Dr Greg Bahnsen - Critical Thinking: Categorized Syllogism Part 2 (Part 11)

Okay, when we come to section 5.5 in the PROPI, we raise the question of existential import because the proposition is said to have existential import. If it is typically uttered to assert the existence of objects of some specified kind, and it's obvious, then that particular proposition that carries some S is P or some S is not P do have existential import. They imply the existence of some S's which either are or are not P. Now, do universal propositions have existential import? Now this is going to depend upon your interpretation. On the traditional square of opposition, it would seem that the universal propositions A and E would have existential import. Otherwise you would not be able by subalternation to infer or imply the I and O propositions from those universal propositions. If universal propositions that all the apples in the barrel are Jonathan is not assumed to have existential import, then you could not validly infer that there are some apples in the barrel that are Jonathan. And so the only way to save subalternation is by presupposing that the universal propositions have existential import. Now that would be nice, because we've already worked through all those crazy exercises of conversion and obversion and composition. So you might think, well, then we want to save that. If that has to be done by assuming or presupposing that universal propositions have existential import, then we would do it. But as Kochu says on the bottom of 182, there are several objections to making the blanket existential presupposition. One of them is it would then be impossible for any standard form categorical proposition to deny the existence of memory of the classes designated by its terms. You wouldn't be able to deny the existence of something in those classes. Secondly, this doesn't really fit into our ordinary usage in all respects. Sometimes we'll say all trespassers will be prosecuted without presupposing that there will be any trespassers necessarily. We don't necessarily assume existing in that category. And then thirdly, there are cases where we often wish to reason and says without making any presuppositions about existence, as in Newtonian physics, the illustration goes. And so for those reasons, modern logicians do not follow the traditional Aristotelian square of opposition, because the air of the ceiling requires me to presuppose that universal propositions are existential, that they are claiming existence for some object. Modern logicians will not follow that existential presupposition. And the modern approach, named after George Boole, is called Boolean logic. Over against error for ceiling logic. On the Boolean interpretation, universal propositions are understood as having no existential import, as Copeland says in page 183. So what we're going to be doing from this point on is when we see a proposition all sec or no sec, we will not automatically assume that there are some Fs, we will not automatically assume existence the existence of some members of that class S. Now, on the Boolean approach, the bottom of page 183 tells you a and E propositions can both be true and are no longer contrary. The biceps. All apples are no, forget apple, because they do exist. I say all Martians are blonde. I think that's the example he uses. And I say no Martians are blonde. Both can be true if there are no Martians, and since the A and E propositions can both be true, they are no longer contrary. And in the same way the I and O propositions can both be false. Some Martians are blonde, it's false since there aren't any Martians. Some Martians are not blonde. It's false since there are no margins and therefore they both can be false. And if both can be false, they are not subcontray. Moreover, since we do not assume the existence of anything in the class of S, in a universal proposition, all S is T or no S is P, subalternation no longer is a legitimate inference because subalternation leading to the sum S is T assumes that there are finesses that exist. So what we have lost now are the contrary relations, the sub contrary relations and the sub alternation relations. Now the square of opposition just looks like an X, right? All you have left are the contradictory. It is still the case that an A proposition contradiction O proposition. If all S is C, then S contradicts the claim that some S is not C and the Greek proposition contradicts the I proposition. If no S is C, that contradicts the statement that some F is C. So on Boolean interpretation, what we have saved is the contradictory from the square of contradiction. Obversion remains valid on the Boolean interpretation, but all the rest is highly qualified. Conversion by limitation is rejected.

Now.

