Dr Greg Bahnsen - Critical Thinking: Categorized Syllogism Part 3 (Part 12)

Let's begin this morning with a word of prayer. My heavenly Father, we do thank you for the privilege of prayer. We thank you that by your Son, allow us to come into your holy presence to make our petitions known to you. We would praise you for who you are, what you have done. Thank you above all for your saving mercy in Christ. We do ask that you would forgive our sins and that you would be with us by your spirit to glorify you and to do well in our task today that you've given to us. We pray especially that you would enable us to serve Christ even with our minds. We thank you that in saving us you saved every aspect of our being, that you have saved us to think in a way that shows our love for you and that glorifies you as well. And toward that end, we ask that you would use this class period in Jesus name. Amen. All right. We have learned what categorical propositions are and categorical syllogisms. You can tell me what are the three ways in which you can tell the categorical syllogism? Three different methods that are mentioned in the book for testing. Categorical syllogism.

Has three premises or two premises and a conclusion.

No, no, I'm asking for methods of testing, not a definition of a syllogism.

Logical analysis, Venn diagrams and the rules.

By the rules, okay, We've looked at logical, not analysis, but analogy. The attempt to. That's okay. The attempt to imitate the structure of your opponent's argument using premises that are obviously true and a conclusion that's obviously false, and thereby showing that the structure must be unreliable, that the conclusion does not follow from the premises. The second method of testing a categorical syllogism is by means of the Venn diagrams. The overlapping circles where you fill in the different quadrants or aspects of the circle, the parts of the circle and their overlap to determine if in fact the premises cover the conclusion. It amounts to a physical, literally a physical method of testing whether the conclusion has been entirely covered by what's stated in the premises. And then thirdly, the method which is preferable and the one that I've asked you to focus on, is that of testing by means of the six rules of syllogism which you find in Cocci, Chapter six, section four. So let's go over those rules and then try to do some of the exercises so you can know how to apply them once you get the hang of this. It's pretty nifty. Six rules is not difficult to memorize and Having those particular rules in mind will enable you to test every categorical syllogism. The first rule that is mentioned by Kofi is in a sense, not so much a rule as it is a reminder of what a syllogism, he says a valid standard form categorical syllogism must contain exactly three terms, each of which is used in the same sense throughout the argument. To say that it uses exactly three terms, you have your major term, your minor term, and your middle term is again, just what we mean by categorical syllogism. If you find an argument or what purports to be an argument that uses four terms or five terms or six, common in ordinary discourse for people to do that, then what you might initially conclude is that the fallacy of four terms has been committed. Now it's called the fallacy of four terms. Even if there's five or six or seven, that just is the nomenclature that is used. But another thing you could say is instead of accusing them of committing a fallacy, you simply say, well, this is not a standard syllogism, so it's not testable. You're going to have to reformulate your argument to make it testable. Another part of the rule that should be noted is that these three terms, each one of them must be used in exactly the same way throughout the argument. Now, that's redundant to you because you've already learned in ordinary language analysis, that is the fallacies of ordinary, that one of the types of fallacies is equivocation. So this is just a restatement of that as well, that if you see a term being used in two different ways, then the argument is fallacious by means of equivocation. All I want to get at then is that with rule number one, this is nothing new, it's just putting in a rule things that you have already mastered. And it's just a matter of course, only three terms, and they have to be used unequivocally. Now, the next two rules for testing the categorical syllogism are rules of distribution. I think it's helpful if you remember you have two rules of distribution. And then on page 209, Cokey says there are two rules, of course, quality having to do with the affirmative or negative quality of the propositions. And then the sixth rule is one that you already know as well, and that is the rule having to do with existential assumption. So when you remember that numbers 1 and 6, in a sense, you've already learned they've not been called rules, but you already have that down. You really only have four rules left. Two of distribution, two of quality. So if we get those, then we'd be able to test every syllabus and without the complication of the Venn diagram or having to be fast on repeat logical analysis. So the two rules of distribution.

What.

