Wisdom (Metaphysics 2006, Colorado)
39. The Three Roads of Knowledge: Natural, Common and Private Ways of Proceeding
https://berquistcourse.com/course/philosophy/7b-wisdom-2006-colorado/039-the-three-roads-of-knowledge-natural-common-and-private-ways/

[0:01] But now it's time for lunch, right? And we'll finish in our next class. Finish talking a little bit about this distinction of the three roads, right? And then we'll go into this consideration of the private roads and how they should be determined here, okay? God our enlightenment. Guardian angels strengthen the lights of our minds, order and illumine our images, and arouse us to consider more correctly. Saint Thomas Aquinas, Angelic Doctor.

[0:42] And help us to understand all that you've written. Name of the Father, the Son, Holy Spirit. Amen. So we're talking about the three roads or the three ways of going forward that can be distinguished in our looking knowledge. In the first road, as you talked about before, is the natural road, right? The road from the senses into reason, and we explained or distinguished a bit the before and after along that road, both the order in different kinds of knowing, right, and the order in things known.

[1:31] And as regards the second, the order in which different things are known along this road, and the order in which even one and the same thing is known along this road. And let's cover those two: that what is more known to us, but less known by nature or less known simply, is before what is more known by nature, more known simply, but less known to us.

[2:01] Now the second and third roads are made by reason, huh? And the second road, Thomas refers to maybe as the common road of reason out knowledge, or perhaps you could say more generally, the road of reason as reason.

[2:21] And that is based upon the fact that reason is used in all reason out knowledge. It's by the use of reason that all reason out knowledge comes. And so, like the other day, we're looking at the before and after in the acts of reason. huh

[2:45] And if you recall, we following Thomas's proemium there to logic, because it's logic that takes up the common road of reason. Thomas had distinguished the first and the second and the third acts of reason: understanding what something is, understanding the true or false like composing in an affirmative statement or dividing in a negative statement, and then reasoning, huh? And you see that exemplified most clearly at common road in Euclid's Elements, huh?

[3:27] Where you have definitions. Helping you to understand what a triangle is, or what some right angle is, or whatever it might be, and then you have postulates, right? Whereby you can understand something true that's kind of obvious, and also the axioms, and then you have the third act, the reasoning, as you go through the theorems of Euclid. Now, to some extent, you do that in every reasoned-out knowledge.

[3:56] You have to understand what something is before you can understand whether it should be affirmed or denied, or has something affirmed or denied of it in a statement, and in every reasoned-out knowledge, statements must come before reasoning, because when you reason, you put together usually two statements, and then you come to a third statement from them.

[4:21] And then we point out some other before and afters in the acts of reason that we guess before we know. Reason does, and that reason thinks about something before understanding it, and that reason discurses before it sees a before and after, and you could unfold each of these to some extent. So, under the idea that we guess before we know, you can say we grasp before we judge, and you could also say that connected with this is dialectical reasoning before demonstrative reasoning, except perhaps in geometry, right, where it's easier arithmetic, and connected with that, perhaps is we see the part before the whole again, and it is in there a bit, because you go from reasonable guesses to knowledge, and reasonable guesses are apt to

[5:35] hit upon some part of the truth, but not the whole truth, so we tend to see a part before the whole, and when we think about something before we understand it, well, if you're thinking out a definition or thinking out a division, so on, you're going from the confused to the distinct, right? And here you see how the natural road is presupposed to this,

[6:06] or when you go, say, from examples of something, you think out the definition of it. Almost all the dialogues of Plato, where Socrates asks the question, "What is something? " Like when he asked Meno, "What is virtue? " or Euthyphro, "What is piety? " or Theaetetus, "What is science? " and so on, he'll get. The man he asks, giving examples of the thing, and then Socrates says, "Well, asked you for one thing, you gave me many.

[6:37] He wants to know what's common to all of them, right? So you have to think out what's common to all those examples. But you can see how that presupposes the natural road. That's why it comes first.

[6:52] A thing is singular when sensed, universal understood. So that's why we give the singular examples, or tend to do so, before we think out the universal definition of something.

[7:08] Same thing is true when you get to reasoning. Aristotle speaks of how induction comes before syllogism. With induction, you go from the many singulars to something universal, but the syllogism begins with something universal. So the reason why induction comes before syllogism is because the natural road that we sense before we understand, and the singular therefore comes before the universal in our knowledge. The same with the rhetoric where he says that example is before enthymeme, because example goes from singular to singular.

[7:48] But the enthymeme is a bit like the syllogism; it starts with often with something, maybe not complete universal, but something that's true for the most part. Boys will be boys, likelihood, or from signs.

