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PHI1101G: Reasoning and Critical Thinking (Fall 2021): Final Exam A
I. True/false questions (4/40):
(a) An invalid argument with all true premises and a false conclusion is unsound.——
(b) An argument which is neither valid nor invalid is sound. ——
(c) Any argument with all true premises and a true conclusion is valid. ——
(d) No sound arguments are invalid.——
II. Put the following arguments into standard form, and then diagram them. (4/40)
(a) Once you have killed someone, there’s no way to bring him back to life. So, if the
state mistakenly executes someone, there’s no way to fix the mistake. Yet the
justice system is known to make mistakes even in trials for murder and other
serious crimes, as is proved by the cases of Donald Marshall and Guy Paul Morin.
Thus, if we reinstate the death penalty, it is entirely possible that we will commit
irreversible injustice by killing innocent people. For this reason, if for no other, we
should not do so.
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(b) If the detective really is a racist—which he is—then he never should have been
allowed to testify at all, since white racists are especially unreliable witness when
the accused is a person of color. So, the detective should not have been allowed to
testify at all.
III. (A) Symbolize the following arguments using the letters provided, and (b) show that
each argument is valid by constructing proofs of their conclusions from their premises using
the rules of inference we have studied in this course. (9/40)
(a) If Smith once beat the fireman at billiards, then Smith is not the fireman. Smith once beat
the fireman at billiards. If the brakeman is Jones, then Jones is not the fireman. The
brakeman is Jones. If Smith is not the fireman and Jones is not the fireman, then Robinson
is the fireman. If the brakeman is Jones and Robinson is the fireman, then Smith is the
engineer. Therefore, Smith is the engineer. (O— Smith once beat the fireman at billiards; M—
Smith is the fireman; B— the brakeman is Jones; N— Jones is the fireman; F— Robinson is the
fireman; G— Smith is the engineer.)
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(b) If Anderson was nominated, then she went to Boston. If she went to Boston, then she
campaigned there. If she campaigned there, she met Douglas. Anderson did not meet
Douglas. Either Anderson was nominated or someone more eligible was selected.
Therefore, someone more eligible was selected. (A— Anderson was nominated; B— Anderson
went to Boston; C— Anderson campaigned in Boston; D— Anderson met Douglas; E— Someone
more eligible was selected.)
(c) If Santacruz is injured, then she will not play. And if Santacruz does not play, then
Khumalo must play. What’s is more, if Khumalo and Nakata both play, then Jones must be
moved to the center. In fact, Santacruz is injured and Nakata will play. Thus, Khumalo will
play Jones will be moved into the center. (I— Santacruz is injured; S— Santacruz will play;
K— Khumalo must play; N— Nakata plays; J— Jones must be moved to the center.)
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IV. Draw a Venn diagram for each of the following categorical syllogisms, and then circle
whether it is valid or invalid. (4/40)
(a) Some students work full time.
Everyone who works full time is busy.
So, some students are busy.
Valid
Invalid
(b) All fascists are extremists.
Some radicals are not extremists.
So, not all radicals are fascists.
Valid
Invalid
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V. Identify exactly why each of the following arguments is unconvincing overall (explain
whether the premise(s) are acceptable, relevant, and sufficient) (5/40).
a) Withholding information is just the same as lying and lying is wrong, so withholding
information is wrong.
b) If you believe in God, you will be happier. That shows that God really does exist.
c) Paul is the best person to be put in charge of the arrangements for our club’s trip to the
International Debate Meet next year. After all, he does hold the number-one position on our team.
d) Most intellectuals cannot explain the mathematical supposition called “Goldbach’s Conjecture.”
My calculus professor is an intellectual, so he wouldn’t know about the Goldbach thing.
e) The days when natural disasters such as earthquakes, hurricanes, or volcanoes had the power to
bring death to thousands are fortunately behind us. Unlike the times of such catastrophes as the
1906 San Francisco earthquake or the hurricane of 1900 in Galveston, these days modern
construction methods for building, sophisticated advanced warning systems, mass communication
and modern health-care developments mean that we are able to keep the toll from even the worst
natural events to tens or at most one or two hundred.
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VI. Discuss the strengths and weaknesses of the following arguments, which involve
inductive and/or causal reasoning. (4/40)
(a) Fewer than 2 percent of people who work in New York live in Connecticut, so you
should infer that Allen, who works in a Times Square bookstore, does not live in
Connecticut.
(b) Your mother always told you to bundle up when the weather is cold, and it turns out
she was right—statistics prove that colds occur much more frequently when the
temperature is lower, so it is obviously exposure to cold temperatures that causes us to
catch colds.
VII. (A) Name the fallacy involved in each passage, and (b) explain it. (10/40)
(a) After-death experiences are a reality. Despite years of attempts at debunking, no one has
ever been able to show that reports from beyond the grave are all due to error, deception, or
simply wishful thinking.
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(b) Nobody wants to say so in public, but we all know that immigrants do not have as strong a
commitment to this country as those of us who were born here.
(c) Dr. Chance Tang told our class that a human embryo is a person just like me or you and
entitled to the same treatment. Dr. Tang is an obstetrician, so I’m prepared to believe what
he says, and reject the destruction of embryos as equivalent to murder.
(d) When can I make up the exam I missed?
(e) The Universe is spherical in form, because all the constituent parts of the universe, that is
the sun, moon, and the planets appear in this form.
(f) Adultery can never be justified, for it is never acceptable for a married person to have sex
with anyone but his or her spouse.
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(g) Why do so many people keep wanting to become friends with me? Is it because I am more
intelligent that others around here? Or do I have something natural leadership qualities?
(h) According to a recent poll 80% of United States citizens think that taxes are too high.
Doesn’t that prove the point?
(i) The economist’s model for determining the price of Gold is absolutely brilliant. No wonder
he won the Noble Prize. It’s true that the predictions produced by the model turned out to
be off by a wide margin in almost all cases. But this is a minor point.
(j) Every society that has collapsed throughout history has done so because of rottenness
within. The collapse has always been preceded and thus triggered by the slackening of
shame typified by widespread public nudity.
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