Even though conversion remains valid for E and I and contraposition remains valid for A and O, we have two limited immediate inferences. Now we have contradictions A and O, E and I, and all the obversions are valid. We have conversions valid for E and I, and we have constant positions valid for A and O. When we turn the page, we are told if it is not assertive, exclusive explicitly That a class has members. It is a mistake to assume that it has. Any argument that turns on this mistake will be said to commit the fallacy of existential assumption, or more briefly, the existential fallacy. This is a good point to make, a remark by way of commentary on what logic itself is. Many times people will present the laws of logic like these are non negotiable, universally extended. No one can break these rules. Everybody agrees on them. That's the laws of logic. People that may not be as dramatic as I am, but that's the way they taught. We need to remember the laws of logic are affected by the presuppositions of brains. And that's why there are different systems of logic. So the next time somebody throws it at you and is trying to pretend he knows all this stuff about logic and that everyone agrees on the laws of logic, you might just remind them, well, there are different laws of logic, different immediate inferences, depending on whether you take an Aristotelian interpretation or a Boolean interpretation of categorical propositions or categorical reasoning. On the Aristotelian interpretation, you assume that universal propositions assert the existence of their subject terms, but you do not assume that in Boolean logic, for reasons which we've already given in the chapter. So this is just a good example of how laws of logic and what you understand by the inferences that can be logically made will be affected by your interpretation or initial presupposition. The exercise calls for us to explain at which step or step the argument that you're going to be considering commits. Fallacy of existential. Yeah, the fallacy of existential assumption. And so number one goes like this. Premise one, no mathematician is one who has squared the circle. Therefore no one who has squared the circle is a mathematician. Does that commit the fallacy of existential assumption?

No.

And how do you get from one to two?

It's a conversion on a D4 proposition.

And that remains valid. Okay, from number two, no one is. No one who has squared the circle is a mathematician. We conclude therefore all who have squared the circle are non mathematicians. How do we get to that?

That's an obversion.

That's an obversion. And is that commit the fallacy of existential assumption.

That's still valid?

Yes, all the inversions are valid. Very good. And then from number three, all who have squared the circle are non mathematicians. We can conclude some non mathematician is one who has squared the circle. And how would you get from three to four?

That would be a conversion by limitation, which is not Valid.

Not valid. On the Gwillion interpretation for a commissary fallacy of exponential assumption. Any questions? No questions. Then we're going to go to number five, which gives us the first premise. It is false that some mermaids are members of college sororities from which it's concluded. 2. It is true that some mermaids are not members of college sororities from which it follows that there exists at least one mermaid. Where in this exercise is the fallacy of existential assumptions committed and the step from what to what? In the transition between the 1 and 2? The first one he states upon us that it is false that some mermaids are members of college sorority. And then in the second one he says it is true that some members are not members of false authorities. And while. Now, what procedure. Let's discuss it. What logical procedures would a person use to go from the falsity of some mermaids are members to the implications that some mermaids are not members? What kind of relationship is that between those two propositions? No, it's not a conversion. The first one is a I proposition. Correct. What's the second one? An O. An O proposition. So what is the move from an I to an O changing from false to true? On what basis would somebody think they might be able to do that? Kind of subconscious. Yeah. On the understanding that subcontraries cannot both be false. If you take the first one to be false, the second one has to be true. So this is a subcontrary immediate relation from false to a true. Now, where is the fallacy of existential assumption committed in that? Because the first one. And so what you're saying is when someone reasons by self contrary that they cannot both be false, then they're committing the fallacy because what they're assuming is the relationship is subcontrariness. And that relationship in the Boolean square opposition is not there. That line doesn't exist. Okay, well, enough on categorical propositions, on the traditional Aristotelian approach, and then the Boolean approach. Now I think you'll find a lot more fun and helpful. Turning to chapter six, categorical syllogism. Everything we've done thus far is going to attempt to understand the propositions and their immediate infancy. Syllogisms are not immediate inferences. Syllogisms are mediated inferences. I want you to show me that you understand the difference here. In an immediate inference, you move from one proposition by some immediate rule to another logically equivalent proposition. Okay. Or the determination of true falsity and determination In a syllogism, you don't have one proposition, then a conclusion. You have a proposition, a second proposition, then a conclusion. And in that case, we say that the first proposition leads to the conclusion through the mediation of the second proposition. Okay, section 6.1. Now we're getting away from immediate inference. We're now going to talk about mediated or median. A syllogism is a deductive argument in which a conclusion is inferred from two premises. A categorical syllogism is a deductive argument consisting of three categorical propositions that contain exactly three terms, each of which occurs in exactly two two of the constituent propositions. The categorical syllogism is said to be in standard form when its premises and conclusion are all standard form categorical propositions that are arranged in a specified standard order. Let's just make sure we understand this. A standard form has only categorical propositions in it. There are only three terms used to appear in each of these propositions, and there is a set form. And he gives an example here, which I'll prioritize on the board for you. No heroes are towers. Some soldiers are cowards. Therefore some soldiers are not heroes. In this particular syllogism, are all three of the propositions categorical propositions?