[8:06] So the natural road gives the reason for some of the things you find in in logic. But for the most part, this road is considered in logic. Does the natural? This may be a tangent, but does the natural road explain why there's no fourth figure? Is it because we proceed from the universal to the particular? No, no, it doesn't explain that. It's more. You have to go into the treatise on the syllogism of the CY, huh?

[8:43] Okay. But we really, it's because people are resolving to imagination rather than to reason, huh? Because the middle term is either between the major and the minor premise, or it's above them or below them, right?

[9:02] So if you speak of a fourth fourth figure, you're just calling it by a different name. That's all. But anyway, let's not go into that right now in great detail. Three is the first number of both. We say all. So we'll leave it at that.

[9:20] But you can see there's no other way for place the middle term to be, right? In the middle between the two ones, or above them, or below them.

[9:32] I used to call that playing checkers. huh The fourth figure is playing checkers. Then there is the what private road of each reasoned-out knowledge, which is we'll learn in here, is going to fit the matter of that reasoned-out knowledge. And

[10:04] as Boethius says, also or adds in the De Trinitate, and how our reason is to that matter in particular. Now there are many elements there of the private road of each reasoned-out knowledge, but limiting myself now to to the parts of looking philosophy, mathematics and natural philosophy and first philosophy or wisdom.

[10:36] You could perhaps distinguish these elements at first into three, because basically looking philosophy is arising because of wonder, okay? And the wonder of the philosopher is most of all wonder what and why, what and why. And that's why the second book of the Posterior Analytics is kind of you know of extreme interest to the man who wonders, because in the second book of the Posterior Analytics, Aristotle

[11:19] talks or compares the question what is it with the question why is it, and compares definition which answers the question what is it with demonstration which answers the question why it is, and what's the connection between definition and demonstration, huh? And so you could talk about the way of defining, huh, in each of the parts of looking philosophy, and the way of what demonstrating, huh? Okay.

[11:56] But in addition to those two, you could add what we call the order of determination, or what Thomas calls the order of determination, I sometimes call it the order of consideration, what things you talk about first and what things you talk about second, and so on. Now going back to the first one, the way of defining, huh?

[12:22] Well, if you know the second book of Natural Hearing. Aristotle distinguishes between natural philosophy and mathematics by the way they define, and the natural philosopher defines with matter and motion, and the geometer without matter and motion. When you get to the sixth book of of wisdom, Aristotle distinguishes between natural philosophy and mathematics and first philosophy, and then sometimes he talks about matter in a kind of extended sense in mathematics, intelligible matter, or he could perhaps call it imaginable matter, this extension that you have in geometry and so on.

[13:09] But wisdom defines even without that extension, without that imaginable matter. So this is kind of the first element there, the way of defining, and that's got to fit the subject. But you also, so basically, use it to distinguish the sciences, and then secondly, you could say more generally the way in which they make known their beginnings.

[13:39] And in natural philosophy, just as you define with sensible matter, that subject to matter, to motion, so on, so you make known your beginnings by the senses. But in mathematics, just as you define without sensible matter, but perhaps as imaginable matter, you make known your beginnings by in the imagination,

[14:09] and so you try to understand what a right angle triangle is. Right? You've got to imagine a line meeting a line, right, making equal angles, and so on. And then

[14:24] you get to a science like wisdom or, if that matter, logic. Then they can't make known their principles so much by the sense and imagination because they're dealing with immaterial things, and this is of course easier to see in logic than in wisdom because logic is before the sciences in the order of learning because it teaches the common way of proceeding. But if you read the dialogue, the Parmenides there, where Parmenides teaches Socrates the Socratic method, Parmenides and Zeno are talking to him, and Socrates is trying to understand the universal, right?

[15:06] He imagines the universal to be like a sail covering things, and so he's trying to resolve, he's resolving to the imagination, and that doesn't work.

[15:19] And you find in the modern mathematician, a geometer, or a logician, sometimes who. Who want to substitute classes for what universal right? The class is a multitude of individuals of the same sort, so it's something more sensible or imaginable. But universal is something what

[15:42] one set of many, right? It's the same in each. Where you see this difficulty in Locke there when he tries to, you know, imagine triangle in general. It's neither scalene nor isosceles equilateral, but it's all none of these. You know, it's all confused.

[16:01] A third thing that that's talked about in the De Trinitati again, in the article there where he's talking about whether, in studying divine things, even in philosophy, in studying divine things, can your judgments resolve to the imagination? Of course, the answer is no. But if by judgment you mean the separation of the truth from the false by some beginning in our knowledge, then there's a connection between the way of judging ultimately, in natural philosophy, and in geometry, and in wisdom, and the way its beginnings are made known.

[16:46] So just as the beginnings of natural philosophy made known by the senses, so the judgment of natural philosophy goes back to the senses, as Aristotle says in many places, like in the book on the Universe huh.

