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Book Reference

A Rulebook for Arguments

Weston, A. (2009). A rulebook for arguments (4th ed.). Indianapolis, IN: Hackett Publishing Company

A Rulebook for Arguments Fourth Edition

Anthony Weston

VI

Deductive Arguments

Consider this argument:

If there are no chance factors in chess, then chess is a game of pure skill.

There are no chance factors in chess.

Therefore, chess is a game of pure skill.

Suppose that the premises of this argument are true. In other words , suppose it's true that if there are no chance factors in chess, then chess is a game of pure skill- and suppose there are no chance factors in chess. You can therefore conclude with perfect assurance that chess is a game of pure skill. There is no way to admit the truth of these premises but deny the conclusion.

Arguments of this type are called deductive arguments. That is, a (properly formed) deductive argument is an argument of such a form that if its premises are true, the conclusion must be true too . Properly formed deductive arguments are called valid arguments.

Deductive arguments differ from the sorts of arguments so far con- sidered, in which even a large number of true premises does not guaran- tee the truth of the conclusion (although sometimes they may make it very likely). In nondeductive arguments, the conclusion unavoidably goes be- yond the premises- that's the very point of arguing by example, author- ity, and so on- whereas the conclusion of a valid deductive argument only makes explicit what is already contained in the premises.

In real life, of course, we can't always be sure of our premises either, so the conclusions of real-life deductive arguments still have to be taken

37

38 22. MoDUS PON£NS

with a few (sometimes many) grains of salt. Still, when strong premises can be found, deductive forms are very useful. And even when the prem- ises are uncertain, deductive forms offer an effective way to organize arguments.

Modus ponens

Using the letters p and q to stand for declarative sentences, the simplest valid deductive form is

If [sentence p] then [sentence q] .

[Sentence p].

Therefore, [sentence q].

Or, more briefly:

lfp then q.

p.

Therefore, q.

This form is called modus ponens ("the mode of putting": put p, get q). Taking p to stand for "There are no chance factors in chess," and q to stand for "Chess is a game of pure skill," our introductory example fol- lows modus ponens (check it out). Here is another:

If drivers on cell phones have more accidents, then drivers should be prohibited from using them.

Drivers on cell phones do have more accidents.

Therefore, drivers should be prohibited from using cell phones.

To develop this argument, you must explain and defend both of its prem- ises, and they require quite different arguments (go back and look). Modus

23. MoousroLLENS 39

ponens gives you a way to lay them out clearly and separately from the start.

A second valid deductive form is modus tollens ("the mode of taking": take q, take p).

Ifp then q.

Not-q.

Therefore, not-p.

Here "Not-q" simply stands for the denial of q, that is, for the sentence "It is not true that q." The same is true for "not-p."

Remember Sherlock Holmes's argument, discussed under Rule 1:

A dog was kept in the stables, and yet, though someone had been in and had fetched out a horse, [the dog] had not barked . ... Obviously the ... visitor was someone whom the dog knew well.

Holmes's argument can be put as a modus tollens:

If the visitor were a stranger, then the dog would have barked.

The dog did not bark.

Therefore, the visitor was not a stranger.

To write this argument in symbols, you could use s for "The visitor was a stranger" and b for "The dog barked."

If s then b.

Not-b.

Therefore, not-s.

40 24. HYPOTHETICAL SYLLOGISM

"Not-b" stands for "The dog did not bark," and "not-s" stands for "The visitor was not a stranger." As Holmes puts it, the visitor was someone whom the dog knew well.

A third valid deductive form is''hypothetical syllogism."

Ifp then q.

If q then r.

Therefore, if p then r.

For instance:

If you study other cultures, then you start to realize the variety of human customs.

If you start to realize the variety of human customs, then you become more tolerant.

Therefore, if you study other cultures, then you become more tolerant.

Using the letters in boldface to stand for the component sentences in this statement, we have:

If s then v.

If v then t.

Therefore, if s then t.

Hypothetical syllogisms are valid for any number of premises, as long as each premise has the form "If p then q" and the q (called the "conse- quent") of one premise becomes the p (the "antecedent") of the next.

25. DISJUNCTIVE SYLLOGISM 41

A fourth valid

p orq.

Not-p.

Therefore, q.

