So, by the end of the Second Meditation, Descartes begun to use that Archimedean point in order to establish some things that go beyond the sheer existence of his own self. In the third meditation, which is tough going, difficult reading, (I don't expect you to be able to get to the bottom of all of it, I don't think that I have yet!) He gives his first version of an argument for the existence of God. Scholars, so far as I know, take this to be what's now referred to as an unusual version of the cosmological argument. A cosmological argument for God's existence tries to show that by thinking about causality, the origins of things, where things could have come from, you can infer that there must have been a God that produce the things that we have in front of us. The most common form of the cosmological argument focuses on the existence of the physical world, and says, "The physical universe must have come from somewhere, and it couldn't have come from just other physical things, therefore, there must be something non-physical, perhaps something divine, that accounts for the existence of the physical universe." That's an interesting argument that I don't want to go to into any depth about. But, Descartes' version of that argument is not about the physical universe, but about something that he finds within himself. Because he's introspecting as we've seen, he finds that he can see close up, so to speak, know for sure that is existing, that he's having thoughts, that he's performing judgments, and willing to do certain things. He finds that the second order thoughts are things that you can be sure of the existence of. But, he also finds himself in the Third Meditation. "I've got the idea of an infinite substance, a thing that is infinitely powerful and has other kinds of perfections." I don't think that I could have created that idea myself. I don't think I could have come up with something so sublimely wonderful as the idea of an infinite substance. Likewise, maybe my parents gave that idea to me. But then again I'm not sure they could've come up with it themselves, and their parents couldn't have come up with it themselves, etc. None of us human beings, none of us finite beings, he says, could have come up with the idea of an infinite substance. So, Descartes infers the only explanation that can make sense of the occurrence inside of my own mind of the idea of an infinite substance, was that it was placed there by an infinite substance itself, namely God. That's kind of like the way in which a painter will sign her painting, put a little signature of herself in order to acknowledge the fact that she was the creator. So, too Descartes suggests, maybe I've got the idea of an infinite substance of the way in which God signed to me as one of its products by saying, "I'm the one who produced you." We're not going to have to figure out whether Descartes has got a valid or sound argument for this conclusion. For our purposes is going to be enough to just understand that by the end of the Third Meditation, he takes himself to have established the existence of God. So by now, he's got, by the end the Third Meditation, that He exists, how things seemed to him to be, even if he can't be sure that's how things are, he can be sure about how things seem, what's sort of being He is, a thing that thinks and wills and judges and denies and imagines, etc. What the properties of external objects would have to be if there are any external objects, that's the idea of primary qualities. Then, the thing that's new as of the end of the third meditation is what it takes to be a proof of God's existence. We won't assess the cogency of that argument, but we'll just give it to Descartes in order to understand what he's going to be doing next, which is Meditation Four. In Meditation Four, to appreciate that, you need to understand a little bit about the problem of evil. The problem of evil is a traditional problem for theists, and even if you're agnostic, you might find yourself swayed in the direction of being an atheist as you look around you, and you confront the amount of evil that there is in the world. Some, types of evil are called moral evil, where for example, a person intentionally and knowingly does something that she takes to be wrong, the example of torturing a child that we mentioned not too long ago, might be a case of that kind. There's also physical evils in which, for example, people die horrible deaths due to earthquakes and hurricanes and lightning strikes and diseases, that is, things that cause suffering, that are not produced by the acts of an intelligent knowing agent. There are other cases that are not so extreme or overt as what are defined as morally evil in which, for example, a person fails to achieve a certain reasonable standard. They did not do their best, so for example, someone who's got a talent that they choose because of laziness can't be bothered, they decided not to develop that talent. You might feel it's a tragedy that they didn't develop their talents into becoming the great musician they could have been, or the great mathematician that they could have been, etc. Likewise, being in error is a form of evil for the following reason: learning about the world, acquiring knowledge is something that Descartes wants to suggest is inherently good. When you don't do your, what I'll call epistemic best, when you're not using your mind, and as rigorous and careful and painstaking ways you can, you're likely to fall into error. But, when you're not using your mind to the most rigorous and painstaking way, that's your fault, you're not doing as well as you could do. If you're not trying as hard as you might, in order to, for example, we're doing mathematics, calculate carefully and without making any computational mistakes, or if you're investigating the world outside of you trying to do some science, you might be using devices that are insufficiently clean, or that are malfunctioning in some way that might give you incorrect results. Descartes formulates this as, what he calls, the notion of clear and distinct perception. By definition, when I engage in clear and distinct perception, I'm using my mind in the most rigorous, careful, painstaking, self-critical way that I can imagine, before I jump to any conclusions. I only conclude something when I've challenged myself and imagined doubts that are as painful and surprising and distressing as I can possibly imagine. It's only if I've allayed those doubts, only if I convince myself those doubts can be overcome, then I'm going to allow myself to come to that conclusion. I clearly and distinctly perceive a piece of wax (if there's any wax outside my mind), by virtue of only ascribing to it these primary qualities such as extension, and shape, and location in space and time. If I think of the wax as being yellow or fragrant, or warm, Descartes will say that I'm engaging in obscure and confused perception, I'm not thinking as rigorous way as I possibly can. So with that background, with that partly theistic background that Descartes hasn't produced up until the end of Meditation Three. In Meditation Four, Descartes argues for what we may even think of it as a new principle of logic. In logic, we have inference rules: given certain things can be accepted as true, for example, the proposition that either A or B is true. If you also know that A is not true, you can infer that B must be true, and likewise Descartes will say, "If you can clearly and distinctly perceive that something is so, then you can infer that that thing is the case too." Why? Because if that proposition in question were not true, then if you were to conclude it is it will be case if you're falling into error. But that is not your fault because you've done your epistemic best to figure out whether P is true or not. Then, it cannot be your fault. It can only be God's, but God's not a deceiver. God will not ever will anything evil to happen. Therefore, Descartes will say, "If I can clearly and distinctly perceive something, then the theistic backing behind my epistemic processes will ensure that if I had come to a conclusion, that is definitely the case. That is definitely true." Here's a clear example. You can clearly and distinctly perceive that there can be no largest integer. How could you know? Well, I can clearly think of some number n, suppose somebody suggests that n, a very, very large number is the largest integer that there is. But, now, we can see clearly with my mind's eye as it were, add one, n plus one is clearly larger than n. Therefore, n, the original n we started with, cannot be the largest integer. I've used the notion, that process known as reductio ad absurdum, to conclude, that there can be no largest integer. We've just proven that there can be no largest integer, and if you thought was largest integer is one, such that you could add one to it, and get one that's even larger. Therefore, Descartes will say, "I've used my mind in a rigorous and painstaking way. I can conclude that there is no largest integer. There are infinitely many integers. God would not, let me go fall into error, given that I've used my mind, and the careful, rigorous, and painstaking way that I just did." Another example, is that Descartes thinks that you can clearly and distinctly perceive the possibility of your existing disembodied. I asked you to think about this a little while ago before we're delved into Descartes' reasoning. I asked you to imagine, well, if you were in a terrible accident that caused the destruction of your body, whether it's conceivable that you could survive the destruction of that body. I'm guessing that many people watching me raise that question thought, "Yeah, I guess that's conceivable. It seems like a possibility." Descartes will say, "Ah, well, if that's the case, then you've got the following is a possibility that you could exist disembodied, that that could happen even if we don't ourselves know that it will happen."