Ep. 229: Descartes’s Rules for Thinking (Part Three)

0:00 Mark: Okay, feel better, Seth. We're going to finish this up.

0:02 Seth: Good night.

0:03 Mark: So we're trying to figure out is a simple thing is as simple a proposition, because a proposition seems to involve subject and predicate. Maybe we should actually turn to another quote here.

0:13 Dylan: So which rule 12. This is the section where he starts talking about the three kinds of simple natures. There are those things which are said to be simple with respect to our intellect are in our view either purely intellectual or purely material, or common to both. Those simple natures which the intellect recognizes by means of a sort of innate light without the aid of any corporeal image, are purely intellectual. That's where that notion of the first simple nature, the incorporeal. And then there is those simple natures on the other hand, which are recognized to be present only in bodies such as shape, extension and motion, are purely material.

Lastly, those simples which are termed common, which are ascribed indifferently now to corporeal things, now to spirits, for instance, existence, unity, duration and the like. To this class we. We must also refer to those common notions which are, as it were, links which connect other simple natures together and whose self evidence is the basis for

1:10 Wes: all rational inferences, we make the purely intellectual stuff. His examples are doubt, ignorance, the action of the will. These are things when you think about them. You don't think about them by imagining something physical. They're purely abstract. And that's a problem that you have when you start talking about the human subject and say faculties of that subject as opposed to the things they're applied to. And then there are these higher level categories which span the gap between those two, like, you know, existence. This reminds me of in our social construction episode, Searle's distinction between ontological and epistemological objectivity. The fact that existence is something that can apply to our thoughts just as much as two things. So we would predicate them of both objects and our thoughts.

2:04 Dylan: Same thing like unity and duration. It's an interesting. The case of the pure material. Are all the ones that shape, extension, motion seem to be like the ones that he wants to focus on mathematically? At least in this book, it seems

2:17 Mark: like there's some philosophical work being done there. I mean, you could just say, oh, this is inner sense versus outer sense.

2:22 Wes: Yeah, you're talking about Kant's distinction, right?

2:24 Mark: Yes, yes. But by saying that there are certain things we grasp purely by an inborn light, you know, those truths of pure mathematics, for instance. That makes it sound like the way that we grasp inner sense is the same sort of intuition as the way we grasp the fact that I doubt my own experience of myself in time. And that's where the two seem to split apart for me, that you can use your inborn light of reason to contemplate eternal truths, sort of taking it back to Plato. Whereas the phenomena of inner sense seem closer to me phenomenologically to the experience of outer sense.

Right. My experience of myself as having a desire of willing something. There's different epistemic grounds. He obviously wants to make a big point that I can't be mistaken about my willing something in the way that I could be mistaken about my picking up a rock. But it seems like the experience. I don't think those come apart in the same way as mathematical truths versus empirical truths. These simple natures are known per se and are wholly free from falsity. We have a notion of number or existence or will or anything else like that. It is somehow you just contemplate it to just even think of it as to know everything there is to know about it.

It doesn't have any hidden properties. That's what makes it a simple nature.

3:46 Seth: Yeah.

3:46 Wes: Or it doesn't involve any judgment Affirmation or denial. Right. So again, that so much of Kant comes out of this. In fact, it having been so long since I've read this, and originally I read this when I was, you know, not even 20. But now it's clear how much Kant has ripped off people like Descartes. I mean, some of this is very direct. The distinction between judgment and intuition is very important and it lines up with this distinction between what is simple and clear from everything else, because what's present to intuition is just present and it doesn't involve us. Does it involve us making it an actual judgment or not? I don't think so.

4:27 Dylan: It doesn't seem like it here involves making an actual judgment. Though it does make you wonder if for some of these things that are simple truths that sound like they are actually more complicated, where you would think about them, where the line is between them being simple and not, like something like let's take shape, extension and motion for the purely material ones, or existence, unity and duration. We could probably, without too much work, come up with existences of whole books that are about each of those ideas. And so it takes so much time to explain it. Even him, when he gets to talking about extension in Rule, Rule 14, it feels like you're still trying to figure out what he means by extension. So taking him at face value that he means something particular about it and it has to be this idea that they're self evident in their simplicity.

5:17 Wes: The important thing to which all of this builds, right, it's foundational for modern science and it's a kind of amazing turn. But the idea is that, yeah, something like spatiotemporality or the extendedness of things, it's not really something you can say anything more about. And science doesn't try to. It works with it and it treats it as a given. But you're not going to do a scholastic thing about, oh, what's the nature of space? It's the, you know, it's the thing that's right around the object or something like that. You just say things are extended. We know what we mean by that. Our awareness of space is intuitive and Kant of course builds on that and that's clear to us. And we're not going to do any metaphysical proofs or judgments about all of that. Foundationally, it's meant to be clear because it's supposed to be the foundation for what is scientific.