Consider, for instance, Bertrand Russell's argument discussed under Rule 2:

Either we hope for progress by improving morals or we hope for progress by improving intelligence.

We can't hope for progress by improving morals.

Therefore, we must hope for progress by improving intelligence.

Again using the boldface letters as symbols, this argument goes

mori.

Not-m.

Therefore, i.

There is one complication. In English the word "or" can have two dif- ferent meanings. Usually "p or q" means that at least one ofp or q is true, and possibly both. This is called an "inclusive" sense of the word "or" and is the sense normally assumed in logic. Sometimes, though, we use "or" in an "exclusive" sense, in which "p or q" means that either p or q is true but not both. "Either they'll come by land or they'll come by sea," for example, suggests that they won ' t come both ways at once. In that case you might be able to infer that if they come one way, then they' re not coming the other way (better be sure!) .

42 26. DILEMMA

Disjunctive syllogisms are valid regardless of which sense of "or" is used (check it out). But what else, if anything, you may be able to infer from a statement like "p or q"-in particular, whether you can conclude not -q if you also know p-depends on the meaning of "or" in the specific "p or q" premise you are considering. Take care!

Dil-emma

p orq.

If p then r.

If q then s.

Therefore, r or s.

Rhetorically, a dilemma is a choice between two options both of which have unappealing consequences. The pessimist philosopher Arthur Schopenhauer, for example, formulated what is sometimes called the "Hedgehog 's dilemma," which we could paraphrase like this:

The closer two hedgehogs get, the more likely they are to poke each other with their spikes; but if they remain apart, they will be lonely. So it is with people: being close to someone inevitably creates conflicts and provocations and opens us to a lot of pain; but on the other hand, we ' re lonely when we stand apart.

In outline this argument might be put:

Either we become close to others or we stand apart.

If we become close to others, we suffer conflict and pain.

If we stand apart, we'll be lonely.

Therefore, either we suffer conflict and pain or we'll be lonely.

2 7, REDUCTIO AD ABSURDUM 43

And in symbols:

Either c or a.

If c then s.

If a then l.

Therefore, either s or l.

A further argument in dilemma form could conclude, even more simply, something like "Either way we'll be unhappy." I'll leave this one to you to write out formally.

Since this is such a jolly little conclusion, maybe I should add that hedgehogs are actually quite able to get close without poking each other. They can be together and comfortable too. Schopenhauer's second prem- ise turns out to be false-at least for hedgehogs.

Reductio ad absurdum

One traditional deductive strategy deserves special mention even though, strictly speaking, it is only a version of modus to/lens. This is the reduc- tio ad absurdum, that is, a "reduction to absurdity. " Arguments by re- ductio (or "indirect proof," as they're sometimes called) establish their conclusions by showing that assuming the opposite leads to absurdity: to a contradictory or silly result. Nothing is left to do, the argument suggests, but to accept the conclusion.

To prove: p.

Assume the opposite: Not-p.

Argue that from the assumption we'd have to conclude: q.

Show that q is false (contradictory, "absurd," morally or practically unacceptable .. . ).

Conclude: p must be true after all.

44 2 7. REDUCTIO AD ABSURDUM

Rule 12 discussed an argument for the existence of a Creator. Houses have creators, the argument goes, and the world is like a house-it too is ordered and beautiful. Thus, the analogy suggests, the world must have a Creator too. Rule 12 also cited David Hume's argument that the world is not relevantly similar enough to a house for this analogy to succeed. In Part V of his Dialogues, Hume also suggested a reductio ad absurdum of the analogy. 8 Developed, it goes something like this:

Suppose the world has a Creator like a house does. Now, when houses are not perfect, we know whom to blame: the carpenters and masons who created them. But the world is also not wholly perfect. Therefore, it would seem to follow that the Creator of the world is not perfect either. But you would consider this conclusion absurd. The only way to avoid the absurdity, however, is to reject the supposition that leads to it. Therefore, the world does not have a Creator in the way a house does.

Spelled out in reductio form, the argument is:

To prove: The world does not have a Creator in the way a house does.

Assume the opposite: The world does have a Creator in the way a house does .

Argue that from the assumption we'd have to conclude: The Creator is imperfect (because the world is imperfect) .

But: God cannot be imperfect.

Conclude: The world does not have a Creator in the way a house does.

