Critical Thinking Lecture 8 An introduction to Categorical Logic

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Critical ThinkingLecture 8An introduction to
Categorical Logic

• By David Kelsey

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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

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Categorical claims

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

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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.

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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

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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

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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 claims terms.
• Find the standard form claim it is logically
  equivalent to.

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Translating A and E claims

• Translating A claims Consider Every X is a Y
• Translating E claims Consider Xs arent Ys

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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.
• An example There were creatures weighing more
  than 4 tons that lived in North America

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Translating Only

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

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The Only

• Now consider the only Xs are Ys, (for some X and
  some Y).
• For example, The only people admitted are people
  over twenty one.
• Is it an A, E, I or O claim?

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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 over
  twenty-one

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Times

• Consider I always get nervous when I take logic
  exams.
• The claim says

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Places

• Now consider He makes trouble wherever he goes.
• The claim says

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Single Individuals

• Claims about a single individual person
• Consider Aristotle is a logician
• Represent the individual with a term that refers
  to only that individual
• 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.