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).
–
•
This is another A claim:
–
•
For example,
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.