Deductive Validity

1. Deductive Validity • Truth preserving: The conclusion logically follows from the premises. It is logically impossible for the premises to be true and the conclusion false, because the conclusion expresses what is implied by the combination of premises. If the premises are true, the conclusion is true. • Because validity is a matter of form, any argument that exhibits the appropriate form is valid, regardless of whether the statements it contains are true. • It is not necessary for the establishment of validity to ascertain the truth of the premises.

2. the Valid argument • May consist in • false premises and a false conclusion, • False premises and a true conclusion, • True premises and a true conclusion, • Yet still be valid in virtue of its form. • But, it is impossible for a Valid argument to have true premises and a false conclusion!

3. MODUS PONENSIf p, then q.p.Therefore, q. If the soup is green (p), then it is poison (q). The soup is green (p). Therefore, the soup is poison (q).

4. MODUS TOLLENSIf p, then q.not q.Therefore, not p. • If mind is immortal (p), then mind is independent of brain activity (q). • Mind does depend on brain activity (not q). • Therefore, the mind is not immortal (not p).

5. HYPOTHETICAL SYLLOGISMIf p, then q.If q, then r.Therefore, if p then r. • If the Fed raises rates (p) , then fewer qualify for loans (q). • If fewer qualify for loans (q) , then home sales plummet (r). • Therefore, if the Fed raises rates (p), then home sales will plummet (r).

6. DISJUNCTIVE SYLLOGISMEither p or q.Not p.Therefore, q. • Either I was there (p) or I failed the test (q). • I was not there (~p). • Therefore, I failed the test (q).

7. Sound Argument • While Validity is a desired condition for a good argument, by itself it is not sufficient. • We also require that an argument be sound: • 1. identify premises and conclusion, • 2. determine whether the argument form is valid. • 3. determine truth of premises.

8. A test for Invalidity The method of counter example • Determine whether there is another argument with the same form that will allow the premises to be true and the conclusion false. If so, the argument is invalid.

9. Some Invalid Argument Forms • Affirming the Consequent • If p, then q. • q. • Therefore, p. • If Houston is the capital of Texas (p), Then Houston is in Texas (q). • Houston is in Texas (q). • Therefore, Houston is the capital of Texas (p)

10. What’s wrong with affirming the consequent • The form inadmissibly allows for the premises to be true and yet the conclusion false! • So any argument with this form does not provide a good reason for accepting its conclusion.

11. Some Invalid Argument Forms • Denying the Antecedent • If p, then q. • Not p. • Therefore , not q. • Imagine a situation in which the premises are true and the conclusion false. • If Bob is a bachelor (p), then male (q). • Bob’s not a bachelor (not p). • Therefore, Bob is not male (not q).

12. Some Invalid Argument Forms • Affirming a Disjunct • Either p or q. • P. • Therefore, not q. • Logical or is interpreted Inclusively . . . either p, or q, or both! • Either the battery is dead (p) or I’m out of gas (q). • The battery is dead (p). • Therefore, I’m not out of gas (~q). Invalid • Can’t rule out the possibility that both conditions obtained.

13. Informal Fallacies. • Unacceptable Premises • Begging the Question • Merely assumes what it purports to show. • He’s a psychic. Therefore he’s able to read minds. • But, it’s a vicious circle. • False Dilemma • Presumes a dichotomy when multiple option are possible. • Science has no explanation or it’s a miracle. • But, Additional option – natural but not yet explained!

14. Informal Fallacies. • Irrelevant Premises • Equivocation • Terms used ambiguously, i.e., differently from use to use. • Man is a rational animal. (man used generically for a species) • No woman is a man. ( man used to specify a sex) • Therefore, no woman is rational. • Composition • Is what’s true of the parts true of the whole ? • Each chemical element is lifeless • Therefore no chemical composition accounts for life. • But the sum of parts may have novel new properties!

15. Informal Fallacies. • Division • Is what’s true of the whole true of the parts? • Argumentum ad Hominem • Argument P is false because Gov. Perry holds it’s true and Perry is just a wanker. • But, the name-calling has nothing to do with the soundness of P. • Genetic Fallacy • I saw argument P written in a toilet stall so P is false. • But, we need not consider the source provided P is sound.

16. Informal Fallacies. • Appeal to Authority • Argument P is true because it’s in the Book. • But, only the soundness of P provides acceptability of P not who published it. • Appeal to the Masses • Everybody said there name isn’t Sonia. So you can’t really be Sonia. • But, being unpopular doesn’t make it go away.

17. Informal Fallacies. • Appeal to Tradition • Traditionally our church grows by killing competitors. So, kill competitors. • But, sound argument guarantees the truth of its outcome, whereas tradition does not guarantee its outcome.

18. Informal Fallacies. • Appeal to Ignorance • Using a lack of disproof as if it was a positive proof. • There’s no proof you cheated on the test. So, Cheating is ruled out. • Using a missing counter proof as failure of opposing view. • You haven’t proved he’s not dead. So, dead he must be.

19. Informal Fallacies. • Appeal to Fear. • Affirm argument P or X results, where x is a feared circumstance.

20. Informal Fallacies. • Insufficient Premises • Hasty Generalization • Jumping to conclusions • Bad Deduction: Some x is y, therefore All x is y. • Bad Induction: small sample x is y, therefore All x is y. • Faulty Analogy • Any two things may have some features in common. Consequently, an argument from analogy can be successful only if the dissimilarities are insignificant. • False Cause • Post hoc, ergo propter hoc • After this, therefore because of this. • Night follows day doesn’t mean night causes day.