Introduction to Philosophy & Logic (1999)
36. Demonstration: Cause, Necessity and Through Itself
https://berquistcourse.com/course/philosophy/1-philosophy-1999/036-demonstration-cause-necessity-and-through-itself/

[0:00] You know, and she'd always be there in the front of the tabernacle on that side, and she'd be taking care of the flowers and the altar and so on. So she died finally. So she was quite good up in years. And Monsieur Delacour, I had for one or two courses when I was at the College of Saint Thomas. He died. He was about eighty-one, I think. So that's a pretty good age, I guess.

[0:21] But anyway, and then Mister Rice there, who I met when I was going off to Rome, you know, he died. So I just he stuck in his wake all the way home. So a number of these. So just remember them a little bit. Okay, let's say a few more words about demonstration and dialectic, and then we'll go and talk a little bit about sophistic, huh? Sophistical refutations.

[0:47] Is Aristotle? His book is entitled "About Sophistical Refutations." You get into the first book of the Posterior Analytics, which is the book on demonstration and the effect of demonstration, which is episteme or using out knowledge. Aristotle gives this definition of demonstration. I don't know if we met this definition yet or not,

[1:15] but he defines demonstration as a syllogism, which is the genus of demonstration. It's a syllogism making us know the cause, okay, and that of which it is the cause,

[1:48] and that it cannot be otherwise, okay. So it's a syllogism making us know the cause and that of which it is the cause, and that it can't be otherwise. So he's seeing a necessary connection there between the cause and the effect, huh?

[2:21] And notice if you've read the great dialogue there, Plato called the Meno, when he's separating knowledge in strict sense from right opinion, and he has pointed out how man can act well sometimes not having knowledge but just having right opinion, and then he's asked by Meno, "Well, is there any what's the difference then between knowledge and right opinion?" And is knowledge any better than right opinion as far as action is concerned?

[2:55] And Socrates says, "Well, if you hold on to the right opinion, right? You are going to be perfectly well off, right? But you might give up the right opinion and go on and give what? Wrong opinion. Yeah, yeah. See? By the case, if you know it, what you think is tied down, so it's not going to get up and go away. It's tied down, he says in the Greek there, by the logismō aitias, by an account of the cause.

[3:30] Okay. So you can see how the great Plato there is anticipating what Aristotle is going to say there, right? The demonstration here is a syllogism that's producing knowledge in the strict sense, and not just an opinion, right? So that Aristotle is anticipated here by Plato. You can see the cause as what enables you to see that it must be so and cannot be otherwise. Okay.

[4:06] You see that also in the great dialogue called the Phaedo, right? Because in the Phaedo, Socrates is reasoning that the human soul is immortal, and Cebes thinks that some of the arguments are are good but not necessary, right? And he's kind of pressuring Socrates to come up with an argument that is altogether necessary. And the final argument that Socrates gives seems to satisfy at least for the time being, Cebes, right?

[4:38] One could examine the argument to see if it really is as necessary as it appears to be, but when Socrates is being pressured to do that, he says, "Well, you are asking for a lot, right? " And then he goes back and recalls his days as a natural philosopher, as if the natural philosopher would most of all know about causes, right? And so why is Socrates going back to his experience as a natural philosopher in order to find a reason why the soul must be what immortal, right?

[5:13] And not just you know probable argument it is. Well, because the natural philosopher most of all seems to know about causes, and he has to know the reason why he's going to give the reason why the soul must be immortal. It must be in terms of the cause, right? Okay. So there you see in both the Meno and the Phaedo that Plato sees, or Socrates, I am going to give Plato more, sees a connection between being sure about something, right, and something being necessary and what cause.

[5:50] Do you see that? Okay. And sometimes, you know, I'll touch upon this to students, and I'll say, you know, you can give many reasons for something, right? Because I think I might have said last time, what is the best reason you can give for a statement? Say, and he goes, "Oh, well, you could say the best reason for a statement."Is the reason why it must be so?

