1. Philosophy 1504: Language and Logic March 28, 2016

2.  A categorical proposition is a proposition that relates two classes. These classes are denoted by a subject term and a predicate term. ◦ Examples:  “All Virginia Tech students are students that love logic.”  “No undergraduates are lazy students.”  “Some GTAs are awesome teachers.”  “Some GTAs are not awesome teachers.”

3.  Since a categorical proposition states that all/part of the class denoted by subject term is included or excluded from the class denoted by the predicate term, there are four kinds of categorical propositions: 1)The whole subject class is included in the predicate class. 2)Part of the subject class is included in the predicate class. 3)The whole subject class is excluded from the predicate class. 4)Part of the subject class is excluded from the predicate class.

4.  A categorical proposition is in standard form if and only if it is a substitution instance of one of the following forms: 1) All S are P. 2) No S are P. 3) Some S are P. 4) Some S are not P. Note: S and P stand for the subject term and predicate term, respectively. ◦ Quantifiers specify how much of the subject class is included or excluded from the predicate class.  “all”, “no”, and “some” ◦ Copula link the subject term and the predicate term.  “are”, “are not”

5.  Exercise: Identify the subject term, predicate term, quantifier, and copula: 1)“All people that drink and drive are irresponsible people.” 2)“Some roses are not red flowers.” 3)“Some artificial medical devices are mechanisms that are prone to failure.” 4)“No ostriches are birds that can fly.”

6.  Quantity ◦ Universal:  All S are P.  No S are P. ◦ Particular:  Some S are P.  Some S are not P.

7.  Quality ◦ Affirmative:  All S are P.  Some S are P. ◦ Negative:  No S are P.  Some S are not P.

8.  Letter Names of Propositions: FormTypeLetter Name All S are P. Universal affirmative A All S are not P. Universal negative E Some S are P. Particular affirmative I Some S are not P. Particular negative O

9.  Distribution ◦ A term is distributed if the proposition makes an assertion about every member of the class denoted by the term; otherwise, it is undistributed. FormType Letter Name Terms Distributed All S are P. Universal affirmative A All S are not P. Universal negative E Some S are P. Particular affirmative I Some S are not P. Particular negative O

10.  Distribution ◦ A term is distributed if the proposition makes an assertion about every member of the class denoted by the term; otherwise, it is undistributed. FormType Letter Name Terms Distributed All S are P. Universal affirmative AS All S are not P. Universal negative E Some S are P. Particular affirmative I Some S are not P. Particular negative O

11.  Distribution ◦ A term is distributed if the proposition makes an assertion about every member of the class denoted by the term; otherwise, it is undistributed. FormType Letter Name Terms Distributed All S are P. Universal affirmative AS All S are not P. Universal negative ES, P Some S are P. Particular affirmative I Some S are not P. Particular negative O

12.  Distribution ◦ A term is distributed if the proposition makes an assertion about every member of the class denoted by the term; otherwise, it is undistributed. FormType Letter Name Terms Distributed All S are P. Universal affirmative AS All S are not P. Universal negative ES, P Some S are P. Particular affirmative Inone Some S are not P. Particular negative O

13.  Distribution ◦ A term is distributed if the proposition makes an assertion about every member of the class denoted by the term; otherwise, it is undistributed. FormType Letter Name Terms Distributed All S are P. Universal affirmative AS All S are not P. Universal negative ES, P Some S are P. Particular affirmative Inone Some S are not P. Particular negative OP

14.  A mnemonic device for distribution: ◦ “Unprepared Students Never Pass”  Universals distribute Subjects.  Negatives distribute Predicates.

15.  Exercise: First, identify the quantity, quality, and letter name. Next, state whether the subject and predicate terms are distributed or undistributed. 1)“All people that drink and drive are irresponsible people.” 2)“Some roses are not red flowers.” 3)“Some artificial medical devices are mechanisms that are prone to failure.” 4)“No ostriches are birds that can fly.”