Kobe labels rules two and three. Remember, distribution means when a subtraction, distributive or so. Then the term is used as ways to refer to every member that is named. Rule 2 says in a valid standard form categorical syllabus, the middle term must be distributed in at least one premeditle term. In at least one. You don't have to have both, but one of the premises must use the middle term in a distributed fashion. Now, does that make any difference whether middle term is mentioned, whether it's in the subject or critical position, major or minor premise? No. So one use of the middle term, and the reason for that should be fairly clear. If the middle term is not distributed, then the way in which the other two terms are related, they may not even touch each other for that matter, because you're not using that middle connecting term in a way that covers the whole field or the whole set of things that it mentions. Okay, then Rule 3 is related, although it doesn't use the middle term. Rule 3 says that if either term is distributed in the conclusion, then it must be distributed in the premises as well. Now, in how many premises? Think about this. In how many premises will that term from the conclusion be found? Only one. That's exactly right. If a term is distributed in the conclusion, then you've got to find that term in the premises. But there's only going to be one premise that mentions it. Correct, because the other premise is going to use the middle term and then the minor or the major premise, whichever is left. So you just have to check one premise and that distributed term in the conclusion and make sure that it's also distributed in the premise. Now, when the term that is distributed in the conclusion is is not distributed in the premise and it's the major term of the argument, then that's the fallacy of illicit major. This terminology comes from the Middle Ages and may seem cumbersome, but in actuality will help you remember the rules. In this particular case. Just remember what you have is the fallacy of illicit major or illicit minor. Can that fallacy be committed if the major or the minor term are not distributed in the conclusion? No, you don't even apply this rule unless you find one of them distributed in the Conclusion. So that's it. Rules of distribution, middle term must be distributed in at least one premise, and then any distributed term in the conclusion must be distributed in its corresponding premise. Now the rules of the quality number four is perhaps the easiest of all the rules to remember. No standard form categorical syllogism having two negative premises is valid. Anytime you have somebody that has an argument where there is a negation in both of the premises, the conclusion is invalid. I know that may seem a little strange. You think, well now how can that be? Well, go ahead and test it. Just try dozen or so like that and you'll finally get the point. You cannot reason from two negative premises to a conclusion that will be valid when you test it in the other methods and the reason is stated on page 210. You might be able to just catch this intuitively. The author says from two negative premises, no relationship whatever between S and P can valibly be inferred. And this is then the fallacy of exclusive premises. I don't have it on the board, but let me remind you what the schema for a negative premise looks like. If I say no S is P, no sailor is a pirate, then I've got two classes, class of sailors and the class of pirates. And I'm saying they don't overlap at all because no S is a P. So there's not going to be any touch at all. So that's what a negative premise does, it separates these classes. So if you have two that do that, then obviously you're not going to be able to draw any conclusion between the S's and the P's in your argument. And that's why it's called the of exclusive premises or negative premises. And then the fifth rule is the last one. We have to talk about another rule having to do with quality. If either premise of a valid standard form categorical syllogism is negative, the conclusion must be negative. If either premise is negative, the conclusion must be negative rather than affirmation affirmative. So when we look at our arguments, one of the things we're going to look for is a negative premise. Or two, if you find a negative premise, then rule five will come into play. You know that the conclusion must be negative. And then if you find two negative premises, you know automatically the argument is invalid. So I hope you can appreciate the elegance and the efficiency of these six rules. They'll cover all the problems that we might have. The author tells you that Rule 5 is not the sort of thing that you ordinarily run into in Discourse. He says arguments breaking this rule are so implausible that they are said seldom encountered in serious discussions anyway. But when we get into formal logic, where we have the ordinary language content or the semantics of the argument stripped away in favor of just the structure and the form of these things, then it's possible to have that fallacy committed and not be aware of it. Unless you're, you know, the rule only watch for that. The middle paragraph on page 210 discusses what would have in classical logic been taken as another rule of syllogism corresponding to number five, where you want to prevent syllogisms with affirmative premises and a negative conclusion. And the reason why Copie does not choose to formulate that rule is that his Rule 6 will cover all such cases. Rule 6 is just what you've already learned about the fallacy of existential assumption. If you have two universal premises, do those premises assert the existence of anything in their classes? If I say all of the coins in my pocket are nickels, does that assert that there are coins in my pocket? No, it does not. Just says that if there are any coins that are going to turn out to be nickels, but there might be no coins. And so a universal premise does not assert the existence of any members of its class. Now, if you have two universal premises or two distributed classes, classes mentioned in the premises, can you then draw a conclusion that there is something that actually exists in the conclusion? No. And so let's remember that in the case of a standard or a valid standard form categorical syllogism, that none of them with a particular conclusion can have two universal premises. And I've already told you we learned that yesterday when we discussed existential assumption. Do you have any questions about these six rules? Because I think applying them probably the best teaching device here. You've all done your exercises. Let's turn to page 211. In Roman numeral 1, Popey inconveniences you a bit by forcing you to remember the mood and diagram of syllogisms. And so we are to name the fallacies committed and the rules broken by invalid syllogisms of the following forms. And number one will begin with Pat this morning, A two syllogism. Just so that we can wake up and be together in this, can you tell me what that syllogism will look like? What is the AAA mood? Figure 2. We'll use P, M and S. The P will be the predicate of the conclusion. The S will be the subject. The conclusion M will be the Middle term. Okay, now what's this look like?

P dash M.

Okay, well, give it to me with the AAA form as well. Not just the figure.

All P is M. Good.

All P is M. All.

S. S.

Is P. All S is P.

Therefore.

All S is P. Wait a minute. You said all S is P. You missed the second premise. It's in the a form. We have all P as M. No, you've already. We have all P is M. Just the first premise. What's the second premise going to be? What's figure two look like? Turn back to that page.

Predicate major.

What page are you on?

Page 193.

Okay. Okay. If this is to be the second figure, then you know that the order of mention is predicate. Middle subject, middle subject predicate. Of course, there are no such predicate laws to there. Okay, so these are all A form propositions. Then it's going to be all S is P, all P is M. All S is.

All S is.

No, that's the conclusion. S and P are the conclusion. The second premise has got to be universal. Affirmative. Where you have the subject. Yeah, the subject and the middle term used. So all S is is M is M. Good. And now the conclusion will be all S is B in every figure. Remember, you don't have to memorize the conclusion because the conclusion is always subject predicate. It's just a question of where the subject and predicate terms are distributed in the premises. That gives you the four figures of C syllogism. Okay, well, now that we've finally got it on the board, what we're supposed to be analyzing. Let's analyze it. Does this commit any fallacy or does it break any of the rules of syllogism?

That undistributed middle.

Undistributed middle. Okay, and that's rule number two. And how do you know that the middle term is undistributed?

The middle is.

Remember our diagram for terms, how they're distributed. I hope the little way I taught you to remember it yesterday would be helpful in doing your homework. If you remember what we saw, then it's always easy to test the distribution. You have A form, E form, form I form and O form. Right. And what is the distribution? Pattern distribution is right there. The top line subject terms are distributed. The right line predicate terms are distributed. So of course E is the most distributed of all, is its subject and predicate terms are distributed. So all you have to do now is look at the form of the proposition. You have an A form proposition Right here. So in A form, what is distributive?

The subject is distributed in the second, second part of the premise. All S is M. It isn't distributed.

Is this an A form? Number one. Is this an A form?

Okay.

Is the predicate distributed? In an A form proposition, the subject is distributed here and the predicate here. This is an A form. Is the subject distributed? Is the predicate distributive?

Yes.

In an A form proposition, only the subject is distributed. Remember, along this line, subjects are distributed. Along this line, predicates are distributed. In an A form proposition, only the subject is distributed. Let's start again. All P is M. What is the predicament in a sentence? Okay, in an A form proposition, is the predicate distributor, M. This case, the middle term. So you have an undistributed middle, right? I'm sorry to belabor the obvious, but I'm just trying to build this up step by step. What's the form of prems 2? A form. Okay. Is the predicate described distributed in an A form proposition? No. Does M stand for the middle term here? So is the middle term distributed in the second premise?

It is in this argument.

No. You have all S is M. M is the predicate. It's an A form proposition. You know that the predicate is not distributed in an A form proposition, only the subject is.

So you have two distributed subjects and no distributed middle.

Exactly. But the point is, you have to see that the middle term's in the predicate position, and in both places it's undistributed. And so you commit the fallacy of undistributed middle. Okay, let's do another one. Number three. Pete, why don't you help us on this one?