6:08 Dylan: So that's a lot easier with the common notions, right? The notion of two things that are the same as the third thing are the same as each other, those kinds of basic logic things. I remember one of the things that I found interesting at St. John's is it made sense to ask a question and try to figure out, well, where do the, the rules of logic come from? Because usually in my experience up to then is you just have the rules of logic, right? And in the posterior analytics, I think it is, Aristotle tries to talk about where all of these sort of common notions come from. But at some level it's just something that you just know is true, right? Like when you say that you have two stones on the ground and another two stones and you say they're equal, what you mean by equal is. I don't know if it's anything other than something self evident.

6:57 Mark: I'm just looking at the next page because he goes on and gives a mathematical example, because he says the union of these things, one with another, is either necessary or contingent. In other words, the simple ideas are if you do make a judgment about them, then it could be a contingent judgment or it could be a necessary judgment. It's a necessary judgment when one of the ideas is so implied in the concept of another in a confused sort of way that we cannot conceive even either distinctly if our thought assigns to them separateness from each other.

So for instance, 4 and 3 are 7. The union is necessary. So I'm going to say that just number and equality, those are simple notions. Four is perhaps a slightly more complex notion because it builds on what number is and you don't really know what 4 is unless you already also know what 3 is and what 7 is and what addition is. And that that is a mathematical truth. What does that mean? So I started by saying number is absolutely simple. You just think number and you know everything there is to know about number. But clearly you don't know everything because there's innumerable mathematical truths.

Even just to kind of get the idea that there's an infinite number of mathematical truths and have a general idea how to do them, seems to involve more than just knowing a simple notion.

8:14 Dylan: Well, and in fact, the great example there is irrational numbers, right? So if there is a self evident number, it's the counting numbers 1, 2, 3, 4. And you might get yourself around to thinking of a ratio as a number, that a half is a number, though you have to do some work to do that. But getting to the diagonal of a square as a number, when you try to figure that out, that becomes a pretty big problem in thinking about it, that it's a number that you, you can't write it down as a fraction, you can't write it down as a finite series of decimal.

And in fact, the way you end up calling it a number is because you make an insistence that you have to be able to number a line. You have to be able to apply number to measure the length of every line that exists. And it's thinking that through and it's making that insistence that you're able to number a line that makes you say that the square root of 2 is a number. At some level, it feels like to your point, Mark, that's become a complicated notion. You've discovered something about number that wasn't part of your self evident truth before.

9:21 Mark: So his next point, I think the only way to try to figure these out is just keep moving and see if it resolves. Fifthly, we remark that no knowledge is at any time possible of anything beyond those simple natures and what may be called their intermixture or combination with each other. Indeed, it is often easier to be aware of several of them in union with each other than to separate one of them from the others.

9:42 Dylan: This is about limits of our understanding.

9:44 Wes: Right?

9:44 Mark: Right. I mean, he's going to give an example from geometry. It seems like a triangle might be simple, but there's an angle, a line, the number three figure, extension, etc. He says, but that does not prevent me from saying that the nature of the triangle is composed of all these natures, that they are better known than the triangle since they're the elements we comprehend in it. So maybe that's what's going on with arithmetic as well, that there is equality, there is succession, some basic things like that that together make a system.

10:14 Dylan: Don't you have a whiff of someone like Russell and Whitehead here in the Principia Mathematica of trying to derive all of mathematics from 0, 1 and plus.

10:27 Mark: But it is interesting, of course, that he's. No knowledge is at any time possible of anything beyond these simple natures of what might be called their intermixture or combination. Okay, well, maybe in math, but really anything. So that is to be shown.

10:43 Wes: So at the triangle example, the point of that example is to say that sometimes it's easier to know the complex thing than the actual simpler things of which it's composed that we will end up analyzing them into.

10:55 Dylan: So just because we don't understand three and shape and extension doesn't mean that we can't understand triangle, which is funny because it sort of flies in the face of. I think this is part of your point, Mark.

11:05 Wes: Right.

11:06 Dylan: That you have these simple natures that are the ones that we're supposed to intuit perfectly or something like that. Those are the only ones we can know. But he seems to be saying that, well, we can know triangle, but not really understand shape.

11:18 Mark: I guess we don't really know it. Let's go on the next point. We say those natures which we call composite are known by us either because experience shows us what they are or because we ourselves are responsible for their composition. This is sounding like it's getting Kantian.

11:32 Dylan: Kant was getting Cartesian.

11:34 Mark: I guess that's an open question, because it's. For Kant, it's not that experience shows us what they are, or we ourselves are responsible for their composition, it's just that's what experience is, is us actually composing things even though they strike us as preformed. So Descartes seems to be drawing a distinction here. I think that Kant does not actually make.

11:55 Wes: I think it's a little complicated because the categories of experience for Kant, of the understanding and intuition, they determine how things are going to appear to us. But of course, the data has to come from somewhere. Like there are mind independent constraints and experience, that's a word that's ambiguous between what's being inserted into the whole system as data and between experience in that specific Kantian sense where you have constructed objects that are already constructed according to all the categories and stuff. To say experience shows us what they are can mean very broadly, just to say that it's a posteriori, let's put it that way, and there is such a thing, obviously, as a posteriori. And Kant, despite the fact that we're

12:41 Dylan: constructing everything, isn't part of this section all about how we go wrong and the conditions under which we go wrong. So he says that the intellect can never be deceived by any experience, provided that when the object is presented to it, it intuits it in a fashion exactly corresponding to the way in which it possesses the object, either within itself or in the imagination. We can go wrong only when we ourselves compose in some way the object of our belief.

