Logic: Deductive Reasoning: The Categorical Syllogism

 

Purpose: To introduce the basic structure of the categorical syllogism and the concept of validity.

 

            "Your mother!"

            "No, your mother!"

            "Look, ferret face..."

            "What, weasel breath?"

 

As entertaining as this may look and sound to those fortunate enough to have tickets, it isn't an argument. It's noise - nasty, brutish, immature noise. You may not know who the speakers are, but you can assume they have acne, strange clothes, and no lives.

 

A true argument is carefully structured and immensely powerful. Those blessed in the art of argument will have no difficulty scoring high marks, confusing teachers, and getting the car on Friday nights.

 

You will notice that I used the word "structured". This implies that there are parts. You knew that? Very good!

 

As you have already gathered, the purpose of an argument is to get others to accept some conclusion you have developed. Ergo, the conclusion is one of the parts. See how well we're doing?

 

Now, to get to the conclusion, we need a series of steps. Usually we call these reasons. These are the other key part. It doesn't matter if we are moving from reasons forward to conclusions or from conclusions back to reasons - as long as we have both parts we have an argument.

 

Let's examine what is probably the world's most famous argument:

 

                        1.            All men are mortal.

                                    Socrates is a man.

                                    Therefore, Socrates is a mortal.

 

Isn't that beautiful? Can you see how powerful it is? Where does that beautiful power come from?

 

It comes from the simple fact that if the first two sentences are true, the conclusion has to be true. You can't escape it! In your face!

 

What shall we call these sentences? We could call them sentences, but the taxpayers who are footing the bill for your education want you to learn big words, and you of course would like to impress various car owning relatives with big words. Why? Consider the following argument:

 

            2. All those who know big words are doing their homework.

                My daughter/nephew/niece/son is a person who knows big words.

                Therefore, my ______ is doing homework.

 

               If my ______ is doing homework, then my _____ deserves the car.

               My ______ is doing homework.

               Therefore, my _______ deserves the car.

 

Let's do the words!

 

The reasons in an argument are called the premises. The conclusion to an argument is called the conclusion. In our first example, we have two premises:

 

                                    All men are mortal.  P1

                                    Socrates is a man.            P2

                                    Therefore, Socrates is a mortal.            C1

 

Our second argument is a little different:

 

            All those who know big words are doing their homework. P1

            My daughter/nephew/niece/son is a person who knows big words. P2

            Therefore, my ______ is doing homework. C1

 

            If my ______ is doing homework, (C1/P3) then my _____ deserves the car (C2).

            My ______ is doing homework. (P3)

            Therefore, my _______ deserves the car. (C2)

 

Here you should admire just how subtle the writer was. The conclusion to the first part of the argument - C1 - became the premise for the second part of the argument. What we have here is a chain of reasoning. Do you know what we call a chain of reasoning when its written down? We call it an essay outline! Are you beginning to understand why we are doing this?

 

Those of you who are very observant and who are not wasting those powers of observation watching the clock will note that argument 2 and argument 3 look different. They are not the same kind of argument. You will also note that argument 1 and argument 2 do look like each other. All of this would suggest (1) that there are different kinds of arguments, and (2) that the kind of argument you are using is determined by its shape or form or pattern. Let's examine this a little further.

 

 

           

            1. All men are mortal.                         3.            All monkeys are perverts

                Socrates is a man.                                         All squirrels are monkeys

               Therefore, Socrates is a mortal.              Therefore, all squirrels are perverts.

 

These two arguments are identical. If you look carefully at the hints we've provided, you will see how this is so. Examine the conclusion. It contains two terms. The first term is the subject term and the second is the predicate term. In arguments like these, the subject term is called the MINOR term and the predicate term is called the MAJOR term. You will notice that there is a third term. It does not appear in the conclusion but it does appear in both premises. It is called the MIDDLE  term. Now we can name the sentences:

 

            The sentence that contains the major term and the middle term is called the MAJOR PREMISE. The sentence that contains the minor term and the middle term is called the MINOR PREMISE. The major premise always goes first. This kind of an argument - major premise; minor premise; conclusion - is called a categorical syllogism.

 

But how are the arguments identical? One is about mortals and men; the other is about monkeys and perverts. They are identical because of the pattern.

 

In both arguments, the middle term is in first place in the major premise and in second place in the minor premise. The major term is in second place in the major premise and in second place in the conclusion. The minor term is in first place in the minor premise and in first place in the conclusion. Thus, the placement of terms is identical.

