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Dr. Robert Barnard

Philosophy 103 Linguistics 103 Yet, still, Even further More and yet more, ad infinitum, Introductory Logic: Critical Thinking. Dr. Robert Barnard. Last Time : . Introduction to Categorical Logic Categorical Propositions Parts and Characteristics Conditional and Conjunctive Equivalents

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Dr. Robert Barnard

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

  2. Last Time: Introduction to Categorical Logic Categorical Propositions Parts and Characteristics Conditional and Conjunctive Equivalents Existential Import

  3. Plan for Today Venn Diagrams for Propositions Existential Import in Diagramming Traditional Square of Opposition

  4. REVIEW: THE 4 TYPES of CATEGORICAL PROPOSITION

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

  6. Diagramming Propositions… Diagramming is a tool that can be used to make explicit information that is both descriptive and relational. • Geometric Diagrams • Blueprints • Road Maps • Flow Charts

  7. …is FUN!!! We can also diagram CATEGORICAL PROPOSITIONS. They describe a relationship between the subject term (class) and the predicate term (class).

  8. Focus on Standard Diagrams • Since there are 4 basic standard form categorical propositions, this means that there are exactly 4 standard diagrams for Categorical Propositions. • BUT – there are two flavors of diagrams we might use!

  9. Euler Diagrams (not Standard) P S P S X X

  10. Pro and Cons: Pro: Euler Diagrams are very intuitive Con: Euler Diagrams can represent single propositions but are difficult to combine and apply to syllogisms. Con: Euler Diagrams Cannot capture Existential Import in both the Aristotelian AND Modern modes. (more later)

  11. Alternative: Venn Diagrams • Venn Diagrams are less intuitive to some people than Euler Diagrams • Venn Diagrams Can easily be combined and used in Syllogisms. • Venn Diagrams CAN represent alternative modes of Existential Import.

  12. The Basic VENN Diagram SUBJECT CIRCLE PREDICATE CIRCLE X LABEL LABEL P S RULE 1: SHADING = EMPTY RULE 2: X in a Circle = at least one thing here!

  13. Questions?

  14. TYPE A : ALL S is P Conceptual Claim THE UNIVERSAL AFFIRMATIVE

  15. TYPE E : No S is P Conceptual Claim THE UNIVERSAL NEGATIVE

  16. TYPE I: Some S is P At least one thing X is Both S and P Existential Claim THE PARTICULAR AFFIRMATIVE

  17. TYPE O: Some S is not P At least one thing X is S and not P Existential Claim THE PARTICULAR NEGATIVE

  18. 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. Diagrams with an X indicate EXISTENTIAL IMPORT.

  19. In CATEGORICAL LOGIC a proper name denotes a class with one member. Fred Rodgers is Beloved by Millions PROPOSITIONS ABOUT INDIVIDUALS Fred Beloved

  20. The Traditional Square of Opposition How are the 4 standard CPs related?

  21. Contraries The A Proposition is related to the E proposition as a CONTRARY X is CONTRARY to Y = X and Y cannot both be true at the same time. Thus if A is true: If E is True: If A is False: E is False A is False E is UNDETERMINED

  22. Contraries: Not Both True A E If both are TRUE then S is all EMPTY and there is no UNIVERSAL Proposition asserted!!!!

  23. The Traditional Square of Opposition

  24. Sub-Contraries The SUBCONTRARY RELATION holds between the I-Proposition and the O-Proposition. Sub-Contrary = Not both False at the same time • If I is False then O is true • If O is False then I is true • If O (or I) is True, then I (or O) is undetermined

  25. Sub-Contrary: Not Both False I O IF both are FALSE, then there is no PARTYICULAR Proposition asserted!!!

  26. The Traditional Square of Opposition

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

  28. A – O Contradiction If BOTH are True then the Non-P region of S is BOTH empty and contains an object! A O

  29. E – I Contradictories • If Both are TRUE, then the overlap Region is EMPTY and contains an object. I E

  30. The Traditional Square of Opposition

  31. 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.

  32. Some Subalternations: • If All dogs are Brown, then Some dogs are brown. • If All Fish have Gills, then Some Fish have Gills. • If All Greeks are Brave, then Some Greeks are Brave

  33. The TRADITIONAL Interpretation The TRADITIONAL or ARISTOTELIAN interpretation allows SUBALTERNATION Because FOR ARISTOTLE all category terms denote REAL objects. -- Every name picks out something in the world.

  34. TRADITIONAL A and E When we want to clearly indicate a TRADITIONAL - ARISTOTELIAN interpretation we need to adapt the A and E Diagrams! E A X X

  35. The Traditional Square of Opposition

  36. Questions?

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