Number three.

Okay, you have a syllogism of the IAO mood. Figure three. Tell me what figure three is.

It's some.

No, figure three.

Okay, Figure three is M dash P.

Okay, Here you're going to have a syllogism where the middle term is the subject.

And then the minor premise is M dash S.

Okay? So we know that that is going to be the figure. Now, let's put it in I. A O form. An I proposition.

Sum M is B.

Correct sum M is P minus 2.

All M is P. Right.

That's an A form. All M is. Did you say P?

Excuse me?

S. It should be S because we have S here in that figure. And in conclusion, it's going to be in O form.

Therefore, some S is not pulling, is.

Not P. We're down Here, the O form proposition. Now, does everyone understand that that's the form of the argument that we're evaluating? This is just setting up the problem, making sure we know how to describe it. Is there a fallacy in this? Yes. What is it?

It's a fallacy of drawing a negative conclusion from affirmative parenthesis.

A negative conclusion from. What did you say?

I said a negative conclusion from affirmative.

Principles or from affirmative premises.

Which would be the opposite of number five.

Yeah, we've already said we don't need the opposite of number five.

Okay.

That if you have that problem, it will be covered by rule number six. And let's see if rule six applies. Do we have two universal premises here?

No.

Okay, so that is not the problem with this syllogism, Jay.

I say we have an illicit major.

Exactly right. Illicit major. Rule number three. Rule three says if either term is distributed in the conclusion, it must be distributed in the premises. Now let's ask ourselves about these terms in the conclusion. Melissa, we'll let you be part of this conversation this morning. Is S distributed in this proposition? Some S is not P. Is S distributed? Does every member of the S class mentioned. No. How about not P? Is every member of the P class mentioned? Yes, it is. Not one of the P's can turn out to be some of the S's. And so that does distribute P. Now, is P distributed in the premise? We look up here, P only appears in premise one. Remember, it's A Molly being one of them. And now what we have here is what form of premise is this? At some M? Is P? Is that A, E, I or O? A particular affirmative? No, E is the universal negative. Okay, now here is my little way of remembering distribution in the I form. That in the I form, which term is distributed.

The benefit?

That was a trick question, Pat. In the I form, if you look at what I've shaded for distribution, it's the only corner that has no distribution at all. There is distribution in the subject term here. There's distribution in the predicate term here. And there's distribution in both terms here. And there is no distribution there. Do you understand what we're talking about? Let me ask you again. What's the form of this proposition? Okay, now we. If we're going to test for the distribution of term P that appears here in an I form, proposition. Is P distributed? No, cannot be, because neither term will be distributed in an I form. And so we have a distributed term in the conclusion that is not distributed in the premise. And now the only question is which term is this? Is this the minor or the major term of the argument? Major. It's the major term of the argument. Why did you say that? What's the definition of the major term of an argument?

It appears in both the original premise.

No, no. Order or premise will not help you, especially when you get sloppy people who don't put it in standard form. There is a specific way of finding the major term in a categorical syllogism. It has nothing to do with the premises, has everything to do with the conclusion and the order of mention. Who can help?

That's the predicate of the conclusion.

Right?

The major term of an argument is the predicate term of the conclusion. The minor term of an argument is the subject. Okay, so now if we have a distributed predicate here, it's not distributed in the premise. Then what illicit step have we taken? An illicit elicit major. You can speak up, okay? In fact, people on tape can't hear you if you don't do that. So let's do this again. We have a distributed predicate term and the conclusion that's not distributed in the premise. Then we have a fallacy of illicit major. That's right. These other ones will be a little bit easier because they don't require us to go back and identify mood and figure. I'm sure you didn't enjoy the exercises in this section for that reason. But then if we forget what we have learned, especially this distribution chart, then we won't be able to test the syllogisms at all. So there's a reason why the author did that. Okay. In number two, you were to do numbers one through five. Name the fallacies committed and the rules broken by any of the following syllogisms that are invalid. Whose turn is it? Okay, well, then we'll have Jay do number one. All textbooks are books intended for text, careful study. Some reference books are books intended for careful study. Therefore, some reference books are textbooks. Before you give the answer, let's see if we can't work through this step by step. Let's schematize this argument using letters that are appropriate to the English language components.

Here.

I know you guys are laughing, but I can understand why you go from the English language abbreviation to another formal language. So then you can test this by the rules and so forth. When you can just use anything you want, you just make it hard on yourself. Okay, let's try it my way, the easy way. All T is S. Okay? So T is going to be textbooks. And S for study. For study. In the expression books intended for careful study. You're using study. You can do anything you want. It's like Alpha. I didn't want to use books. You can choose X if you want, but I would think B would be the thing that would help you keep it in mind, since that's the beginning of a description. All T is B. Number two sum.

R is B.

Good. Some reference. Whatever books are B and the conclusions.

Therefore, some R.

Is T is what?

Some R is T. That's okay.

Very good. Shall we go through the rules one by one, See if they're broken? Let's start at the end here. Do we have two universal premises leading to a particular conclusion? Why not?

There's a particular name in it. In the minor premise.

That's right. The second premise is particular. So we haven't broken rule six. What's rule five?

Negative.

Rule five is if you have two. If you have a negative conclusion, there must be at least one negative premise, right? No, no, no. If you have a negative premise, then you must have a negative conclusion. I hope you catch the difference between the way you work. You look at the premise. Any negative premises here? So that rule doesn't even apply. Back up another one. Rule four.

Yeah.

If you have two negative premises, then it invalidates the argument. Are there any negative premises here, Pat?

No.

Okay, so Rule 4 doesn't apply. Rule 3. If either term is distributed in the conclusion, it must be distributed in the premises. Well, no term is distributed in the conclusion. Some R is D. No termist distribution. No. Thank you. Don't let me push you off what you know. I already gave you the diagram's distribution. What form of.

It's in the I form.

I form down here. What have we learned? There's no distribution in I form propositions. Okay, so we don't have to worry about rule three. Wow, this is going to be easy then, huh? One or two or left? We know it's easy because here you don't have to decide if it's valid. He tells you it's invalid. You just have to find which rule is broken. You want to take a 5050 stamp at this? Is it Rule 1 or Rule 2? I say it was Rule 2, which is the fallacy of. I'm just going to do middle. Okay, what is the middle term out of TV R? What is the middle term? B. B is here. And here is the predicate term distributed in an A form proposition? No. Okay. Is the predicate term distributed in an I form proposition?