13:09 Wes: Yeah. And the composition will be something like the intuition of something as it presents itself to us, and then a judgment to the effect that, hey, this is the way the world really is in itself.

13:21 Dylan: Yeah. So when you look at a stick that's in the water and it looks bent, you would not say that, oh, my senses got fooled. You would say that you made a mistake. Right. So it's not that the world appears to your senses As a bent stick. It's that you are wrong in your judgments about making that composite.

13:40 Wes: Yeah. Or his examples of jaundice. You know, I'm looking at everything and it seems yellow. And there's nothing wrong in and of itself with that data. Right. As long as I treat it as such. When I say, oh, it seems. Everything seems yellow to me. That's true. It's when I say everything seems yellow to me and the world is yellow. Everything is yellow. I have compounded two things and that composition is what's led to the error. The two things are the judgment and then the initial experience.

14:11 Mark: What the imagination represents to him and then what he assumes on his own account. Namely that the imagination reflects what is in the external world.

14:21 Wes: Right. Moreover, we ourselves are responsible for the composition of the things present to our understanding when we believe that there is something in them which our mind never experiences when exercising direct perception.

14:33 Mark: Yeah. The correspondence with the external world. That is the thing that we are never actually experiencing when exercising direct perception. The thing that Searle hates.

14:41 Wes: So, yeah, that's actually really fascinating.

14:43 Mark: We're only ever perceiving the contents of our minds and never the things in the world themselves. All right. And then he just goes on that there are lots of different mental habits that would make us make these judgments about the world. We need to go back and look at the other rules and use intuition and deduction.

15:02 Dylan: Your version says what three forms of composition?

15:06 Mark: I was trying to summarize.

15:08 Wes: Impulse, conjecture and deduction.

15:10 Mark: Our second conclusion. To know these simple natures, no pains need be taken because they are of themselves sufficiently well known. This is that they're entirely self contained. Application comes in only in isolating them from each other and scrutinizing them separately with steadfast mental gaze? Anybody can, by focusing, can pick these things out.

15:30 Wes: So his example is sitting and standing. The difference between me sitting and standing is just position and nothing else I haven't altered in any other way. Is that a satisfying example?

15:45 Dylan: In this section he's slamming Aristotle.

15:49 Wes: Yeah. He's going to get into that whole theory of the place is the surface of the body surrounding us. That's what he doesn't like here. And this idea that that's what's changed when we're sitting or standing is just our position and not relative to other things we might even say, but not some sort of metaphysical property of place that's surrounding us or something like that.

16:12 Dylan: For example, can anyone fail to perceive all the respects in which change occurs when we change our place and when Told that place is the surface of the surrounding body, which is from Aristotle, would anyone conceive of the matter in the same way? For the surface of the surrounding body can change even though I do not move or change my place. Conversely, it may move along with me, so that although it still surrounds me, I am no longer in the same place. And then again, when people say that motion, something perfectly familiar to everyone, is the actuality of a potential being insofar as it is potential, do they not give the impression of uttering magic words which may have hidden meaning beyond the grasp of the human mind?

For who can understand these expressions? Who does not know what motion is? Who would deny that these people are finding a difficulty where none exists? It must be said, then, that we should never explain things of this sort by definitions, in case we take hold of composite things instead of simple ones. Rather, each of us, according to the light of his own mind, must attentively intuit only those things which are distinguished from all others.

17:16 Wes: So that's a really good example to get at what he means by its being simple and being evident to us without any further. We can't do the philosopher thing with motion. It's not helpful, according to Descartes, and say it's an actualization of potentiality. We just have to treat it as basic. We have to treat it as something that we know, even if we can't give a, you know, say what it is exactly in a metaphysical way.

17:44 Mark: So, yeah, someday we will actually read that part of Aristotle and figure out why someone would want to say that about motion. But the next paragraph here, the next section, is illustrative because he's actually getting, to use a scientific example, he just repeats what we said earlier, that the whole of human knowledge consists in distinct perception of the way in which simple natures combine to build up other objects. Consider the question, what is the nature of the magnet? He says people at once prognosticate difficulty and toil in the inquiry in dismissing from mind every well known fact, fasten on whatever is most difficult, vaguely hoping that by ranging over the fruitless field where multifarious causes lie, they will find something fresh.

Is that what physicists do? Like, it does seem like we would want to find that there are invisible particles flying between the magnet and the piece of iron. You know, at the very least we want to come up with a formula for, like, how strong the magnetic pull is. And hopefully this would lead to some actual mechanistic interpretation. Certainly a mechanism is the aim, but he says he reflects that there can Be nothing to know in the magnet, which does not consist of certain simple natures evident in themselves, will have no doubt how to proceed.

