Phil 1100 – Critical Reasoning
Final Exam – July, 2015
Name __________Answer Key___________
1. _________ is a statement that expresses an opinion or point of view, ____________ is a statement
that expresses a reason to believe, and together they make ________________.
a) A claim, a premise, a conclusion
b) A claim, a premise, a fact
c) A claim, a premise, an argument
d) An issue, a premise, an argument
e) An issue, an argument, a fact
2. An opinion that expresses that something ought to be done is:
a) always a moral judgment
b) a logical fallacy
c) always totally subjective
d) a normative claim
e) always rhetorical
3. Critical thinking:
a) sometimes involves attacking other people
b) generally requires defending the truth from skeptics
c) will always lead to finding the truth
d) is sometimes subjective
e) expects you to have good reasons for believing what you believe
4. Why do you need to identify the primary claim clearly before you proceed to evaluate an argument?
Without knowing the primary claim, you don’t know what the argument is in any
meaningful sense, and in particular, you have no way to evaluate whether any other
assertions can serve as premises by providing relevant evidence.
5. A strong inductive argument is one in which
a) if the premises are true, then the conclusion necessarily is (I.e. has to be) true.
b) the premises are always true
c) the conclusion is always true.
d) the premises do not give support to the conclusion, but the conclusion might be true.
e) none of the above.
6. An invalid deductive argument is one in which
a) if the premises are true, then the conclusion necessarily is (I.e. has to be) false.
b) the premises are false and thus the conclusion is false.
c) the conclusion is always true when the premises are true but the premises are false.
d) the premises give good support to the conclusion but do not “prove” it..
e) if the premises are true, then the conclusion may be true but may not be.
7. “You didn’t fire her already? This is the second time you have caught her stealing.”
a. this is not an argument but an explanation
b. this is clearly an argument with a normative claim and a normative premise but needs also a
factual premise.
c. this is a complete argument with a factual premise and a factual claim
d. this is a complete argument with a normative premise and a normative claim.
e. this may seem to be a good argument, but actually it contains rhetoric and at best an unstated
premise AND an unstated conclusion.
8.
Logical arguments should avoid both vagueness and ambiguity. Ambiguity and vagueness differ in that:
a) An ambiguous statement has multiple meanings but a vague statement only has one
meaning but that meaning is easily misunderstood
b) A vague statement has multiple meanings but an ambiguous statement only has one
meaning but that meaning is easily misunderstood
c) Both vague and ambiguous statements have only one real meaning, but vague
statements always suggest something that they don’t really say.
d) Both vague and ambiguous statements have multiple meanings, so they are really the
same thing.
e) Vague statements are usually understood by their context but ambiguous statements are
not
9. Consider the following argument: If it is Feb. 14, it is St. Valentine's Day. It is St. Valentine's Day. It
must be Feb 14:
a)
b)
c)
d)
e)
this is a valid deductive argument because of its logical form.
this is a invalid deductive argument because of its logical form.
this is a strong inductive argument because of its logical form.
this is a weak inductive argument because of its logical form
none of the above.
10. “The U.S. landing on the moon didn’t really happen because nobody has given evidence that it did.”
This statement:
a) is a good logical argument because it shows that there is no evidence for a commonly
held misconception
b) perhaps a bit skeptical, but a fairly good argument
c) absolutely ridiculous. We don’t need evidence for what we know.
d) seems to be the logical fallacy of “shifting the burden of proof.”
e) true if everyone agrees it is true
11. A rhetorical device that distracts from the current issue but may make a good point about a related
issue is:
a) an innuendo
b) a rhetorical analogy
c) a dysphemism
d) an ad hominem
e) a red herring
12. The following is true about ambiguity:
a. An ambiguous claim is a problem in a logical argument until the ambiguity is resolved.
b. In a logical argument, sometimes ambiguity can be used effectively.
c. What is ambiguous may be resolved by the context.
d. (a) and (c) are both true.
e. In an ambiguous claim, the problem is that only one meaning is understood by all parties in the
argument but there could possibly be other meanings in another argument.
