Richard L Epstein

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by Critical Thinking (3rd Edition) (pdf)


  The minor term is "police officers." The middle term is "thieves." The major

  premise is "Some thieves are sent to prison." The minor premise is "No police

  officers are thieves."

  The main focus of Aristotelian logic, as traditionally presented, is to show that

  we can mechanically determine of any given categorical syllogism whether it is valid

  or invalid. One way to do that is by inspecting its form. We list all possible forms of

  syllogisms in standard form: All the claims are in standard form, and the major

  premise comes first, then the minor premise, then the conclusion. For example,

  "No S is M; All M are P; so No S is P" has form EAE. We determine for each form

  whether it is valid or invalid; this one is valid. Given any categorical syllogism, we

  can first rewrite it in standard form and then check whether it is one of the valid

  forms.

  But instead of listing all the forms, Aristotelians have shown how we can start

  with knowing whether a few are valid or invalid, and then convert any other form

  into one of those by a detailed reduction procedure.

  Alternatively, we can take any categorical syllogism, rewrite it in standard

  form, and then use the method of diagrams presented in Chapter 8 to determine

  whether it is valid. Or we can use one of several other well-known diagram

  methods, similar to but distinct from the methods of Chapter 8.

  Once we've checked for validity, we still have to decide whether the syllogism

  is a good argument. We know that a valid argument need not be good, for a premise

  could be false, or the premises may not be more plausible than the conclusion.

  Indeed, many valid Aristotelian syllogisms beg the question. For example, with "All

  dogs eat meat. Spot is a dog. So Spot eats meat.", it's more plausible that Spot eats

  meat than that all dogs do. Categorical syllogisms, as originally used by Aristotle,

  are really a logic of explanations, not arguments. In an explanation the conclusion is

  supposed to be more plausible than the premises, as when someone tries to explain

  why "The sky is blue" is true. (The Science Workbook for this text teaches how to

  reason about explanations.)

  In any case, in ordinary speech we first have to decide how the person giving

  the argument intends "all" and "some" to be understood, and many times those

  readings won't be compatible with the assumptions of Aristotelian logic. Even if

  those readings are compatible, we often have to do a lot of work to rewrite the claims

  into standard categorical form. Then we have to check against a (memorized?) list of

  valid Aristotelian forms. Then we have to ask about the plausibility of the premises

  to determine whether the syllogism is a good argument. Even then, many simple

  arguments using "some" or "all" can't be analyzed as categorical syllogisms, such as

  "Some dogs like cats; some cats like dogs; so some dogs and cats like each other."

  For hundreds and hundreds of years students and scholars preoccupied

  themselves with the methods of Aristotelian logic as the primary focus of their

  EXERCISES for Section D 383

  analysis of reasoning. They could rely on standard methods and checkable rules.

  But that tradition missed most of the important work in critical thinking that has been

  incorporated into the foundations of reasoning analysis only in the last 150 years,

  even though much of that can also be traced to Aristotle.

  For reasoning in your daily life, being able to listen and analyze as you read

  and speak, the methods and work we did in Chapter 8 will be more useful than the

  formal methods of Aristotelian logic. To decide whether a categorical syllogism is

  valid, do what we've always done: See if there is a possible way for the premises to

  be true and the conclusion false.

  Exercises for Section D

  1. What is a categorical syllogism?

  2. What is the major term of a categorical syllogism?

  3. What is the minor term of a categorical syllogism?

  4. What is the middle term of a categorical syllogism?

  5. What is the major premise of a categorical syllogism?

  6. What is the minor premise of a categorical syllogism?

  7. What is the standard form for a categorical syllogism?

  Which of the forms of categorical syllogisms in Exercises 8-15 are forms of arguments that

  must be valid? The forms are presented by giving the letter name of the standard form of the

  major premise, then the minor premise, then the conclusion.

  8. EAE (No S is M; all M are P; so no S is P.)

  9. AAA

  10. AEO

  11. IAO

  12. Ill

  13. AEE

  14. AOO

  15. AAI

  For each of the following arguments, either rewrite it in the standard form of a categorical

  syllogism and identify the form, or explain why it cannot be rewritten that way. In either

  case, determine if the argument is valid.

  16. All students at this school pay tuition. Some people who pay tuition at this school will

  fail. So some students at this school will fail.

  17. There aren't any wasps that will not sting. Some bumblebees will not sting. So some

  bumblebees aren't wasps.

  384 APPENDIX: Aristotelian Logic

  18. Badly managed businesses are unprofitable. No oyster cultivating business in North

  Carolina is badly managed. So some oyster cultivating business in North Carolina is

  profitable.

  19. Most critical thinking books do not teach Aristotelian logic. Chemistry textbooks never

  teach Aristotelian logic. So most chemistry books are not critical thinking textbooks.

  20. Nothing that's smarter than a dog will cough up hair balls. Cats cough up hair balls.

  So cats are not smarter than dogs.

