Dr. Robert Barnard

2. Philosophy 103Linguistics 103Yet, still, even further more, expanded,Introductory Logic: Critical Thinking Dr. Robert Barnard

3. Last Time: • Definitions • Lexical • Theoretical • Precising • Pursuasive • Logical Form • Form and Validity

4. Plan for Today • Deductive Argument Forms • Formal Fallacies • Counter-Example Construction

5. Validity and Form • DeductiveValidity – IF the premises are true THEN the conclusion MUST be true. • DeductiveSoundness – the deductive argument is valid AND premises are all true • Form - The structure of an argument. Validity is a Property of Form.

6. Common Deductive Logical Forms • Modus Ponens • Modus Tollens • Disjunctive Syllogism • Hypothetical Syllogism • Reductio Ad Absurdum

7. Common Logical Forms • Modus Ponens If P then Q, P --- Therefore Q • Modus Tollens If P then Q, Q is false --- Therefore P is false

8. Modus Ponens Example

9. Modus Tollens Example

10. Common Logical Forms • Disjunctive Syllogism P or Q, P is false --- Therefore Q • Hypothetical SyllogismIf P then Q , If Q then R--- Therefore If P then R

11. Disjunctive Syllogism Example

12. Inclusive OR vs Exclusive OR Assume: Tom is a Lawyer or Tom is a Doctor If Tom is a Lawyer does that require that he is not a Doctor? Inclusive-OR: No - (Lawyer and/or Doctor) Exclusive- OR: Yes - ( Either doctor or lawyer, not both)

13. Hypothetical Syllogism Example

14. Common Forms • Reductio Ad Absurdum(Reduces to Absurdity)a) Assume that P b) On the basis of the assumption if you can prove ANY contradiction, then you may infer that P is false Case of : Thales and Anaximander

15. Thales and Anaximander • Arché - Table of Elements - Thales: Water - Anaximander: Aperion

16. The Presocratic Reductio • Everything is Water (Thales’ Assumption) • If everything is water then the universe contains an infinite amount of water and nothing else. (From 1) • If there is more water than fire in a place, then the water extinguishes the fire. (observed truth) • We observe fire. (observed truth) • Where we observe fire there must be more fire than water. (from 3 & 4) • Therefore, everything is water and something is not water (Contradiction from 5 and 1) • Thus, (1) is false.

17. Common Formal Fallacies • Affirming the Consequent • Denying the Antecedent • Illicit Hypothetical Syllogism • Illicit Disjunctive Syllogism

18. Common Formal Fallacies • Affirming The Consequent If P then Q, Q --- Therefore P • Denying the Antecedent If P then Q, P is false --- Therefore Q is false

19. Affirming the Consequent

20. Denying the Antecedent

21. Common Formal Fallacies • Illicit Disjunctive Syllogism -P or Q, P is true -- Therefore not-Q -P or Q, Q is true -- Therefore not-P • Illicit Hypothetical Syllogism(*)If P then not-Q , If Q then not-R--- Therefore If P then not-R * - there is more than one form of IHS

22. Illicit Disjunctive Syllogism

23. Illicit Hypothetical Syllogism

24. Testing for Validity The central question we ask in deductive logic is this: IS THIS ARGUMENT VALID? To answer this question we can try several strategies (including): • Counter-example (proof of invalidity) • Formal Analysis

25. Counter-Example Test for Validity • Start with a given argument • Determine its form (Important to do correctly – best to isolate conclusion first) • Formulate another argument: a) With the same form b) with true premises c) with a false conclusion.

26. An example counter-example… • If Lincoln was shot, then Lincoln is dead. • Lincoln is dead. • Therefore, Lincoln was shot. The FORM IS: • If Lincoln was shot, then Lincoln is dead. • Lincoln is dead. • Therefore, Lincoln was shot. • 1. IF --P-- , THEN --Q--. • --Q-- • Therefore -- P--

27. NEXT: We go from FORM back to ARGUMENT… • IF --P-- , THEN --Q--. • --Q-- • Therefore -- P-- • IF Ed passes Phil 101, then Ed has perfect attendance. • Ed has perfect attendance. • Therefore, Ed Passes Phil 101

28. NO WAY! Ed’s Perfect Attendance does NOT make it necessary that Ed pass PHIL 101. SO: Even if it is true that • IF Ed passes Phil 101, then Ed has perfect attendance. • ..AND that..Ed has perfect attendance.

29. IT DOES NOT FOLLOW THAT ED MUST PASS PHIL 101! • It is possible to have perfect attendance and not pass • It is also possible to pass and have imperfect attendance • This shows that the original LINCOLN argument is INVALID.

30. This is ED…

31. Another Example? • All fruit have seeds • All plants have seeds • Therefore, all fruit are plants Form: All F are S All P are S Therefore All F are P

32. Another example….cont. Form: All F are S All P are S Therefore All F are P • All Balls (F) are round (S). • All Planets (P) are round (S). • Therefore, All Balls (F)are (P)lanets.

33. Formal Evaluation? The counter-example test for validity has limits. • Counter-Examples should be obvious. • Our ability to construct an Counter-Example is limited by our concepts and imagination. • Every invalid argument has a possible counter-example, but no human may be able to find it.