4.2 QUALITY, QUANTITY, AND DISTRIBUTION

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4 Categorical Propositions

• 4.2 QUALITY, QUANTITY, AND DISTRIBUTION

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Quantity, Quality, and Distribution

• Quantities there are just two quantities
• 1 Universal (All or None)
• 2 Particular (Some at least one).
• Qualities there are just two qualities
• 1 Affirmative
• 2 Negative

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Quantity, Quality and Distribution

• Proposition Letter Name Quantity Quality
• All S are P A Universal Affirmative
• No S are P E Universal Negative
• Some S are P I Particular Affirmative
• Some S are not P O Particular Negative
• Quantity and Quality are properties of
  Propositions.
• A proposition is what a sentence asserts, or what
  we assert with a sentence.
• I love the girl and Puellam Amo are two
  different sentences that assert the same
  proposition.

4
Quantity, Quality, and Distribution

• Distribution is a property of terms, not
  propositions.
• A term is distributed if the proposition asserts
  something about every member of the class the
  term refers to, so
• In All S are P, something is asserted about
  every member of the class referred to by the term
  S, and so S is distributed.
• For instance, All Salads are Priced to sell
  something is asserted about every salad, but not
  about everything that is priced to sell (on
  sale).
• All S are P assigns or distributes a property
  to every member of S (being priced to sell)

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Quantity, Quality, and Distribution

• All S are P can be symbolized like this

S
P
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Quantity, Quality, and Distribution

• No S are P looks like this
• No S are P, on our grocery interpretation, says
  something about everything Priced to sell, and
  every Salad.
• Therefore, both S and P are distributed.

S
P
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Quantity, Quality, and Distribution

• Some S are P
• This says that at least one member of S is also a
  P (at least one salad is priced to sell). This
  I proposition asserts something about at least
  one member of S and at least one member of P, so
  neither term is distributed.

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Quantity, Quality and Distribution

• Some S are not P
• This propositions asserts that at least one Salad
  is not Priced to sell (it says nothing about all
  salads, but it does say something about all the
  sale items none of them is that particular
  salador subclass of salads).

S
P
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Quantity, Quality and Distribution

• Summary
• All SD are P
• No SD are PD
• Some S are P
• Some S are not PD
• Proposition Letter Name Quantity Quality Distrib
  ution
• All S are P A Universal Affirmative Subject
  only
• No S are P E Universal Negative Sub Pred
• Some S are P I Particular Affirmative Neither
• Some S are not P O Particular Negative Predicat
  e only