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

0:00 Mark: You're listening to the Partially Examined Life, a podcast by some guys who at one point set on doing philosophy for a living, but then thought better of it. Our question for episode 229 is something like, are there mental habits to optimize our approach to philosophical and scientific problems? And we read Rules for Direction of the Mind by Rene Descartes, written around 1628. The for more information, please check out partiallyexaminedlife.com this is Mark Linsenmayer with truths growing from my brain like Athena from Zeus in Madison, Wisconsin.

0:29 Seth: This is Seth Paskin intuiting simple truths in Austin, Texas.

0:33 Dylan: This is Dylan Casey extending myself in multiple ways of knowing in Madison, Wisconsin.

0:38 Wes: This is Wes Alwan in Cambridge, Massachusetts.

0:42 Mark: All right, this had been on the table for a long time. I think, Dylan, you might have brought it up first right after we did our Objectivism episode, because that purported to be some kind of version of this. Like these are the basic ways to think about stuff. And it seemed like at that point reading Descartes as a different take on what it is to be rational might have been useful, but we punted it down the road years. So here we go. What sort of past experiences or initial impressions have you guys had about this text?

1:13 Seth: I guess I was unaware that Wittgenstein was a devout Cartesian.

1:18 Dylan: Why do you put it that way?

1:19 Mark: Like the Tractatus or which part of

1:20 Seth: You mean the Tractatus? You could read the Tractatus as a manifestation of Descartes, Rules for the Direction of the mind in a weird, perverted, but to me interesting kind of way. I didn't realize I was going to throw everybody for a loop with that.

1:36 Mark: No, that's interesting.

1:37 Dylan: I first heard of the Rules when I was started at St. John's I find Descartes himself kind of pleasant to read. But what I really liked about the rules was just a kind of workmanlike way of going through and then just setting out these rules. So his way of thinking about figuring out problems resonated with me deeply. When I read that, that was the first time I thought, you know what? I probably am way more Cartesian than I ever imagined I was.

2:07 Seth: Aren't we all?

2:08 Mark: Yeah, I feel like analytic philosophy as a whole, whether folks actually buy any of Descartes specific derivations or think it makes sense to think that the entirety of philosophy can be made into one deductive pseudo mathematical enterprise, still, the idea of we want to think clearly, we want to analyze, we want to look at problems, break them down to their smallest bits and just really stare at it until you, you know, we can have something that we can all intersubjectively agree about. What is the meaning of this term? What is the relationship of this issue to this issue? And just really trying to cut through all the bullshit, cut through all the massive disagreements, the political grandstanding, by just being calm and rational and methodical.

2:54 Seth: It's not just that there's a reason I thought of Wittgenstein when I read this, but it's also an articulation of the highest aspirations of the Enlightenment, this faith in human reason. Descartes has this idea of clarity and distinctness in our conceptions is what he uses the term in this text. But there's this essential faith in human reason to be able to grasp things in such a way or to conceive of things in such a way that it can be without doubt, indisputable. And that's not simply an analytic parsing of language trying to figure out the terms things. It's a faith in the rational enterprise that springs from the Enlightenment. Yeah.

3:39 Mark: Any sort of other higher level structural things before we just dive right in. This is definitely a text where we can just start with rule one and kind of move forward until we run out of time. There are only 20 some. And the last couple are like, this is a text he never actually finished. He gives a rule and then he gives some commentary on the rule. And that could be short or it could be pages and pages and pages, as it is, with some of them toward the end.

4:04 Seth: Yes. Rule one is you do not talk about the rules for the direction of the mind.

4:11 Mark: And they seem to, even though this is not a deduction in itself. Like Descartes Meditations, which I should point people at. So our episode, is it two or three? Four, really.

4:22 Seth: You should point people to the Meditations, the text that everybody reads in Intro to Philosophy.

4:28 Mark: I'm sure that we're going to be kind of taking for granted a little bit what his ultimate conclusions are, which I feel like he had the idea for the Meditations first.

4:37 Wes: Rules of the Direction of the Mind is the earliest thing he wrote. Right?

4:40 Dylan: Yeah, it's like when he was a kid, so to speak. Yeah, it's like a really smart college student writing.

4:44 Wes: It's never published and then discovered.

4:47 Mark: But you can't tell me he didn't kind of have in mind in general how the structure of the Meditations would go even by this point. Like, it seems so obvious. I don't recall if he specifically points to God and how. How Knowledge of God grounds every other bit of knowledge. But I was definitely reading that into what I was reading in here.

5:05 Dylan: That part is definitely in the method, but it's not in this.

5:09 Wes: Completely absent from the text.

5:12 Dylan: Yep. If you picked something you'd say it was math, it was founding how we understand math with pointing out towards saying that we can understand everything else in the world by extension. Extension is a technical term, Mark.

5:24 Seth: You're relying too much on memory and you haven't inculcated the method appropriately. Prone to error. It's totally understandable.

5:34 Dylan: You just have to close the gap between the things that you see clearly from one to the other to make sure the chain of reasoning is perfectly clear.