[6:27] Okay, that's the best reason you can give, isn't it? Huh? You can't always give that kind of reason for everything, but the best kind of reason you can give for a statement is the reason why it must be so. Okay. Now notice when you use the word why there, as I do, you're touching upon the what? Cause, because cause answers the question why, and also the question what for that matter too.

[6:56] But it's more obvious that it answers the question why. And you see again the connection with what? Necessity, right? Okay. So in geometry, huh, when straight lines intersect, these opposite angles will be what? Equal. And these two for the same reason. Now I say to students,

[7:25] what's the reason for saying those angles will be equal, right? Well, they look equal. Well, that's not the best reason you can give, right? Okay. Well, Euclid says they're equal. Well, that's the reason, but is that the best reason you can give? What if you measured these two and they're equal, right? Well, that would be reason to think that they're equal, right? Would that would that tell you universally that they're always equal?

[7:50] Because this particular one is equal, right? Well, let's measure a few more. Okay. But even so, that's not the best reason you can give, right? Euclid gives the best reason for those being equal. The reason why they must be equal, right? And that reason is that because, and because means the cause being, because this is a straight line, a plus x must either be two right angles or be equal to two right angles.

[8:21] Okay. And because this is a straight line, this is a straight line meaning it, because huh, b plus x must equal two right angles. Okay. And the rest is those axioms that are obvious to everybody, right? Quantities equal to the same equal to each other. And quantities equal to subtract from equals to the result are equal, right? But notice the basic reason why comes from the fact that these lines are straight, right?

[8:58] Because this is a straight line meaning a straight line, because of that, these two angles have got to be either two right angles or equal to two right angles, huh? Okay. That's something you see early in first year geometry. So that's the best reason you can give. The reason why it must be so. So the demonstration.

[9:21] Is that kind of a syllogism that makes known the cause, right? And that of which it is a cause, it cannot be otherwise. So in this demonstration, Euclid makes known the cause. The lines intersecting is the cause of their being angles, right? But the straightness of the lines is the cause of the angles being what? Equal, right? Okay. So you see the cause, the straightness of the lines, that of which is a cause, the equality of these angles, and they cannot be what?

[9:51] Otherwise, it's impossible for it to be otherwise. Okay. So you're the man from Missouri, there, right? Missouri you've got to show it to me, right? Well, this comes to that word to show it. You've really, shown that, right? Okay.

[10:20] Now, when you study the fifth book of wisdom, the fifth book of the metaphysics, Aristotle, in that whole book, he takes up the words, right? That are used most of all in wisdom, but these are also the words that are used in the axioms,

[10:46] and these are also the words that to some extent are used everywhere. Okay. And the first group of words he takes up are words that pertain to cause in some way, and so he takes up the word beginning, the word cause, the word element, and meets them again in the very first sentence of the thoughts of nature, the word nature, right? And these are all in some way names of causes, but he attaches to them the word necessary.

[11:20] Okay. And Thomas says he attaches the word necessary to the words for cause because a cause is that to which something else necessarily follows, just like necessarily follows upon those lines being straight that those angles will be equal, right? It follows necessarily upon a number being two that it's half of four and a third of six, and the other things follow necessarily. So you see, there's an intimate connection between cause and what?

[11:55] Necessary, right? And so sometimes we define, as I define it here, as Aristotle did, demonstration there with emphasis upon making known the cause, but sometimes we say that a demonstration is a syllogism from premises that are necessarily true, right? And our seeing is necessarily true, right? Okay. So there is a connection then between cause and necessarily true, right? And cause and necessary. So those are two key words, right?

[12:36] Now later on, when Aristotle is talking about the properties, the words that pertain to the properties of being as being, in the middle he talks about being in one and their parts. But the first word he takes up is perfect,

[12:54] and it's kind of interesting what he does. He explains the three basic meanings of perfect, right? And then he distinguishes a sense in which God is said to be perfect and creatures are said to be perfect. But after he gets through the word perfect, then he takes up three words that are related to perfect. It's very unusual what he does here. The first word he takes up is limit or end.

[13:26] You can translate it if you please by. The second word he takes up is through itself, per se, and Latin "kath' hauto And the third meaning he takes, or word he takes up, is have and having, right?