Okay.

And then the specified order is given. Here you have a major premise and a minor premise. Then you preclude. But in order to tell what is the major premise, you have to know what is the major term. Here we have no ace is two. No heroes are powered. Then you have some soldier from S. Some soldiers are college. Therefore we'll draw the line. And the conclusion is sum, S is not H. Now, do we have only three terms? Here we have H and C and F. We have zeros, powers and soldiers those in spine. And he tells us we can identify. The major and the minor term by looking at the conclusion. The term that occurs as the predicate of the conclusion is called the major term of the syllogism. The term that occurs as the subject of the conclusion is called, called the minor term of the cylinder term. So when they have it written out like this, the predicate term becomes the major thing and the conclusion, the subject term, is the minor. Okay? Now the reason why you have to be able to identify this is because this will determine what is the major premise and the minor premise in the syllogism. In a syllogism, the major term occurs as the subject term of the first premise. The minor term occurs as the subject term of the second term. And that means that you have something out here at the end of each one. The predicate term for premise one and the predicate term for premise two. You notice how it's the same. So it turns out we are relating the heroes to the soldiers, the aces to the S's in terms of their intersection at the predicate times involved these premises which. So through the interaction of Coward, we're going to find out what the relationship between those soldiers is. Can you all see that? When I see the president on the board. This is the point, very simply, is that the predicate term in your conclusion is what's going to be called the major term. And that determines the major premise because it appears in the major premise. And then the subject term in the conclusion will be called the minor term, and it will appear in the second premise of the argument. And the remaining term then is going to be the middle term. When Copy discusses the mood of syllogism, she calls on us to look at each of the three propositions in the argument, the premises and the conclusion, the two premises and the one conclusion, and consider what form they are in. Are they in the universal affirmative, universal negative, particular affirmative or particular negative? The A, E, I and O forms, and then put them in the order of mention. If the first proposition is a universal negative, then it's E. And then you write that down. If an X proposition is a universal affirmative, then that's going to be an I, not a universal affirmative. It's going to be an A. And then if the next proposition, the conclusion, is just making this up, a particular negative, then it's going to be an O. So in that case you'd have an E, A, O for the mood. So the mood is just a summary of the three different kinds of propositions that are found in the argument in the order in which they're found. The figure on the other hand, has to do with the the placement of the middle term in the argument. Remember, the middle term does not appear in the conclusion. The major term appears and the minor term appears in the conclusion, but the middle term does not appear in the conclusion. The middle term must then appear in both of the premises in order to link 1 and 2 together. If the two premises are going to have any relationship, they're going to be related through the middle term. But now where does the middle term appear? As subject or prefix? And there are four different possibilities given to us, and they're respectively called first, second, third and fourth figure of the syllogism. In the first figure you have the Middle term as the subject of premise 1, the predicate of premise 2. You can see that in the middle of page 193, in the second figure, the middle term is the predicate of both premise one and Premise two. In the third figure, the middle term is the subject of both premise one and Premise two. And then in the fourth figure, the middle term is going to be the predicate term of Premiere, Premise 1 and the subject term of Premise 2. Let me give you an easy way of remembering this. 1 and 2 have got a diagonal relationship to each other if you look at the M's on the chart. Whereas in Figures 2 and 3, the M lines up. Okay, so now in Figure 1, M begins in the subject position. So now you know it's going to be predicates in Figure 2 because of the diagonal in Figure 4, it's going to have that's the other diagonal. So it's going to have to be the other way around. M will be in the predicate position for premise 1 and in the subject position for premise 2. And then you have to remember on the second that M appears in the predicate position for 2 and in the subject position for 3. Figures 1, 2, 3 and 4. Exercises began on the bottom page. 193. Rewrite each of the following syllogisms in standard form and name its mood and figure. He says this means the first, identify the conclusion. Notice the predicate term, which is the major term of the syllogism. Third, identify the major premise, which is the premise containing the major term. Fourth, verify that the other premise is the minor premise through its containing the syllogism minor terms, which is the subject term of the conclusion. Fifth, rewrite the argument in standard form with the major premise first, the minor premise second, and the conclusion third. And then finally, name the mood and figure of the pilot. All right. Number one says no nuclear powered submarines are commercial vessels. So no warships are commercial vessels, since all nuclear powered submarines are warships.

