Module 2, Lesson 2 - SkeletalOutline

PHI 1100 MODULE 2, LESSON 2 SKELETAL OUTLINE ADDITIONAL FORMS OF SENTENTIAL ARGUMENTS & RELATED FALLACIES Important Concepts: - Disjunction Inclusive “or” - Exclusive “or” Truth Table - Disjunctive Syllogism Hypothetical Syllogism - Constructive Dilemma Destructive Dilemma - False Dilemma 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? Additional connectives (terms used to form compound sentences)— expressed in english by “or,” “and,” as well as “if and only if” 4. What are the two important principles of Sentential Logic? 1. The principle of the excluded middle: every sentence is either true or false. 2. The 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.

2 If p, then q If q, then r --------------- If p, then r 6. What is the logical definition of dilemma? Another meaning of dilemma refers to a conditional form of argument with a premiss that states alternatives. 7. What is a constructive dilemma? What is its logical form?_ constructive dilemma is similar to affirming the antecedent. It has two conditional premisses, a third premiss that states that one or the other of the antecedents is true, and a conclusion that states that one or the other of the consequents is true. If p, then q If r, then s p or r -------------- q or s 8. What is a disjunction? compound sentences that are connected by or are called disjunctions. 9. What sense of “or” do logicians use and what does this mean? some disjunctions are exclusive, in which case or means “one or the other, but not both. Other disjunctions are inclusive. In these sentences, or means “one or the other, or possibly both.” 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? Another version of the dilemma, called the destructive dilemma, is closely related to denying the consequent (modus tollens). 12. Explain the fallacy: false dilemma - when presented with two choices, we often consider the consequences of each and reason about them using one or another of the dilemma forms. to avoid the fallacy of black-and-white thinking, we must be careful to avoid being misled into thinking that the number of alternatives is always limited to two.

4 Hypothetical syllogism, this statement draws logical conclusions based on conditional relationships. 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. Disjunctive Syllogism, this statement illustrates disjunctive syllogism, where the truth of one disjunct leads to the negation of the other. 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. Constructive dilemma, the statement illustrates the difficult predicament challenging the individual in their preparation for the exam. 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. Disjunctive syllogism, this statement presents two mutually exclusive options and concludes the truth of one based on the falsity of the other.