Philosophical Method

1. Philosophical Method • Logic: A Calculus For Good Reason • Clarification, Not Obfuscation • Distinctions and Disambiguation • Examples and Counterexamples • Revealing Our Deepest Convictions • Testing Our Principles and Definitions

2. Logic: Primary Philosophical Tool • Logic Gives Us Rules For Reasoning • Arguments And Their Parts • Premises • Sub and Main Conclusions • Note: Relation Between Premises and Conclusion Is What Matters • Calculus For Generating New Beliefs On Basis Of Old Ones

3. Types Of Argument: Two Main Forms Of Inference • Deductive Inference • Validity: If The Premises Are True, The Conclusion Must Be True • Distinguishing Validity From Truth • Arguments: Valid Or Invalid; Not True Or False • Premises: True Or False; Not Valid Or Invalid • Logicians Care More About Truth Preservation Than Truth • Soundness: Valid AND True Premises

4. Non-Deductive Reasoning • Inductive Inference • Probability: If The Premises Are True, The Conclusion is Probably True • Inference To Next Case • Universal Generalization • Inference To Best Explanation • Appealing To Best Hypothesis • Fallacies

5. Syllogisms • Is a systematic arrangement of arguments containing Major premise All A’s are B’s Minor Premise C is an A Conclusion C is a B

6. Categorical Syllogisms • Contain words like all, every, each etc • Major premise All students (A’s) are Intelligent (B’s) • Minor Premise You (C ) are a student (A) • Conclusion You (C ) are intelligent (B) • Not all premises are true ! 

7. Disjunctive Syllogisms • Contain mutually exclusive choices. Words such as either, or , neither, but etc • Major Premise Either students will attend classes or work at home • Minor Premise Students do not attend classes • Conclusion Therefore they work at home! • Now you KNOW not all premises are true ! 

8. Conditional Syllogisms • This is based upon a notion of hypothetical or future events/actions. It uses words such as if, supposing etc • The major premise has antecedent and subsequent statements. • IF the antecedent occurs then the subsequent will followand become the conclusion

9. Conditional Syllogisms (cont..) • Major Premise Students will pass the course if their work is good enough • Minor Premise Your work is good enough • Conclusion Therefore you will pass

10. Categorical Syllogisms • Always have two premises • Consist entirely of categorical claims • May be presented with unstated premise or conclusion • May be stated formally or informally • Are intended to be valid

11. Categorical Syllogisms • All P are T • Some T are D • Some P are D • Things to notice: • • Two premises and a conclusion • • Three terms, each used twice

12. All T are ZNo Z are FNo F are T

13. All T are ZNo Z are FNo F are T F T Z

14. All T are ZNo Z are FNo F are T F T Z

15. Some voters are alcoholics.No alcoholics are happy people.So some voters are not happy people.

16. Some voters are alcoholics.No alcoholics are happy people.So some voters are not happy people. V - voters H - happy people A - alcoholics

17. Some voters are alcoholics.No alcoholics are happy people.So some voters are not happy people. V H A

18. Some voters are alcoholics.No alcoholics are happy people.So some voters are not happy people. V H A

19. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals

20. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals First, put the claims into a standard form.

21. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals First, put the claims into a standard form. All people who may shop here are members.

22. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals First, put the claims into a standard form. All people who may shop here are members. Some members are professionals.

23. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals First, put the claims into a standard form. All people who may shop here are members. Some members are professionals. Some people who may shop here are non- professionals.

24. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals Second, determine the categories. All people who may shop here are members. Some members are professionals. Some people who may shop here are non- professionals.

25. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals Second, determine the categories. All people who may shop here are members. Some members are professionals. Some people who may shop here are non- professionals.

26. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals Second, determine the categories. All people who may shop here are members. Some members are professionals. Some people who may shop here are non- professionals.

27. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals Second, determine the categories. All people who may shop here are members. Some members are professionals. Some people who may shop here are non- professionals.

28. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals Second, determine the categories. All people who may shop here are members. Some members are professionals. Some people who may shop here are non- professionals.

29. Only members may shop here. But only some of our members are professionals. So, some of the people who shop here are non-professionals • It makes things easier to assign variables to the categories. • M - members • S - people who may shop here • P - professionals • non-P - non-professionals

30. Only members may shop here. But only some of our members areprofessionals.So, some of thepeople who shop herearenon-professionals. • All S are M • Some M are P • Some S are non-P

31. Only members may shop here. But only some of our members areprofessionals.So, some of thepeople who shop herearenon-professionals. • All S are M • Some M are P • Some S are non-P • But there is still work to do before validity can be determined. The problem is that there are four categories. At least one claim must be rewritten if this is to become a proper syllogism.

32. Only members may shop here. But only some of our members areprofessionals.So, some of thepeople who shop herearenon-professionals. • All S are M • Some M are P • Some S are non-P • Rewriting one of these claims requires use of at least one of the forms of immediate inference: conversion, contraposition, or obversion. In this case, either the second premise or the conclusion must be rewritten. Does it matter which one?

33. Only members may shop here. But only some of our members areprofessionals.So, some of thepeople who shop herearenon-professionals. • All S are M • Some M are P • Some S are non-P • Logically, it makes no difference which claim is rewritten. But since the conclusion states the issue of the argument in a way that someone presumably wants to think about it, let’s leave the conclusion as close to the original statement as possible.

34. Only members may shop here. But only some of our members areprofessionals.So, some of thepeople who shop herearenon-professionals. • All S are M • Some M are P • Some S are non-P • Only one of the immediate inference rules will change the second premise in the way needed to create a well-formed syllogism.

35. Only members may shop here. But only some of our members areprofessionals.So, some of thepeople who shop herearenon-professionals. • All S are M • Some M are P --> Some M are not non-P • Some S are non-P • Obversion (valid for all claim types) • 1. Move horizontally across the Square of Opposition. • 2. Replace the predicate term with its complement.