All nuclear power, therefore no worship.

Okay, that's right. Let's make sure we understand why it is. So what is the conclusion? How did you know what the conclusion was?

Because. The planet is the major defense.

You're not hearing my question. How do you know which of these propositions is the concluding proposition? The conclusion of the argument? I'm not asking you a difficult question. This goes all the way back to the beginning of our course. Is there any conclusion indicator in this? Okay, so that's how you figure out that that was the conclusion. Now, once you know the conclusion you can figure out the minor and the major term. Right. Okay. So what is the major term in this argument?

The major term is conservative.

And why is that? The predicate in the conclusion is the major term. So that means that whatever premise contains the expression commercial vessel must be the first premise of the argument, which is what you gave, of course. And then the other is going to have to be with the minor one. That's easy enough. What's the middle term here?

Nuclear power.

Okay. And what is the mood.

Is bae, which is universal matters.

Right. Given your answer was number one, no, nuclear is commercial.

I can abbreviate it.

And so that's E form. Your second premise was all nuclear is warship, and that's an A premise. And then your conclusion was no warship do commercial. And so that's the E form. And then what figure do we have here?

Because both of those times are in the public position.

Very good. So we have an EAE3, just so we make sure we know what we're doing here. Okay, let's do another one. These are fun, aren't they? Almost too easy. Number two. Let me read it. Some evergreens are objects of worship because all fir trees are evergreens and some objects of worship are fir trees. What is the conclusion here? The conclusion that some evergreens are objects of worship. And just for review, how do you know that? Because right after that. Right. Okay. And then what is the major term of this argument? No, no, I'm not asking for the premise, I'm asking for the major term. Okay, so then what becomes the major premise? Okay, and then what will be the minor term in this argument for evergreens? Evergreens. And then what is the minor premise then? All first trees are evergreens. Okay, then what is the mood of this argument? Affirmative. Particular. Affirmative. I, A, I. Not the fourth mood. Mood is the three figures. It's the three letters. Yeah, the fourth figure. Because the middle term F appears in the first position in the first premise and the subject's position in the second. And again, the only way you can remember this by looking at that chart on page 193. Very good. Let's move ahead then. 6.2. We're now going to get into doing some real logic here. After the immediate inferences, which of course were logic, we're dealing with telogism in this chapter and with this introduction, we now want to talk about performance nature of syllogistic arguments. On page 195, the author tells us a valid syllogism is a formally valid argument, valid by virtue of its form alone. This implies that if a given syllogism is valid, any other syllabus of the same form will also be valid. This is crucial. Also, any other syllogism of the same form, if it's invalid, will be invalid. Here we're stripping away all the content. Now, ordinary language, natural language is gone, and we're completely into a formal language where we have S's and C's and A's and B's and all the rest of the. Now you know why it's called formal logic. It's in a formal notation. And now we're going to be testing the validity of an argument pattern, not on the basis of whether fallacies like composition or ambiguity or hasty generalization are made, all of which was determined by the content of the argument. Now we're going to be looking only at the form of the argument. So let me repeat, we're dealing with a formal notation and considering the validity of the argument based only on its form or structure, and that this is formal logic. We know what the syllogism is. Syllogism has three premises, a major premise, a minor premise, and a conclusion. You know that the first premise, the conclusion, is mediated from the first premise through the second premise. You know what the mood of the syllogism is and you know the figure of the syllogism. Now, there are a lot of different possibilities. At one point he probably gives you, what is it? How many different possibilities are there? 256. 56 possibilities. Now, it's pretty hard for people to memorize. 256. This is valid. That's invalid. This is valid. You can teach a computer that, you know, no problem, but hard for the human beings. Pay attention to that boring, long list of valid invalid stuff. So how are we going to test televisions for validity? Remember, the validity depends simply on the structure of the cosmic. How are we going to test it? Your author will give you three ways of testing the categorical syllogism. I wish you would make it clear that he's doing this. I'm now I'm taking the helicopter up above the forest, saying, who, by the way. This is the lay of the land, you guys. He's going to discuss three ways of testing the validity of the syllogism. The first is by logical analogy, or dip, actually is a way of showing the fallacious character of a syllogism. The second will be by Venn diagrams, diagramming them in terms of circles standing for sets that overlap each other. And the Third will be by means of certain rules that apply to the construction of syllogism. So, you all listening? Three ways to test the validity of a categorical syllogism. One, by logical analogy. Two, by Venn diagram, three, by certain rules that are laid down. Let's look at the first method, which is discussed on page 195 at the bottom. He says, by far the best way of exposing the pellacious character of some syllogism would be to