No.

The I form is the easy one. There is no distribution in an I form. Okay? So neither mention that the middle term is distributed. And so we have the fallacy of undistributed middle. Any question about number one? All right, let's do number three?

Green.

No. Tragic actors are idiots. Some comedians are not idiots. Therefore, some comedians are not tragic actors. Schematize it.

Okay. No t are I.

No t is I.

Some t.

Are not I, some t.

Some c are not c. Okay.

Some c is not.

Therefore some c are not t.

Okay, what fallacy is committed here? The fallacy. Hint. I said this is the easiest one to spot. Easiest rule to remember. Maybe I should have said, but. All right, Pete, what fallacy is committed here?

It's fallacy of exclusive premises.

Exclusive premises. Because the two premises are what quality?

Negative.

Okay, can you show the negation in the first one?

1.

Where's the negative quality?

It's universal negative.

No. And the second one, it's the copula, is.

No, there is not.

Copula has nothing to do with the quality.

Some is not.

This is a particular negative. Negative. Particular because it says some negative. Because that's right. So that's the fallacy of exclusive premises. Let's back up and look at number two. Pat, I think it's your turn. Let's schematize it on the board quickly.

Okay. Policy.

Is W. Okay.

All P is C. Therefore all P is W.

Okay. What rule does that violate?

Equivocation rule number one. Violation of four terms. What he does is he takes criminal actions in both places, and he means two divisions.

Exactly. Right. Now, what I want to know is, did you go through all the other rules until you came down to rule one? You said, this is the only one left. It doesn't break any of the others. Oh, that's too bad. I was hoping that. See, by putting it up on the board, then I got all the semantics stripped out of it. And you go through and you start testing these things. I said, well, it doesn't break rule number six. Shouldn't break rule number five. Doesn't break rule number four. You work backwards and you say, well, what rule is broken? And then you look at it and say, oh, criminal actions is taken in two different ways. And it's kind of a funny argument, isn't it? All criminal actions are wicked deeds. That is the things that criminals do are wicked. The next premise is all prosecutions for murder are criminal actions. That is to say, it's an action in a criminal law court. And so criminal action is being used in two different ways. And that's the fallacy. Very good. Okay, number four. Jamatize it for me.

Some p.

Is.

Not.

Let's use another word.

In a case like this, you're just going to have to Q something. Q.

Okay, let's let her down better.

All.

A is.

Oh, wait a minute.

All P. Excuse me. Okay, I got my toes. Basically, all P is A, therefore no, A is Q.

Pets. It really messes you up when you have parrots, pests and pets. So as long as we remember what we're talking about, what fallacy is committed here? Let's just go to the part of the matter.

Okay.

Both terms are the way I figured this. Both terms are distributed in the.

Conclusions.

So they both need to be distributed in the.

That's right. This is E form. Right.

And I found that.

What's the pattern of distribution path?

A?

E? No, I think this is an E form. You get total distribution. Right. That means both of them have to be distributed in the premises. Are they?

And the minor term is not.

Okay, what's the minor term in an argument? How do you identify it?

Pat.

Minor term is the subject of inclusion.

Very good. So now let's find A in the premises. It's up here. What form of proposition is All P is A. A form is the predicate term distributed in an A form proposition. So we have the fallacy of illicit.

Minor.

Minor. Very good. And now Melissa will let you do number five.

All p is m.

All p is m. Go ahead.

All m is b.

B.

Yes. And therefore some b. Rm. I mean RP.

Okay.

Balison race. Rule 6. It has two universal premises and a particular conclusion.

Exactly.

We have an A form. A form. Those are both universal. But here we have a particular conclusion. And so from its 1000 name broke rule number six, you're correct. What's the name of that fallacy?

The fallacy of.

Existential assumption. Because existence is asserted in the conclusion and illicitly assumed then in the premises. But in universal premises. On Boolean logic, no. Existence by mistake. All the coins in my pocket are nickels. Does not tell you that I have any coins in my pocket. Just tells you that if there are any coins, you'll be nickels. Okay, now number three, you were to do numbers one and three in section three. Name the fallacies committed in the rules broken by any of the following syllogisms that are invalid. So now you've got to be willing to say that the syllogism is invalid and show a rule or declare that it is valid. Number one. J.

Okay, I said it's broken rule.

This we got to reconstruct. Here we have it in not in anything close to standard form. All chocolate eclairs are fattening foods because all chocolate eclairs are rich desserts. And some fattening foods are rich desserts. That's a good argument. We'll detest it. What's the conclusion?

All chocolate eclairs are fattening food.

But how do you know that's the conclusion rather than a premise?

Because after that you have the word because and two more pronounces.

All right, so because is usually a premise indicator. So the conclusion schematize it for me. All C is F. Very good. I will now adopt the procedure of not using the copula when I schematize. But just the dash, obviously fill in will be are, has been, is whatever we all see is F. Then the first premise.

First premise is all C is R.

Oh, wait a minute. Hold on. Let's go through our rules again. You are right.

Let's look at those cases.

We're going to find out what mistake you made.

I know what mistake I made.

What mistake did you make?

I was putting the minor premises of major.

Okay, how do you know what is the major premise?

The major premise is the one with the predicate.

I just wasn't thinking. That's all right, give it to me now.

Okay, Some F is R is not.

R is not R. Okay, and then.

The minor premise is all C is R. Right.

Now that it's up there, it should be easy to analyze. What is the fallacy committed, if any?

We have a problem because we are drawing an affirmative conclusion from a negative premise.

Notice there's a negative premise. And as long as there's even one negative premise, the conclusion must be negative. The conclusion is not negative. So it's a fallacy of. Don't you love the fancy term for this one? All the others have got undistributed. Middle implicit, major existential assumption. But this is the fact that fallacy.

Of drawing an affirmative conclusion.

In other words, we're just going to. In the title. We're just going to describe it all over again. Okay, one more and then we're done with these. Number three. Pete, what is the conclusion? I'll read it. Some snakes are not dangerous animals, but all snakes are reptiles. Therefore some dangerous animals are not reptiles.