He will first collect all the observations with which experience can supply him about this stone, and from these he will next try to deduce the character of that intermixture of simple natures which is necessary to produce all those effects which he has seen to take place in connection with the magnet. This achieved, he can boldly assert that he has discovered the real nature of the magnet insofar as human intelligence and the given experimental observations can supply him with this knowledge. So that's very abstract. Does that sound like, oh, he's just stating in a shorthand way what actually science does, or does this just sound bizarre?

19:27 Wes: No, I think he's saying what science does, especially in the context of what comes later. But I wish I knew more about magnetism and maybe Dylan can help us. But part of this is just instead of giving some metaphysical speculations about where magnetism comes from, you do a lot of work in quantifying it, saying, okay, what happens when I put such and such an object in a magnetic field? How does the magnetic field vary with the distance to the object or, you know, and all of that stuff, and you find ways to quantify it. And ultimately, if you can give a lower level theory about what's going on, maybe at a subatomic level, you're still within the realm of spatiotemporal correlations between extended things, at least metaphorically extended. I don't know once we get to the quantum level, how that works. But Dylan, can you help us with that?

20:19 Dylan: Putting aside for a second what the current scientific account of magnetism would be, what I hear him saying is that you're going to take your observations and you're going to account for them, presuming that there is a group of simple natures that are composed together to give you that result, and you're going to presume that you can know them. It's going to be, for lack of a better term, mechanical in some way.

20:46 Seth: Yeah.

20:47 Wes: And you're going to presume that they involve extension and duration and all of these quantifiable noble, these simples.

20:54 Mark: But the simples would have to be things that are macroscopic. Right. So it's like the weight of something, you know, its mass. Maybe attraction is just a simple notion in itself. We see some things are attracted to other things. Once we get a formula that figures out exactly what kinds of materials are going to be attracted to the magnet, which ones Aren't whether if it's heavier or lighter, whether it's going to affect how strong the pull is. Like that's the stuff that we can find out and we can't know anything more than that. Like that's the limit of human knowledge.

21:26 Dylan: Yep. In this realm. Like the idea that you would have an account of nature that was based upon four fundamental forces and a bunch of particles that just existed. That idea, even if you wanted to try to go further that kind of account is what he would be driving for.

21:46 Mark: Yeah. His last point is here that there's no kind of knowledge that's more obscure than any other kind. It's just all just combining what is self evident.

21:56 Dylan: What's interesting about this is how complicated something that is progressively built up of self evident things is. Which I think he would not deny.

22:06 Wes: So obscure doesn't mean that it can't be a difficult problem with lots of steps. It just means it's a difference in quantity of steps. Not in some fundamental difference in kind.

22:18 Mark: And then the remainder of this section he sets up what's going to happen in the rest of this extant text. Which is what constitutes a scientific or any other kind of question. Legitimate question.

22:28 Wes: So we get these different types of deduction.

22:30 Dylan: Yeah. Different types of problems.

22:32 Wes: Things from words, cause from effect or effect from cause. And then parts of the whole or the whole from the parts. So these three different sorts of relationships are what's at stake when we are conducting investigations. Want to figure out what the causes are. We want to figure out what something is composed of. Or we might be in the domain of figuring out. Is it a meaning thing is conceptual analysis.

22:58 Dylan: I mean my translation. He calls them perfectly understood problems and imperfectly understood problems. The perfectly understood problems, even though we don't know the solutions to them. They can be understood perfectly. And you can count it as perfectly understood only if we have a distinct perception of the following three points. What the criteria are which enable us to recognize what we are looking for. For when we come upon it. What exactly is the basis from which we ought to deduce it and how it is to be proved that the two are so mutually independent that one cannot alter in any respect without there being a corresponding alteration to the other

23:34 Mark: that sets up what questions are going to be. Which you can see how very limited it is compared to what we might consider legitimate philosophical questions. Like we can really see the roots or at least one link in the chain to get to something like logical positivism. That a question like why does the world exist? Or something just wouldn't even make any sense.

23:53 Dylan: I think on this account it's an imperfectly understood problem. I mean, this idea of stating the problem in the right way, such that there is a way to answer it, is that I would consider it a core principle of science, of quantitative modern science. Half of the battle is stating the problem in the right way so that it admits of an answer.

24:15 Mark: So even the example I just gave, why does the world exist? That could be, you know, give a causal account, or it could be looking for a reason in God's mind or something. And maybe the causal account question makes sense and the reason God's mind question doesn't make sense. Or maybe you think more about God and you find there is a sense to, you know, we could further clarify that question. I feel like Descartes would have a response to that, you know, something about the perfection of his nature and extending out and, you know, then Leibniz will give us a whole theodicy based on that. So finally done with Rule 12, Rule 13.

24:53 Wes: Once a question is perfectly understood, we must free it of every conception superfluous to its meaning, stated in its simplest terms, and having recourse to an enumeration, split it up into the various sections beyond which analysis cannot go in minuteness.

