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Introduction to Deductive Logic and Fallacies in Critical Thinking

This session covers fundamental concepts in introductory logic with a focus on critical thinking. Topics include various definitions of logic, logical forms, validity, and soundness of deductive arguments. Key deductive argument forms such as Modus Ponens, Modus Tollens, Disjunctive Syllogism, and Hypothetical Syllogism are explored, alongside common formal fallacies like Affirming the Consequent and Denying the Antecedent. You will learn to evaluate arguments for validity using counter-example construction and understand the distinction between inclusive and exclusive OR.

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Introduction to Deductive Logic and Fallacies in Critical Thinking

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

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

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

  4. 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.

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

  6. 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

  7. Modus Ponens Example

  8. Modus Tollens Example

  9. 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

  10. Disjunctive Syllogism Example

  11. 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)

  12. Hypothetical Syllogism Example

  13. 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

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

  15. 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.

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

  17. 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

  18. Affirming the Consequent

  19. Denying the Antecedent

  20. 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

  21. Illicit Disjunctive Syllogism

  22. Illicit Hypothetical Syllogism

  23. 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

  24. 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.

  25. 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--

  26. 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

  27. 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.

  28. 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.

  29. This is ED…

  30. 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

  31. 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.

  32. 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.

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