 

The arguments are identical in one other key way. Sentences in categorical syllogisms are said to express quantity and quality. They will say something about all or only some of the members of some group. This is the quantity factor. They will also say something affirmative or something negative. This is the quality factor. If this sounds complicated, consider that these arguments can include only four different kinds of sentences. Two refer to all members of a group. These are called universals. Two refer to only some members of a group. These are called particulars. The four kinds of sentences are listed below:

 

            All S are P                universal affirmative

            Some S are P                particular affirmative

            No S is P                      universal negative

            Some S are not P            particular negative

 

So the other reason arguments 1 and 3 are the same has to do with the fact that all the sentences in each argument are universal affirmatives. 

 

Yes, I know that was confusing. But you are all clever young people and your lives would lose meaning if there were no challenges.

We now come to the last of the big opening concepts. If arguments 1 and 3 are identical in their patterns, and if argument 1 leads to an inescapable conclusion, then argument 3 must lead to an inescapable conclusion. So do we have to accept the conclusion that all squirrels are perverts? Some of you may have spent many hours watching squirrels and may therefore be in a position to tell us more about their sexual habits, but given that you are likely too smart to admit that you are squirrel peepers, we will have to assume that the argument, however beautiful its pattern, is false. Its pattern gives it a great deal of power but that is not enough.

 

Now, consider this final argument:

 

                        4.            All men are mortal.

                                    Socrates is mortal.

                                    Therefore, Socrates is a man.

 

In this case, does the conclusion follow from the premises? Think before you speak. Is Socrates necessarily a man? Nope! Socrates could be a goldfish! A perverted squirrel! A non-perverted squirrel. Knowing that he is mortal does not necessarily allow us to assume that he is a man - even though we all know that he was. Let's use another identical argument to show you the problem more clearly:

 

            5a.            All people who live in Alberta live in Canada

                        Jerby Frumpquat  lives in Canada.

                        Therefore, Jerby Frumquat lives in Alberta.

 

 

We all know that the conclusion could be wrong. Good old Jerby could live in any one of many other provinces. But look what happens when we alter the position of the terms:

 

            5b.            All people who live in Alberta live in Canada

                        Jerby Frumpquat  lives in Alberta.

                        Therefore, Jerby Frumquat lives in Canada.

 

 

Now the conclusion follows necessarily from the premises.

 

When the form of the argument guarantees that the conclusion will follow, that argument is considered valid.

 

When the premises can be assumed to be telling the truth, the argument is said to be true.

 

If an argument is both true and valid, that argument is said to be sound.

 

Identify the follwing sentences as  (A)universal affirmatives,  (I) particular affirmatives, (E) universal negatives,  (O) particlar negatives, or (X) none of the above:

 

1. Some of my best friends are squirrels.

 

2. Acts of self defence are not immoral.

 

3. Those trees are deciduous.

 

4. Cheating is wrong

 

5. A few of my friends are not going to Harvard.

 

6. The cat barfed.

 

7. Abortion is murder.

 

8. Abortion is not murder.

 

9. I hate liver.

 

All sentences in Categorical syllogisms state that the subject of the sentence does or does not fall into a certain group or category.

 

 

For each of the following, fill in the conclusion.  BE CAREFUL! 

 

            All P are M               No P are M               No M are P

            No M are S                Some S are M   All S are M

 

            _________                  ___________            _________

 

 

By now, you should be able to identify the following in any categorical syllogism:

 

            the major premise            the major term

            the minor premise            the conclusion

            the minor term            the middle term

 

You should be able to define:

 

            valid                 true                  sound               invalid  

 

 

 

 

ENT3A0 Review of Logic

 

For each of the following, fill in the missing sentence:

 

1.         1.  All merchants are profit motivated.

            2.

            C: All salespersons are profit motivated.

 

2.         1. No-one from Mars likes purple grapes.

            2. All Seinfeld fans are from Mars.

            C:

 

3.         1.

            2.  Some religious leaders are scientists.

            C: Some religious leaders are people who believe in facts.

 

4.         1.  No monster is an effective babysitter.

            2.  Some Garneau students are monsters.

            C:

 

5.         1.  No ENT students are over thirty.

            2.

            C: No Leaside student is an ENT student

 

6.         Of course he voted against the tax increase.  He's from Ontario.

 

7.         She should try for the basketball team.  She's from Flemingdon.

 

For each of the following, underline the conclusion:

 

            Since politicians sometimes try to divert our attention from the real issues, the

            American's bombing of the Khartoum factory was a fraud, because it made                         Americans forget about Monica Lewinsky.

 

            The town will have a good crop this year since the lottery was held and the                  lottery guarantees good crops.

 

            The school has cancelled morning prayers on the P.A.  Canadians have the                    right to practice religion freely.  Prayers on the P.A. force religion on those who do        not want to participate.

 

            The Olympic games are very expensive.  They also lead to overcrowding of city               roads. Toronto should not bid for the games.