5:41 Seth: That's right, exactly.

5:43 Mark: But do you not think that at least these rules and the progression of them is non arbitrary, that you use the rules to generate more rules? Like that's how he came up with it in the first place.

5:54 Dylan: I would bracket that as an interpretive point because I think that you're careening down the question of interpreting the whole of Descartes oeuvre and saying something like, well, it seems like the same guy wrote all these things and that makes sense.

6:08 Wes: What she's saying about the generating more rules thing is out of the Internet Encyclopedia philosophy article quite possibly.

6:16 Seth: Oh, I love the way this has started.

6:18 Dylan: One of the things I love about this book is you can start with the title and go from there and it pretty much just unfolds before you in that way. Yes, there's all kinds of other super interesting connections like to the method that we're going to do next, but I think it works pretty well.

6:36 Mark: All right. The direction of the mind, number one, south. That's all it says. So we're dealing with multiple translations here. The one that all of us have that we will link folks to is

6:48 Wes: by Elizabeth Anscombe and Peter Geach.

6:53 Mark: No, that's a short one. Okay, so it's Elizabeth S. Haldane and GRT Ross.

6:58 Wes: So I'm using Anscombe.

7:00 Mark: Oh, you found the long version of that.

7:02 Wes: I got the Kindle version.

7:03 Dylan: I'm using Cottingham.

7:05 Seth: Haldane and Ross. Yeah, that's the one I used.

7:08 Mark: And I think that was also identical to what was in the Essential Descartes that I had. It's the same one that was on the PDF that we'll pass out. This version of the Anscombe that I found online, which is what I thought the whole text was, is just highly abbreviated. It's on wikisource.org, i'll link folks to it. And it's a great way to sort of remember what they are. But the whole thing comes out to like seven pages the way that particular one is.

7:31 Dylan: That's called abridged.

7:33 Mark: So. Yes.

7:39 Dylan: No, it's not very long though, in itself, it's not particularly long.

7:42 Seth: So, I mean, why don't we just read this thing instead of having a conversation? We can just read the text and.

7:47 Mark: Well, all right, go ahead, read. Number one.

7:49 Seth: The end of study should be to direct the mind towards the enunciation of sound and correct judgments on all matters that come before it. That's rule number one.

8:00 Wes: So that's definitely inferior to Anscombe.

8:04 Seth: Oh.

8:05 Wes: The aim of our study should be to direct the mind with a view to forming true and sound judgments about whatever comes before it.

8:10 Dylan: That's exactly what the Cottingham is.

8:12 Seth: That didn't sound terribly different.

8:14 Wes: It's exactly the same.

8:15 Dylan: It's exactly word for word the same as Cottingham.

8:17 Wes: The end of our studies is confusing because it's a technical use of end that won't become clear until the rest of the sentence is uttered. And aim avoids that. And there's several other things you could say. But anyway, I like Anscombe.

8:31 Seth: Oh my God. That's not gonna be the conversation tonight, is it?

8:35 Wes: Is it?

8:36 Seth: Comparing translations?

8:37 Mark: I just was trying to sound you guys out as to whether I could just read the Anscombe ones. Cause those are the ones that were copy and pasteable from my PDF. So those are the ones that are in my notes as opposed to paging through the longer version. So I'm happy that somebody else used those. But I did kind of compare both as we were going, and they're pretty damn similar. So, yeah, the explanation of this, and maybe this is different than what analytic philosophy does now is when it comes to science, don't specialize. Knowing truth in one area helps you in knowing it in others. Knowledge in specific areas is chiefly valuable insofar as it contributes to universal wisdom. Once you have the light of wisdom, it will guide the will to its proper choices in all the contingencies of life. It's a pretty ambitious gauntlet throwing right here at the beginning.

9:20 Seth: He's not just talking about the unification of the sciences. He's also trying to break down the barriers, distinctions between science and the arts.

9:28 Mark: Well, he mentions, like harp playing as one of the examples.

9:32 Seth: Yeah. I mean, he's trying to lay the foundation for it's leading up to the notion of the universal mathematics. But here, let's read Whenever men notice some similarity between two things, they are wont to ascribe to each, even in those respects in which the two differ, what they have found to be true of the other. Thus they erroneously compare the sciences, which entirely consist in the cognitive exercise of the mind, with the arts, which depend upon an exercise and disposition of the body.

10:00 Mark: And the reason he's saying that is because not all the arts can be acquired by the same man.

10:05 Seth: Yes, exactly right.

10:07 Mark: If you learn farming and learn harp playing, those are different things. Learning harp playing is not going to make you a better farmer. But that's not true when it comes to the sciences, by which he just means intellectual pursuits in general.

