Dr. Robert Barnard

2. Philosophy 103Linguistics 103Yet, still, Even further More and yet more, etc., ad infinitum,Introductory Logic: Critical Thinking Dr. Robert Barnard

3. Last Time: Venn Diagrams for Propositions Existential Import in Diagramming Traditional Square of Opposition

4. Plan for Today Review: Venn Diagrams for Propositions Modern Square of Opposition The Existential Fallacy

5. Today is DAY 10 • In 10 Days an embryonic Chick goes from nothing to this: HAVE YOU DEVELOPED AS MUCH IN the LAST 10 Days???

6. REVIEW: THE 4 TYPES of CATEGORICAL PROPOSITION

7. REVIEW: A, E, I, and O

8. Review: The Traditional Square of Opposition

9. Subalternation What is the relation between the UNIVERSAL and the PARTICULAR? • If All S is P, what about Some S is P? • If No S is P, what about Some S is not P? Subalternation claims that if the Universal is true, then the corresponding Particular is true.

10. TRADITIONAL A and E In Traditional Logic we need to capture the Existential Assumption: That everything we can name with a category term or description, exists! E A X X

11. Traditional vs. Modern Categorical Logic The KEY difference between Traditional (Aristotelian) and Modern (Boolean) categorical Logic is that Traditional Logic ASSUMES that category terms all refer to actual objects. Modern Logic does NOT make the Existential Assumption.

12. Thanks to: George Boole • English Mathematician and Grandfather of computer Science. • Wrote The Laws of Thought (1854) • Invented Boolean Algebra 1815-1864

13. Boole and the Existential Fallacy • Boole recognized that many Syllogistic Arguments assume that every category or class referred to is NON-EMPTY. • But it is possible to denote an EMPTY CLASS • What Happens to Categorical Logic if EMPTY CLASSES are allowed?

14. Traditional Square using Venn Diagrams X X The Existential Assumption allows the inference from Universal to Particular

15. Where is the Fallacy? Basically, the EXISTENTIAL FALLACY is this: • Deductive validity requires that it be IMPOSSIBLE to infer a FALSE CONCLUSION from TRUE PREMISES. • Reasoning by SUBALTERNATION always requires that the SUBJECT CLASS is non-empty. • It is POSSIBLE that a UNIVERSAL Proposition is true but has an empty SUBJECT CLASS • Therefore, it is possible to reason from True Premises to a false Conclusion by Subalternation. • So Subalternation is INVALID.

16. BUT Hurley Disagrees with ME!!! • The Author of our Logic Text claims that the Existential Fallacy only occurs when the subject is some sort of Mythic or Fictional being. • He thinks that traditional logic only sanctions SOME sub-alternations. • I disagree: I think Aristotle would not have drawn the line in THAT place. I think that relying upon individuals to decide on what is Mythic or Fictional takes us beyond LOGIC.

17. Take THAT Patrick J Hurley!

18. Avoiding the Existential Fallacy In order to avoid the Existential Fallacy we need to modify traditional categorical logic to remove the existential assumption. The Result is Modern or Boolean Categorical Logic

19. The Modern Square of Opposition Without the Traditional Existential Assumption, ONLY Contradiction is Valid

20. Modern Square using Venn Diagrams

21. Contradictories Contradictory Propositions ALWAYS take opposite TRUTH VALUES • A and O are Contradictories • E and I are Contradictories

22. Questions?

23. The Class So FAR (roughly)

24. Next Week Tuesday: Mid Term Exam Thursday: Immediate Inferences in Categorical Logic

25. Test Format The Midterm will be 150 Points • Section 1 (30 points) Basic Concepts/Vocabulary • Section 2 (30 Points) Fallacies • Section 3 (30 Points) Categorical Logic Concepts • Section 4 (60 Points) Applications