[17:00] But in geometry, just as the beginnings are made known in imagination, so the judgment goes back to the what imagination. And I remember my brother Mark remarking about how people call the fifth postulate the parallel postulate. Don't they call it that? Well, it's not about parallel lines; it's about lines meeting. And and why do you have a postulate about lines meeting rather than about parallel lines? Well, you can't reimagine parallel lines as such because the lines which extended forever never meet.

[17:36] Well, you can't imagine something infinite extent, can you? But you can imagine lines meeting. So you have to go back to something that you can what imagine, right? And these things like the the fourth theorem, which my brother Mark pointed out, not really a theorem, it may be the full sense. The fourth theorem, if you recall, was that if two triangles have what an equal angle contained by equal sides, those two triangles will be equal, right?

[18:04] But you've got to imagine a triangle, right? And then you place the other triangle upon it. At the point that the angle is, and put this line down there, and since the angles equal, the two lines are going to coincide, right? And because they have the same length, their endpoints will be the same. And then you can kind of see in your imagination, yeah, yeah. If they have an equal angle, contained equal sides, the triangles must be equal.

[18:34] And I know myself in kind of confirmation of what everybody's saying there. When Euclid talks about the circle, he defines the circle, right? And then he defines diameter, and then he gives kind of like a postulate. That's not in the list of postulates. That the diameter bisects a circle, that is to say, divides it into two equal parts. And I say to the students, now, is that obvious, right?

[19:06] And some students want to say, well, it's just by definition it divides it into two parts equal. No, no. The definition of diameter is not that divides is not that it's a line dividing a circle into equal parts. The definition of a diameter is that it's a line drawn from any point in the circumference of the circle to the center and through the opposite side, right? And must such a line divide it into two equal parts?

[19:33] Yeah, but maybe that has to be kind of manifested in your imagination. And they said that Thales did this, huh? A little bit like the fourth theorem. That if you imagine one side of the circle, right, flipped over the other one, right, you've got obviously the same base there, because the diameter. And if the two circumferences coincide, then obviously they're equal, right? But if they don't, then the radii are not all equal, which contradicts, right?

[20:07] But you got to kind of look at it in your imagination. And likewise, when you get to the fifth, the fifth postulate, that all radii angles are equal, right? You say, well, some people want to kind of jump right away and say, well, isn't that the way you define right angles? When a straight line meets a straight line and makes equal angles, then we call them right angles.

[20:34] Yeah, but you got another theorem, if you recall, about dividing a line into two equal parts, right? But if you have two lines divided into equal parts, the parts in both lines equal, not necessarily, right? So maybe a little bit of manifestation there in the imagination. And so, if you imagine, let's say, this straight line meeting this straight line and making equal angles, and this line meeting this one, right?

[21:02] And then you place the points, right, on top of each other, and the lines on top of each other, right? If the two lines upright. Coincide, well then obviously they're all equal, right? But if they don't coincide and one goes over here, then you are going to get into an easy contradiction, right? Because since this one is equal to that, right? Let's take part of this one over here where the other line fell, and then this here is bigger is bigger than that because the whole is bigger than the part.

[21:38] Then you add this other part there, and it's much bigger. But according to the original hypothesis, it was also dividing equal parts. So you kind of kind of go back to imagination to see, yeah, it has to be so. Yeah, if two straight lines meet two straight lines and make equal angles in both cases, all those four angles must be equal, right? So you got to go back to imagination to to judge these things, huh?

[22:03] And but can you go back to the imagination to judge the way God is, or the way an angel is, or even the way your soul is, right? Something immaterial, or the way the universal is? Can you imagine the universal? No, if you imagine something, you make it singular, right? And that's a problem with with Locke, right? He's trying to imagine triangle in general when it can only be understood.

[22:28] So that's kind of the third thing, but I put it even though it might pertain more to judgment and to demonstration almost, because the term to which your judgments go back is also what was the beginning of your knowledge. Well, then, just as they differ by the way of defining and the way they make their beginnings known, so by the way they judge or by the term of the judgment, so those three are all different, right?

[22:58] Now, again, they'll talk about them from time to time, like probably an article where Thomas is taking up what Boethius says that can in divine things can one resolve your judgment's imagination, and of course he answers no, but then Thomas will point out that you don't resolve to the same thing in natural philosophy or in geometry or in logic or in wisdom, right? When theology resolved, maybe back to what the church teaches or something like that, right?

[23:31] So different forms of knowledge there have different things by which you judge, right? And a judgment is separating the true from the false by beginning in your knowledge, and the beginnings are different, or made known in a different way, then the term of the judgment that to which your judgments go back is going to be different. So I distinguish those three things, but the first one I use the way of defining, right?