[13:59] Now why do I mention all this stuff here? Because we can speak of what perfect and all kinds of things, right? A perfect dinner, right? A perfect tragedy, a perfect chair, a perfect argument, right? This is a perfect argument, right? Okay.

[14:22] Now you say, why is the demonstration the perfect argument? Well, because of two things: because the conclusion follows necessarily from the premises, and because the premises themselves are necessarily true. In other kinds of arguments, either the conclusion doesn't follow necessarily, right? Or the premises are not necessarily true, right? In some cases, maybe both, right? Okay, they fall away from the perfection of demonstration. So demonstration in a way is the measure of all other arguments, and you can see how they kind of have sometimes something of demonstration, like the dialectical syllogism.

[15:16] The conclusion follows necessarily, but the premises are not necessarily true, right? So the conclusion is only probable, right? But in this most perfect argument, both the form and the matter, you might say, are perfect, right? But more could you ask in an argument, as far as the form is concerned, than that the conclusion should follow necessarily from the premises? What more could you demand of the premises?

[15:47] Well obviously you want them to be true and not false, right? And that they be necessarily true, right? Seeing is necessarily true, right? But then Aristotle will reason that the demonstration is about premises that are what kath' hauto per se, through itself.

[16:13] That's interesting, huh? He sees through itself. As a word that pertains to the perfection of things, huh? And you see that if you study love and friendship, for example, that if I love you because you're useful to me, or I love you even because you please me, right? I'm not loving you to yourself, right? Not loving you for what you are in yourself, right? But in the highest and the best and the most perfect kind of friendship, I love you to yourself, huh?

[16:47] Not to what you do for me. Okay? It may do a lot for me, but that's not the primary basis in the highest friendship for my my loving you, right? Okay.

[17:03] Um. So Aristotle goes on and he talks about the various senses of through itself, right? And he talks about how the premises in a demonstration involve through itself, right? So in that simple example I gave you before, I think you say man is an animal with reason, and because he's an animal with reason, he's capable of laughter, right? Okay. Well, to be an animal with reason belongs to man through being a man, right?

[17:38] It belongs to man as such, right? And to be capable of laughter belongs to a rational animal as such, huh? Through itself, huh? So the connection between through itself and what necessary, right? And through itself and what cause, huh?

[18:05] The reason you say two is what half a four? Take a very simple example. But why is two half a four? It just happens to be half a four. Like a triangle happens to be green, huh? No, no. Ah, two is half a four because it is two, right? Okay. So you have the word cause, right? But you could say also that to be half a four belongs to two as such, or it belongs to two through itself, huh?

[18:42] What does that mean? It belongs to two through being two, right? Okay. But it doesn't belong to what a triangle because it is a triangle to be green, right? Does it? It doesn't belong to triangle through being a triangle that it be green, right? Okay. It doesn't belong to triangle as triangle to be green, right? That's something that happens to it, right? See? So you see the connection between as such through itself with both cause and what necessary, right?

[19:18] It's necessary for two. To be what half of four, right? Huh? And this tied up with the fact that two as two is half of four. Two through being two is half of four, right? But it isn't necessary the triangle be green because it's not green through being a triangle. It's not as triangle is green, right? That's something accidental that happens. So could is that truly then that through itself or as such, being another way, expressed in another way by its very nature, just saying that instead of saying through itself or it is by its very nature Yeah you could say it yeah ultimately by its nature yeah yeah yeah yeah.

[20:06] But Aristotle will in the Posterior Analytics distinguish four senses of through itself, right? In one sense, the first sense is when what is in the definition of a thing is said of that thing, right? Okay. So square as such is equilateral, or square as such is a quadrilateral, right? Okay, and then what belongs to something like a property, right? Those are the two basic ones, huh? Okay.

[20:37] T here is another sense of through itself, which in Greek, you know, is more idiomatic than ours. It means by yourself, right? So if you are in your room by yourself, you are kath' hauto right, and by yourself, right? Okay. And then sometimes you apply it to the other causes. They move in the end too. Yeah.