10:19 Seth: Yes. For since the sciences taken altogether are identical with human wisdom, which always remains one and the same, however applied to

10:27 Dylan: different subjects, if therefore, someone seriously wishes to investigate the truth of things, he ought not to select one science in particular, for they are all interconnected and interdependent. He should rather consider simply how to increase the natural light of his reason, not with a view to solving this or that scholastic problem, but in order that his intellect should show his will, what decision it ought to make in each of life's contingencies. One thing that's worth pointing out here is when he drops this scholastic problem question, and this is peppered throughout the Rules, is his utter disdain for a particular way of talking about philosophy and engaging in philosophical thinking and thinking about the natural world going at the time, scholasticism in his pejorative point of view, a universe of syllogisms and spending a lot of time talking about stuff that doesn't make a hill of beans a difference.

And so he'll point us to being concerned about what the truth of the actual things you are reasoning about are and how you get there. He'll point us to a kind of empiricism about that getting this data from the world. And he'll point us to how again, things are related to one another, that we look at them individually, but then reason about them to come to conclusions about them more broadly, and also lastly, that anyone can do it. This is another thing that's a theme. I would call it a kind of decidedly democratic or universal accessibility theme, anti authoritarian theme.

11:58 Seth: I don't want to push on that right now, but I didn't pick that up in my version.

12:02 Mark: I definitely got that. And this is, I think, where some of my prejudice against the idea of genius comes in that no, when, if you can actually break problems down to bite sized bits, then clear thinking people have pretty much the Same ability to figure out truth in any given instance and learning how to cut it up, as he describes here, is a method is something that one can learn. I have a lot of sympathy to that. And that kind of deflates the whole process of philosophy, that of course some people are smarter than others, are better able to synthesize things. But what actually cuts to making true judgments maybe is more common. And it's just that what's uncommon is focused attention.

12:46 Seth: I agree with that with respect to historical authority, I don't see it as a democratic principle in what I read in the text, but that's not worth arguing about at the spine. Next,

12:58 Dylan: rule number two. We should attend only to those objects of which our minds seem capable of having certain and indubitable cognition. All knowledge is certain and evident. Cognition, that's the first sentence. So focus on the things that we can know.

13:15 Mark: Yeah, he sounds a lot like Bacon here. I'm so glad that we read Bacon. This is what I really firmly had in mind throughout this text, is comparing it to what we just read in Bacon's attempt to develop experimental science. And here it's not that Descartes, as we'll see, says, don't pay attention to experience. You could just figure everything out from an armchair. He specifically says, you can't do that. But he is known as a rationalist, as opposed to empiricists. So it's something to look at specifically what that means. But they both definitely had in common a disdain for the way the Scholastics did philosophy, and really just how speculative they are and how certain they seem to be about so many things over which these guys don't see any way we could have reasonable knowledge about at all, if anything.

14:00 Dylan: He's trying to say, look, don't say you know something that you don't really know. At the end of this first paragraph, he says, men of learning are perhaps convinced that there is very little indubitable knowledge, since, owing to a common human failing, they have disdained to reflect upon such indubitable truths, taking them to be too easy and obvious to everyone. But there are, I insist, a lot more of these truths than such people think. Truths which suffice for the sure demonstration of countless propositions which so far they have managed to treat as no more than probable because they have thought it unbecoming for a man of learning to admit to being ignorant on any matter. They have got so used to elaborating their contrived doctrines that they have gradually become to believe them and pass them off. As true.

14:46 Mark: Yeah. He had a similar experience, I think, to what Socrates describes as going around searching for wisdom, and he finds actually nobody knows much of anything. So as we're going to read in this discourse on method, he actually has a little biographical section where you can see the realization that he had, presumably talking about around the time or the years just before he wrote this. You know, this was the time where you could actually be a scholar of just about everything in the intellectual world that was known because it was just so much more unified, you know, more canonical. Less had been discovered. And so he felt like he did that and that it was a wasteland, that he really had to shed all this stuff that had been passed down to him and use his own brain to build it up from scratch. That's what we're seeing here, to be

15:33 Seth: fair, he says that that was a disposition he had from the very beginning, that he would rather not have somebody teach him something, so much as figure it out for himself. And through that process, he oftentimes discovered different methods that were in his mind, probably superior. So seems to be a disposition as well as an artifact of his experience.

15:56 Mark: And you got to think he's talking about his math classes. Like, even though he kind of says,

16:00 Seth: since he invented math, like this is generally applicable.

16:04 Dylan: Yeah, Well, I mean, he points here that as math, if my reckoning is correct, out of all the sciences so far devised, we are restricted to just arithmetic and geometry, if we stick to this rule. So this is another aspect of it, while he has these rules, and this is, I think, a characteristic of the method, that it's a set of guideposts, but they're not a strict formula. They're not a crank that you go through. They're a way of doing things. And I think we should take him seriously in that. Sometimes they point to a character of things. But arithmetic and geometry are like the canonical example of indubitable knowledge. But that doesn't mean that they're the only kind.

16:44 Seth: Yeah.

