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Categorical Logic

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.”.

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Categorical Logic

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

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

  3. 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 Xs The only Xs are Ys

  4. 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 Xs The only Xs are Ys Note: X and Y must be nouns or noun phrases.

  5. Categorical Claims • A: All X are Y • E: No X are Y

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

  7. 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.

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

  9. Categorical Claims The direct way of reasoning with ALL All S are P A is s VALID Therefore, a is P

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

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

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