13. Tracy said her son’s grandmother told her that “her son walked out” on his job. Tracy thought this
unclear in regard to whether the person in question quit his job permanently or not, but thought it was
clear in regard to whom was being discussed, namely Tracy’s son’s father. Do you agree or not?
Please give your reasons and identify whether any lack of clarity here is due to ambiguity or vagueness.
Actually, the statement is ambiguous whether it was Tracy’s son or Tracy‘s son’s
grandmother’s son (who may or may not even be Tracy’s son’s father) who “walked out” on
her job. Tracy seems to be assuming a context here which is not explicit in the actual
statements. Tracy is correct however that “her son walked out on his job” is unclear whether he
quit his job permanently or not. Again, this is a matter of ambiguity, not vagueness.
14. What kind of ambiguity if any exists in the statement “The average secretary’s salary is $45,000?”
a) Syntactic ambiguity
b) Semantic ambiguity
c) Grouping ambiguity
d) There is no ambiguity
e) (a), (b), and (c) are all true.
15. Rhetoric:
a) Is an attempt to persuade through the emotional use of language and thus has no logical value
b) Is an attempt to persuade through critical thinking and thus is a useful skill
c) Is an attempt to persuade through any means available and thus logical argument is one way
to provide good rhetoric
d) Is simply an attempt to confuse someone with more facts than they need
e) Will never influence us if we listen carefully and commit to thinking critically.
16. Joan: “All this criticism of the President is baloney. It just comes from the Republicans wanting to
get elected.” Joan seems to committing what logical fallacy?
a) begging the question
b) a dysphemism
c) wishful thinking
d) a genetic fallacy
e) a straw man
17. The claim “If we legalized marijuana, it would lead to greater use of harder drugs such as heroin.
Marijuana is a gateway drug.” is:
a) Clearly an example of “slippery slope” logical fallacy
b) Could be a “slippery slope” logical fallacy if evidence is not presented for the claim.
c) Is an indisputable fact.
d) Is a good argument, although inductive.
e) Is a sound argument.
NOTE: Although (b) is the best answer since we are only told the claim and not that this is all the argument
given. However if one assumes in the context of this question that “this was all that was said” (which is not
an unreasonable assumption), then (a) is also a possible answer. Thus, I accepted answer (a) or (b).
18. The shading in a Venn Diagram in Categorical Logic represents:
a) all things that may or may not exist.
b) what cannot exist.
c) what can exist.
d) particular things that are asserted to exist
e) what is already known to exist.
19. The claim “All Christians are not atheists” where the classes are understood to be “Christians” and
“Atheists” is:
a) an A-claim
b) an E-claim
c) an I-claim
d) an O-claim
e) not a valid claim in categorical logic
20. If a claim uses the phrase “the only”, you know immediately that:
a) it is an O-claim
b) it is an A-claim and “only” introduces the subject
c) it is an A-claim and “only” introduces the predicate
d) it is an E-claim and “only” introduces the middle term
21. For all four types of logical forms in Categorical Logic, a claim is equivalent to its:
a) converse
b) obverse
c) contrapositive
d) converse and contrapositive
e) obverse and contrapositive
22-24. Determine whether the following argument is valid or invalid using the long form truth table method.
Show all steps!!!
25. You have drawn an overlapping three-circle Venn Diagram representing the premises of a categorical
syllogism. You notice that to draw the conclusion, you just need move an “x” off of a line. Dude, you have
just:
a) Proven the argument valid
b) Proven the argument invalid
c) Demonstrated that the argument was NOT a categorical syllogism in the first place.
d) Not done squat yet to determine if the argument is valid
e) Proven that the premise and conclusion are not both true.