16:44 Mark: So he says here that arithmetic and geometry are alone free from any taint of falsity or uncertainty. We must note, then, that there are two ways by which we arrive at knowledge of facts, viz, by experience and by deduction. Let's further observe that while our inferences from experience are frequently fallacious, deduction or the pure relation of one thing from another, though it may be passed over if it is not seen through, cannot be erroneous when performed by an understanding that is in the least degree rational. Pretty strong there.

17:13 Wes: So he'll Go on to say when there's errors in deduction, it's not the inference itself that's the problem, but bad premises, basically, poorly comprehended experiences, hasty propositions. The deduction itself, if it's a direct movement from one proposition to another, is not something that itself can be faulty. Now, he is going to end all of this, by the way, by backing out of the whole geometry and arithmetic thing, right? He's going to say, no, these aren't the only sciences to be studied, they're models. But it seems that way in the beginning. But we can get an extension of them.

17:48 Dylan: Ha ha, Extension, sorry, yeah.

17:51 Mark: This was just another place where I felt a resonance from the text because I have often felt in kind of accordance with the whole point of philosophy is not to know everything, but to know how to approach any given problem. And if you feel like deduction is something that is always going to be accurate, then I feel like the things that we can know for certain are a lot of if, then conditional phrases like I don't know if there is a God, but I know that if these certain experiences are veridical, then there is a God. You know, I don't know the ultimate answers, but I know how much we don't know.

And what can be concluded from what we seem to know and what we don't know and therefore can kind of feel situated, even though you actually don't know very much. That's another way of expressing the Socratic. The only thing that I know is that I know nothing because I can sort of see the logical hinges between the various things that I don't know. At least that's the idea that you

18:43 Wes: can talk about nothing intelligently with math though, right? We're out of the realm of doubt in arithmetic and geometry at least, right? So our deductions don't go astray. But also we have very certain intuitions of the objects that we're dealing with, which is not the case in things involving experience. So it's not like we just get an axiomatization of if, then propositions. We get a lot of stuff that's actually grounded in something intuitive.

19:13 Seth: That's a great and important word there, Wes. Intuition. So in this section he talks about using your own judgment and this democratic approach of not bowing to authority. And he says you have to pass everything you have learned, you know, through the lens of your own judgment. Otherwise it's just history. Which is a nice little phrase, but he mentions here two methods of knowledge. Intuition. And you've moved on to rule Three, right? Yeah. I'm on rule three. Is that not.

19:40 Dylan: We didn't read rule three yet.

19:41 Seth: Were you still on two?

19:42 Wes: We were still on rule two.

19:44 Seth: Apologies.

19:45 Mark: Well, let's read three. We're here already. Let's do it.

19:48 Wes: We got there. But we should also linger at some point on whether or not we think that deduction is foolproof.

19:54 Dylan: That's a really important thing for us to linger on. But I think he's got a couple more things to add to it that'll help us or maybe hinder us.

20:02 Mark: Number three, concerning objects proposed for study, we ought to investigate what we can clearly and evidently intuit or deduce with certainty and not what other people have thought or what we ourselves conjecture. For knowledge can be attained in no other way. So we've touched on points at this already. Don't bow to authority. But then it's this new term, intuition.

20:21 Seth: What he says is that an intuition is an undoubting conception of an unclouded and attentive mind. So in other words, if you are in the proper state of mind, you're attentive, you're clear thinking, you grasp these simple facts in a way that makes it indubitable. And this is one of the things that I wanted to talk about tonight was trying to understand what that might be, what a simple fact might be. But it's the idea that there's some sort of thing in the world, or some sort of simple fact is the word he used. And that we have the capacity as human beings using our understanding. Not in the case of deduction, not in the case of intuition, but a kind of, he calls it intuition, an intentional grasping of a thing directly to apprehend it. And if you are in the proper state of mind, you cannot be mistaken about grasping that fact.

21:16 Wes: So, by the way, deduction will turn out to be a form of intuition. But intuition is also a way in which you can grasp propositions that go into the deduction, which, confusingly, he also uses the word induction synonymously. But he makes the statement that basically there's neither the senses nor the imagination are involved in this type of intuition. So what we're getting is intellectual intuition. So let me just read on here a little bit.

21:45 Seth: I thought that was later that he talks about imagination and the senses, because I have a lot of questions about that.

21:51 Wes: Well, by intuition I mean not the wavering assurance of the senses or the deceitful judgment of a misconstructed imagination. So I might be wrong there. Maybe he's just qualifying. But A conception formed by unclouded mental attention so easy and distinct as to leave no room for doubt in regard to the thing we are understanding. And then down a little bit. Here are some examples. Thus anyone can see by mental intuition that he himself exists, that he thinks that a triangle is bounded by just three lines and a globe by a single surface, and so on. There are far more of such truths that most people observe. These sorts of intuitions look like things that are divorced from either typical sensation or the imagination. Right? We get this idea of our own existence. We get mathematical objects.

22:39 Seth: It's not just that they're divorced from imagination and senses. It's also that you don't come to them through a chain of reasoning. There's a more immediate experience of grasping these truths as opposed to some kind of continuous chain of thought.