construct another argument having exactly the same form, but whose invalidity was immediately apparent. And Kolky illustrates this for us. He says, we might seek to expose the given argument by replying in the following way, but let's make sure we know what that argument was. Somebody says, all liberals are proponent of national health insurance. Some members of the administration are proponents of national health insurance. Therefore some members of the administration are liberal. If we look at the form of that, we get all L's are P's, some M's are P's, therefore some M's are L's. Now all you need to do is to construct an argument that has that very same form, changing the terms where when a person hears, well, that doesn't make any sense. That's fallacious. And this is very powerful tool to expose the invalidity or the fallacious nature of the syllogism. And your author does this by using all rabbits are very fast runners. Some horses are very fast runners, therefore some horses are rabbits. And anybody listening to, oh, well, obviously horses aren't rabbits. And yet this syllogism would make you draw that conclusion. So if it's invalid in the case of horses and rabbits, that form of argument is invalid. When you're talking about liberals, proponents of national health insurance, and members of the administration, this is a matter of showing the absurdity of an argument by mimicking its form to show that the form alone is. Now this. If we were all able to do it, if we were all very creative and fast on our feet or even, you know, laborious at home, this method of refuting the syllogism would be very helpful. It would be very powerful in debate. I want you to remember that in a debate setting, for talking to people, it's probably easier to give a limiting argument than it is to explain minor premise and major premise and middle premise and, you know, mood and figure and all the rules of syllogism. If you want to show the invalidity, instead of going through all the steps like that, just give an alternative that mimics the form and yet it's an absurd kind of argument. But then, as COCI says in 196, I want to really promote this. I think it will help you to learn to think, what's the pattern? Of what my opponent or who I'm talking to is saying, what's the pattern? Can I imitate that pattern until it can be fallacious? But Copy points out in one night he said, this method of testing the validity of arguments has serious limitations. It has great power for communication and debate. Serious limitations first, sometimes a logical analogy is difficult to think up on the spur of the moment. We're all smiling and agreeing with that. Wouldn't we love it if every time we heard an argument and he'd say, okay, I see the form and I got an illustration, boom, boom, boom. But sometimes you can't do that. And there are far too many invalid forms of argument for us to prepare and try to remember. Refuting analogies for each one of them. I mean, that would be as hard, if not harder than remembering for the 256 possibilities. Valid, invalid, invalid, valid, and so forth. You have to remember all the illustrations as well. So that's not going to be very helpful. And then this is even more detrimental. Not being able to think of one that is one of these alternatives that shows not being able to think of one does not prove the form valid, for it may only reflect the limitations of our thinking. Let's say I go through it and I say, well, I can't think of any counter example to this structure of reasoning, so I guess it's valid. Well, I mean, you couldn't draw that conclusion. The only conclusion you can draw is, well, you haven't been able to think of one. Maybe there is one, but you haven't come up with it yet. And so co the very end of this section, a more effective method of establishing the formal validity or invalidity of syllogism is required. It is to the explanation of effective methods of testing syllogism that the remaining sections of this chapter are devoted. So now back up in the helicopter looking over the lay of the land. Three ways to test logical analogy. So you think that has a lot of problems. Maybe you can't think of one. The second will be Venn diagrams, which I am excluding is just too cumbersome and unnecessary for this particular course. Although you may want to look at it for fun. Venn diagrams will do the job if you can learn to master the technique and so forth. And then thirdly, rules of syllogism, which I think to me is just to use what nasty looks rule. And then you can test everyone one by just six steps rather than having to go through the diagrams or all this logical analogy stuff. The exercises that appear on page 196 and 7, however, are to try stimulate our creativity to come up with counter examples. And so we'll look at a couple of those anyway. Okay, number one, we're put to refute by if it is invalid by logical analogy. All business executives are active opponents of increased corporation taxes. And the reason for that completion is all active opponents of increased corporation taxes are members of the Chamber of commerce. And all members of the Chamber of Commerce are business executives. In order to effectively refute somebody by logical analogy, you have to have exactly the same form of argument as they did. And on top of it, you need to have two premises which are known to be true, which are not controversial. And so if your premises are known to be true and yet the conclusion is obviously false, then you assume this can't be valid. So in order to effectively do this exercise, we have to mimic the form exactly and our premises have got to be true premises. But the conclusion and obviously false. Well, it has the obviously true premise and an obviously false conclusion in order for the technique to work. So in this particular illustration, what is the form of the argument? Just schematize it for me.