26. A good translation in categorical logic for “A few holidays fall on Saturday” is:
a) Not all holidays are days that fall on Sunday.
b) Some holidays are days that fall on Sunday.
c) No holidays” are days that fall on Sunday.
d) Some holidays are not days that fall on Sunday.
e) It is not the case that most holidays are days that fall on Sunday.
Oops. Typo. FREE QUESTION. Everybody got it right. I typed “Saturday” rather than “Sunday.” I was
wanting you to translate “ A few holidays fall on Sunday. Of course, the question as is has NO translation.
Note however that if the mis-typed claim were true, then (a) is certainly true and can be proven from it. But
of course the original claim could not in turn be proven from (a) and thus they are not equivalent and not a
good translation. (b) in that case would be an invalid conclusion from the original assertion
27. A good translation in categorical logic for “Only outlaws own guns” is:
a) All outlaws are gun-owners.
b) Some outlaws are gun-owners.
c) All gun-owners are outlaws.
d) Some gun-owners are outlaws.
e) None of the above
28. The contrapositive of “No students who passed this exam are students who graduated from Millard
North” is:
a) All students who passed this exam are not Millard North graduates.
b) All students who passed this exam are students who didn’t graduate from Millard
North.
c) All Millard North graduates are students who passed this exam.
d) All Millard North graduates are students who didn’t pass this exam.
e) No students who didn’t graduate from Millard North are students who didn’t pass this
exam.
29. “No students who passed this exam are students who graduated from Millard North” is equivalent to
which of the following properly stated claims:
a) All students who passed this exam are not Millard North graduates.
b) All students who passed this exam are students who didn’t graduate from Millard
North.
c) All Millard North graduates are students who passed this exam.
d) All Millard North graduates are students who didn’t pass this exam.
e) No students who didn’t graduate from Millard North are students who didn’t pass this
exam.
30. Consider the following Categorical Syllogism using the Rules Method of Testing for Validity:
Some A are not B
Some B are C
________
Thus, Some C are not A
a)
b)
c)
d)
e)
The argument breaks Rule #1 and thus is invalid.
The argument breaks Rule #2 and thus is invalid.
The argument breaks Rule #3 and thus is invalid.
The argument breaks no rules and thus is valid.
Whether the argument is valid or not cannot be determined by the rules.
31-34. Determine if the following Categorical Syllogism is valid or invalid by using the Venn Diagram
method. Define the variables that you use with appropriate class descriptions and state the premises and
conclusion in standard logical forms. If you need to perform any operations, please show your
transformations and label them.
All ears of corn with white tassels are unripe, but some ears are ripe even though their kernels are
not full sized. Therefore, some ears with full-sized kernels are not ears with white tassels.
W=”White tasseled ears of corn,” U-“Unripe ears of corn, “F” = Full-sized ears of corn.
Tentative Syllogism:
P1: All W are U
P2: Some non-U are not F
______
Claim: Some F are not W.
However, P2 is not in a logical form. But the contrapositive of it is: “Some F are not U” This latter
claim is a logical form (i.e. an O-claim) and thus we can use the rules of operation to show that it is
equivalent (by means of a contrapositive on an O-claim) to the original tentative translation.
Thus we can now restate our syllogism in logical form:
P1: All W are U
P2: Some F are not U
______
Claim: Some F are not W
35. Consider the following argument: “Scarlet is not guilty of the crime. If Scarlet were guilty, then Ms.
White would have left the back door unlocked and the colonel would have retired before ten o’clock.
However, either Ms. White did not leave the back door unlocked, or the colonel did not retire before ten.”
a)
b)
c)
d)
e)
36.
To translate the conclusion into T-F (truth-functional) logic, one requires only one elementary
variable.
To translate the conclusion into T-F logic, one requires two elementary variables: “Scarlet is
guilty” and “Scarlet is not guilty.”
To translate the argument into T-F logic, one requires three variables.
Both (a) and (c) are correct.
It is impossible to translate this argument into T-F logic.