The conclusion is some dangerous animals are not reptiles. Some A is not R. Some A animal.

Animal.

Must want me to do sp.

Again, some D is not R. There's. There's a math. I mean, There's a reason for this madness here. Usually the predicate will turn out to be the defining or specific term in class designation. And so that's why I usually look for the major or controlling predicate. You could have done it the way you did it, but let's just stick with dangerous animal rather than animal. Some. D is not R is the conclusion. What is the premise? The first premise? Some.

Or, excuse me all. S is not D is not B. D D D as in dog, which.

Doesn'T appear in the syllogism, but that's okay. Very good, you schematized it correctly. What fallacy, if any, is committed?

I said it was illicit.

Major. Good. What's the major term in the conclusion?

The major term in the conclusion is R.

Because it's the predicate. R is found up here. All S's. R is what form of proposition?

An A form.

Is the predicate distributed in an A form.

No.

No. Okay, so we have an undistributed major term. Do you have any questions about how to test syllogisms? Does it? The end of the line on doing it the easy way. As you know, we're going to go into the next chapter and we're going to run into the ones that, as he says, are not chemically pure. Then we run into the kinds of syllogisms you actually encounter in ordinary discourse, where people have not been careful to have only three terms and to put them in the right order and using expressions other than some, all you have accepted propositions and things like that. Are we ready to go into the more complicated cases where this requires translation? Why did we bother to do this with these artificial or easy cases? Because if you know how to test them once they're in standard form, then the next step is learning how to translate anything you hear in ordinary discourse into standard form. You can translate then into standard form, you can apply the six rules and you can test any syllogism you run into. And so that's why the next chapter, at least first 2/3 of it, deal with that particular problem. Alright. We come then finally to chapter seven in Kopi, which he calls argument in ordinary language. This chapter, actually, as I see it in the development of the book, continues our discussion of categorical syllogism. Now, by dealing with the complication of ordinary language not having exactly three terms when people present arguments or they don't have exactly three premises. And so the chapter begins by dealing with translation issues, reducing the terms, translating into standard form and uniform translation. And then it deals with Arguments that aren't in the pure form because they have more than or less than three premises, enthymemes and sorites. And at that point the author turns to a different kind of argumentation altogether. He turns away from class inclusion logic, the all, some and not. And he begins a discussion in ordinary language of what I have called the connective logic, or he calls compound proposition logic, where propositions are related by and or if then and so if I were doing the book, I would have divided this chapter to make that division a little clearer. But we have the job of getting through the entire thing trying to be introduced to symbolic logic before we then turn actually to chapter eight, which is symbolic logic dealing with connectives and or if Then so page 214. The first section deals with reducing the number of terms in a syllogistic argument. He tells us the process of reformulating a syllogistic argument as a standard form Categorical syllogism will be called translation or reduction to standard form. Page 215 reminds us that a syllogistic argument that we run into in the real world instead of the stilted artificial arguments that are found in textbooks. Those syllogistic arguments may deviate from standard form in a couple of ways. The component propositions may not be standard form categorical propositions, or they may involve more than three terms. Now, how are we going to deal with this? Essentially, the rest of this section just tells you two ways of doing it. I could simplify it for you. He says. Look to eliminate synonyms if you can. Here's one guideline. Try to find synonyms that can be eliminated so that you don't have as many terms. And the second thing he tells you is that we can use our valid immediate inferences of conversion, obversion and contraposition. So the synonym route and the immediate inference route may be helpful in eliminating some of the terms in a non standard syllogistic argument. But in order for us to use the inferences of conversion, obversion and contraposition, we need to remember which ones actually are valid inferences or are reliable inferences on Boolean interpretation we know. Let me put up here on the board our familiar A, E, I, O and see if this will help you remember which of these types of propositions A, E, I or O may be converted validly. Anybody, E. And I notice that right across here. So this is the conversion line, if you will, which may be obverted. All of the may be obversed. So you don't need a chart for that. Let's Put that up here. All obversions are still helpful. Then which contrapositions are legitimate on Boolean interpretation A and O. Going this way. Now I put this up on the board scheme. It has it on the board just to help you see it. If you remember. Conversion, obversion, contraposition. The conversion line runs at a slant here the EI obversion all of them contraposition the other slant A to O. Sometimes seeing it like that helps you remember. It's not a big deal. Now the exercises translate the following system syllogistic arguments into standard form and test their validity by one of the methods that we have learned. Let's look at number two. Number two says some metals are rare and costly substances. But no welders materials are non metals. Hence some welders materials are rare and costly substances. Now what's the problem with this?

It's not set in correct form.

We have four terms to be more specific and which is the most likely to be used? What's the easiest way to reduce this to three terms? But what are we looking for when we start the reduction process? The author says we look for complements. Right. Now do we have any complements mentioned in this illustration?

Well, metals and non metals.

That's right. Metals and non metals. And so if we could get rid of one of those terms through one of the methods given to us, then we would have reduced things to three terms and we can test the syllogism. So what do you suggest we do here? Well.

I first of all set it up in the correct form so that I mean.

Okay, let's hear it.

Do you want me to use just initials or do you want me. Okay. Sum. Sum M or R?

Okay.

No W R. N. No, no, no, we haven't changed it yet.

Why don't you just say non M? Non M. Okay, so the complement class is made clear.

Oh, okay.

And then the conclusion.

Sum W R R. That's right.

Sum W is R. We can just use is Is.

Okay.

Now how are we going to get rid of M or non M? What do you suggest?

Using the. Contradiction. I did it in my head and where the steps out. That's why I'm not sure what to use. I think I used the obverse of the. Second premise.

Exactly. You look at the second premise where you see non metal. If you use the obversion inference pattern you can get rid of the non metal. That becomes metal. You have to change the quality of the proposition. So instead of no W is not M, you get all W is M. Okay, now we have Syllogism we can test. And what does it come out?

I came out with some M is R. All W is M. Therefore sum.

W. Therefore sum W is R. Okay, now is it valid? You were supposed to translate and test.

Now is valid.

No, not necessarily. Now it's just in standard form. Now it's set up so it can be tested. Now you got to apply the rules. Now, do you all understand that there's two steps here? The translation step is just to get it into a form that it can be tested. But translating it does not test it for validity. It just sets it up for the test. And so now we must test for validity.

