Chapter 3
Evaluating Arguments
A. (pp. 45 - 46)
2. Not valid. It could be that many people who do not watch daytime
TV also have corrupted minds. Maybe Herbert reads romance novels all day every day and
that is why he has a corrupted mind.
3. Valid. If he cuts himself shaving, he cuts himself. And the
premise says he does this every morning.
5. not valid. Most mammals do not have wings, but bats
could be among those that do. The fact that bats are in fact among those that have wings
makes the answer even more obvious, but strictly speaking that does not matter for
validity.
6 Not valid. For instance, all the horoscope people are
superstitious. And while some of these
superstitious people will not stay on the 13th floor of hotels, others among them will. Under these conditions, the
premises are true but some superstitious people will stay on the 13th floor. Thus, the
conclusion is false.
Because the second premise says “some people” and the
conclusion says “no one” students immediately recognize that this argument is
not valid. Ask whether the argument would be valid if the conclusion were changed to
“some who read the horoscope column...will not stay on the 13th floor...” But
with the proposed change it is essentially like #22 below and still is not valid.
8. Valid.
9. Not valid. Even it could well be that all pleasurable things are
good, but some good things are not pleasurable.
Self-sacrifice is one possibility.
11. Not valid. Jake could well have failed and not have been out
partying. For instance, he might have simply chosen not to study calculus but instead
spent the night reading Moby Dick. Or maybe Jake
just has aptitude for math.
12. Valid. Do not be misled by both the premises and the
conclusion being false.
13. Not valid. The premises are the same as in #12, but in this
case the arguer has stumbled into a true conclusion. (If the premises are true, then not
only can we conceive of the conclusion being false; we cannot conceive of it being true.)
14. Valid. If there is literally no water anywhere in the
desert, then any place in the desert must be without water.
15. It is sometimes said that “real-life” arguments
are seldom valid. That is not close to being correct. This argument, given by a TV
commentator, is clearly valid. Tennessee gets either 5 yards or 15 yards. Either is more
than 4 yards.
16. Valid. Each flying squirrel has the characteristic of being a
mammal. Each bird does not have this characteristic. So obviously not a single flying
squirrel can be a bird.
18. Not valid. Suppose the premises are true but you fail to take the
medicine as prescribed and die.
21. Not valid. We can easily see how the premises could be true
and the conclusion false. Dumbo!
22. Not valid. Suppose that all vegetarians lack protein in
their diets, and so they are undernourished. They do, however, get plenty of vitamins from
the seaweed they eat. Further, some very poor people who are not vegetarians at all are
undernourished because they cannot afford enough food. We then have undernourished
vegetarians who do not need vitamins and some undernourished poor people who do need them.
The premises are true and the conclusion is false under these conditions.
23. Valid. Since squash and beans are vegetables, having squash
or having beans means having vegetables. Discussed in class (definitions)
24. Valid. Since 20 is a larger number than 19, even if I give out
the first 19 pieces of candy as evenly as possible, the 20th piece must go to a student
who already has one.
B. (p. 47)
--In cases where there is no question of formal validity, whether an
invalid argument is deductive or nondeductive is probably not of much importance. Without
some clue, (such as, “it follows with complete certainty” in #10), we cannot be
sure and the question seems mainly psychological--what does the arguer mean?--and of
little importance. On the other hand, arguments such as #1 and #9 are clearly supposed to be valid in a non-psychological
sense. That is, if there is no mistake in the reasoning, they would be valid. That the
reasoning is of the sort that gives validity (if correct) is well worth knowing.
2. Deductive but not valid.
3. Deductive but not valid. Conceptual mistakes in arguing from most
A’s are B’s to most B’s are A’s are common.
5. Deductive and valid. We can reasonably take this to mean.
“Every person...” and “You are a
person.”
6. Deductive and valid.
7. Deductive but not valid. This is supposed to be a valid
inference based on what is involved in being a pair. The question is an old riddle that
most people get wrong at first, saying, as here, that one must take out eleven to be sure
of getting a pair. We need remove only three of course (eleven to be sure of getting different colors).
10. Deductive but not valid. “It follows with complete
certainty” indicates that the argument is supposed to be valid, and so it is
deductive. It is not valid, however, since there could well be creatures other than birds
who also have wings. (And there are.)
C. (pp. 57 - 60)
1. This statistical syllogism obviously is quite successful,
making the conclusion 84% likely.
4. This is a statistical syllogism that makes its conclusion
slightly over 98% likely.
7. This inductive generalization attempts to establish either
(a) that Professor Crator’s Intro class is boring or (b) more generally, that she is
a really boring teacher. In regard to (a), the sample size is vaguely stated and probably
rather small (“several”) and the sample is not random, since it is made up of
entirely of students in the Advanced Algebra class. The argument is even weaker if the
conclusion is (b). For (b) would apparently mean that all (or at least most) of Professor
Crator’s classes are boring. For this more sweeping claim, the sample size (whatever
it is exactly) is relatively smaller.