Not everyone would find the idea of an imperfect God "absurd," but Hume knew that the Christians with whom he was arguing would not ac- cept it.

8 David Hume, Dialogues Concerning Natural Religion, pp. 34-37.

28. DEDUCTIVE ARGUMENTS IN SEVERAL STEPS 45

Deductive arguments in several steps

Many valid deductive arguments are combinations of the basic forms in- troduced in Rules 22- 27. Here, for example, is Sherlock Holmes per- forming a simple deduction for Doctor Watson's edification, meanwhile commenting on the relative roles of observation and deduction. Holmes has casually remarked that Watson visited a certain post office that morn- ing, and furthermore that he sent off a telegram while there. "Right! " replies Watson, amazed, "Right on both points! But I confess that I don 't see how you arrived at it." Holmes replies:

"It is simplicity itself .. . . Observation tells me that you have a little reddish mold adhering to your instep. Just opposite the Wigmore Street Post Office they have taken up the pavement and thrown up some earth, which lies in such a way that it is difficult to avoid treading in it in entering. The earth is of this peculiar reddish tint which is found, as far as I know, nowhere else in the neighborhood. So much is observation. The rest is deduction."

[Watson]: "How, then , did you deduce the telegram?"

[Holmes]: "Why, of course I knew that you had not written a letter, since I sat opposite to you all morning. I see also in your open desk there that you have a sheet of stamps and a thick bundle of postcards. What could you go into the post office for, then, but to send a wire? Eliminate all other factors, and the one which remains must be the truth. "9

Putting Holmes's deduction into explicit premises, we might have:

1. Watson has a little reddish mold on his boots.

2. If Watson has a little reddish mold on his boots, then he has been to the Wigmore Street Post Office this morning (because there and only there is reddish dirt of that sort thrown up, and in a way difficult to avoid stepping in).

9 Sir Arthur Conan Doyle, "The Sign of Four," in The Complete Sherlock Holmes, pp. 91-92.

46 28. DEDUCTIVE ARGUMENTS IN SEVERAL STEPS

3. If Watson has been to the Wigmore Street Post Office this morning, he either mailed a letter, bought stamps or cards, or sent a wire.

4. If Watson had mailed a letter, he would have written the letter this morning.

S. Watson wrote no letter this morning.

6. If Watson had bought stamps or cards, he would not already have a drawer full of stamps and cards.

7 . Watson already has a drawer full of stamps and cards.

8. Therefore, Watson sent a wire at the Wigmore Street Post Office this morning.

We now need to break the argument down into a series of valid argu- ments in the simple forms presented in Rules 22-27. We might start with a modus ponens:

2. If Watson has a little reddish mold on his boots, then he has been to the Wigmore Street Post Office this morning.

1. Watson has a little reddish mold on his boots .

I. Therefore, Watson has been to Wigmore Street Post Office this morning .

(I will use I, II, etc. to stand for the conclusions of simple arguments, which then can be used as premises to draw further conclusions.)

Another modus ponens follows:

3. If Watson has been to the Wigmore Street Post Office this morning, he either mailed a letter, bought stamps or cards, or sent a wire.

I. Watson has been to Wigmore Street Post Office this morning.

II. Therefore, Watson either mailed a letter, bought stamps or cards, or sent a wire.

Two of these three possibilities now can be ruled out, both by modus to !lens:

l

28. DEDUCTIVE ARGUMENTS IN SEVERAL STEPS

4. If Watson had gone to the post office to mail a letter, he would have written the letter this morning.

5. Watson wrote no letter this morning.

III. Therefore, Watson did not go to the post office to mail a letter.

and

6. If Watson had gone to the post office to buy stamps or cards, he would not already have a drawer full of stamps and cards.

7. Watson already has a drawer full of stamps and cards.

IV. Therefore, Watson did not go to the post office to buy stamps or cards.

Finally we can put it all together:

II. Watson either mailed a letter, bought stamps or cards, or sent a wire at the Wigmore Street Post Office this morning.

III. Watson did not mail a letter.

IV. Watson did not buy stamps or cards.

8. Therefore, Watson sent a wire at the Wigmore Street Post Office this morning.

47

This last inference is an extended disjunctive syllogism: "Eliminate all other factors, and the one which remains must be the truth ."

