Dr. Robert Barnard

3. Philosophy 103Linguistics 103Yet, still, Even further More and yet moreIntroductory Logic: Critical Thinking Dr. Robert Barnard

4. Last Time: Introduction to Categorical Logic Aristotle’s Categories Leibniz, Concepts, and Identity Analytic – Synthetic Distinction Essence and Accident Necessary and Sufficient Conditions

5. Plan for Today Categorical Propositions Parts and Characteristics Conditional and Conjunctive Equivalents Existential Import

6. Reminder !!!!! Thursday, September 13, 2007 4:00 PM Bryant 209 Philosophy Forum Talk – “Einstein on the Role of History and Philosophy of Science in Physics” Dr. Don Howard – University of Notre Dame Extra Credit: 1 page reaction, due in 2 weeks (9/27)

7. Categorical Propositions Categorical Propositions relate one category (in whole or part) as indicated by the SUBJECT TERM to another category, indicated by the PREDICATE TERM (either affirmatively or negatively): • All houses have roofs • Some buildings are houses • No eggs are shatterproof • Some people are not paying attention

8. UNIVERSAL CATEGORICAL PROPOSITIONS A Categorical Proposition that makes a claim about the entire SUBJECT CLASS is called a UNIVERSAL CATEGORICAL PROPOSITION • All Toys… • No Fish… • All Bugs… • No people from Georgia…

9. PARTICULAR CATEGORICAL PROPOSITIONS A Categorical Proposition that makes a claim about one or more members of the SUBJECT CLASS is called a PARTICULAR CATEGORICAL PROPOSITION • Some Eggs… • Some men… • Some Lithuanians…

10. QUANTITY All categorical propositions are either: UNIVERSAL or PARTICULAR We call this the QUANTITY of the proposition.

11. AFFIRMATIVE AND NEGATIVE PROPOSITIONS When a categorical proposition asserts the existence of a relationship between the Subject term and the Predicate term we say that the proposition is AFFIRMATIVE. When a categorical proposition denies the relationship between the Subject term and the Predicate term we say that the proposition is NEGATIVE

12. QUALITY All categorical propositions are either: AFFIRMATIVE or NEGATIVE We call this the QUALITY of the proposition.

13. THE 4 TYPES of CATEGORICAL PROPOSITION

14. Questions?

15. ALL S is P TYPE A If (x is S) then (x is P) Conceptual Claim THE UNIVERSAL AFFIRMATIVE

16. No S is P TYPE E If (x is S) then (x is not P) Conceptual Claim THE UNIVERSAL NEGATIVE

17. In CATEGORICAL LOGIC a proper name denotes a class with one member. Socrates: the class containing Socrates Al Gore: the class of Al Gore Brad Pitt: The class containing Brad Pitt …etc… SO, a proposition like ‘Socrates is a man’ is really about the whole class Socrates, so… It is a UNIVERSAL proposition!!! PROPOSITIONS ABOUT INDIVIDUALS

18. Universal Propositions • All Dogs are Brown • All Houses are residences • No Pigs have wings • No Cars are Airships • No Humans have quills • All Wisdom is not Folly • John Jay was the first Chief Justice

19. Some S is P TYPE I At least one thing X is Both S and P For at least one x (x is S) and (x is P) Existential Claim THE PARTICULAR AFFIRMATIVE

20. Some S is not P TYPE O At least one thing X is S and not P For at least one x (x is S) and (x is not P) Existential Claim THE PARTICULAR NEGATIVE

21. Particular Propositions • Some Cats are red. • Some Pigs are not Sows • Some lettuce is not endive. • Some Men are not Women • Some Flowers are plants. • Some Presidents of the United States served two terms • Some Ole Miss coaches used to win games.

22. EXISTENTIAL IMPORT ONLY a proposition with EXISTENTIAL IMPORT requires that there be an instance of the SUBJECT TERM in reality for the proposition to be true. • All Dogs have 4 Legs (Conceptual – no EI) • Some Fish are Red (Existential – EI)

23. The Term which determines the QUANTITY of the proposition is called THE QUANTIFIER ALL – NO -- SOME The term that determines the QUALITY of the proposition is called the QUALIFIER ALL – NO – IS – IS NOT QUANTIFIER AND QUALIFIER

24. A, E, I, and O

25. Every Categorical Proposition has a Quantity and Quality, a Subject term and a Predicate Term. There is one more part: THE COPULA All S is P No S is P Some S is P Some S is not P COPULATION!!!!

26. Questions?

30. Questions?

37. Week - • Categorical Propositions • Conditional and Conjunctive equivalents • Existential Import • Traditional Square of Opposition • Modern Square of Opposition • Existential Fallacy • Venn Diagrams for Propositions

38. Week- • Immediate Inferences • Conversion • Contraposition • Obversion

39. Week- • Syllogistic Logic • Form- Mood- Figure • Medieval Logic • Venn Diagrams for Syllogisms (Modern)

40. Week - • Venn Diagrams for Syllogisms (traditional) • Limits of Syllogistic Logic • Review of Counter-Example Method

41. Week - • Logic of Propositions • Decision Problem for Propositional Logic • Symbolization and Definition • Translation Basics

42. Week - • Truth Tables for Propositions • Tautology • Contingency • Self-Contradiction

43. Week - • Truth Tables for Propositions II • Consistency • Inconsistency • Equivalence

44. Week - • Truth Table for Arguments • Validity / Invalidity • Soundness

45. Week - • Indirect Truth Tables • Formal Construction of Counter-Examples

46. Week - • Logical Truths • Necessity • Possibility • Impossibility