Philosophy 4: Logic and Critical Thinking                                             Sierra College

Instructor: Al Cinelli                                                                                          Fall 2004

Categorical Logic Cues

Claims: Statement that is either true or false

Categorical: dealing with categories, classes, groups

Standard form categorical claims:

          A: All S are P; E: No S are P; I: Some S are P; O: Some S are not P

Correspondence: two standard form categorical claims have the same subject and predicate terms

          The Square of Opposition

Contraries: A-E: the two claims cannot both be true at the same time

Contradictories: A-O, E-I: if one claim is true, the other is false, and vice versa

Sub-contraries: I-O: both claims cannot be false at the same time

Complementary term, Complementary class: the “non-“ class, in a given universe of discourse, all things outside a given class; term that refers to the complementary class

          The Three Categorical Operations:

Conversion, converse: switching subject and predicate terms of a standard form categorical claim: E, I are valid; A, O are not

Obversion, obverse: change affirmative to negative, negative to affirmative; change predicate term to its complement. A, E, I, O all have valid obverses.

Contraposition, contrapositive: switch subject and predicate and change both to their complementary terms. A and O are valid. E and I are not.

Categorical Syllogisms: consist of two premises and a conclusion, three categorical claims, three terms, each used twice

Major term: the predicate of the conclusion

Minor term: the subject of the conclusion

Middle term: term that appears in the premises but not in the conclusion

Venn Diagram Testing: Diagrams for standard form categorical claims:

Using Venn Diagrams to test categorical syllogisms for validity:

Step 1: Translate all claims into standard form categorical claims

Step 2: Convert, contrapose or otherwise remove complementary classes

Step 3: Assign letters to stand for classes of the argument

Step 4: Draw three intersecting circles. Assign a letter to each circle to stand for each class. Suggestion: put minor term left, major term right, middle term above or below.

Step 5: Diagram universal premise first according to examples above. (If the syllogism does not have at least one universal premise, it is invalid).

Step 6: Diagram particular premise, if present. Place X in unshaded areas.

Step 7: To determine whether the argument is valid, consider how conclusion would be diagramed. If the conclusion is already diagramed by the premises, the argument is valid. If the conclusion is not already diagramed by the premises, the argument is invalid.

Example

	P1. All S are M P2. No P are M C. No S are P Valid		No P are M Some M are S Some S are not P Valid  Note: diagram par-ticular premise 2 after universal premise 1
	No S are M No M are P No S are P Invalid		All S are M Some M are P Some S are P Invalid Diagram particular premise 2 after uni-versal premise 1

Rules for Distribution:

In syllogistic logic, distribution means the application of a term of a claim to the entire class that the term represents.

Table for Distribution:

Three Rules of the syllogism: Use these rules to test syllogisms for validity.

A syllogism is valid IFF(if and only if) all of these conditions are met: if a syllogism fails at least one of these tests, it is invalid. If it passes all of the tests, it is valid.

1.       The number of negative claims in the premises must be the same as the number of negative claims in the conclusion

2.       At least one premise must distribute the middle term

3.       Any term that is distributed in the conclusion of the syllogism must be distributed in the premises.