Appendix I

Some Common Fallacies

Fallacies are misleading types of arguments . Many of them are so tempt- ing, and therefore so common, that they even have their own names. This may make them seem like a separate and new topic . Actually, though, to call something a fallacy is usually just another way of saying that it vio- lates one of the rules for good arguments . The fallacy of "false cause," for example, is a questionable conclusion about causes, and you can look to Chapter V for explanation.

Here is a short list and explanation of some of the classical fallacies, including their Latin names when frequently used.

ad hominem (literally, "to the man"): attacking the person of a source rather than his or her qualifications or reliability, or the actual argument he or she makes. You know from Chapter IV that supposed authorities may be disqualified if they are not informed, impartial, or largely in agreement. But other sorts of attacks on supposed authorities are typically not legitimate .

It's no surprise that Carl Sagan argues for life on Mars-after all, he was a well-known atheist. I don't believe it for a minute.

Alhough Sagan did take part in the public discussion about religion and science, there is no reason to think that his views about religion colored his scientific judgment about Martian life. Look to the argument, not "the man."

ad ignorantiam (appeal to ignorance): arguing that a claim is true just be- cause it has not been shown to be false . A classic example is this state-

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74 APPENDIX I: SOME COMMON FALLACIES

ment by Senator Joseph McCarthy when he was asked for evidence to back up his accusation that a certain person was a Communist:

I do not have much information on this except the general statement of the agency that there is nothing in the files to disprove his Commu- nist connections.

ad misericordiam (appeal to pity): appealing to pity as an argument for special treatment.

I know I flunked every exam, but if I don't pass this course, I'll have to retake it in summer school. You have to let me pass!

Pity is sometimes a good reason to help, but it is certainly inappropriate when objective evaluation is called for.

ad populum: appealing to the emotions of a crowd; also, appealing to a person to go along with the crowd ("Everyone's doing it!"). Arguments ad populum are good examples of bad arguments from authority. No rea- sons are offered to show that "everybody" is any kind of knowledgeable or reliable source.

affirming the consequent: a deductive mistake of the form

Ifp then q.

q.

Therefore, p.

Remember that in the statement "if p then q," p is called the "antecedent" and q the "consequent." The second premise of modus ponens-a valid form-affirms (asserts) the antecedent, p (go back to Rule 22 and check). Affirming the consequent (q), though, yields quite a different-and invalid-form. A true conclusion is not guaranteed even if the premises are true. For example:

When the roads are icy, the mail is late.

APPENDIX /: SOME COMMON fALLACIES 75

The mail is late.

Therefore, the roads are icy.

Although the mail would be late if the roads were icy, it may be late for other reasons too. This argument overlooks alternatives.

begging the question: implicitly using your conclusion as a premise.

God exists because it says so in the Bible, which I know is true be- cause God wrote it, after all!

To put this argument in premise-and-conclusion form, you'd have to write:

The Bible is true, because God wrote it.

The Bible says that God exists.

Therefore, God exists.

To defend the claim that the Bible is true, the arguer claims that God wrote it. But, obviously, if God wrote the Bible, then God exists . Thus the ar- gument assumes just what it is trying to prove.

circular argument: same as begging the question.

You can count on WARP News for the facts , because they constantly say on the air that "we just give you the facts, " so that must be a fact too!

Real-life circular arguments often follow a bigger circle, but they all eventually end up starting in the same place they want to end.

complex question: posing a question in such a way that people cannot agree or disagree with you without committing themselves to some other claim you wish to promote. A simple example: "Are you still as self- centered as you used to be?" Answering either "yes" or "no" commits you to agreeing that you used to be self-centered. A more subtle example: "Will you follow your conscience instead of your pocketbook and donate to the

76 APPENDIX I: SoME CoMMON FALLACIES

cause?" Saying "no," regardless of their real reasons for not donating, makes people feel guilty. Saying "yes," regardless of their real reasons for donating , makes them noble. If you want a donation, just ask for it.

denying the antecedent: a deductive mistake of the form

Ifp then q.

Not-p.

Therefore, not-q.

Remember that, in the statement "If p then q," p is called the "antecedent" and q the "consequent." The second premise of a modus tollens-a valid form-denies the consequent, q (go back to Rule 23 and check). Deny- ing the antecedent (p), though, yields quite a different-and invalid- form. A true conclusion is not guaranteed even if the premises are true. For example:

When the roads are icy, the mail is late.