22:53 Wes: It's confusing because later on he is going to say deduction as a species of intuition.

22:57 Dylan: But, well, I mean, in fact, in practically the next paragraph, so I mean, what Seth said is true. That's not the same. But in the next paragraph he says the self evidence and certainty of intuition is required not only for apprehending single propositions, but also for any train of reasoning whatsoever. Take for example the inference that 2, 2, 3, 1. Not only must we intuitively perceive that 2 plus 2 make 4 and that 3 plus 1 make 4, but also that the original proposition falls necessarily from the other two.

23:27 Seth: This much math I can handle, Dylan. So is that not him saying something to the effect of I have an intuitive proposition or an intuitive fact? 2, 2, 4. I have an intuitive fact that 3 and 1 equals 4 and then there needs to be some intuitive experience of four and four are identical. But to then create the chain of reasoning that says two plus two equals three plus one, it's constructed out of this intuitive apprehension of these simples. But when you look at the chain of thought that brings them all together like that, then you're talking about, well,

24:02 Wes: this is a case where we can actually do this quite intuitively, right? If you're imagining 2 dots plus 2 dots next to 3 dots plus 1.it's a weird thing to call this an inference, I think. Let's just say specifically what he's saying, right? The third proposition is that three plus one is the same as two plus two.

24:21 Dylan: It's not deductive.

24:23 Mark: I feel like if you can fit it all in one imaginative grasp. And again, maybe imagination is the wrong word here, but the way you just described it is imagine the dots. And this is a way to make it make sense to me. And you could do it through sensation, too. You could just actually put objects in front of you. But in either case, and maybe part of the intuition is recognizing that those are the same, whether you're imagining the dots or you're looking at actual objects. Then in this case, as long as you can fit the whole chain of reasoning in your head at the same time, then you've grasped it via a single intuition. And it's just when you chain a bunch of these together that it becomes a deduction, I guess, why it would be necessary to distinguish those two. I think he is explaining exactly the point you were trying to make, Wes, why deduction is a form of intuition or derived from that.

25:08 Wes: Maybe another example would be more helpful, like modus ponens, like some rule of logic. So all men are mortal. Socrates is a man. Socrates is mortal. There's no justification that we're ever going to do for that rule itself. Right. So in many ways you could reduce a rule of inference to an axiom, which we learned to do, Mark, at University of Texas. They forced us to do that type of thing where you just say if A then B and A then B, as circular as that sounds. So you could treat some of these, or you could try to, I guess, treat these rules as sort of axiomatic propositions.

But the main thing that I think about in this context is just the idea that the inference itself is this unjustified thing that we somehow intuitively grasp. We know that inference from all men are mortal. Socrates is a man. Socrates is mortal. We know that it holds. We know that with a great certainty. But we'd never be able to justify that.

26:06 Dylan: The justification proceeds from the light of our reason, which is just another way of saying we intuit it, we grasp it clearly and distinctly, and that the character of truth that that has is the highest standard of truth. For Descartes, and there's examples of these trains of reasoning. They are going to have the same character of truthness that a fundamental axiom has insofar as it's being true.

26:34 Wes: Yeah. So the theorems, even when you get very, very complex theorems that rest on lots of different axioms and deductive steps, they will inherit all that certainty as long as everything is done right.

26:46 Mark: I think there's something later that he says that clarifies what intuition is here and how this relates to deduction. It's actually in the Description under Rule 14. It's very natural for us to give syllogisms like you just gave Wes as examples here. But he specifically doesn't do that because he hates the.

27:01 Dylan: He hates syllogism.

27:02 Mark: Yeah, syllogisms, right. He says all we can know other than the simple and naked intuition of single independent objects is a matter of the comparison of two things or more with each other. So that's really what's going on when we're comparing. You know, we have this naked intuition that two and two plus four and we have another naked intuition that three and one make four, and then we compare the two. That's all you can do. So that's how, if we're going to say that raw intuitions add up to deductions, comparison is the only actual way, which is something obviously that can take place in imagination or in perception. But he's saying intuition is sort of the intellectual thing that is common to all those, that abstracts from the tricky stuff about both of those realms.

27:45 Wes: So just two things to say about that when we're doing it in the comparison, in the empirical realm. Right. There's reason to think that it's still an intellectual thing that's happening. That's why Plato even goes on about it. Is there a Platonic idea of similarity and so on that we need to make all that work? But the other thing is, I don't see how we're going to get any real inference going if we're just stuck with comparison. I think we'll need logic, and I think he'd be happier with contemporary symbolic logic. And once it's divested of all the scholastic associations, he might be happier, but I don't know.

28:20 Dylan: There's places in here where he basically takes the form of the syllogism itself as being patently true, in a similar way that he just talked about this arithmetic. But then the great failing of a syllogism is the most interesting part of it are the terms themselves and whether they're true or not. And he's claiming that his method is going to get us to that. So in some ways it's inverting the learning of the scholastics and saying, okay, well, all that syllogism stuff is fine, but what I need to get to is why those things that are the terms are actually true or not, and my method is going to help me get there.

