Disjunctive & Hypothetical Syllogisms

1. Disjunctive & Hypothetical Syllogisms Alternatives, conditions, and validly choosing.

2. The Three Principal Kinds of Syllogisms

3. Review: Categorical Syllogism

4. Differences

5. Disjunctive Syllogisms • The case of the logical dog PATH A PATH B PATH C

6. Disjunctive Syllogisms STRUCTURE Either P is true or Q is true. P is not true. Therefore Q is true. *disjunctional proposition, disjuncts

7. A Valid Disjunctive Syllogism • The disjuncts are not both false or both true. The meaning of “or” [inclusive and exclusive] • Example: He was captured either dead or alive. He was not captured dead. Therefore, he was captured alive.

8. A Valid Disjunctive Syllogism 2. The alternatives must be mutually exhaustive. • Example: You are either a Catholic or an Aglipayan. You are not a Catholic. Therefore, you are an Aglipayan. = the fallacy of possibilities not exhaustive

9. A Valid Disjunctive Syllogism 3. The alternatives must be mutually exclusive. • Example Juan is either stupid or dishonest. Juan is not stupid. Therefore, Juan is dishonest. = the fallacy of alternatives not mutually exclusive

10. An objection • Disjunctive • Either P is true or Q is true. • P is not true. • Therefore Q is true. • Either Smith is in New York or Smith is in Paris. • Smith is in New York. • Therefore Smith is not in Paris. The disjunction plays no role in the argument. The conclusion is based from the second categorical premise with the unexpressed additional premise being the obviously true proposition that “Smith cannot be both in New York and in Paris.” In disjunctive form, it can be stated as, =>Either Smith is not in New York or Smith is not in Paris. P is true. Therefore Q is not true.

11. Hypothetical Syllogisms • contain one or more compound, hypothetical (or conditional) propositions • affirms that if one of its components (the antecedent) is true => then the other of its components (the consequent) is true

12. Conditional (or hypothetical) Proposition • has two component propositions: • the antecedent • follows the “if” • states the condition or limitation • the consequent • comes after the “then” • states the result • asserts something as true on condition that the “if clause” is true.

13. Conditional (or hypothetical) Proposition • This kind of compound proposition can be further categorized according to the nature of the propositions they contain. • Pure hypothetical • Mixed hypothetical

14. Pure Hypothetical Syllogism • contains conditional propositions only • The first premise and the conclusion have the same antecedent, the second premise and the conclusion have the same consequent, and the consequent of the first premise is the same as the antecedent of the second premise. • If P is true, then Q is true. • If Q is true, then R is true. • Therefore if P is true, then R is true. Same consequent Same antecedent

15. Pure Hypothetical Syllogism

16. Mixed Hypothetical Syllogism • 1 conditional premise + 1 categorical premise • two valid forms: Modus Ponens & Modus Tollens 1. Modus Ponens • in the affirmative mood • first premise is a statement of alternatives. In this form, the categorical premise affirms the antecedent of the conditional premise and the conclusion affirms its consequent. If P is true, then Q is true. Pis true. Therefore Q is true

17. Mixed Hypothetical Syllogism

18. Form Mixed Hypothetical Syllogism • If P is true, then Q is true. • P is true. • Therefore Q is true • invalid form: • If Bacon wrote Hamlet, then Bacon was a great writer. • Bacon was a great writer. • Therefore Bacon wrote Hamlet. its categorical premise affirms the consequent, rather than the antecedent, of the conditional premise. => the fallacy of affirming the consequent. Q is true. P is true.

19. Mixed Hypothetical Syllogism • the fallacy of affirming the consequent. Another example: • If I have the flu, then I have a sore throat. • I have a sore throat. • Therefore, I have the flu.

20. Mixed Hypothetical Syllogism 2. Modus Tollens • categorical premise denies the consequent of the conditional premise, and the conclusion denies its antecedent If P is true, then Q is true. Q is false. Therefore P is false.

21. Mixed Hypothetical Syllogism

22. Mixed Hypothetical Syllogism • Invalid form: • If Pedro marries Juana, she will be happy. • Pedro will not marry Juana. • Therefore, Juana will not be happy. • its categorical premise denies the antecedent, rather than the consequent, or the conditional premise. • the fallacy of denying the antecedent.

23. 4-Square http://faculty.unlv.edu/beisecker/Courses/Phi-102/HypotheticalSyllogisms.htm

25. *Conjunctive Syllogism • Contains a CONJUNCTIVE PROPOSITION (and) NEGATIVE CONJUNCTIVE SYLLOGISM - Denies the possibility of 2 alternatives • If not "P and Q" • Then, either "not P" or "not Q" or "not P and not Q" • Ex: You cannot serve God and the devil at the same time. You cannot both be in two place at the same time.

26. “Both and…” • "P and Q" is true if and only if "P" is true, and "Q" is true. - the only kind that yield two conclusions (or more) from only one premise. - we can separate them and affirm each as a separate conclusion. If both terms together are true, then each one separately is true also. 1. Roses are red and violets are blue. 2. Roses are red. 3. Violets are blue.