  21. Dick will not visit Tom tonight if Zoe cooks dinner. Zoe didn't cook dinner. So Dick

  visited Tom tonight.

  22. No pacifists will fight in a war. Dick is a pacifist. So Dick will not fight in a war.

  23. Police chiefs who interfere with the arrest of city officials are always fired. People who

  are fired collect unemployment. So some police chiefs who interfere with the arrest of

  city officials collect unemployment.

  24. Some temporary employment agencies do not give employee benefits. All employees of

  Zee Zee Frap's restaurant get employee benefits. So no employee of Zee Zee Frap's is

  hired through a temporary employment agency.

  Key Words categorical claim A claim

  standard form of a E claim

  categorical claim I claim

  universal categorical claim O claim

  particular categorical claim subalternate

  affirmative categorical claim Square of Opposition

  negative categorical claim categorical syllogism

  quantity of a categorical claim major term

  quality of a categorical claim minor term

  subject of a categorical claim middle term

  predicate of a categorical claim major premise

  contradictory minor premise

  contrary standard form of a

  subcontrary categorical syllogism

  Further Study There are many textbooks that present the "traditional" Aristotelian

  logic with lots of diagrams and a listing of all valid and invalid forms of categorical

  syllogisms. But to see the real power of the Aristotelian tradition, you need to study

  m
edieval logic in the work of Buridan, Duns Scotus, Peter of Spain, and others.

  There are some good translations and expositions of the work of those logicians, but

  you're best off taking a philosophy course on the history of logic.

  Diagramming Arguments

  A. Diagrams 385

  • Exercises for Section A 388

  B. Counterarguments 389

  • Exercises for Section B 390

  A. Diagrams

  This appendix is a supplement to the section Complex Arguments for Analysis. It

  provides a way to visualize the structure of complex arguments. For example:

  Spot chases rabbits. 1

  Spot chases squirrels. 2

  Therefore, Spot chases all small animals. 3

  To picture this argument, we number the premises and conclusion. Then we

  ask which claim is meant to support which other. Here support just means that it's

  a reason to believe the other claim.

  The conclusion will have to be at the bottom, since all the premises are supposed to

  support it. And both do. The picture we'll draw is:

  Neither 1 supports 2, nor does 2 support 1. So there is no arrow from one to the other. But both support 3, so we have arrows there. That's simple.

  Now consider:

  Dogs are mammals. 1

  Cats are mammals. 2

  Some dogs hate cats. 3

  Therefore, some dogs hate mammals. 4

  385

  386 APPENDIX: Diagramming

  We number the claims. It's easy to see which is the conclusion (it's labeled

  with the word "therefore"). Which claims are meant to support which others? We

  need 2 and 3 to get the conclusion 4. But what's 1 doing? Nothing. The

  argument doesn't get any better by adding it, since it doesn't support any of the

  other claims. So our picture is:

  We also need a way to represent premises that are dependent, that is, they are

  meant together to support another claim, in the sense that if one is false, the other(s)

  do not give support.

  In a diagram we indicate that premises are dependent by putting '+'

  between them and drawing a line under them.

  Dogs are loyal. 1

  Dogs are friendly. 2

  Anything that is friendly and loyal makes a great pet. 3

  Hence, dogs are great pets. 4

  Recall now the argument discussed on pp. 221-222:

  Whatever you do, don't take the critical thinking course from Dr. E. 1

  He's a really tough grader 2, much more demanding than the other

  professors that teach that course. 3 You could end up getting a bad

  grade. 4

  We rewrote 1 as "You shouldn't take the critical thinking course from Dr. E."

  And we rewrote 3 as "He's much more demanding than the other professors that

  teach that course." It wasn't clear which claim was supposed to support which other.

  We had two choices:

  We chose to repair this argument with:

  SECTION A Diagrams 387

  If you take critical thinking from someone who's more demanding than

  other professors who teach that course and who is a really tough grader,

  then you could end up getting a bad grade, a

  That makes the second diagram a better choice, though we still need to get from 4

  to 1. We can use:

  You shouldn't take any course where you might get a bad grade, b

  We can see that the argument is only as good as the unsupported premise b.

  Let's see how adding a series of unstated premises can affect the picture.

  Consider:

  My buddies John, Marilyn, and Joe all took Dr. E's critical thinking class and

  did well. 1 So I'm going to sign up for it, too. 2 I need a good grade. 3

  First, we need to rewrite 2 as a claim "I should sign up for Dr. E's critical thinking

  class." I take this to be the conclusion (try the other possibilities, asking where you

  could put "therefore" or "because"). Initially we might take the diagram:

  But we need some glue for this to be even moderately strong. To begin with, why do

  1 and 3 yield 2 ? A (fairly weak) assumption might be:

  Usually if John, Marilyn, and Joe all do well in a class, I'll do well, a

  But even that plus 3 won't give us 2. We need some further assumption like:

  I should sign up for classes in which I know I'll get a good grade, b

  Then the argument becomes:

  Still, there's something missing. We need:

  I'll do well in Dr. E's course, c

  And that changes the picture entirely:

  388 APPENDIX: Diagramming

  We have a strong argument, in which we see a dependence between 3 and

  what we get from 1. Whether this is a good argument depends on whether the

  premises are plausible.