[21:00] Maybe I missed something. You mentioned that Aristotle, I guess, in the Posterior Analytics makes a distinction between necessary and as such and the through itself. Yeah, but they're connected. They're connected. Yeah. Yeah. Okay. So then, while while we can say it is necessary that two is a number, yeah, it is also necessary that two is half of four. Yeah. Even though you could also say two through itself is half of four.

[21:33] Yeah. Yeah. Okay. So. But two different senses of through itself, right? Okay. You talk about the property. You are talking about the definition of some part of it, right? So

[21:48] Aristotle takes up this phrase. if. You want to call it that through itself, both in the fifth book of wisdom and in the first book of the Posterior Analytics, huh? That's relevant to both, right? He takes it up in the fifth book of wisdom because it's something that follows or is connected with the word perfect, right? He takes it up in the Posterior Analytics because it's connected with necessary, right?

[22:12] Okay. But as I say, if you realize that demonstration is is the perfect argument, right? One should not be surprised that, through itself and as such, should be very important in demonstration. Okay. Now, this word "limit or" "end" is very interesting. You know, a lot of people think of the,

[22:39] you know, opening up people's, you know, horizons and all this kind of stuff. You know, kind of, you know. And I used to joke up and write a book entitled "How to Limit Your Thinking." Yeah. How to perfect your thinking, right?

[22:55] But notice now the importance for demonstration of definition, right? And how definition enables one to what have certitude, right? To see something as being necessarily so, right? Okay.

[23:17] Now, one of the meanings of "limit" is definition. We look at the Latin word definition comes from the Latin word "finis," meaning what end or limit. Okay. So one should not be surprised to see that definition is an extremely important thing in demonstration. In fact, the middle term of a demonstration would tend to be a what definition, right? Okay. And there's other ways in which you could see "limiter" "end."

[23:54] Um. You know, we spoke about the the square of opposition and and statements that are contradictorily opposed, right? Okay. And how we sometimes, Aristotle does in the Prior Analytics, he distinguishes between the demonstrator and the dialectician by the fact that the demonstrator takes one half of a contradiction, lays it down, you know, and excludes and throws away, so to speak, the other half. But dialectician says, "Which do you think?"

[24:28] You know. Okay. And although you might incline to one more than the other, there's a little bit of what fear you might, you know, a little bit of. See, that is a word "determined" to one half of the contradiction. So when they ask, "Socrates, can virtue be taught?" and Socrates says, "Well, we haven't defined yet virtue, right?" He doesn't think he can know for sure yet whether virtue can or cannot be taught, right?

[24:56] Okay. But then he argues that virtue can be taught, right? Then he argues that virtue cannot be taught, right? There's a kind of what lack of determination, right? In the dialectician, huh? And so sometimes Aristotle says dialectic is reasoning for probable opinions, even to contradictory conclusions. And that's what Socrates does in the third part of the Meno, right? He reasons that virtue can be taught with probability, then he reasons probability cannot be taught, right?

[25:29] Okay. Thomas does that in the Quaestiones disputatae, right? He may have had 15 arguments, yes, and 10 no, right? And then finally he will start to resolve, right? But notice, huh? That's tied up with the perfection of demonstration that the mind is determined or limited, you might say, to one half of a contradiction, both in the premises and in the what conclusion, right? So what never demonstrates the contradictory of what's been demonstrated?

[26:05] It's impossible, okay? And the demonstrator never reasons from both sides of a contradiction, But dialectically we can. Because sometimes both sides have some probability. Do you see that? So again, you see in many ways the connection of demonstration with limit, huh? Limit in the sense of definition. Definition is tends to be the middle term in a demonstration. And also you see that the mind in demonstration is limited to one half of a contradiction, both in the premises and the conclusion.

[26:49] While dialectic is kind of unlimited, right? You're being inclined more to one than the other. That's not firm there. So in demonstration you have the truth, right? In dialectic you're still what? Guessing the truth, right? You may have a reasonable guess, right? But you don't really have the truth yet, huh? Not any firmly. You don't have hold of it, right? Okay. I got you now, right? No chess or something, right?