8. This is a very unconvincing plausibility argument. We do not
know whether the criteria (expert on the eighteenth century, well-regarded teacher) are
even relevant for this particular position. And, even if they are relevant, to know he is best qualified we would have to know the
qualifications of other potential applicants.
9. This rather vaguely stated statistical syllogism (“the
great majority”) is quite successful.
10. Here we have a plausibility argument that makes the
conclusion more likely than not. It could go wrong in many ways: maybe Notre Dame has poor
coaching or is overconfident. But at least we know they are superior in the mentioned
aspects. Suppose that you had to bet, and all
you know is that Notre Dame is bigger, stronger, and quicker. We all know which team we
would bet on. Discussed in class
11. The inductive generalization here is successful. We do not
know just how many “hundreds” includes, but if even two hundred have been
investigated and every one of those has been shown to be fraudulent, we have good reason
to accept the conclusion—Debated in class
13. Gorillas in zoos cannot be expected to exhibit behavioral
characteristics typical of gorillas in general. The generalization is unsuccessful.
14. Even if this plausibility argument makes a decent case that
some mammal is in the campground, it gives no reason to think it is a giant rat rather
than any number of other mammals.
15. This argument contains two inferences, both statistical
syllogisms. The first makes the intermediate conclusion 90% likely; the second, in itself,
would make its conclusion 50+% likely. If the majority in the second inference is just 51%
(which is all we have the right to assume), the conclusion is only about 45% likely, and
so the argument is unsuccessful. (See the discussion in the text on pp. 56 - 57.)
**understand that several pretty good inferences may not make
for a rationally convincing argument.
18. If this is meant to be a statistical syllogism, it fails. Since many is not the same as most, it does not make the conclusion (“You
will be [energized] too.”) more likely than not. Whether or not the conclusion is
more than 50% likely is probably of secondary importance in a case such as this. If this
product helps many people (some significant minority, even), then it may be worth you
giving it a try. (The assumption here is that there is little to lose and some possibility
of gain.)
19. The first inference is the implicit generalization to the
unreliability of the installation processes for CD’s in general (60% of all CD’s are difficult to install). The second
inference is a statistical syllogism from the generalization to your CD in particular. As
in #18, whether the conclusion is made more than 50% likely (that depends on how well the
magazine carried out its poll) is not crucial. Most
do not want to risk disappointment on Christmas.
22. The plausibility argument appears to make a strong case for her
guilt. (Of course there could be unmentioned considerations that would change the picture.
That is why we have attorneys for the defense.)
23. This complex argument first has three valid inferences,
then a successful
24. We should not rely on the outcome of the series of three
individually successful inferences. Altogether much too much doubt is introduced.
D. (pp. 54--55)
Overall
evaluation is much more accurate and helpful if we recognize the exact source and nature
of the problems. Are there false premises? inadequate support? etc.
Recognizing that a premise is false involves going
outside the argument in one sense. The sense of “relevant outside evidence” that
matters only for nondeductive arguments concerns evidence that itself bears on the
conclusion, rather on the truth of a premise.
2. This argument has
two separable problems: first, the support is not adequate.
Assuming we really do need protection at times, why should we rely on hand grenades rather
than, say, a gun or a dog? Second, there is obvious outside information
we must take into account. We would blow up ourselves and our houses with a grenade.
5. The premise is not
relevant to the conclusion. Being the best debater gives no support to the claim that
he is the best person to make the arrangements. (Anyone who thinks it is relevant must
make a case for that unlikely idea.)
7. Most of us would say that the premises are not relevant
to the moral claim that it is all right to take the bracelet. A view that entailed that
the premises are morally relevant would certainly need justification.—Some may not—this
is a different matter that could be debated (take more ethics courses)
8. The barking could be a big terrier, but it also could have
many other sources. The support is not adequate.
9. The premise is false.
10. The relevant outside
information is that President Bill Clinton is
from Arkansas.
12. As with #11 we can question both the truth and the relevance of the premise. If we think the premise
is relevant, we can still wonder if it provides adequate support for the conclusion. (That
it makes you happy may count in favor of believing, but so do other factors.) A very
ambitious discussion could bring in James’ Will to Believe,” Pascal’s
“wager,” and even pragmatism in general.
13. Support for going to a gym is not adequate.
Why not run or play tennis? Support for going to Bailey’s Gym in particular is even
weaker. Explained well by students in class
14. Known relevant outside
information is omitted. We know that premed
students must take organic chemistry.
15. Answer in text.
Remember: ARG Conditions from class
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