[24:02] I never put the thing is. So the way of defining is different. The Way in general, they make known their beginnings, and the way they judge, or that to which their judgments go back,

[24:23] and then you have the the way of demonstrating, and there the first thing to be considered is whether you demonstrate going from the cause to the effect, or going from the effect to the cause. Well, geometry demonstrates more by going from the cause to the effect, by natural philosophy and maybe even wisdom at first, going from the effect to the cause, the most part,

[24:54] and then maybe later on you see you know sciences why right something is so, and then the second thing is by what causes do you demonstrate? What causes do you use? And geometry might use just one, the the formal cause. Natural philosophy might use all four, and wisdom might use the end of the form chiefly, but the mover to some extent, and not properly the matter at all, right?

[25:23] So there are differences as to the kinds of causes you use in demonstrations, but that goes back to what your your subject matter is, huh?

[25:36] And then the third thing you'd say is about how rigorous the demonstrations are, because in geometry they're much more rigorous, and something is going to be true universally, but in natural philosophy and a fortiori, if you get into practical philosophy, you're going to have things that are true for the most part, right?

[25:58] Even maybe that great rule of two or three, right? Might have a few exceptions, huh? So you might have you know things that are true for the most part in some sciences, because they involve matter or human free will or something else, right? And so because of the matter, you can't have complete universality, or maybe you can't have complete certitude. I'll be talking about that, especially here in this last reading, right?

[26:31] So the three and three there, those are six elements that are going to be found in the private road, the private way of going forward in science. They won't define in the same way, they won't make known their beginnings in the same way, they won't judge in the same way, right? It's in a way that's appropriate to their matter, right? I'm talking about dogs, I have to judge by the senses.

[26:59] If I'm talking about triangles, I have to go back to my imagination, because I'm talking about the universal in logic, I got to go back to reason itself. Can't judge it by what can be sensed or imagined. Yeah, I may have missed this, but you spoke of or elaborate on the way of demonstrating, and also give three elements underneath the way of sorry the way of demonstrating.

[27:24] Also, give one or the order of consideration. No, I haven't come to the order of consideration. Oh, you haven't. Okay. No. Okay. I just got six elements so far. Okay. So, in imagination,

[27:40] you don't have either in the imagination or the senses perfectly straight line or. Well, in the imagination, you could have a flat surface, right? But you have to go and find out here a flat surface in order to talk about a flat surface in geometry. You have things you sense that you can't tell that they're not perfect until you go up closer. So the appearance is such, and then you imagine that, and then you, in your imagination, go in as much as you want.

[28:10] It doesn't change. Oh. I don't know if the circles in my imagination are perfectly circular. Well, that's that's a defect in your imagination, then, Father.

[28:27] I mean, the point is, you know, you can talk about a flat surface in your imagination without going out to the senses and finding a flat surface, huh? Aren't you, in a way, also going back to your reason there? Well, yeah, but I mean, see, if you try to understand

[28:47] examples, if you go back to examples I gave you, right? You know, like in the fourth theorem of Book One, or the uh diameter bisecting, you know, dividing the several equal parts, or you go back to the parallel theorem, which is actually not parallel theorem, but our parallel postulate. Um, you can see

[29:10] that you have to be able to imagine these things. Huh? That's why solid geometry is more difficult because it's more difficult to imagine these things. Huh? Some of the things they got to make a little cardboard one and hang it up over the lamp and while doing these theorems, and I had one hanging down the kitchen table there one time, and but that's because the weakness of my imagination.

[29:35] See, the same we might use a piece of paper or something like that because of the weakness of your imagination, and sometimes I'm trying to to recall a theorem. I have to take a piece of paper or something like that, but that's kind of a crutch from imagination, right? A great mathematician wouldn't have to maybe use a piece of paper like that, but you got to go back to imagination and and and see them somehow in the imagination, huh?

[29:59] But you can't do that in natural philosophy. I go all the way back to the senses ultimately, but with the case of universal, then, um, and you can see the difficulty in Parmenides that if you try to imagine universal, right. You're going to be deceived by false imagination. It cannot be imagined. You don't always have to imagine all of it. You can do some of it by you can see parts, and then use the reasoning for the rest.

[30:32] Yeah, but you got to go back to imagination. You see, that's a part. Yeah, yeah. And that's kind of interesting that Euclid begins the Elements with plane geometry rather than arithmetic, as the geometry is is more imaginable than the numbers, right? And of course, even in the use of these lines to represent the numbers, you can kind of see that.

[31:03] So. I distinguish then between the way of defining, but I attach to that these other two things, and the way of demonstrating, by from cause to effect, effect to cause, but then these other two I add on there. But now, apart from these six elements of the private road of looking, looking philosophy, you have the order of determination or consideration that I think we talked about another day.

[31:33] But as far as the three parts of looking philosophy are concerned, in natural philosophy you go from the general to the particular, and you go towards matter.

