Categorical Syllogisms

1. 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

2. 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

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

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

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

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

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

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

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

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

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

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 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.

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 It makes things easier to assign variables to the categories. M - members S - people who may shop here P - professionals non-P - non-professionals

21. 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

22. 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.

23. 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?

24. 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.

25. 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.

26. 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.

27. Obversion (valid for all claim types) 1. Move horizontally across the Square of Opposition. 2. Replace the predicate term with its complement.