25:09 Dylan: This seems just sort of a stepping stone to 14.

25:12 Mark: I had a note here under this. Something we don't know is designated by something we do already know, right? So this is Plato's concern. In order to look for something, we must vaguely know it in the first place. I think that Descartes is giving a later version of that.

25:25 Wes: I mean, ultimately for Descartes, we're going to give a symbolic representation of what we don't know and put it in relation to all the things that we do know. So the simplest example of that is just equations where I'm representing known quantities, say as A, B and C, and then unknown quantities as X or Y. And then I can put things in relation to each other and solve the equation.

25:51 Dylan: Is there a deeper point of saying that I have to have something, no matter how fuzzy or unarticulated, to which I'm directing that thinking? And until I get that, I'm never going to have a place to even start.

26:06 Wes: If I'm asking a question, I need to know, in a sense, what counts as an answer, what category of thing the answer would be in. Is it going to be a number? Is it going to be something else? And then again, as Mark pointed out, if you knew nothing about it, it's not just. I mean, it is Meno's paradox, right? I have to have some fuzzy sense of the thing before I investigate it. But to investigate something, there actually have to be some elements of it that I know really well or well enough that I can put them in relation to the stuff I don't know and then solve. In other words, I have to have these very well known noble things there that'll end up forming a basis of an account that I construct to explain the unknown thing.

26:51 Mark: So that makes me think of like a crossword puzzle. You know, you've got the scheme, maybe you've got some letters already filled in, and you just need, you know, three down or whatever. Now, is that comparable to. He says a little more about magnets here. We already know what is meant by the problem. If the problem be the nature of the magnet, we already know what is meant by the two words, magnet and nature. And this knowledge determines us to seek one sort of answer rather than another, and so on. Maybe that's better in Latin. So that's not helpful as far as I'm concerned, like, because I don't really know what. Maybe nature meant something very particular to him in Latin, you know, whatever Latin term he's using there.

27:28 Wes: Well, he talks about the experiments by this guy Gilbert, who wrote the book on Lodestone. Maybe it's better to do the example of the strings. So the question may be, if you're saying, you know, what is the nature of sound, right, you could try to give a metaphysical what is account by some sort of speculation. Or you could do an experiment. The one he gives is, you know, strings of different lengths and thicknesses holding different weights and whether they make identical sounds. And you can get the same sound out of them by increasing the weight as you would of the other by, I don't know, decreasing the thickness of the string or something like that.

So you develop all these relationships between these different dimensions, you know, weights and lengths and thicknesses. And then the sound, which we ultimately assume to be correlated to pitch, he's talking about, it'd be correlated to a certain frequency oscillation. That's one way of conceiving of the nature of something as involving all those sorts of relationships. And it's one that can be investigated.

28:30 Mark: Yeah, the rest of this is just look at everything that is stated in the problem. Don't add anything, just restate the problem clearly, try to get rid of assumptions. He brings up the riddle of the Sphinx. You know, walks on four legs in the morning, two legs in the afternoon. Three legs at night. He says, don't bring in the assumption that foot refers to an actual animal foot. So I'm not sure. What do you think of that as advice for how to solve a riddle like that even? Because, I mean, the whole point is to kind of think outside the box.

29:00 Wes: Well, it's good advice for solving riddles because that's what you do to solve the riddle. You think of all the words and you try to figure out the double entendre, basically.

29:09 Dylan: Exactly.

29:10 Mark: But saying don't bring in the assumption that foot refers to an actual animal foot. Like it's. Don't assume that the words mean what you think they mean or have their usual meaning.

29:20 Wes: Can we think of an analogy, though, in science?

29:23 Mark: Yeah, exactly. I mean, we want to isolate the different potential causes. So maybe that's something by picking apart each word in a riddle for looking for the double entendre. That's kind of like picking out the various causes in a phenomenon and then trying to figure out by varying this thing. Does it.

29:42 Wes: Well, I think. Doesn't he bring up the Earth later on? We don't make the assumption of geocentricity, for instance, just because it looks like the sun is going around the Earth. We try to get more abstract than that. So that, I think is analogous to saying, even though it's the word foot, even though it's the sun going around the Earth, in some sense we want to get really non literal about it. You get to a different level of abstraction that way. So it could be that the Earth is going around the sun and you get the same effect.

30:13 Mark: Is that example under 14? Can we move to 14?

30:16 Wes: Okay, we're skipping over a lot of.

30:18 Mark: I just don't have any notes previous to that, but if you had anything that you wanted to bring up, just.

30:22 Wes: Yeah, what I said is towards the end of this, about the Earth. And we seek to extract and recorded observations of the stars in answer to the question as to what we can assert about their motion. It is not to be gratuitously assumed that the Earth is immovable and established in the midst of the universe, as the ancients would have it, because from our earliest years it appears to be so. We ought to regard this as dubious in order afterwards to examine what certainty there is in this matter to which we are able to attain. This sort of lines up with this distinction he made between appearance and things appearing to us and then making judgments on top of that.