I thought the problem was rule one, and that way after we changed it, it would be okay.

That's why I didn't think, okay, that's good that this mistake has come out so we can all learn from it. No, the problem is that there's more than three terms. But after you get rid of some of the terms, you might have other rules that are broken. And so all we're doing now is setting things up for testing. You've learned the test, in essence, by mastering those six rules, you've learned the test. The problem is you go out in the world and people don't hand you arguments that fit into your test mechanism. And so what you're doing now is you're learning a technique for translating into the form that is testable. Now you've done the translation, now it's testable. But to say it's testable is not to say it's been tested. Let's test it. Okay, what's the. Is there a problem with number two? Yes.

The middle term is undistributed in both.

The middle term is going to turn out to be metals. And the term metals in the first premise is some metals are rare and costly, so that's not distributed. And then the second premise, which we obverted becomes all. What does W stands for? Welder's materials. All welders materials are metals, but that too does not distribute the term metals. And so metals is not distributed in either premise. Very good. It. Let's do another one. These are fun. Number four, some non drinkers are athletes because no drinkers are persons in perfect physical condition. And some people in perfect physical condition are not non athletes. In number four, the first thing we have to notice apparently is there are going to be five terms. We have non drinkers, athletes. Drinkers, persons in perfect physical condition, and non athletes. And so with five terms we're going to have to Apply some kind of procedure to eliminate two of them. Actually, there are six terms if you count persons in perfect physical condition as different from people in perfect physical condition. So the first thing we're going to do is we're going to apply the synonym guide here and we'll eliminate that. So from six, now it's down to five, and that's what I was originally describing. Let's translate this as much as we can into standard form and then find out what our problem areas are going to be. The conclusion of this argument is what pat?

Therefore, some drinkers are not athletes.

Okay, the opening proposition is the conclusion some non drinkers are athletes. So we'll put that down as some non d is a. And then what would be the major premise? What's got to be mentioned in the major premise? Athletes. Athletes, because that's the predicate term of the conclusion. So what's the first premise as we find it in the book?

Some people in perfect physical condition are not non athletes.

Okay, so we're to going to put down some P is not non a. And then the second premise will be the remaining one. No drinkers are persons in perfect physical condition. No D is P. Let me repeat this to make sure we all have it right. First premise, some P is not non a. Second premise, no D is P. Conclusion, sum non d is a Given the form that it's now in, let's look at the conclusion first of all and see if we can't get rid of the non D as a term. If we apply conversion to the conclusion, sum non d is a by conversion becomes sum a is non D. No problem there, because conversion can apply to an I form proposition. And then we apply obversion to our converted premise. In obversion, we're going to change the quality and use the complement for the predicate. And so by changing the quality, instead of sum a is non D, we have sum a is not. And then instead of non D we have the complement of non d, which is D. Therefore we have sum A is not D. We've eliminated the non through conversion and obversion. So now the conclusion reads sum a A is not D. This means we have two other complementary terms remaining. We have a and non a. Non a appears in our first premise. First premise says some P is not non a. If we obvert that, we can eliminate the not and non a becomes its complement, which is A. And therefore by obverting the first premise, we get sum p is A. Now let me put this all together through the steps we have taken. Premise 1 is sum, P is A, premise 2 know D is P, and the conclusion sum A is is not D. And all we have to do now is look at this to see what rules of syllogism may or may not be violated. If it appears that none of the rules are violated, then we're going to say this is a valid syllogism. So let's real quickly run through our rules backwards again. Existential assumption. Do you have two universal premises? No. So that rule doesn't apply. Rule five, do we have a negative premise? Yeah. The second premise is negative, so the conclusion must be negative. Is it? Yes. Yes, it is. So Rule 5 is not violated. Rule 4 says you can't have two negative premises. Do we? No, because the first premise is affirmative. Rule 3, if either term is distributed in the conclusion, it must be distributed in the premises. Our conclusion is in the form of an O proposition, and therefore only the predicate is distributed, which means D is distributed.

Neither are distributed. I thought. Oh, no, okay. Oh, never mind.