Truth-functional logic and categorical logic are similar in that:
a)
b)
c)
d)
e)
Both are concerned with relationships between classes.
Both are types of deductive logic and thus are concerned with proving arguments through
logical form.
Both are types of deductive logic and thus are concerned with evaluating evidence.
Both are types of inductive logic and thus are concerned with proving arguments through
evaluating evidence.
Both are concerned with proofs based on truth tables.
37-38. Symbolize the following argument correctly. Be sure to identify your elementary claims and state
your translations appropriately. (But you do not have to prove it):
“R” = Rob autographs the book, “K” = “Kellie will be happy, and “B” = “Beth will buy it.”
Premise: If Rob autographs the book then Kellie will be happy. Either way Beth will buy it.
(R->K) & B
Conclusion: If Rob autographs the book, then Kellie will be happy and Beth will buy it.
R -> (K & B)
39. The definition of a “truth-functional statement” is:
a) a statement generally true when the simpler statements that comprise it are true, but not
always
b) a statement whose truth always depends entirely on the truth of elementary statements
properly arranged and thus comprise the meaning of the statement
c) a statement within a language such as English that could be true.
d) a statement that could be true even if it is believed to be false, e.g. Mary believes that the New
Orleans Saints won the Super Bowl.
e) c) and (d) are both correct
40.
One primary difference working with categorical logic and truth-functional logic is that:
a)
b)
c)
d)
In categorical logic we represent claims as variables such as P and Q but in truth-functional
logic we do not use variables.
In categorical logic we represent classes as variables such as P and Q but in truth-functional
logic we do not use variables.
In categorical logic we represent claims as variables such as P and Q but in truth-functional
logic we represent “states of the world” as variables.
In categorical logic we represent classes as variables such as P and Q but in truth-functional
logic we represent claims as variables.
41. Paul claims that he did a categorical logic proof by both the Venn Diagram method and the Rules
Method and in one he got the result that the argument was valid but with the other, he got the result that the
argument was invalid. Dottie suggested to him that one of the proofs must be wrong. Your opinion is:
a) Dottie is right. The two methods always give the same results.
b) Paul might have done the proofs correctly, but it is not likely. The two methods
almost always give the same result but not always.
c) Paul may be right. The answer depends on context and interpretation frequently.
d) Paul is right only if he and Dottie translated the premises the same way.
e) Paul is likely right. These are two different methods and their results are usually very
different.
42. Consider the conditional claim in T-F logic: If Justin would have brought enchiladas (or whatever it was
he was eating) for all to class, we would have enjoyed it. But of course, we all know that he did not. In the
truth table for the conditional operation in T-F Logic, if the antecedent is false, the result of the conditional is:
a) sometimes true, sometimes false
b) always false
c) always true
d) undetermined
e) none of the above
43. Mary claims that being home-schooled was a great experience. Sarah said she did not like being
home-schooled. Based on this, what clearly must a critical thinker conclude?
a. Mary is exercising wishful thinking.
b. Sarah is exercising rationalization.
c. Home schooling doesn’t work for half of the students that are home schooled in the
United Sates today.
d. This is an example of a false dilemma logical fallacy.
e. None of the above.
44. Kim suggested that rhetoric is often “good.” She said it is a very effective way to make an angry
customer forget their complaint at work and sometimes it is a good way to resolve an issue with her kids or
get them motivated to do their school work. As a critical thinker, what might we say?
a)
b)
c)
d)
e)
No, rhetoric is always wrong and hurtful and morally repugnant.
No, Kim is wrong. Rhetoric never helps anyone achieve any objectives.
Kim is probably right. Rhetoric can be a good premise for constructing a good
argument.
Kim is both right and wrong. Rhetoric can be useful to achieve certain aims, but
it still is never useful in any way when we are trying to think critically.
Kim may be right if she clarifies what she means by “good”, but regardless what
use rhetoric can serve for various aims including perhaps motivating someone to
think critically at times, it is NEVER actual support for an argument.