28:59 Mark: Why you're bringing up Rule 4. There is a need of a method for finding out the truth, which I actually like better than the Anscombe. We need a method if we are to investigate the truth of things, because I don't like things Seems to introduce a complication there.

29:13 Dylan: I like it much better because of the word investigate. In fact, I like it a lot better because of that. Because the investigation is a process and you can have doubt and be wrong about it. There's an activity involved. Whereas find is more of the end point rather than the process.

29:32 Mark: He could have said we need a method if we are to successfully investigate the truth of things. But. So, yeah, this doesn't seem deducible from the earlier rules. These all seem to come in a pool. They're all just intuitively obvious. What could you use to justify this other than just. I've looked at people that don't have rules and they see lots of. They disagree.

29:53 Dylan: And that's what he says, essentially. So, you know, it's basically saying it's undisciplined. What typically happens. So blind is the curiosity with which mortals are possessed that they often direct their minds down uncharted paths in the groundless hope that they will chance upon what they are seeking.

30:08 Wes: It would be a weird world, right, in which to say there's not a. We don't need a method for finding out the truth is the same as just saying that any method will do and anything means of investigation someone might be using is adequate.

30:20 Dylan: Yeah. And this is one of the reasons why I think that he is explicitly in some places and sort of continually implicitly criticizing authority. In that the method is of attestation by people who have power and authority. And he's undermining that by providing a method by which anybody can figure this out that's available to anybody who shares the light of reason.

30:43 Wes: The method itself becomes the authority.

30:45 Dylan: Yes. And so at the end of this paragraph. So it's quite certain that such haphazard studies in obscure reflections blur the natural light and blind our intelligence. Those who are accustomed to walking in the dark weaken their eyesight, the result being that they can no longer bear to be in broad daylight. Experience confirms this. For we often find that people who have never devoted their time to learned studies make sounder and clearer judgments on matters which arise than those who have spent all their time in the schools. By a method, I mean reliable rules which are easy to apply such that if one follows them exactly, one will never take what is false to be true or fruitlessly expend one's mental efforts, but will gradually and constantly increase one's knowledge till one arrives at a true understanding of everything within one's capacity.

So this is also like a encomium to the authority of the self in evaluating the world.

31:42 Wes: But the method is also. There's something impersonal about it. It's hard not to think about the stuff with equations later on, which is reminiscent of what goes on in his geometry. This idea that you can create a kind of calculus or an algebra that has these kind of steps that are forced on you, or you can follow them almost without even thinking. Right. And then today we know that they can be instantiated in mechanical machines. They can be done almost mechanically, they can work almost like the laws of nature and unfold that way, and so do away with any sort of contingency corruption that might enter the process. I don't know. Does that comparison make sense?

32:22 Mark: Yeah. And it makes me feel like maybe the finding out is better than investigating, because that's just how pretentious Descartes is like. He thinks that you're actually going to use his method to find out whatever can be found out, whatever is within his capacities. What you just said, all that does not surpass his powers is what my translation says. I don't know that we've emphasized enough, even in some of the rules that we've already read. He's also intending to not just bracket off ways of talking about things, but certain whole areas of discourse that there are things. So he's kind of prefiguring Kant. There might be just whole areas of metaphysics that are just not within human understanding. And so not only does this method make you think clearly, but it determines what you should be thinking about at all.

33:08 Wes: Descartes would never do metaphysics. He must be 17 here.

33:17 Dylan: That kind of setting up the problem and choosing problems well, that are solvable problems is central to the way he thinks about stuff. Don't solve a problem that has no hope of being solved. And there's a kind of judgment involved in doing that.

33:32 Mark: Or maybe you can't even articulate a problem.

33:35 Dylan: If you can't articulate it, then you definitely can't solve it.

33:37 Mark: Yeah. Yes. I'm just thinking whether this is like, you know, prefiguring not just Kant, but like logical positivism. Again, that's the thing that I think analytic philosophy picked up. Not just that, you know, we want our students to think clearly. But I don't understand what your question even is. If you can't phrase your question in a way that makes it clear what kind of answer would count as a successful answer, then I'm just not going to admit it as a question. So why does existence exist or something like that? That might be a kind of question that that kind of thinker, and maybe Descartes himself would just say, you don't even know what you're talking about. Just shut up.

34:12 Seth: Yeah.

34:13 Dylan: The reason that I like that word investigation, even though I agree that he is a big proponent of the final conclusions, is the very existence of the method and him thinking about how to do what he's doing. And when you read his work, the constant clear joy in talking not only about what he's found, but also the way in which he's found it, makes him equally interesting, in fact, even more interesting about the way in which he came to his conclusions than necessarily always what he came to his conclusions about. And in fact, I think that that energy for speculation, even if he might come up with something that is wrong in some way, is alive and well in his thinking, even though he's constantly pointing to how we won't ever get anything wrong if we do this right, he employs that. And mathematics is the central example. But in his writing in general, he ends up being very speculative.