AA1.

No, schematize it in terms of. Just let something spin for the class. Business executive. You have. The conclusion is stated at the very beginning. All business executives are active opponents of increased corporation taxes. So I put down all B is A.

Okay, I used all S is key for subject and credit. That's how he did it all through here.

That's fine. Go ahead.

All S. So my major premise is all P is M. P being active opponents of increased corporation taxes and M being all members of the Chamber of commerce. And then my minor premise was M equals S. All M is R. Or excuse me, all M is S. Therefore all S is T.

Okay, so we've got the form of the argument Using your notation. We have alt P is M. Alt M is S. All S is P. Okay, there's the form. Now give me a couple of premises that fit that form which are obviously true.

One premise would be all men are opponents of me.

And that's not obviously true. It is not obvious that all men are your opponents. If you were trying to use this, they'd say, oh, yeah, that looks real clever. But the point is, the premises aren't true to show invalidity. You must have True premises and a false conclusion. That's the key to all of this stuff here in deductive logic. True premises and a false conclusion. That's why I've been belaboring this, because when I first heard what you were going to propose, the person that jumped out at me. Well, that's not obviously true, that all men are your opponents. So you're not going to convince me of anything unless you. So you've got to kind of draw me in by giving me true premises. And I say, oh, yeah, and then you show by the structure. That would mean the following conclusion. If you know that that conclusion doesn't follow, and therefore the structure must be wrong. Okay, Greg, let's see if you have one. I said taking. Taking the form. Okay. All tulips are flowers. All flowers. Okay, that's obvious enough that all tulips are flowers. All flowers are plants. All flowers are plants. Wait a minute, wait a minute. Are all flowers plants? That's not true. Well, depends on what you mean by the word plant. I'm using it as it would be. We're not talking about plastic. We're talking about organic. Yeah, but as you say all flowers are plants. Are you distinguishing between. Can you go to the nursery between plants and flowers, or are you just saying they're all plants since they are something that you plant in the ground? Well, I'm just thinking that's the organic term. The rest should have said all flowers are organic. Okay, well, then you're.

In the ground.

Right. But they're still organic. They're living organs. Okay. The defect in your illustration, although it may be worked out equally, I don't know. But the defect at this point is. You see, immediately an ambiguity jumps out. You've got to give premises where your listener, or you look at it and say, well, this is obviously true. This is obviously true and clear. But the conclusion doesn't follow. And so that structure's got to be wrong. So we're gonna. You're taking plants in the sense of what, Over against a mineral or an animal? Yeah. Okay, so it's in the plant category. I should have said all flowers are in the plant. Okay, I'm not sure if it's gonna work there, but let's see if it does. Start again. All tulips are flowers. All flowers are plants. All plants are tulips. Okay, I got you. Very good. I'm just sorry. There was an ambiguity of the word plant. I didn't realize that. Okay, I'd like to catch the size. The same one. What did you Come up with all billy goats are nasty troll. All billy goats are nasty. Well, this relies on some specialized knowledge of trolls and cannibalism and dilly goats, right? And when you say that all dilly goats are nasty trolls, that is not something that's going to be an obvious truth to people. Okay, well, maybe it's good we did stop on this one. The use of logical analogy is totally ineffective if you don't have obviously true premises with an obviously false conclusion. That's the whole point of this, is to show that the structure of argument is unreliable. And I'm going to show you that that structure is unreliable by mimicking the structure where we have true premises and a false conclusion. And that's the classic definition of invalidity. Where the premises are true and the conclusion is false, the conclusion does not follow from those premises. What did you have?

I had as my first premise, all puppies are dogs.

All puppies are dogs, okay?

My second premise was all dogs are animals, okay? And then my concluded, all animals are puppies.

That's very good. Very good. And now you see how if you presented that to somebody, they'd say, hey, that doesn't follow because we know that it's, you know, false when you say that all animals are puppies.

