CHAPTER 2
MORE ON DEDUCTION AND INDUCTION
I.
Brief Chapter Outline
1. Deductive Validity
Exercise 2-1
2. Deductive Invalidity
Exercise 2-2
3. Syllogisms
Exercise 2-3
4. Indirect Proofs
5. Tautologies, Contradictions, and Contingent Statements
Exercise 2-4
6. Inductive Validity (Correctness) and Invalidity (Incorrectness)
Reasoning by Analogy
Statistical induction
Higher-level Inductions
Reasoning to Causal Connections
Concatenated inductions
Exercise 2-5
7. A Misconception About Deduction and Induction
8. Reasoning Cogently Versus Being Right in Fact
Summary of Chapter 2
II.
List of Key Terms
Affirming the consequent
Analogy
Categorical proposition
Causes
Concatenated
Contingent
Contradiction
Denying the antecedent
Disjunctive syllogism
Higher-level induction
Hypothetical syllogism
Indirect proof
Induction by enumeration
Major term
Middle term
Minor term
Modus ponens
Modus tollens
Mood
Particular affirmative
Particular negative
Predicate class
Proof
Reductio ad absurdum
Statistical induction
Structure
Subject class
Syllogisms
Tautology
Thesis
Universal affirmative
Universal negative
III.
Chapter Summary
In this Chapter the authors outline various different forms of argument, including modus
tollens, modus ponens, hypothetical syllogism, and disjunctive syllogism. They then
outline the concepts of validity and invalidity, and outline the fallacies of denying the
antecedent and affirming the consequent. They then discuss further traditional syllogistic
logic, noting that categorical propositions assert or deny relationships between a subject
class and a predicate class; these assertions or denials give rise to four kinds of
categorical propositions. Having discussed syllogistic logic the authors then discuss
indirect reasoning, and then the definitions of tautologies, contradictions, and contingent
statements, offering examples of each.
The authors then move from deductive logic to discuss inductive validity and
invalidity. Here, they outline various types of induction, including induction by
enumeration, reasoning by analogy, statistical induction, higher-level inductions,
reasoning to causal connections, and concatenated inductions. They then note that it is
not true that in deductive reasoning we go from the general to the particular, while in
inductive reasoning we go from the particular to the general. They then discuss the
difference between reasoning cogently and being right in fact.
IV.
Practice Questions
A. Objective Multiple Choice
1. “If A, then B. A. Therefore B” is an example of the argument form
a. Modus ponens
b. Modus tollens
c. Hypothetical syllogism
d. Disjunctive syllogism
2. “If A, then B. Not B. Therefore, Not A” is an example of the argument form
a. Modus ponens
b. Modus tollens
c. Hypothetical syllogism
d. Disjunctive syllogism
3. “If A then B. If B then C. Therefore, if A, then C” is an example of the
argument form
a. Modus ponens
b. Modus tollens
c. Hypothetical syllogism
d. Disjunctive syllogism
4. “A or B. Not A. Therefore, B” is an example of the argument form
a. Modus ponens
b. Modus tollens
c. Hypothetical syllogism
d. Disjunctive syllogism
5. “If A then B. Not A. Not B” is an example of the fallacy of
a. Denying the antecedent
b. Affirming the consequent
c. Hypothetical syllogism
d. Disjunctive syllogism
6. “If A then B. B. Therefore, A” is an example of the fallacy of
a. Denying the antecedent
b. Affirming the consequent
c. Hypothetical syllogism
d. Disjunctive syllogism
7. A categorical proposition is
a. An unconditional offer
b. A subject-predicate proposition
c. A syllogistic proposition
d. A conditional offer
8. The predicate of the conclusion in a syllogism is the syllogism’s
a. Major term
b. Minor term
c. Middle term
d. Propositional term
9. The subject of the conclusion in a syllogism is the syllogism’s
a. Major term
b. Minor term
c. Middle term
d. Propositional term
10. The term that occurs in each premise but not in the conclusion is the
syllogism’s
a. Major term
b. Minor term
c. Middle term
d. Propositional term
11. “Some S are P” is a
a. Universal affirmative proposition
b. Universal negative proposition
c. Particular affirmative proposition
d. Particular negative proposition
12. “No S are P” is a
a. Universal affirmative proposition
b. Universal negative proposition
c. Particular affirmative proposition
d. Particular negative proposition
13. “All S are P” is a
a. Universal affirmative proposition
b. Universal negative proposition
c. Particular affirmative proposition
d. Particular negative proposition
14. A particular negative proposition is an
a. A proposition
b. E proposition
c. I proposition
d. O proposition
15. A universal affirmative proposition is an
a. A proposition
b. E proposition
c. I proposition
d. O proposition
16. A universal negative proposition is an
a. A proposition
b. E proposition
c. I proposition
d. O proposition
17. “No dogs are smart” is an example of a
a. Universal affirmative proposition
b. Universal negative proposition
c. Particular affirmative proposition
d. Particular negative proposition
18. “Some parrots are not linguists” is an example of an
a. A proposition
b. E proposition
c. I proposition
d. O proposition
19. A contradiction is a statement
a. That is necessarily true
b. That can be true or false
c. That is neither true nor false
d. That is necessarily false
20. “Either you will pass this class or you won’t pass this class” is an example of
a. A tautology
b. A contradiction
c. A contingent statement
d. A false statement
B. True/False
1. In induction by enumeration, we reason from the fact that all As observed so far
have been Bs to the conclusion that all are Bs.