  Exercises for Section A

  For each of the following, if it is an argument, diagram it, repairing as necessary.

  1. Dr. E is a teacher. All teachers are men. So Dr. E is a man.

  2. No one under sixteen has a driver's license. So Zoe must be at least sixteen.

  3. Sheep are the dumbest animals. If the one in front walks off a cliff, all the rest will

  follow him. And if they get rolled over on their backs, they can't right themselves.

  4. I'm on my way to school. I left five minutes late. Traffic is heavy. Therefore, I'll be

  late for class. So I might as well stop and get breakfast.

  5. Pigs are very intelligent animals. They make great pets. They learn to do tricks as

  well as any dog can. They can be housetrained, too. And they are affectionate, since

  they like to cuddle. Pigs are known as one of the smartest animals there are. And if

  you get bored with them or they become unruly, you can eat them.

  6. Smoking is disgusting. It makes your breath smell horrid. If you've ever kissed

  someone after they smoked a cigarette you feel as though you're going to vomit.

  Besides, it will kill you.

  7. You're good at numbers. You sort of like business. You should major in accounting—

  accountants make really good money.

  8. Inherited property such as real estate, stocks, bonds, etc. is given a fresh start basis

  when inherited. That is, for purposes of future capital gains tax computations, it is

  treated as though it were purchased at its market value at the time of inheritance. Thus,

  when you sell property which was acquired by inheritance, tax is due only on the

  appreciation in value since the time it was inherited. No tax is ever paid on the increase

  in value that took place when the property belonged to the previous owner.

  1994 Tax Guide for College Teachers

  SECTION B Counterarguments 389

  B. Counterarguments

  Recall the conversation between Dick and Zoe we looked at in Chapter 7:

  We ought to get another dog. 1

  (objection) We already have Spot. 2

  The other dog will keep Spot company. 3

  (objection) Spot already has us for company. 4

  We are gone a lot. 5

  He is always escaping from the yard. 6

  He's lonely. 7

  We don't give him enough time. 8

  He should be out running around more. 9

  (objection) It will be a lot of work to have a new dog. 10

  (objection) We will have to feed the new dog. 11

  (objection) It will take a lot of time to train the new dog. 12

  Dick will train him. 13

  We can feed him at the same time as Spot. 14

  Dog food is cheap. 75

  We can diagram this if we have a way to r
epresent that a claim is an objection, not

  support, for another claim.

  To diagram the argument, then, note that it seems that Dick intends but never says:

  Spot needs company, a

  That with 3 will be what gets the conclusion.

  14 15 13

  11 12 9 8 7 6 5 4

  V 3 ^

  v. 3 + a

  Claim 4 is an objection to a. That is, it's an attempt to show that a crucial

  premise of Dick is false. It must be answered. And Dick answers it by amassing

  390 APPENDIX: Diagramming

  enough other evidence for a. Claim 10 is a direct challenge to the conclusion. If it is true, the conclusion is in doubt. So it must be answered. Dick doesn't try to show

  that it is false directly. Rather he shows that the two claims Zoe uses to support 10

  are false. So there is no reason to believe 10.

  When we finish diagramming we can see at a glance whether the argument has

  left some objection to a premise or objection to the conclusion unanswered. Either

  the objection is knocked off with a counterclaim above the support for it (as with

  13-15 against 10) or other claims are amassed as evidence (as with 5-9 against 4). Of course you'll still need to evaluate whether the various claims are plausible.

  Exercises for Section B

  Diagram and evaluate the following arguments:

  1. You should not take illegal drugs. They can kill you. If you overdose, you can die.

  If you share a needle, you could get AIDS and then die. If you don't die, you could end

  up a vegetable or otherwise permanently incapacitated. By using drugs you run the risk

  of getting arrested and possibly going to jail. Or at least having a hefty fine against you.

  Although some think the "high" from drugs is worth all the risks, the truth is that they

  are addicted and are only trying to justify supporting their habit.

  2. Zoe: I think sex is the answer to almost everyone's problems.

  Dick: How can you say that?

  Zoe: It takes away your tensions, right?

  Dick: Not if you're involved with someone you don't like.

  Zoe: Well, anyway, it makes you feel better.

  Dick: Not if it's against your morals. Anyway, heroin makes you feel good, too.

  Zoe: But it's healthy, natural, just like eating and drinking.

  Dick: Sure, and you can catch terrible diseases. Sex should be confined to marriage.

  Zoe: Is that a proposal?

 

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