Critical Thinking Lecture 8 An introduction to Categorical Logic

1. Critical ThinkingLecture 8An introduction to Categorical Logic By David Kelsey

2. Categorical Logic • Categorical logic is based on the relations of exclusion and inclusion among classes. • A class is a set of things • Example: • Categorical logic gives us a set of rules for making justified inferences about classes of things. • Example:

3. Categorical claims • Categorical claims: A claim is categorical if it is about classes of things. • Philosophy 110 example:

4. Standard formcategorical claims • A standard form categorical claim: • results from putting names or descriptions of classes in the blanks of any of the following 4 sentence forms: • A: All ___ are ___. • E: No ___ are ___. • I: Some ___ are ___. • O: Some ___ are not ___. • Terms go in the blanks above. • Terms can be either nouns or noun phrases.

5. Terms • The subject term: the term that goes in the first blank of a standard form categorical claim. • The predicate term: • The term that goes in the second blank. • The predicate of the claim. • It is predicated of the subject term, • Examples

6. Affirmative andnegative claims • Affirmative claims include one class or part of one class in another. • These include all A and I claims. • Example: • Negative claims exclude one class or part of one class from another. • These include all E and O claims. • Example:

7. Translating a categorical claiminto standard form • Turning a categorical claim into standard form: • we can take an ordinary categorical claim and turn it into one of standard form. • figure out which type of claim it is, A E I or O, and then just substitute in the claim’s terms. • Find the standard form claim it is logically equivalent to.

8. Translating A and E claims • Translating A claims: Consider Every X is a Y • Translating E claims: Consider Xs aren’t Ys

9. Translating into present tense • All standard form categorical claims must be in the present tense. • Talking about the past: we can still use standard form claims to talk about the past. • link the subject and predicate which are about the past with the present tense of the verb ‘to be’.

10. Translating Only • Consider only Xs are Ys, (for some X and some Y). • For example: • Turning this into standard form: • 1.) Determine what its terms are. • 2.) Determine the form of the claim, A E I or O.

11. Only Sophomores are eligible candidates • Consider: Only sophomores are eligible candidates: • An A claim: a careful reading of the claim indicates it is an A claim but which one: • All sophomores are eligible candidates. • All eligible candidates are sophomores.

12. The Only • Now consider the only Xs are Ys, (for some X and some Y). • For example, • This is another A claim: • We are talking about one class of things being included in another. • Which A claim is it?

13. Rules for Only &The Only • The word ‘only’: • introduces the predicate term of an A claim. • Only sophomores are eligible candidates: • The phrase ‘the only’: • introduces the subject term of an A claim. • The only people admitted are people that are over twenty-one:

14. Times • Consider ‘I always get nervous when I take logic exams.’ • The clue: when • The claim says:

15. Places • Now consider ‘He makes trouble wherever he goes’. • The clue: wherever • The claim says:

16. Single Individuals • Claims about a single individual person: • For example, • The class of things identical to an individual:

17. Aristotle is a logician • Consider ‘Aristotle is a logician’: • Logicians and Aristotle: • This claim is about two classes: • All claims about single individuals are either A or E claims. • Individual places: What has just been said about individual persons can also be said about individual places.