The roads are not icy.

Therefore, the mail is not late.

Although the mail would be late if the roads were icy, it may be late for other reasons too . This argument overlooks alternatives.

equivocation: sliding from one meaning of a term to another in the mid- dle of an argument.

Women and men are physically and emotionally different. The sexes are not "equal," then, and therefore the law should not pretend that we are.

Between premise and conclusion this argument shifts the meaning of the term "equal." The sexes are not physically and emotionally "equal" in the sense in which "equal" means simply "identical." Equality before the law, however, does not mean "physicaily and emotionally identical" but

APPENDIX /: SOME COMMON fALLACIES 77

"entitled to the same rights and opportunities." Rephrased with the two different senses of "equal" made clear, the argument goes:

Women and men are not physically and emotionally identical. There- fore, women and men are not entitled to the same rights and oppor- tunities.

Once the equivocation is removed, it is clear that the argument's conclu- sion is neither supported by nor even related to the premise. No reason is offered to show that physical and emotional differences imply different rights and opportunities.

false cause: generic term for any questionable conclusion about cause and effect. To figure out specifically why the conclusion is (said to be) questionable, go back to Chapter V.

false dilemma: reducing the options you consider to just two, often diametrically opposed to each other and unfair to the people against whom the dilemma is posed. For example, "America: Love It or Leave It." A more subtle example from a student paper: "Since the universe could not have been created out of nothingness, it must have been created by an in- telligent life force .... "Well, maybe, but is creation by an intelligent life force the only other possibility? This argument overlooks alternatives.

Ethical arguments seem especially prone to false dilemmas. Either the fetus is a human being with all the rights you and I have, we say, or else it is a lump of tissue with no moral significance at all. Either every use of animal products is wrong, or all of the current uses are acceptable. In fact, other possibilities usually exist. Try to increase the number of options you consider, not narrow them!

loaded language: language that primarily plays on the emotions. It does not make an argument at all, in truth, but is only a form of manipu- lation. See Rule 5.

non sequitur: drawing a conclusion that "does not follow," that is, a conclusion that is not a reasonable inference from, or even related to, the evidence. This is a very general term for a bad argument. Try to figure out specifically what is supposed to be wrong with it.

78 APPENDIX I: SoME CoMMON FALLACIES

overgeneralizing: generalizing from too few examples. Just because your student friends are all athletes or business majors or vegetarians, it doesn ' t follow that all of your fellow students are the same (remember Rules 7 and 8). You can't even generalize from a large sample unless it is demonstrably representative. Take care!

overlooking alternatives: forgetting that things may happen for a va- riety of reasons, not just one. For example, Rule 19 pointed out that just because events E

1 and E

2 may correlate, it does not follow that E

1 causes

E 2

. E 2

could cause E 1

; something else could cause both E 1

and E 2

; E 1

may cause E 2

and E 2

may cause E 1

; or E 1

and E 2

might not even be re- lated. False dilemma is another example: there are usually many more options than two!

persuasive definition: defining a term in a way that may seem to be straightforward but in fact is loaded. For example, someone might define "Evolution" as "the atheistic view that species develop as a result of mere chance events over a supposed period of billions of years." Persuasive definitions may be favorably loaded too: for example, someone might de- fine a "conservative" as "a person with a realistic view of human limits."

petitio principii: Latin for begging the question

poisoning the well: using loaded language to disparage an argument before even mentioning it

I'm confident you haven't been taken in by those few holdouts who still haven't outgrown the superstition that .. .

More subtly:

No sensitive person thinks that ...

post hoc, ergo propter hoc (literally, "after this, therefore because of this"; sometimes just called the post hoc fallacy): assuming causation too readily on the basis of mere succession in time. Again a very general term for what Chapter V tries to make precise. Return to Chapter V and try to figure out if other causal explanations are more plausible.

APPENDIX I: SoME CoMMON FALLACIES 79

red herring: introducing an irrelevant or secondary subject and thereby diverting attention from the main subject. Usually the red herring is an issue about which people get heated quickly, so that no one notices how their attention is being diverted. In a discussion of the relative safety of different makes of cars, for instance, the issue of which cars are made in America is a red herring.

straw man: a caricature of an opposing view, exaggerated from what anyone is likely to hold, so that it is easy to refute . See Rule 5.