2. In induction by enumeration, a greater sample size yields lower probability.
3. More than one counterexample is needed to shoot down induction by
enumeration.
4. Higher-level inductions are used to evaluate those that are more general.
5. Statistical induction is a weak form of induction.
6. Concatenated reasoning joins together inductions and deductions to find a pattern.
7. If you reason correctly you will always get a true conclusion.
8. If you have a true conclusion you will have reasoned correctly.
9. Deductively valid reasoning progresses from the general to the particular.
10. It is not the case that inductively valid reasoning goes from the particular to the
general.
11. “No As are Bs” is a universal negative statement.
12. “Some Ps are Qs” is a universal affirmative statement.
13. Denying the antecedent is a fallacy.
14. “If A, then B. B. Therefore, A” is an example of modus tollens.
15. When we reason inductively we are often looking for causes.
C. Fill-in-the-Blanks
1. An argument that doesn’t have a deductively valid form is said to be _____.
2. The fallacy of affirming the consequent is of the form _____ .
3. A hypothetical syllogism is not a true ____ .
4. A categorical proposition expresses a relationship between a _____ class and a
____ class.
5. “No men are mortal” is a ______ proposition.
6. Every syllogism has _____ terms.
7. Indirect proofs are sometimes called ________ proofs.
8. “Barry Bonds didn’t take steroids” is a ______ statement.
9. Only _____ resemblances count in drawing correct analogies.
10. Unfortunately, we can reason correctly and get a ______ conclusion.
D. Essay Questions
1. Why were hypothethical syllogisms not considered to be syllogism by Aristotle?
In answering this question you should explain Aristotle’s reasoning, and not
merely state his view. Does this affect their potential validity in any way?
2. Provide an example of concatenated reasoning that draws on at least four different
types of reasoning process, and evaluate it for correctness.
3. It is often claimed that deductive reasoning moves from the general to the
particular, while inductive reasoning moves from the particular to the general. Do
you agree with this view? Explain your answer, taking care to explain why some
people might be persuaded by this account of deductive and inductive reasoning.
4. If it is possible for us to reason correctly and yet be wrong in fact, what is the use
of reasoning at all? Explain your answer, and provide examples to illustrate it.
5. Provide an example of two different deductively invalid arguments, and explain
where they go wrong.
V.
Additional Sources for Study and Research
A. InfoTrac Search Terms
Analogy, Antecedent, Causality, Claims, Disjunctive Syllogism, Fallacies,
Hypothetical Syllogism, Induction, Inductive Reasoning, Necessity, predicate,
Premise, Probability, Medieval Logic, Reasoning, Syllogism, Tautology, True, Valid.
B. Internet sites
Wikipedia; inductive reasoning
http://en.wikipedia.org/wiki/Inductive_reasoning
Wikipedia; deductive reasoning
http://en.wikipedia.org/wiki/Deductive_reasoning
Sparknotes: inductive and deductive reasoning
http://www.sparknotes.com/math/geometry3/inductiveanddeductivereasoning/section1.ht
ml
Informal fallacies
http://www.drury.edu/ess/Logic/Informal/Overview.html
VI.
Answer Key
A. Objective Multiple Choice
1. a
2. b
3. c
4. d
5. a
6. b
7. b
8. a
9. b
10. c
11. c
12. b
13. a
14. d
15. a
16. b
17. b
18. d
19. d
20. a
B. True/False
1.T
2. F
3. F
4. F
5. F
6. T
7. F
8. F
9. F
10. T
11. T
12. F
13. T
14. F
15. T
C. Fill-in-the-Blanks
1. Deductively invalid
2. If A, then B, B, therefore A
3. syllogism
4. subject/predicate
5. universal negative
6. three
7. reductio ad absurdum
8. contingent
9. relevant
10. false