Module 2, Lesson 2 - SkeletalOutline (1)
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PHI 1100
MODULE 2, LESSON 2
SKELETAL OUTLINE
ADDITIONAL FORMS OF SENTENTIAL ARGUMENTS & RELATED FALLACIES
Important Concepts:
Notes on Text (Salmon’s Introduction to Logic and Critical Thinking
, sixth edition)
I.
Chapter 8, VI: Additional Forms of Sentential Arguments (pp. 317-326)
1.
Write out the truth table for “if…then” (conditional sentence) p
q
If p, then q
True True
True
True False
False
False True
True
False False
True
2.
Write out the truth table for “not” (negation)
p
Not
p
True
False
False
True
3.
What are some of the other logical connectives that can be assigned truth-functional
definitions? "And","Or","If and only if" 4.
What are the two important principles of Sentential Logic? Principle of the excluded middle: Every sentence is either true or false and Principle of contradiction: No sentence is both true and false.
5.
Give an example of a hypothetical syllogism and the give its logical form (by using letters to stand for component sentences) If inflation can be controlled, then businesses will expand.
If businesses expand, then unemployment will decrease.
If inflation can be controlled, then unemployment will decrease.
Logical form:
If p, then q
If q, then r
If p, then r
2
6.
What is the logical definition of dilemma? A dilemma is a conditional form of argument with a premise that states alternatives.
7.
What is a constructive dilemma? What is its logical form? A constructive dilemma presents two conditional premises and a conclusion stating that one or the other of the consequents is true.
Logical form:
If p, then q
If r, then s
p or r
q or s
8.
What is a disjunction? A disjunction is a compound sentence formed by joining two sentences with "or," indicating that at least one of the sentences is true.
9.
What sense of “or” do logicians use and what does this mean? Logicians use the inclusive sense of "or," meaning that a disjunction is true whenever one or both of its components (disjuncts) is true.
10. Write out the truth table for “or” (disjunction)
p
q
p or
q
True
True True True False True False True True False
False False 11. What is a destructive dilemma? What is its form? A destructive dilemma presents two conditional premises and a conclusion stating that one or the other of the antecedents is false.
Form:
If p, then q
If r, then s
Not q or not s
Not p or not r
12. Explain the fallacy: false dilemma The fallacy of false dilemma occurs when only two options are presented as if they were the only ones available, neglecting other possible alternatives.
13. What is a disjunctive syllogism? What is its form? A disjunctive syllogism presents a disjunction as one premise and the denial of one of the disjuncts as the other premise, with the conclusion affirming the truth of the other disjunct.
Form:
p or q
Not q
Therefore, p
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14. Explain the fallacy: affirming a disjunct The fallacy of affirming a disjunct occurs when one disjunct of a disjunction is affirmed, leading to the conclusion that the other disjunct must be false, which is not necessarily the case
. 15. How can we symbolize an exclusive or without introducing a new logical connective (e-or)? An exclusive "or" can be symbolized using "or" and "and" as follows:
p or q, and not both p and q
16. Other Notes:
Practice Exercise - Exercise Set 8.6, Pt 1. (pp. 324-325)
Complete the following problems for your own practice. They will not be graded, but similar problems will appear on Assignment 3 and the Module 2 Test. (The answers to these problems can be found in your textbook on p. 470-471)
Instructions:
Which of the valid argument forms or fallacies discussed in this section best characterizes each of the following English-language arguments?
2. The government must either raise taxes or cut spending for education. If the government raises taxes, the citizens will be unhappy, but they will also be unhappy if spending for education is cut. So either way, the citizens will be unhappy.
Constructive dilemma This argument indeed fits the structure of a constructive dilemma, where two conditional statements lead to a disjunction. It suggests that either raising taxes or cutting spending will result in unhappy citizens.
4. If Lyme disease is recognized at an early stage, antibiotics can halt its progress. If antibiotics half the progress of the disease, the patient can recover completely. So if Lyme disease is recognized at an early stage, the patient can recover completely.
It presents a series of conditional statements that logically lead to a conclusion. Hypothetical syllogism
6. Either you buy a lottery ticket, or you won’t win the lottery. But surely you won’t win the lottery, so you’ll not buy a ticket.
It becomes an instance of affirming the consequent fallacy. It mistakenly concludes that not buying a lottery ticket leads to not winning the lottery. Affirming the consequent fallacy
8. If I stay up late to cram for the exam, I’ll do it poorly because I am so tired. If I don’t stay up late to cram, I’ll do poorly because I haven’t read the material. So it looks as if I’ll do poorly on the exam.
Two conditional statements leading to a disjunction. It suggests that either studying late and being tired or not studying late and being unprepared will both lead to doing poorly on the exam
. Constructive dilemma
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12. Either people must forego such amenities as personal automobiles, air conditionining, and consumption of large quantities of beef, or global warming will continue. But people are not willing to forego their present lifestyles, so global warming will be a fact of life.
While the structure of the argument resembles a disjunctive syllogism, it is noted that it may involve black-and-white thinking, implying that there are only two extreme options without considering potential middle grounds or alternative solutions.