Critical ThinkingLecture 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 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.

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 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:

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.

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.