences, in Descartes' view. It is too subjective, too variable, and too vague. If asked to describe the room, the best I could offer is that it feels somewhat warm — and that is not a measurement precise enough to build an experiment on.
A good measurement, by contrast, would be 78.3 degrees. That is something you can reproduce on the other side of the world or twenty years from now. It is exact and perfectly objective. You and I may disagree about how pleasant or comfortable the room feels, but we will both agree that it is 78.3 degrees. Measurement transforms the subjective into the objective.
Measuring quantifies what is otherwise vague. It makes experience exact, precise, replicable, and universal — the number is the same for everyone. What we need to do to put science on the right track, Descartes argues in this book, is take whatever empirical observations we make and transform them into numbers. That is what Cartesian coordinates are: a method for taking a shape and turning it into numbers. Shape is vague and rough; numbers are perfect and exact.
Once we have numbers, we can record, communicate, and replicate our findings. This transforms experience from the first two groups — the empirical — into the third group, the a priori. What we are doing is taking all of this vague sensory data and absorbing it into the mind, turning it into a mental structure that the mind can use, control, and understand. It is accomplished through something deceptively simple: taking measurements.
Taking measurements quantifies the qualitative. It transforms Groups 1 and 2 into Group 3, and Group 3 survived the skeptical arguments that Groups 1 and 2 fell to. A priori beliefs are certain; a priori beliefs are exact. What Descartes is saying is that of course we need to use our senses — the senses are the only way we come to know the world outside us — but we have to correct for them.
The senses are still deceptive. If I look at a star, it appears exactly as bright as a candle; my eyes report that the two emit the same amount of light. But I am not going to believe that — my reasoning overrules my senses. Similarly, if I look at a section of air, my eyes say it is empty, but my reason knows it is filled with germs, chemicals, and radio waves I cannot perceive. The senses are necessary, but according to Descartes they are not very reliable.
We must use reason to correct for the senses, and the single best way to do this for science is by transforming everything subjective, qualitative, and relative into exact numbers.
This is the moment when everything changes — the moment when all of Western civilization gets put onto a different track. Up until this point, knowledge of love was considered the same kind of thing as knowledge of numbers. They were simply different types of knowledge, neither ranked above the other. But now, Descartes, along with a handful of others — Galileo chief among them — established a rule: the only things science should deal with are things that can be quantified. If something cannot be expressed in numbers, it cannot be the subject of science.
That is not to say such things are unreal or without value, only that they fall outside the proper domain of scientific inquiry. The sole legitimate subject of scientific knowledge is what can be measured. And with that one small rule, modern science was born.
Consider what followed from it. The reason you can see me through a computer is that everything — the image, the color, even the timbre of my voice — has been reduced to ones and zeros. A computer is nothing but numbers. We have doubled the human lifespan, cured diseases, and walked on the moon because of mathematics. As Galileo put it, the book of nature is written in the language of math.
That single change was not foreordained. It was not obvious. Yet it is the reason we have computers, televisions, and airplanes — all of it traceable to this one strange little thought experiment that a French philosopher conducted on a snowy evening in 1619, and that we have now worked through together.