Yes, it looks yellow, but we don't need to assume that at a metaphysical level, we just Treat that as an appearance to be explained. Also, you don't conflate explanation with the phenomenon to be explained. Right. You're not saying, hey, everything looks yellow because everything is yellow, or, hey, so the sun goes around the earth because it looks like that. You disentangle phenomena to be explained from the possible mechanisms of that explanation, which can actually be various and need to be investigated.

31:25 Mark: All right. Extension Rule 14. The same rule is to be applied also to the real extension of bodies. It must be set before the imagination by means of mere figures. For this is the best way to make it clear to the understanding.

31:37 Dylan: The beginning of your version of it is a little bit different in an important way.

31:42 Mark: Yeah.

31:42 Dylan: Mine says the problem should be re expressed in terms of the real extension of bodies. It should be pictured in our imagination entirely by means of bare figures.

31:52 Mark: I like that much better.

31:53 Dylan: Thus, it will be perceived much more distinctly by our intellect. So Rule 13 was all about breaking it into the smallest possible parts, but now this is in terms of what kinds of parts they should be. This is like the mechanization of the world by science.

32:10 Wes: This is the idea that all these things we take for granted. So it's hard to see how radical and amazing that it is. But the idea that all these various phenomena can be explained by spatiotemporal relationships between things, by relationships between different magnitudes, different quantifiable things, it's quite counterintuitive. Again, we saw this in Lucretius. I think it's the idea that if I'm explaining some qualitative thing like color, I'm not just reaching for, hey, it's because there's lots of little colored things that add up to that.

I'm not searching for color qualitative foundations for this qualitative thing. I'm searching for quantitative foundations. I'm saying color is grounded on atoms and their shapes and interactions and things like that, which is purely spatiotemporal. And that's the radical jump that we're making. The ancients, you know, all the stuff that Lucretius goes over about the homunculi and all that stuff, they're caught in that trap of not being able to get their heads around that idea that certain phenomena might be explained by these qualitative things might be explained by something that just seems radically incongruous with them, which is motion and duration and extension and all that stuff.

33:29 Seth: Yeah.

33:30 Mark: What is idiosyncratic to Descartes here is by saying we should quantify everything is to say we should represent it in the imagination by mere figures. In other words, what makes quantification so clear is ultimately because we can imagine different lengths of things and hold them side by side in our head. Like, that's the only reason why we know, you know, one number is bigger than another number is because we can do that little thought experiment where we hold three up next to two and kind of use that knowledge to go from there.

34:00 Dylan: And in fact, it's just generalized in terms of magnitude. So we should note, nothing can be reduced to such an equality except when admits of differences of degree and everything covered by the term magnitude. Consequently, when the terms of a problem have been abstracted from every subject in accordance with the preceding rule, then we understand that all we have to deal with here are magnitudes in general. So we number everything.

34:26 Mark: Yep. And then he specifically talks about ratios. But it's complicated with certain other relations or ratios. I just, from our Heraclitus discussion, jumped on that as, oh, that's what reason comes down to is finding the ratios

34:39 Wes: between things, the relations.

34:43 Dylan: It's rational.

34:45 Mark: Learn your fractions, kids. That's what thinking's all about. So whenever we have a problem with one of these texts, stop. Draw some lines.

34:56 Wes: That's right.

34:56 Mark: This line is longer than that line. I understand.

34:59 Dylan: Now, he's doing things here that just cast a gigantic shadow from here now. I mean, making everything be in terms of magnitude. And then a little bit later, he expands the method. Right. Mathematics is the quintessential example. But he goes on to say, the rules that I'm about to expound are much more readily employed in the study of sciences than in any other sort of problem. Moreover, these rules are so useful in the pursuit of deeper wisdom that I have no hesitation in saying that this part of our method was designed not just for the sake of mathematical problems.

Our intention was rather that the mathematical problems should be studied almost exclusively for the sake of the excellent practice which they give us in the method. So math is just training ground for doing the actual science that he wants to do, which is numbering the world world and establishing relations of magnitude to understand how things work.

36:02 Wes: Yeah.

36:02 Mark: So you had an example here of. Unless somebody asked something earlier. I'm looking at page 30. Why is it okay to say extension is not body? The concepts are different, even though there's a necessary conjunction between them. So you might think that extension and body just mean the same thing. He says these negative distinctions must be taken altogether outside the bounds of the imagination if they are to be true. So it sounds like he's anticipating the sense reference distinction here. Right. In other words, in every body you see, it has extension, but it's kind of picking out different aspects of it or something.

36:35 Wes: This also reminds me of Khan a little bit because he's pointing to the way some of these metaphysical paradoxes arise. And the paradox is you would say everything that's extended is corporeal, and everything that's corporeal is extended. Aren't they just the same thing? And then you say, so isn't it the case that extension just is body, then? And don't we mean the same thing by them? But then you realize, of course, that you don't, and you get this sort of paradox.