35:16 Seth: Right.

35:16 Mark: The last paragraph. Conscious as I am of my inadequacy, I have resolved that in my investigation into truth I shall follow obstinately such an order as will require me first to start with what is simplest and easiest. Never permit me to proceed farther in until the first sphere. There seems nothing further to be done. So that's why up to the present time he's made a study of this universal mathematics. Consequently, I believe that when I go on to deal in turn with more profound sciences, as I hope to do soon, my efforts will not be premature. So, yeah, he's open to the idea of metaphysics. It's just he's not there yet.

35:49 Dylan: I think we have to read this section where he quotes universal mathematics, brings that up. This is just, you know, in the very long paragraph before which you read, he's pointing to mathematics as being the canonical example, and he gives a little bit of background of different kinds of mathematics. Yet it is evident that almost anyone with the slightest education can easily tell the difference in any context between what relates to mathematics and what to the other disciplines. When I considered the matter more closely, I came to see that the exclusive concern of mathematics is with questions of order or measure, and that it is relevant whether the measure in question involves numbers, shapes, stars, sounds, or any other object whatsoever.

This made me realize that there must be a general science which explains all the points that can be raised concerning order and measure and irrespective of the subject matter, and that this science should be termed mathesis Universalis a venerable term with well established meaning for it covers everything that entitles these other sciences to be called branches of mathematics.

36:55 Mark: Yeah, I guess it's easy to read that as like, you know, the essence of science is quantifiability, order and measure.

37:02 Dylan: Yep, those terms come back up later.

37:05 Mark: That's included in a universal mathematics, like all of natural science, basically. Do you think, are you reading that as that's going to be covered by this mathesis universalis?

37:15 Dylan: I mean, I think that he would, in his ambition would say anything and everything. But you're right, I think it ends up being what we would call quantitative

37:24 Mark: science because he is saying then in the part that I read that there would be more profound things that he would get to after that. So maybe that's, you know, when you start doing theology or something. We move to number five. Do you want to read your translation, Seth?

37:39 Seth: Sure. Method consists entirely in the order and disposition of the objects towards which our mental vision must be directed. If we would find out any truth, we shall comply with it exactly. If we reduce involved and obscure propositions step by step to those that are simpler, and then starting with an intuitive apprehension of all those that are absolutely simple, attempt to ascend to the knowledge of all others by precisely similar steps. And this is his follow up. In this alone lies the sum of all human endeavor. And he who would approach the investigation of truth must hold to this rule as closely as he who enters the labyrinth must follow the thread which guided Theseus. Here it is the biggie.

38:28 Dylan: Except the next rule is the main secret.

38:33 Mark: So he specifically picks out astrologers in ignorance of the heavens without having made proper observations of the movements of the heavenly bodies, expect to be able to indicate their effects. So if you do purely practical science mechanics, apart from understanding physics, it's basically just trial and error. Right. It's a techne as opposed to actual knowledge. How's your translation, Wes? And Number six, In order to distinguish

38:56 Wes: the simplest things from those that are complicated and to set them out in an orderly manner, we should attend to what is most simple in each series of things in which we have directly deduced some truths from others and should observe how all the rest are more or less or equally removed from the simplest.

39:13 Mark: Yeah, this is where I was starting to feel like, yeah, these follow from the earlier rules. They're just a little more detail about that whole just long discussion we had on whether deduction is the same as intuition. Like he's now explicitly treating chains of reasoning and getting at the simple bits and focusing on Each link in the chain and all that kind of stuff. That's several of these rules.

39:33 Seth: Here he is trying to outline a method. So he's describing a process or a path, a habit of mind. And although it seems ultimately to boil down to the same thing in several of these propositions, I think what he's trying to do is the rules of conduct, not necessarily rules of understanding. He's trying to articulate the way in which you should approach a thing or to do a thing, as opposed to saying simply that this is something that you must internalize and obey. What I find interesting, and this throws back to my Wittgenstein comment when we started this whole thing off, is we struggled when we were talking about Tractatus, to understand what an atomic fact was.

I don't think we ever got to any kind of agreement about it, and I don't know that anybody else has either. But this notion that he believes in, this decomposition of facts in the world to our mental facilities that we have understanding, understanding comprises of intuition, induction and deduction, right? And we have an imagination, memory and senses. He's trying to articulate a taxonomy where there are some kind of simple facts that we can. Let me go back. Undoubtingly conceive of, right? When we have an unclouded and attentive mind. I feel in much the same way that we had the experience when we talked about Tractatus, that he's saying the same thing over and over again in different ways to try to get us to this comfortable place where we feel like, yeah, we can buy into his concept of intuition.

And I don't know that I'm there, but that's why I feel like there's some redundancy in these rules that you just outlined.

41:22 Dylan: Mark, I don't think his simple nature is an atomic fact. Atomic facts, the way I understand them, are. Are atomic in the sense that they build up to form a whole. But these simple natures, they may form a whole, but they aren't necessarily the smallest thing. Their characteristic of being simple has to do with their character as being individual wholes themselves. That can be intuited. So the paragraph starts with, the secret of this technique consists entirely in our attentive noting in all things that which is absolute in the highest degree.