[31:48] And to some extent, those are moving in the same direction. You can see them almost the same thing, but not exactly the same. So we say both of them. And you go from a study of motion or change in general in the eight books of natural hearing to the particular kinds of change in the later books of natural philosophy. But even there, we study change of place first before change of quality, leading to change of substance, and that before growth and the other changes in living bodies.

[32:25] As change of place is somewhat broader than change of quality, in order to have a chemical change, you got to bring the bodies together in the same place. Of course, for Aristotle, that's even more clear because the heavenly bodies seem to have change of place but not change of quality. But even if every body is subject to change of quality, you can have bodies move around in place without a change of quality, but not vice versa.

[32:53] Got to bring bodies together in the same place to have a chemical reaction or something like that. And likewise, change of quality, or chemical change, to use a modern term, there is more general than growth, because there must be chemical changes in the body for growth to take place. But there can be chemical change even in the non-living world, right? So even in talking about the particular kinds of change, you are to some extent going from the general to particular.

[33:26] But in the whole, where you study change in general and the particular kinds of change, you're obviously going from the general to the particular. But as you go from towards matter, you go from the eight books of natural hearing to the book on the universe, to the books on generation and corruption and so on. You're going down towards matter, and then you do it again when you go with the soul, right?

[33:50] And you go from the soul and the books afterwards. As Thomas explains in the beginning of the next book, Aristotle is going more and more into matters he goes forward in the study of life. But life, as life is most known to us from our inward experience of being alive. And so that's why we begin the study of life with the what soul, strange it might seem to the outside world.

[34:19] Life as life is more known to us from this inward experience, and that's what is a starting point for considering the soul. Now geometry goes from the simple to the composed for the most part,

[34:40] and we said even the first theorem right a bit, we go from the circle to the what equilateral triangle, and you construct it by reason of making two circles right, right and drawing the lines. But you see it especially in the whole geometry where you do plane geometry before solid geometry.

[35:08] But I think you could also say that for the most part in geometry the equal is before the what unequal, and you see that even in the definitions you'll define right angle before acute and obtuse. You'll define equilateral triangle before isosceles and isosceles before scalene. Even the order of the axioms you give the axioms of equality first, like quantities equal to the same to each other, and last the the axiom of inequality, the whole is more than the part.

[35:46] You see it in the theorems and take a striking example in the first two books. The first book ends with the great Pythagorean theorem, which is that the square on the side opposite the right angle is exactly equal to the squares on the sides containing it. But it's in the second book towards the end that you learn that in the obtuse angle triangle the square on the side opposite the obtuse angle is greater than the squares right.

[36:16] Kind of more idea of inequality, and then the theorem about the acute angle that acute angle triangle, the square opposite the acute angle is less than the squares on the sides containing it. But if you examine the twelfth and thirteenth theorem in the second book, they are proven by the Pythagorean theorem. So you not only take up the equal before the unequal, but the equal is used to prove the unequal.

[36:43] Just like in definitions you define the right angle before acute and obtuse, and then acute and obtuse are defined by right angle. You don't define acute and obtuse by saying if a straight line meets a straight line right and makes unequal angles, the greater one is called obtuse, the lesser one acute. Wouldn't be so useful, huh? No, you define the obtuse angle as an angle greater than a right angle and acute angle less than right.

[37:13] So, not only is the equal defined before the unequal, so to speak, but the unequal in this case is defined to the equal. Okay.

[37:25] So that's the order of consideration in geometry, for the most part, huh? That you consider the simple before the composed, like the triangle before the parallelogram, or something like that, and the equal before the what? Unequal. Now, in in wisdom,

[37:52] huh? We saw in the ninth book part of the order of consideration. In a way, it goes from the less universal to the more universal, as you can see in the consideration of act and ability, where you talk about act and abilities are found in motion or in reference to motion, in the first part of Book Nine, and then you ascend to complete the universal consideration of act and ability.

[38:22] And to some extent, you do that, not as clearly as you do in the ninth book, but to some extent you do that in the consideration of substance, huh? Because you begin in the seventh and eighth books from material substance, and then you rise to kind of a general understanding of substance that's useful even in talking about the immaterial substances. Just as you had a rise to a more general understanding of act and ability to be able to talk about the act and ability of immaterial things, and if you study the the one, and and even historically you see that people have a difficult time distinguishing between the one that is the beginning of number, which is what we first think of when we think

[39:12] the one, and then the one that is convertible with being. So you have to ascend from the one that's the beginning of number to the one that is convertible with being, and we ascend from seeing the one that is the beginning of number to be a measure, right? The other one is not so much a measure, but we kind of eventually see it as a measure of some sort, huh?