37:02 Dylan: I mean, this is all in the section of that. We're always going to use our imagination for everything. Abstract entities are never formed in the imagination in isolation from subjects. Henceforth, we shall not be undertaking anything without. Without the aid of the imagination. And here imagination literally means making images of things.

37:23 Wes: Yeah. So when I say all extended bodies are extended, and I can imagine a body and the extended thing, and I can imagine its extendedness. But at the level of saying extension is not body, I'm speaking of these abstract terms, how do you picture that?

37:40 Mark: Well, you don't, because you can't picture a place where they split apart.

37:44 Unknown speaker: Yeah.

37:44 Wes: In this case, that's the thing. You have to be careful to make the distinction about what you're doing. Are you doing something that's picturable in the imagination, or are you working at a different level of abstraction? You don't want to get the two confused.

37:56 Mark: This is what sounds like going back to that inner versus outer sense thing, where when you say extension is not body, it's because extension and body are both simples. And you're just reflecting on the simples and that those are different. And there's something that just the natural light of reason lets you do this. There's no picturing of anything. I guess I'm trying to hook up what he said before about, you know, when you actually imagine something, then you're pulling stuff from experience, even if it's just in your imagination. You're pulling from outer sense. You're picturing representative bodies and the fact that they're all extended. And then by bringing that into imagination, then the lateral light of reason can reflect on it.

38:36 Wes: The error that he's pointing to is that I imagine, I say is extension body, and I imagine bodies, and I know that they're extended, and I know that they're always extended and that extended things are always Bodies. And I'm tempted to rise to this level of abstraction and say, hey, extension is just body. This is the way he puts it. This is a stumbling block for many who, not perceiving that extension so taken, cannot be grasped by the imagination representative themselves by means of a genuine image. So now such an idea necessarily involves the concept of body. And if they say that extension so conceived is not body, their heedlessness involves them in the contradiction of saying that the same thing is at the same time body and not body.

39:15 Mark: He's giving a clarification. You thought that you could just use your imagination, basically by comparing lines next to each other and seeing which one is longer, that you've reduced the problem to a problem of quantity. And that is something that can be studied by the imagination. But clearly concepts, unless they're the same type of thing, the number three and the number four are both numbers, but color and shape are. Well, they're both perceivable attributes, or something like. You'd have to come up with a genre of which the two examples are species, and then you could compare them. But extension and body are fundamentally different types of simples, even though, as a matter of fact, they always accompany one another in the world.

40:04 Wes: Well, his analogy is that extension is not body. He's saying, is like saying that number is not the thing that is counted.

40:12 Dylan: Well, in this case, extension is not body. There's no specific idea corresponding to it in the imagination. And this expression is entirely the work of the pure intellectual. And he goes on to give his examples, and then he's going to conclude with all these and similar propositions. He gives a bunch of examples that are like, extension is not body should be removed completely from the imagination if they are to be true. That is why we shall not be concerned with them in what follows. So all these kinds of correspondences, because they're acts of pure intellect, not of imagination, just don't even fall in these terms.

40:49 Mark: I think what we just did there is in order to say that extension is not body, we actually have come up with some higher level of category to therefore say that one is not the same as the other. It's like saying, oh, you can't compare apples and oranges. Well, yes, because you have the concept of fruit. And so you can say an apple is not an orange. But that's different from saying, this apple is greener than that apple or bigger than that apple. You're finding the genre in a different level of analysis. So when you get too abstract, then you're out of the realm where the imagination is useful here.

But to me, that just says that extension is comparable to body. You can compare the two terms and say for sure that one is not the other. And that just means that there are ways of comparing, in a very basic way, things that cannot be reduced to quantitative differences. And so why could that not also be the case for. I want to say more complicated things, but just other things. I mean, clearly he wants to say mind is not body. And those seem to be, you know, if you bought my phenomenological take, you don't just contemplate the mind in the way that you contemplate timeless mathematical truths.

It's more like there's an inner sense versus an outer sense. And those are comparable in that they are both parts of our phenomenology. But you can't take the inner sense and line it up against the outer sense as you would two lengths of twine and say one is bigger than the other. So I think Descartes is just pointing out that maybe just within the realm of science, but not sort of within the realm of philosophy as a whole, you can't make everything into analysis of quantity.

42:30 Dylan: Well, I think he's certainly saying that that's not what his method is pointing to. His method is all about quantification. Whether he's saying that there's no other forms of legitimate thinking, I think that's a separate question.

42:43 Mark: Wes, do you think that he's saying very strongly that really every type of careful thinking, as opposed to this fuzzy Aristotelian stuff that he's trying to reject, involves being able to abstract from the things you're talking about and come up with some quantitative analysis? So we already talked about the magnetic that it seems like there's a lot of qualities involved, you know, the basic quality of attraction or the basic quality of weight. But when you actually zoom in, do the analyses, you can do them as individual quantitative analyses and then try to insofar as you can relate those to each other. So it's not just comparing weights to weights or attraction level to attraction level, but trying to actually correlate attraction level to weight, et cetera.

43:31 Wes: Yeah, you're doing causal analysis. You're saying how certain quantities change in relation to each other over time.

