Critical Thinking Lecture 8 An introduction to Categorical Logic By David Kelsey

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:

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

Standard form categorical 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.

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

Affirmative and negative 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:

Translating a categorical claim into 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.

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

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’.

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.

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.

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?

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:

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

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

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

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.