[39:40] But more important, more basically, the order in wisdom is said to be towards the immaterial, huh? Okay. And you can see this in the main things being considered there. You consider things like being and the one and the many in Books Six or Five through Ten, which can be in matter, right? But need not be in matter, right? And then you go towards the immaterial substances, which cannot be in matter, cannot involve matter.

[40:15] So you're going towards. The what the less immaterial what does not depend upon matter for can be without matter but can be in matter right to what cannot be immaterial at all so you're going towards the immaterial so in those two things you can see that the way of proceeding in wisdom is almost the what reverse of natural philosophy

[40:47] the one is going towards matter the other is going towards the immaterial the one is going from the general to the particular from the more universal to the less universal and the other to some extent is going from the less universal towards the what more universal

[41:09] and that's why one reason why the more you go on in natural philosophy the more you go into matter and the harder it would become to to pursue wisdom because of the way you're accustomed to think

[41:28] okay so that's the seventh thing the order of determination as Thomas calls it the I call it usually the order of consideration right What you consider before what you know

[41:44] so there's a lot of elements there and Aristotle and Thomas would talk About them in various places, but this was my attempt to kind of bring them together.

[41:59] Thomas distinguishes in the physics one place there between the order, ordo demonstrandi, the order of demonstrating, and the ordo determinandi, which is the order of determination or consideration. that he talked about. When, you talk about going from the general particular. You're talking about the order of determination, right? You're talking about going from effects to causes. You're talking about the order of demonstrating. So he'll make these distinctions, but maybe you're not bringing them all together, right?

[42:31] Or he'll talk in another place about how you judge by going back to the senses in natural philosophy. You don't judge that way in geometry or in logic. There are different ways of judging, right? So kind of a way of of distinguishing and ordering these things is to speak of the way of defining and some things that are connected with that, and the way of demonstrating, and then the order of determination, so we can get a nice distinction into three, right?

[42:58] But then the way of defining, since that's a beginning, right, definition in reason of knowledge, you could say in general the way of making known is beginnings,

[43:11] and in ethics it'll be different from all these, right? You know, Thomas's example there is that concupiscence diminishes by abstinence. We got to have some experience that you don't have any experience of your concupiscence diminishing, right? By abstinence, then you don't have the experience necessary to do ethics, right? I used to notice in the days where the fast was more vigorously enforced, the full fast in in Lent.

[43:44] You know, in the first part of Lent you get kind of hungry, right? Eating less in food. Towards the end of Lent it became less difficult because your your desire had diminished, your size I suppose had diminished somewhat, and we get no experience of this, right?

[44:05] You lack the starting point for ethics and for how these things are acquired. If you've no experience of being better disposed by repeated acts of some sort, how are you going to know these things? So the way the beginnings are made known is different, right? And then, although judgment maybe is more proper to demonstration than to definition, but there is a connection with definition too, and Thomas sometimes says that the the most authoritative, almost judgment, is by the definitive, the definition.

[44:46] You can see that, right? You know, I have a very vigorous judgment myself that no odd number is even, don't you? And by what do I judge so so rigorously and with so much certitude that no odd number is even, right? Well, it's by definition, right? And you know, when when Simmias is is pushing Socrates to the wall there in the Phaedo, he wants Socrates to give a reason why the soul, the human soul, must be immortal, right?

[45:19] Then Socrates goes back to something more known to him, and so on. And he goes back to to definition, right? And tries to bring out that he goes back to the proposition that one opposite cannot be the other, right?

[45:41] And then, the next subtle thing now, if one opposite is in the definition of a third thing, that third thing cannot admit the other opposite.

[45:59] So, for example, if good and bad are opposites or contraries, then one can't be the other, right? But if there's a third thing, like let's say virtue, and good is in the very definition of virtue, can virtue be bad? Not as such, right? See. And then he say, well, life and death are contrary, right? So life cannot be death, and death cannot be life.

[46:30] Now, can a body that is alive admit of death? Yeah. Why? Well, because life is not the definition of body, right? If you define body, you would not put life into its definition. But life is in the very definition of soul,

[46:52] and therefore soul can in no way admit of the opposite of life, which is death. I don't want to say what the argument is entirely good, but see what Socrates is doing, right? He sees the importance

[47:06] of definition, right, for judgment, right. And this might be a more controversial example, but you can see in my earlier example of the no odd number is even, right? How definition enables you to make a very rigorous judgment, or no, no perfect number is a prime number.

[47:37] The prime number is measured by what? Well you have one, and so what measures it can't add up to it, can't it? So there's some rigor there, right, from definition, and even the first proof of existence of God, which is much more difficult than any of these things. But you know the definition of motion is underlying that. So there's a connection between definition and judgment, right? But the connection I was making in putting the way of judging along with the way of making known your beginnings, with with defining the way of making known your beginnings, because definition is a beginning, right?

