Categorical Logic A useful type of “real world” logic commonly used for characterizing relationships Applications in law, business contracts, natural and social sciences

Categorical Claims A: All X are Y All means “Every single one, no exceptions.” “And there is at least one.”

Categorical Claims A: All X are Y In natural language: Every X is a Y.Each X is a Y. If it is an X, then it is a Y.All Xs are Ys. Any X is a Y.All non-Ys are non-Xs. Only Ys are XsThe only Xs are Ys

Categorical Claims A: All X are Y In natural language: Every X is a Y.Each X is a Y. If it is an X, then it is a Y.All Xs are Ys. Any X is a Y.All non-Ys are non-Xs. Only Ys are XsThe only Xs are Ys Note: X and Y must be nouns or noun phrases.

Categorical Claims A: All X are Y E: No X are Y

Categorical Claims A: All X are Y E: No X are Y I: Some X are Y

Categorical Claims A: All X are Y E: No X are Y I: Some X are Y Note: The range of “some” in categorical logic is from as few as one to as many as all of the things in the category.

Categorical Claims A: All X are Y E: No X are Y I: Some X are Y O: Some X are not Y

Categorical Claims The direct way of reasoning with ALL All S are P A is sVALID Therefore, a is P

Categorical Claims Reasoning in a chain with All All S are P All P are QVALID Therefore, all S are Q (This works with All not Some)

Categorical Claims Direct way of reasoning with NO All S are P No Q is a PVALID Therefore, no Q is a S