[27:28] I got you. No way out you can go, right? I got you. Yeah. So it's interesting to see how those words that pertain to perfect can be applied, among other perfect things, to what? Demonstration, right?

[27:45] I was thinking about this again when Aristotle takes up the word limit or end. He says sometimes we contrast the end with the beginning, right? Okay. So we've got a line here, and you begin here. You see, this is the beginning, and you call that over here the what? The end, right? But then he says sometimes we call both the beginning and the end an end, right?

[28:12] We speak of the endpoints of a line, right? Okay. That's interesting, huh? God is the most perfect thing there is, right? And he's what? Beginning and the end of all things, right? But more like a circle, as they say, right? You know, but the beginning and the end are the same, right? But he's the beginning and the end of all things, huh? And the interesting Aristotle saw limit or end as a name associated with what?

[28:44] Perfect, right? And pertains to the perfection of God, not that he has limit, right? But that he's the limit of all things, both in the sense of the beginning and the end. I am the alpha and the omega, beginning and the end. That's kind of amazing, right?

[29:06] And God is being to himself, right? He's good to himself, right? And he has everything, right? Huh? The problem about the Euthyphro you know, how can you give God something? He's got everything, right? You know, this is a Christmas time. You know, what do you give the man who has everything, right? You know, this who kind of find a gift for somebody, right? Why don't you give God a gift, right?

[29:33] He got, he does, in the full sense, have everything, right? Huh? You know, he has it all. You know, Thomas explains, you know, the way of speaking there in Scripture, where God says, "to Moses it Abraham or Moses? You know, follow me, and I will show you every good." Thomas says that is myself. He has everything, right? Huh? Yeah. When Aristotle is what contrasting the sense in which God is perfect from the sense in which a creature can be perfect.

[30:08] A creature can be perfect in its kind, right? It have all that its kind requires, right? But it doesn't have the perfection of other genera, right? But God is everything. He has perfections of of every genus, of every kind of thing, without their imperfections, of course, right?

[30:29] But to have an imperfection is not really to have something. It's not to have something, right? It's a metaphor, right? Like to say, I have what blindness, or I have poverty, or I have ignorance. I have a lot of ignorance. Well, that's really not having strictly speaking, right? Not having knowledge, yeah. Very precious. Thank you. Some question. Would you say that comparing, say, speculative theology with say moral theology, or something, or biological theology, you would encounter a greater use of demonstration in a certain sense in say sacred doctrine or dogmatics as distinct.

[31:27] Maybe you would encounter more dialectical syllogism and practical moral theology. But as you descend to the particular, right, you get less what? Sort of certainty, yeah. There's so many more things to be considered, right? Huh? Okay. And in some cases, you know, it becomes very hard to have necessary reason, right?

[31:56] How many bites of steaks I have? Well, I had two bites. see? You know, It's hard to give a precise reason there, right? Yeah, okay.

[32:13] like the moral manuals and things like that, probable opinions about such and such, you know, very probable. Yeah, it's a different state. If you look at the Summa the Secunda Secundae the Summa Theologiae right? It gives you, you know, the common principles there in ethics, right, and moral theology. But you have to go to maybe Saint Alphonsus de Liguori right, to get the the proper ones and more particular ones, right?

[32:39] You see, and I haven't I haven't read that much Saint Alphonsus de Liguori, but he was made the patron saint of all moral theologians and of all confessors, right? Okay, now why was that, right? Because he's he's descending more to particular, and sometimes I can solve it on certain sins, right? And you can see maybe that if you were a confessor, you might have to have something more particular than the Summa Theologiae or even the Secunda Secundae right?

[33:10] Okay, the Secunda Secundae is is much larger than probably larger than the rest of the Summa together, almost, right? You see, because you you have to descend to particular, right, to perfect these things.

[33:27] Now let me mention something else that comes up in the first book of the Posterior Analytics. Aristotle speaks of another kind of demonstration that goes from the effect towards the cause, right? Okay, and sometimes you know you you see, these referred to from the Latin, the demonstration we've just spoken about is sometimes called demonstration propter quid. But that propter quid means on account of what, right? Okay, it's a demonstration who's going from the cause to the effect.