[48:16] As you can see in Euclid. But the way of judging kind of corresponds to that because judgment is a separation of the true and false by some beginning in our knowledge.

[48:31] So we separate the true from the false in geometry by going back to the axioms and the postulates and the definitions, the beginnings, there, right? Ultimately our judgments go back to the senses, but it's always by some beginning, right?

[48:46] And then I distinguished the way of demonstrating, and that's fairly easy to see. but the first distinction goes all the way back to Posterior Analytics, demonstration from cause to effect or effect to cause, demonstration demonstration quia they call it in Latin, and demonstration quia, which is characteristic of this science. Well, because in geometry you're dealing with accidents in a kind of abstract way, and the and the properties are all what the effects are all relations, right, following upon the quantity.

[49:22] You can kind of go from cause to effect, right? But in natural philosophy you're dealing with sensible things and substances and so on, and the senses know only the outward accidents of these things, and so you tend to know the effects before the cause. And a fortiori in wisdom we're going to be dealing with immaterial things, and we only know these things through their effects. But then you have to say, but you do talk about causes, and try to explain why.

[49:53] What causes do you use? And then you see they don't all use the same causes. When Warren Murray was going to the University of Minnesota, was it Allen? The the Aristotelian so called over there, but you know his explanation of the four causes, Aristotle looks at four causes everywhere. You know, it's four causes. He looked for the four causes, and Warren used to, you know, playfully ask me what are the four causes of triangle, you know, and see what's the first of triangle, you know.

[50:24] Aristotle was not saying, you know, you know I got this, you know, this is some system, you know, where everything is going to, you know, no, there are four kinds of causes, but in any. Reason out knowledge. You got to say now of these four kinds of causes, which ones are what relevant, right? And so I'll take the students to geometry where maybe only the form is really relevant.

[50:49] Why are these angles equal? Because the lines are straight. That's the form, right? And then, but you go to some things and you might bring in all four causes, like the natural things. You go and say God is a cause. Well, turns out that He's a cause in two and a half of these senses. He's a mover or maker and an end, and maybe a cause in the sense of exemplar, but not intrinsic form of things.

[51:18] That's why I say two and a half, and of course not matter at all. So you've got to consider which of the four kinds of causes are relevant, right, to this matter you're considering. And

[51:42] even within the same science, you might not use all four causes; these are relevant in that science for every phenomenon. Okay. And then the thing that we emphasize here a lot in this reading, the the certitude, right, of the demonstrations or something like that, the the accuracy or precision of them. And Aristotle talks about this in some ways more abundantly there in the first book of Nicomachean Ethics, where he says you can't have the same certitude, right, in every science, just like the arts can't have the same precision.

[52:27] So if I'm cutting out a dress, my wife is cutting out a dress in cloth, she can be more accurate, maybe, than a guy chipping away at wood or marble, where can't be quite as exact. Or the guy's making the busts of the presidents out there in the Dakotas, you know, and dynamiting rock, you know, you can't expect the same precision because because rock does not as you know doesn't admit of being as exact, you know, cutting cutting through it.

[52:56] At least with the ordinary tools we have. So Aristotle has a beautiful thing there in the in the Nicomachean Ethics for a man who has the liberal arts. It's equally absurd to demand the rhetorician that he demonstrate, right? Because that's a more rigorous argument than his matter admits. huh? He, demonstrate who's going to be the next president of the United States? Well, it's ridiculous to demand that kind of precision, right?

[53:23] And even during the last election, I thought that Bush was going to win. But if someone says, "Do you know? Show me that it must be so," I said, "No, we're going to wait till election night and maybe the next day or next week or the next month." But so, yeah, I'm not going to know in the strict sense. But he says equally absurd to demand that the rhetorician demonstrate, huh?

[53:45] And then to allow the geometer to what persuade you, you know, with intuitions or examples or something like that, huh? And sometimes, you know, with this theorem here, for example, take a simple example. Students want to go up there and measure whether they're equal or not, right? And start kind of induction. Well, you can give a more rigorous argument than that, right? You should allow the student to do that, huh?

[54:08] But the one is demanding more certitude than is possible, and the other is accepting less than is so, and both are mistakes. You've got to find the certitude or the precision, either one, that is, that this matter seems to admit of. And so Aristotle is in the ethics there. You know, he says that we have to talk often about what is so for the most part, right?

[54:33] Conclusions about what is so for the most part. There's no exception. Boys will be boys, but not always. Sometimes a boy does what you expect a man would do. Sometimes a man does what you expect a boy would do.

[54:51] What What do you do about nothing? Yeah. Could you say a bit about how arithmetic results to imagination? Well, that's a hard thing to see, you know, huh? Because arithmetic is more abstract, right? And I remember this year running across. I don't know where it is now, but I probably have my computer somewhere. A place where Thomas almost speaks or does speak as if the the one that is the beginning of number, right, abstracts from continuous quantity, right, abstracts from intelligible matter.