43:37 Dylan: Well, I want to say that the distinction you might be getting at, Mark, is perfectly versus imperfectly posed problems, so

43:45 Mark: that if you pose it perfectly, then it can be made quantitative, Whereas when you start, then you just don't know how to make it quantitative. Is that what you're saying, I'm not

43:53 Dylan: 100% certain, but I guess that's the direction I was going to.

43:57 Seth: Mm.

43:57 Mark: He either has to say, everything when you think about it carefully enough is quantitative, or there are just some basic things, like knowing that body and extension don't refer to the same thing, even though they're always accompanying each other. That you don't have to do this trick with that you only need to do this quantitative trick when you're talking about composites. I think that's where he's been going in talking about this. You know, that he didn't introduce this stuff about comparing lines when he was talking about simple natures. It's only when we got to composite natures.

44:30 Dylan: Well, in fact, in Rule 12, the end of Rule 12, you have a little bit of his way. He's intending to break up the rules for the direction of the mind. So the first 12 rules were all about the simples, and the next 12 would be about perfect problems. And then the last 12 would be, which don't exist, would be about the imperfectly understood problems.

44:53 Mark: So we'll have to look to discourse on method to find out, presumably, hopefully, the imperfectly posed problems.

45:01 Dylan: Maybe.

45:01 Mark: You guys have anything else here, you know, in the end of 14 or beyond?

45:07 Dylan: Only that you get the foreshadowing of the geometry in a big way. You get things being dimensioned in that they can have some unit of measure with respect to them, and then that you have a unity, so that you're referring everything to that one common magnitude. This is at the heart of book one in the geometry.

45:30 Mark: Yeah, he gets very specifically mathematical by the end of this. By 18, only four operations are addition, subtraction, multiplication and division. So he's getting to the foundations of mathematics. And very much as we've compared to Russell and Whitehead's Principa mathematica.

45:45 Dylan: Up till 14, you're still kind of abstract about the way in which you solve problems, but once you get there past that, you're really getting into much more specific mathematical characteristics.

45:57 Mark: As he gets more specific, he gets less verbose about them. Or maybe my notes were just less verbose. I say, actually, there's quite a bit for Rule 16. Say that I just did not bother.

46:09 Wes: Yeah, it gets complicated once I start seeing square root symbols.

46:14 Dylan: I myself always stopped at 14. I think I've read the other ones, but 14 is where the juice kind of ends for me.

46:21 Mark: Once you get to the idea that you should try to quantify everything, well, okay. What from there? Well, can you use abbreviations so that your quantifications are short. Use all A is B, all B is C. Therefore all A is C. Don't just spell out what the sentences A and B and C. You can remember more stuff. So this is just applying the earlier rules where he was like to get algebra, contemplate each step and then connect them together and then contemplate the stream and try to keep that whole thing in your head. It's just he's applying to this specifically to doing math and science.

46:57 Wes: I mean, it's profoundly important. It's just we're so used to it because we live in his. The matrix that he created. We all did coordinate geometry in high

47:07 Dylan: school called Cartesian coordinates.

47:10 Wes: We're in Descartes matrix. He is the evil genius.

47:15 Mark: Today's closing song is called Perfect Design, fitting for a perfectly designed episode describing a perfectly designed set of epistemological rules in a perfectly designed text, which Descartes never actually finished. The song is by Ian Moore. I talked to Ian on Nakedly Examined Music Episode 94. Check that out at nakedlyexaminedmusic.com so we're going to actually take a break before we come back to Descartes in Discourse on Method. We are going to read some. Bruno Latour has been often requested that we cover. And since we were just doing the kind of science war stuff in our social construction episode, we have a Linda Walsh from our Oppenheimer et al. Science communicators, whatever the hell that episode was called, had suggested. We have never been modern, so come back for that. And then we'll have more Descartes and good night, everybody.

48:12 Dylan: Good night.

48:12 Wes: Good night.

48:30 Unknown speaker: I'm not saying that we're wrong. Just that we should look around, Take stock on all the things that we let slip by in the blank of an eye you could throw it away. But today is a good day with my friends just laughing and singing out songs. Tell your mom not to worry, the kid's all right. Just refining the thought till you're fine. That perfect design, yeah. This light sometimes less than kind Disappointment clouds the rise. Always think that we should reach for something more? You live your life like a ghost? You just float in any direction the wind blows.

But today is a good day with our friends just laughing and singing our songs. Tell your mama not to worry, kids all right. Just refining the thought till it finds that perfect design. So just take off your cynical eyes. Wasn't wisdom that broke up your dreams Back in your tender years. And yeah, you survived all the low tides and rocky shoals A steely demeanor

50:32 Mark: in an ocean of

50:37 Wes: yeah.

50:47 Unknown speaker: So today is a good day with our friends just laughing and singing our songs Tell your mom Mama not to worry, child Kids. All right. Just refining the thoughts you'll define that perfect design yeah Today is a good day oh, today is a good day oh, today is a good day in this life.