[34:14] But sometimes you see what is called demonstration quia, demonstration that it is so, and this is a syllogism going from the effect to the what, the cause, and we tend to use that more in natural philosophy than we do, let's say, in geometry, huh?

[34:39] Because usually the effect is more known to us than the cause, and geometry things on the surface, so you can go from the cause to the effect.

[34:50] Now, when Aristotle gets to the second book of the Posterior Analytics, he begins by discussing the four questions in speculative knowledge, and they are the questions: Does it exist, and what is it? And is this that? And if this is that, why is this that? And he talks about the order of his questions. Right? The question does it exist comes before the question what is it? And the question is this that comes before the question why is this that?

[35:35] Right? Okay. So if you ask me, do unicorns exist? And the answer is no. You don't really ask what is a unicorn. You talk about the word means, but there's no such thing there to be known, right? Okay. And you might say, is the light of the sun eclipsed? If the light of the sun is eclipsed, then you ask why is the light of the sun eclipsed?

[36:02] Right? Okay. Does snow melt? The answer is yes. And why does snow melt? Right? Okay. Now Aristotle shows. How these questions are very closely connected, really, and you can almost change one into the other. And he takes an example there of the eclipse of the sun. He says, "If I ask, 'What is an eclipse of the sun? ' Right? I'm asking a question of that type. What is something?

[36:37] If I ask, 'Why is the light of the sun eclipsed? ' I'm asking a question of the second time, Right? But in either case, I would answer the question really by the cause. If you want to really define what an eclipse of the sun is, right, you'd have to say it's a cutting off of the light of the sun by the moon coming between the sun and the earth.

[36:58] But if you ask, 'Why is the light of the sun being eclipsed in the middle of the day? ' Because the moon is coming between the sun and the earth, right? Okay. So he points out that the questions 'what' and 'why' are both answered by the cause.

[37:18] And you know, you ask me, 'What is a sacrament? ' Right? Okay. So a sacrament is an outward sign instituted by Christ to give grace, right? I'm giving really the causes of the sacrament, aren't I? Instituted by Christ, the Maker, to give grace, the end or purpose. These are different kinds of causes, huh? Outward, huh? That's the matter of the sacrament, huh? The sensible matter, sign, you know, the words and so on, right?

[37:46] Okay. Twinkle, twinkle, little star, how I wonder what you are, right? But you want to know what the star is made out of, right? And so on, and those are the causes of the star, right? Okay. So in the very beginning of natural philosophy, Aristotle referred to understanding, meaning understanding what, knowing why, right? And how they're both answered by knowing beginnings and causes and elements, right? Okay.

[38:20] And to some extent, you can say that that second book of the Posterior Analytics is kind of the centerpiece of logic, because logic is the tool of the man who wonders. Wonder is the beginning of philosophy, right? And wonder is a natural desire to know the cause, or you could define it as a natural desire to know what and why, huh? In that reading I gave you from Plato's Theaetetus, right?

[38:49] You have mention of what and why, right? But you see that in the childhood saying, at least our childhood saying, "Twinkle, twinkle, little star, how I wonder what you are," okay? No, that's in trochee meter, right? It's like the kind

[39:08] of what the unusual. It's like the wonder about, huh? Like the witches, huh? In Shakespeare. Fair is foul and foul is fair. Hover through the fog and filthy air. Twinkle, twinkle, little star. How I wonder what you are! Fall in the first syllable. Twinkle, twinkle, little star. But they always cut it short, so you get another accent.

[39:34] So that's really kind of the key thing, you know. The only Aristotle when he does logic talks about those things, right? Now what the other guys are talking about, what's this for? The stuff that they got, right? One of the University of Minnesota logicians said to one of my professors, you know, symbolic logic is useless for knowing reality. What are you studying it for? You know, yeah.

[40:01] It's because you wonder about things, right? You wonder what and why. You're interested in what definition and demonstration, right? You want to answer the questions what and why. Okay, and they're both answered in a way by knowing the cause.