Yeah, O form. The predicate is distributed, so that means D. D in our schema must be distributed in the premise. We find that in premise two that says no, D is P, so it is distributed. Rule 2 says that the middle term must be distributed in at least one premise. In this case, the middle term is going to be P. And if you notice premise two, no, D is P, the predicate and the subject are distributed. Therefore rule two is not violated. Rule one is what we've been working on to get this down to three terms. And having gone through all the rules, we can then conclude that number four is a valid syllogism. So that's been very helpful. Let's turn to the next section in copie then, which continues with learning to translate into standard form, entitled Translating Categorical Propositions into standard form Form. He says in ordinary language, or he says ordinary language is too rich and multiform to permit a complete set of rules for the translations. In every case, the crucial element is the ability to understand what is being argued. And again, I keep pointing that out over and over in my logic classes. Formal logic does someone no good if he does not have the ability to translate from an ordinary language. That means you have to understand what the person is trying to say and what the thrust of their argument is. So there's no mechanical rule that logicians can come and apply and say, okay, these statements now have to be this. You say, no, wait a minute, that isn't. I mean, you schematized it this way. But that isn't what I was really getting at. Understanding of ordinary language is crucial. Now, having said that, he does give us some guidelines, nine of them. See if we can go through them quickly and try some exercises. Singular propositions. That is a proposition that does not refer to a class of objects, but to just one item, sometimes called a one membered class or a unit class. Dr. Bonson is a one membered class class. Many people are happy about that. There's only one of those guys out there, okay? Socrates is a one membered class and so forth. Ordinarily, one membered classes are treated as universal propositions. So all Socrates. Now, the problem with that is that the singular proposition contains more information than the universal statement would give us, because in Boolean interpretation, a universal statement does not assert existence for any member of the class. And yet, when you deal with particular, such as Socrates or Dr. Bonson, then you're dealing with something whose existence you do assert. And so the only way to get around this, according to copi, is to treat singular propositions as really implicitly two propositions. He says, construe singular propositions as conjunctions of standard form. Categorical propositions. Either I and E both. Excuse me, I'll say this right. A and I both, or E and O both. Okay? You understand that? So if you have a proposition that says Dr. Bonson is a Lakers fan, then that's going to come out. All Dr. Bonsons are Lakers fans and some Dr. Bonsons are Lakers fans. So that asserts that there is one, the sun, and that all of those are. And that way we'll cover everything that is said. The second guideline is found on page 220 here. In ordinary language, we'll run into adjectives or adjectival phrases. Rather than substantives or class terms. He uses the example some flowers are beautiful. This should not have been any trouble to you if you understand set theory. Obviously, sunflowers are beautiful is the same as saying sunflowers are beautiful things. Beautiful defines a class. The things which are beautiful. Three main verbs other than to be, should be treated in the same way. They are predicate terms that define a class. All people desire recognition becomes all people are things that desire recognition. Number four is hardly worth mentioning when it's not arranged in standard form order. You have to rewrite the English sentence so that you can get the form of the syllogism number five. This gets a little more complicated. Quantities that are indicated in a sentence, but not with the words all, some, or not or no, all, some and no. You remember A while back, when we had introductory lectures on logic, I said, the ironic thing is, the funny thing is when you master categorical syllogism, you've only mastered three words in the English language, all some and not or no, that's all it amounts to. So now, if you're going to use categorical syllogism, you have to translate all the other quantity type expressions into one of those. And he gives some guidelines here. Every and any reduced to all. He tells us that the indefinite indefinite article sometimes tell us something about the quantity of a sentence, but it's not automatic. The definite article can refer to a particular individual, or the definite article can refer to a class of things as well. At the end of this section, on page 221, please note, he says negative statements beginning with not every and not any are different from the way you treat every and any. Not every means some is not, whereas not any means no. S is P. That's a very important guideline to remember. Number six. We have exclusive propositions sometimes that say only or none, but. And he says, turning the page, that they can be translated into a propositions whose subject and predicate terms are the same respectively as the predicate and subject terms of the exclusive proposition. So now I'm going to fudge a little bit here and give it to you in a little bit easier way. If you do a conversion on the ordinary language sentence and then put it in a form, then that will accomplish the translation of only or none. But only drunkards are sailors becomes all sailors are drunkards. He says you translate it into an a proposition where the subject and predicate terms have been reversed. Number seven. Sometimes you have sentences where there's no indication of quantity at all. And in this case the sentence what it intends to express may be doubtful. Copy says we may be able to determine its meaning only by examining the context. That's not much more of a guideline than to say the sentence may not tell you. You're going to have to look at the broader context. Okay, let's jump to number nine. Eight wasn't all that important, I don't think. Number nine. He talks about propositions that mention quantity more specifically than all or some because numerical or quasi numerical quantifiers are used. You'll have two or three, many, a few, most. And then he goes on to talk about those quasi numerical quantifiers, almost all or not quite all. Almost everyone, all but a few. And he says propositions in which these phrases appear as quantifiers are acceptive propositions which make two assertions rather than one. And he shows us how to translate them into two separate assertions. And then the problem is, if there are two assertions, you can't test them in the standard way. The strategy then is to test each one of them separately. If the proposition amounts to two propositions, then run it through your test mechanism twice with each of the implicit propositions being used. Now, what happens if you run it through once and the syllogism is invalid? You run it through the second time with the other proposition that was implicit and it comes out valid? He says, then it's valid. As long as what's implicit in the premise will give you a valid syllogism, then the whole syllogism is valid. And then he tells us on page 224, if the premises of an argument are both categorical propositions and its conclusion is acceptive, then we know it to be invalid. I think that's a helpful rule that I want to pick out for you. If you see the acceptive proposition as the conclusion, you know that the syllogism is invalid because it's going to be stating more than can be found in the premises. Accepted propositions, like almost all, not quite all, but a few, almost everyone. When you find those in a conclusion, the syllogism will prove to be invalid. We have some exercises now on page 224, And maybe we can go through a few of them, make sure we understand what we're doing here. We'll begin with number one. Translate the following into standard form. Categorical proposition. Roses are fragrant. Go ahead. What's the translation?

All roses are fragrant.

Plants.

Okay. I don't think you need to put plants in there. That just complicates it all the more. You could just say all roses are things that are fragrant or fragrant things. All roses are fragile. In the class of things that are fragrant. Number two. Orchids are not fragrant.

No orchids are fragrant things.

Okay, if we would have said all orchids are not things that are fragrant, what would have been the problem? If we would have said all orchids are not things that are fragrant, all S is not P, what would have been the problem with that?

You can't do that, can you? Well, it has to be some S.

Is not P. What's wrong with all S is not P?

It's a universal. It's got a.

It's not standard form.

Oh, okay.

We've only got four forms. A, E, I and O. And so when I say all S is not P, that's not one of the forms. But now that's what the sentence says. Orchids are not fragment. To begin with. You've got to say orchids are being here used as a universal class. All orchids are not fragment. Now what do you have to do in order to put it into standard form? Well, we have to understand the sentence that's the key to logic. And when we do, we see that these are intended as exclusive classes. And the way to express an exclusive class is an E form proposition. No, this is that in an E form proposition you notice that conversion is always allowable. So you could put it either way. You could say no orchids are fragrant things, or no fragrant things are orchids, either would be acceptable. And number three, many a person has lived to regret a misspent youth.

I said some people are people who have lived to regret a misspent youth, and some people are not people who have lived to regret misspent youth.

I divided it into two. Is the two really necessary given the sentence where it says many a person has lived to regret a misspent youth? It probably is the feeling of the speaker that other people have not lived to regret it. But the sentence itself doesn't contain that information. The sentence, it seems to me, can be translated as simply about some people. Some people are people that have regrets. Just using that as a summary so that you don't need both of those.

Is it, is it all right to use the same same term in the subject as it is in the predicate like you guys have? Some people are people.

Yeah, but in the second it's not people, it's some people are people who have regrets.

Right?

Okay, okay, enough. Excuse me, Number four, Not everyone worth meeting is worth having as a friend.

Some people worth meeting are not people worth having as a friend.

All right, and we'll take one more here. Number five, if it's a junco, it's the best that money can buy. I don't know what a junco is, but how would you translate that into standard form?

All juncos are the best money can buy.

