Philosophy 103 Linguistics 103 Yet still even further

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

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

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

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

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

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

Modus Ponens Example If P then Q, P --- Therefore Q If Peter is from Ohio then Peter is an American Peter is from Ohio --- Therefore Peter is an American.

Modus Tollens Example If P then Q Q is false Therefore P is false If Paul is a potter then Paul has worked with clay Paul has not worked with clay. Therefore Paul is not a potter.

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

Disjunctive Syllogism Example P or Q P is false Therefore Q Pizza is yummy or Quiche is manly. Pizza is not yummy. Therefore Quiche is manly.

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)

Hypothetical Syllogism Example If P then Q If Q then R Therefore If P then R If Pigs fly then Cows kiss. If Cows kiss then Otters sing. Therefore If Pigs fly then Otters sing

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

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

The Presocratic Reductio 1. Everything is Water (Thales’ Assumption) 2. If everything is water then the universe contains an infinite amount of water and nothing else. (From 1) 3. If there is more water than fire in a place, then the water extinguishes the fire. (observed truth) 4. We observe fire. (observed truth) 5. Where we observe fire there must be more fire than water. (from 3 & 4) 6. Therefore, everything is water and something is not water (Contradiction from 5 and 1) 7. Thus, (1) is false.

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

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

Affirming the Consequent If P then Q Q is true Therefore P 1. If it rained last night then the grass is wet 2. The grass is wet. 3. Therefore, it rained last night.

Denying the Antecedent If P then Q P is false Therefore Q is false 1. If Tom is not hungry then Tom ate lunch 2. Tom is Hungry 3. Therefore Tom did not eat lunch.

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

Illicit Disjunctive Syllogism P or Q P is true Therefore not-Q John is Tim’s father or Sally is Tim’s mother John is Tim’s Father Therefore Sally is not Tim’s mother

Illicit Hypothetical Syllogism If P then not-Q If Q then not-R Therefore If P then not-R 1. If I like fish then I won’t eat beef 2. If I eat beef then I won’t eat cheese 3. Therefore, If I like fish then I won’t eat cheese.

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): a) Counter-example (proof of invalidity) b) Formal Analysis

Counter-Example Test for Validity 1) Start with a given argument 2) Determine its form (Important to do correctly – best to isolate conclusion first) 3) Formulate another argument: a) With the same form b) with true premises c) with a false conclusion.

An example counter-example… 1. If Lincoln was shot, then Lincoln is dead. 2. Lincoln is dead. 3. Therefore, Lincoln was shot. The FORM IS: 1. If Lincoln was shot, then Lincoln is dead. 2. Lincoln is dead. 3. Therefore, Lincoln was shot. 1. IF --P-- , THEN --Q--. 2. --Q-3. Therefore -- P--

NEXT: We go from FORM back to ARGUMENT… 1. IF --P-- , THEN --Q--. 2. --Q-3. Therefore -- P- 1. IF Ed passes Phil 101, then Ed has perfect attendance. 2. Ed has perfect attendance. 3. Therefore, Ed Passes Phil 101

NO WAY! Ed’s Perfect Attendance does NOT make it necessary that Ed pass PHIL 101. SO: Even if it is true that 1. IF Ed passes Phil 101, then Ed has perfect attendance. 2. . . AND that. . Ed has perfect attendance.

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.

This is ED…

Another Example? 1. All fruit have seeds 2. All plants have seeds 3. Therefore, all fruit are plants Form: All F are S All P are S Therefore All F are P

Another example…. cont. Form: All F are S All P are S Therefore All F are P 1. All Balls (F) are round (S). 2. All Planets (P) are round (S). 3. Therefore, All Balls (F)are (P)lanets.

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 counterexample, but no human may be able to find it.