Took me a long time to get to that.

But once you catch on to what you're doing here, you're basically, what you have is a broader category, animal and puppy. In this illustration, you had the structure, and you got to make sure you're using obviously true premises and obviously false conclusion. Let's try to work through number four on page 197. Together. We have no college graduates or persons having an IQ of less than 70, but all persons having an IQ of less than 70 are morons. So no college graduates are morons. What's the conclusion here? Somebody.

No college graduates are math.

And we know that because we have the conclusion indicator. So, okay, so we have no F is P, where S will be college graduates, P will be morons, Okay? And then the predicate term in that conclusion is morons. And so that gives us our first premise, which is mentioned second in the illustration. But all persons having an IQ less than 70 are. So the person having an IQ less than 70 is M. So all M is P, that is to say, are morons. And then the next premise, the minor premise, is no college graduates, which is S in our schematism. Our person's having an IQ of less than 70, which is M. I like my way of doing it. I'm Going from this to one kind of abbreviation to another, it seems like. But anyway, so now the argument is in this form. All M is P. No S is M, therefore no S is P. And we want to get a couple of premises that are obviously true, but the conclusion comes out obviously false. Who can answer?

One of my analogies was all rabbits are fast runners. No person is a rabbit, therefore no person is a fast runner.

That'll do it. Instead of person, let's say human. I think it'll be stronger. Okay, you have all rabbits are fast runners. No human is a rabbit. No. Therefore no human is a fast runner. Now, I do think there will be a possible challenge to this in terms of equivocation on Fast Runner. What's a fast runner for a rabbit? What's a fast runner for a human? And I think between the premise and the conclusion, you're using Fast Runner in two different ways. The reason I'm jumping on this is I want to show you we have to keep remembering what we've learned previously. What I'm saying is I think you may have committed an informal fallacy because you're using Fast Runner in two different ways. Now, how could you get rid of that informal fallacy? Get rid of the ambiguous fast runner aspect of it. And you could do that by saying all rabbits run faster than 80 miles an hour. I don't even know if that's true. True.

It's probably not true.

All rabbits run faster than 20 miles an hour. No human is a rabbit. Therefore no human runs faster than 20 miles an hour, which may be true. So you see, by specifying, you've gotten rid of the ambiguity, but you may not have a good illustration.

Would it be better to use just a completely different word, like a vet, like non carnit?

Well, you can choose anything you want that is true of rabbits and not true of humans. That's the point you want to make here. So what is true of rabbits? Not true of humans? Ordinarily hop. Yeah, but then you're going to have the equivocation on long ears. How about ordinarily hop? Or maybe we should just get away from rabbits and humans to get a better illustration. But I think you could say all rabbits are things that ordinarily hop. No human is a rabbit, therefore no human is something to ordinarily hop. Well, that's true, isn't it? No human is something that ordinarily hops. So now we got to work harder at it. Let's get rid of humans and rabbits. Who else has them? I said all Squares are geometric shapes. No triangle, no triangle are squared. So no, triangles are geometric shapes.

Very good.

You have to catch on to the class relationships, because that's what categorical reasoning is all about, class inclusion and exclusion. So once we see a real obvious one, as you have here in geometric shapes, triangles and squares, then you can put it together and show its invalidity. Well, this is the method of logical analogy. It's fun, it's enjoyable, and it's rhetorically powerful. It's also cumbersome, as you can see, just from what we've had to work through in this exercise ourselves. What we're going to do now then, is jump over Venn diagrams, that section showing us how to test validity in a mechanical fashion, and we'll go to Section 6.4, Rules and Fallacies. COPI will lay out for us six rules by which we can test syllogisms. And if they keep all the rules, that's good. And if they break one, then they're invalid. And we'll summarize the rules and do some exercises in our next class session. Also for that class session, I would like you to read copy all of chapter seven and do the assigned exercises that I'll mention in a moment. Copie, chapter seven, and then QPI chapter eight, sections one, two and three. So the new reading assignment is QOPI seven through 8.3, the first three sections of chapter eight. And then we'll take sections four and five in our next class session after that. Okay, so read COPI chapter 7 through 8.3, and I'll give you some homework assignments to work on. And tomorrow we'll pick up with the end of categorical syllogisms.