Okay, does that also assert that there is such a junco?

Uh huh.

No. You know what should have tipped you off to that this is ordinary language analysis is that it's put in the hypothetical mood, if it's a junco, it's the best that money can buy. But can't you imagine the next sentence being but unfortunately there are no junco. Please, the sentence does not assert the existence of a junco. It just says that all juncos are the best money can buy. All J's are B's. Is that understandable?

Yeah.

Okay, very good. Now, if the sentence had said a junco is the best that money can buy, or actually if it had said the junco is the best that money can buy, if junco is a particular, if it's an individual like Socrates or Dr. Bonson, then you might have said all juncos are the best monies can buy and some juncos are the best money to buy so that you get the exact distance claim in there as well. But in this case, since it says if it's a junco, you know that it is not making a definite claim that such a junco exists. And for that reason you don't need to treat it as a particular or one class or one member class. My car is the best that money can buy. It's translated as everything in the category of my car is the best money can buy and something in the category of my car is the best money can buy. There I'm asserting that there is such a thing my car and it's the best that money can buy. But if I would have said if that's my car, it's the best money can buy, you see, I might not own a car. I might just be saying, but I won't own anything less than the best. So if it's my car, it's the best that I can buy. There's no existence claim in that proposition. And so you don't have to translate it into two, you can just use the universal form. All right, we have some more to learn about uniform translation. 7.3 introduces the concept of parameters. Parameters make this much easier for us though. The author says people have a hard time with this sometimes for some reason it's never struck me as all that difficult. It was a real convenient way to get out of the bind of having all these non standard expressions. You can take a term like all to mean at all times. Okay, so all times would be in standard form all T. All times. He says using the word times here is like a parameter. There are other parameters such as places or cases. And the thing that I've been riding like a hobby horse in this class you'll see on page 225. Again he says care should be taken not to introduce and use parameters in a mechanical and thinking fashion. One must always be guided by an understanding of the proposition to be translated. If you don't understand ordinary Language analysis. If you don't catch the drift of what people are saying, you can't translate into. Into logical notation anyway. At the bottom of the page it says, introduction of parameters is often necessary for the uniform translation of all three constituent propositions of a syllogistic argument into standard form. So just remember that's a tool at your disposal. If you can use times, places, cases, and then translate what the person is saying so you have only three terms left. Cases like this, times like this, places like that, then you'll be able to test the syllogisms with ease. And we are going to do a few of these exercises as well. First of all, in Roman 1, translate the following propositions into standard form using parameters where necessary. Number one. He groans whenever he is reminded of his loss.

Pete.

All times when he is reminded of his loss are times when he groans.

Very good.

Very good.

You have to hang out. This isn't too difficult. Number two. She never drives her car to work.

No places to which she drives. There are places where she works. I don't know if that's acceptable or not.

Well, that's an interesting way of doing it. She never drives her car to work. Would be no places to which she drives are places where she works.

The reason I took that route is because it's talking about where she drives her car.

About places. Yeah, you can do it that way. I probably would have thought.

I don't think it's the best way. If it was all I could come up with at no time zone thing.

She never drives her car to work. Could be there. There are no times she drives her car. There are times she drives her car to work, but I think either parameter would be useful there. Number three. He walks where he chooses. Who's that? Me.

All places he walks, the places he chooses.

Good. Four, he always orders the most expensive item on the menu.

All his orders from the menu are the most expensive item.

All things he orders are things which are most expensive on the menu.

Does that make his things universal? I was thinking about that. Please. No, maybe not. Because I was thinking that all things he orders.

Right. Sometimes you might order and not be ordering from the menu. Yeah. So you want to say all things he orders from a menu. All things which are the most expensive on that menu. Do you understand why we made this a little more precise? Because otherwise you get a situation where you have all of his orders are from menus. And that isn't necessarily true. It's kind of like the example in the book. That was something to the Effect. Every time he plays billiards, he wins. You're not careful. You translate that. That everything that he does is. Is when it billiards or something. You don't want to say that he's playing billiards all the time. By your translation number five. She does not give her opinion unless she is asked to do so.

All the time she gives her opinion are the times she is asked to give it.

Okay, could you say all times she is asked to give her opinion are times that she does so? Could you say all times she is asked to give her opinion are times that she does so?

No, because she might not always. She might not have an opinion to give.

That is one counterexample. What I'm getting at here is you have to be careful. This word unless carries a certain thrust or meaning to it. And if someone says all times she's asked to give her opinion, every time she does so indicates that she always cooperates by offering an opinion if she's asked for it. But the sentence is not trying to tell you that. It's trying to tell you that anytime she's giving an opinion, she has been asked for it. And so that's why you did it. Right. And my counter should have been faulted. And I think you can intuitively see that it must be in Roman numeral 2. We're not going to worry about the then test for these, but let's take a few illustrations, translate each of the following arguments into standard form, name the mood and figure of its standard form translation, test its validity, and if invalid, name the fallacy number one. Since all knowledge comes from sensory impressions, and since there's no sensory impressions of substance itself, it follows logically that there is no knowledge of substance.

I have a little trouble though.

Okay, what's the conclusion of this?

The conclusion that's the first thing I found though was the conclusion is it follows logically that there is no knowledge of substance.

And how would you translate that?

And I said no things of knowledge are things of knowledge of substance itself.

Okay, so no cases of knowledge are cases of knowing substance. Right. Okay. And then what would be the major premise?

The major premise is. Okay, that'd be the second part. Since there was no sensory impression of substance itself.

And how would you translate that?

No item, no cases of knowledge of sensory perception or cases of knowledge of substance itself.

Okay, no cases of sensory impression. I think you said perception. No cases of sensory impression are cases of a knowledge of substance. So no I is s. And then the second premise would be all cases.

Of knowledge are cases from.

Are cases of sensory impressions. Okay, so you have no I is S. All K is all I. Therefore, no K is S.

Just E.

A, E, A, E. That's right. Okay. Is there any fallacy committed here?

I could not find one.

Are there two uniform premises? Yeah, but there's also a universal conclusion, right? Yes. So that's not a fallacy. Is there a distributed middle term? Yes. Which is the middle term?

Items of cases of knowledge?

No, that's not the middle term that appears in the component.

Excuse me.