45. A claim is “subjective” if:
a. it is somebody's opinion.
b. no premises are given for the claim.
c. it is full of rhetoric
d. it is impossible in principle to give a logical argument for it.
e. no one knows if it is true or not.
46. The instructor was a bit hyperbolic and perhaps even crazy in the class by insisting that the word “proof”
be used only as the result of a valid, deductive argument and not as a term referring to “good evidence” in
an inductive argument. Everyone of course realized that both definitions are acceptable definitions
depending on the context. By being “borderline” hyperbolic, the instructor:
a)
b)
c)
d)
e)
definitely wanted to convince us that Webster is WRONG!
wanted to convince us that his definition was “better” than any other.
wanted to convince us that we should stop using the term in everyday life as we do.
wanted to suggest to us that we need to be more aware of the difference between
deductive and inductive arguments and the nature of evidence vs. logical form.
Who knows? When someone uses hyperbole, they are just being crazy and there is
no way to figure out what they mean.
47-49. (3 points) Propose a strong inductive argument for someone’s belief that they should get a degree
at Metropolitan Community College. What is the issue you are addressing? Clearly state if there is
ambiguity in this issue. Be sure your claim is clear and the argument has all the necessary elements.
Identify whether the claim is factual or normative, and evaluate how strong the argument is. If I proposed a
counter-example to your argument, would that make it weaker? Try to imagine a possible an argument with
premises that someone might make to refute your argument? If he makes a good argument does that mean
your argument is NOT good? Could you both be right about your claim?
One possible way to answer the question:
The question is ambiguous in regard to what issue may be being raised here. Perhaps the issue
is whether the student should get a degree at Metro vs. “just taking some courses at Metro,” Or
perhaps the issue is whether the student should get a degree at Metro before going to another
school to get a degree. That ambiguity needs to be clarified. For purposes of my argument, I will
take the issue to be whether a student should get a degree at Metro BEFORE transferring to a 4year degree program at another school. My claim will be that a particular student, call him Jack,
should do so. Thus, my argument is a normative argument. It is prescribing an action Jack
should take.
My premises are: 1) It is likely that the degree at Metropolitan will better prepare Jack for his
eventual 4-year studies (factual premise); 2. If Jack fails to complete his 4-year studies, the
tangible degree that he has from Metro will provide him a better resume than a series of classes
without any degree from two schools (factual premise) and 3) Jack should do what will give him a
better chance of success in life. (normative premise). I believe this is a moderately strong
argument. A counter-argument (that is, an argument for the contradictory claim) could be that: 1)
Jack is already fully prepared to do well in his 4-year studies, and 2: Jack has every intention of
completing his four-year program.
In this case, the premises given in the counter-argument when added to my original argument
seems to make the likelihood that my conclusion is right LESS PROBABLE and thus has made
my argument weaker. I must re-evaluate how strong my argument seems to me now. Probably I
need to seek out further evidence in order to make a better argument. What is the likelihood that
Jack will not finish his 4-year degree? How prepared IS Jack right now to begin those studies?
Nonetheless, the claim that Jack should finish his degree at Metro is an objective claim and
therefore both arguments can not ultimately be right,
50. (If you miss this question, you fail the course!!! …. Well, not really but maybe you should …..)
You overhear the instructor make the following comment, “After the last Congressional election, it is clear we
no longer live in the United States of America. We live in the “United States of Rhetoric.” A good critical
response would be:
a)
b)
c)
d)
e)
“He’s the teacher, so I guess I gotta believe it.”
“I know he’s the teacher, but as a critical thinker myself, I know that is hyperbole and am not
even sure what his claim is.”
“It is a good argument, but I am still not sure he is right.”
“It is just subjective anyway. He can believe that if he wants to, I suppose, but I don’t myself.”
“I can’t believe the idiot said such a thing. It just shows how ridiculous the class was.”