He goes on, for example, the universal is more absolute than the particular in virtue of it having a simpler nature. But it can also be said to be more relative than the particular in that it depends upon particulars for existence, etc. You can have things that are combinations of chains of reasoning, as Wes pointed out earlier, that you end up calling them and holding them as one whole, that you would have the same kind of simple nature as the things that were part of that chain of reasoning. They're simple in their individual truthness, but they're not atomic facts.

You don't build up the world from them one after the other.

42:39 Mark: So I'm pretty sure that later in this text he distinguishes between metaphysical simplicity and epistemic simplicity here they do seem kind of squished together because it does seem like these whole rules are for the mind. They're for. They're epistemic rules. So if you are going to understand something complicated, you should first understand the simple things and then build up to that. And he will go on, you know, it's not entirely clear what are the simple things. Like, is number a simple thing or is it complex? Because you see so many instances of it, so many places, you know, you have to abstract it from so many places.

So it seems like in that sense it's complicated because it's an abstraction. But on the other hand, when you're thinking of it in isolation, it seems very simple. So there's definitely like some complexities to ferret out here. Does he have examples here we want to focus on?

43:33 Seth: His example in this particular section isn't, I don't think, very helpful. But we have to make an appeal to later in the text to be able to understand the notion of what is simple and complex. Anything that's complex relies upon something simpler than itself in order for it to make sense or to be known. The relationship of simple to complex or relative to absolute has to do with. Can you have a conception of the more complex thing without first the conception of the simpler thing? There's a causal relationship in the sense of. It's an epistemic causal relationship that you can't concept conceive of that thing without conceiving of the simpler constitutive elements.

But in his example here, he talks about 3 and 6, 12, 24 and 48. He's talking about the relation that if you can grasp the relation of magnitude between 3 and 6 and 6 and 12, then you can understand the relationship of magnitude between 12 and 24 and 24 and 48. But if you try to look at 3 relative to 48 or 3 relative to 12, you have to fill in a bunch of gaps. It's not as intuitively graspable that you would be able to understand the relationship of magnitude.

44:54 Dylan: He gives this example because of wanting to make it clear, as he says, there's no better way of doing this than accustoming ourselves to reflecting with some discernment on the minute details of things which we have already perceived. So he's going through this, looking at this very, very closely. And part of it is illustrating the way in which the chains of reasoning composes the larger reasoning. But then also that the larger reasoning becomes plain and has a kind of level of knowledge that is like the lower level intuition. But it's also that we want to be asking the right question, testing the method itself and then training ourselves in our thinking so that we just get better and better at it.

And it's not just that the particular thing that we know, we become more certain of it by going over the individual pieces of the chain to close the gap. But we also get fewer and fewer gaps, or there's less and less space to fill in. And also that we just get better at seeing what is clear and distinct. That the natural light of our reason doesn't come out fully formed and operating at the best it possibly can be. That's one of the things to me that's so beautiful and wonderful about his notion of a method is that we have this innate capacity that needs to be trained and honed so that it operates as best as possible.

And that's what the method itself is aimed at doing, or some kind of methodology is. Whether you think it's just one method or a kind of semi related set of things.

46:35 Mark: I'm trying to figure out if the absolute and the simple are really one and the same thing. I mean, he says, I call that absolute, which contains within itself the pure and simple essence of which we are in quest. And this is why I was reading the meditations into this, because elsewhere in here he talks about the simple ideas, which I think again are the absolute ones as being that which as soon as you think it's, you know, the whole thing, there's just no more to it. There's no like rotating to see the other side. There's no having to connect it to other properties because it just is it a simple idea in itself.

So like maybe number is one of those. You know, you can know lots of things about number, but that is not a matter of dissecting what number is. It's a matter of kind of combining it with other things. But the reason that maybe he would not want to just say the absolute is simple, but it contains within it the pure and simple essence. And this whole chain of the more complex, the relative has to Come from the simple. The absolute is because he already had in mind this idea that God is the absolute, the simple. As soon as you contemplate the notion of God, you actually know everything there is to know about its essential properties.

Like that's going to be really important for the Meditations. That's the paradigm case of an absolute. That would be absolute with a capital A. I should say absolute here does not have a capital.

48:00 Dylan: Yeah, I mean, the examples of absolutes here are a cause, simple, universal, single, equal, similar, straight, and other qualities of

48:08 Mark: that sort, which not all those make sense to talk about dependence or logical dependence. This whole absolute versus relative thing is the first place where the text kind of started to break down for me. Like something that was not intuitively graspful to me was being brought up here. That he seemed like to me to be smuggling in stuff that I was taking to be from the Meditations. But like that maybe is scholastic in origin, despite his attempts to abandon that whole paradigm. So we are up to Rule 7. Dylan, what's your translation like on that?