[55:32] And to some extent, that seems to be true, right? But in that case, you would have the one that's convertible with being, huh? And and I was remarking to Warren Murray, I was pointing out this text, and I said, you know, this is very striking because it shows you how difficult it is, right, to separate the two. Count the angels. Huh? Yeah, yeah, but also because you know you have a point here and a point there and a point there, right?

[56:01] And that's obviously not the one that's convertible with things, but the one that is the beginning of number is not here or there, right? See, but.

[56:11] If you realize that that number arises from the division of the continuous, then you realize that although it's more abstract than geometry, it's not completely abstract in the continuous. And the reason why numbers can go on forever is because the continuous is divisible forever. So it shows how difficult that is, how difficult it is. And Thomas will will speak too that when you distinguish the kinds of philosophy by their

[56:49] relation to matter and how immaterial they are and so on. But even within one science, one part is more immersed in matter than another, right? So the diagram is not as immersed in matter as the books that come later on, right? And within mathematics, you can say that geometry is more material in the sense of at least intelligible matter than than arithmetic. Arithmetic is more

[57:17] abstract, right? It's not as material, and that's why you know one of the most difficult things when you're studying the treatise of the Trinity. You know what does this number three mean here, right? And you know if you study that, you know or if you recall studying it, you realize how difficult that was, right? But it involves separating the one that is convertible with being from the one that is the what beginning of number.

[57:51] And the three persons of the Trinity are not more than two. What do you mean? The two are not more than one, right? But you know, we study that with the summa open in front of us, right? You don't, you know, but you can see how difficult that is, right? Okay.

[58:13] Now the the. These three roads. The first road is presupposed the second road, and the first road enters into the explanation of why some things are in the second road. And I mentioned in particular that when you learn in the natural road that we know things in a confused way before distinctly, then you see why, in reasoned out knowledge, we must define and divide and in general what distinguish right.

[58:52] And you've heard me talking here about the importance of what distinction, right? And just noticing that in that book, they're talking about Eutyches, right? But if you go back to the heresies, right? I mean, a lot of them involve not distinguishing the human nature and the divine nature of Christ, or not distinguishing the Father and the Son really, or you know. But in general, why why must our reason define, divide, and distinguish?

[59:23] The angels don't. God doesn't have to do this, but defining and dividing are two ways of going from the confused to the what distinct, right? And we have to distinguish the senses of a word equivocal by reason. Otherwise, we're going to be confusing the senses of it as the moderns do, ad nauseum and people do in general, right? They're always making that mistake.

[59:53] So, what belongs to the natural road, the confused before the distinct, is the reason why in the second road there are things that reason does like define, divide, distinguish. But then, in turn, the second road explains something about the private road. Why why is it so important in the private road to talk about the way you define? Well, you learn in the second road that definition is the beginning of what demonstration, right?

[1:00:26] Definition is the starting point for demonstration. And you learn the Posterior Analytics that the premises and the conclusion have to be in the same genus. I mean, Thomas is talking about how ethics proceeds. He says, and as we're taught in the art of demonstrating, right, the principles and conclusions must agree. Well, that's got to be true then down in ethics that if the that if the principle is only true for the most part, then the conclusion is only true for the most part, and so on.

[1:00:56] So there is a real order among these three roads, huh? And you have to see the distinction of the three roads, though, and understand them before you see and to see the order among them, huh? Why does induction come before syllogism? Right. That goes back to the fact that a thing is singular when sensed, and universal when understood. But. Why does giving examples in the dialogues of Plato?

[1:01:30] you realize that's kind of natural, right? That these people, when they're asked by Socrates what is piety, what is virtue, what is science, they give examples of the thing, right? Rather than a universal definition. And Socrates has to kind of explain the difference between giving examples of the thing and defining it. And when you define, you want to bring out what's common to all of them, right?

[1:01:51] And sometimes he makes a joke. I asked you for one thing, and you gave me many, right? But you're looking for that one definition, right? But that's Plato's representing in the dialogue what's natural for men to do, huh? To start with the singular before the universal. So, in a sense, the reason for the things that we see in logic goes back to the natural road. Now, one might know, one might know from experience of asking people to define things that they tend to give examples, right?

[1:02:28] Before a definition, huh? He asks a little boy or a girl, What's a nose? " They're not going to give a definition, are they? Say, "That's a nose. That's a nose. That's a nose thing. " They'll start naturally with examples, huh? And but the reason why they do that, huh, goes back to the natural road, huh? As nature enters into the irrational, huh, and the common road enters into the third roads, huh?

[1:03:04] Okay. So, an order among these roads. Let's look now at the.