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Categorical Proposition

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- 1. Categorical Propositions Theory of Deduction
- 2. Theory of Deduction • The theory of deduction is intended to explain the relationship between premisses and conclusion of a valid argument, and to provide techniques for the appraisal of deductive arguments, that is, for discriminating between valid and invalid deductions.
- 3. Two Theories to Accomplish this Task • “Classical” or “Aristotelian” Logic • “Modern” or “Modern Symbolic” Logic
- 4. Aristotelian Logic • The Aristotelian study of deduction focused on arguments containing propositions called “categorical propositions” which involve categories or classes.
- 5. Categorical Propositions • Such propositions affirm or deny, that some class S is included in some other class P, in whole or in part.
- 6. Example No athletes are vegetarians. All football players are athletes. Therefore ??????
- 7. Explanation In the argument the three categorical propositions are about: the class of all athletes , the class of all vegetarians, and the class of all vegetarians.
- 8. Class Defined • A class is a collection of all objects that have some specified characteristics in common
- 9. Relationships Between Classes • There are various ways in which two classes may be related to each other. • These various relationships between classes are affirmed or denied by categorical propositions. • There can be just four standard forms of categorical propositions.
- 10. Standard-form categorical propositions • universal affirmative A • universal negative E • particular affirmative I • particular negative O
- 11. Examples 1. All politicians are liars. 2. No politicians are liars 3. Some politicians are liars 4. Some politicians are not liars.
- 12. Universal affirmative proposition (A) • All politicians are liars is a universal affirmative proposition. It contains two classes, the class of all politicians and the class of all liars, saying that the first class is included in the second. • A universal affirmative proposition says that every member of the first class is also the member of the second class.
- 13. A • In this example, the subject term “politicians” designates the class of all politicians, and the predicate term “liars” designates the class of all liars. • Any universal affirmative proposition may be written schematically as • All S is P • Where the letters S and P represent the subject and predicate terms, respectively.
- 14. Universal negative proposition (E) • No politicians are liars is a universal negative proposition. It denies of politicians that they are liars. • A universal negative propositions says that the firs class is wholly excluded from the second, which is to say that there is no member of the first class that is also a member of the second.
- 15. E • Any universal negative proposition may be written schematically as • No S is P. Where the letters S and P represent the subject and predicate terms.
- 16. Particular affirmative proposition (I) • Some politicians are liars is a particular affirmative proposition. • It affirms that some members of the class of all politicians are (also) members of the class of all liars. • This proposition neither affirms nor denies that all politicians are liars.
- 17. I • It is written schematically as • Some S is P • Says that at least one member of the class designated by the subject term S is also a member of the class designated by the predicate term P.
- 18. Particular negative proposition ( O) • Some politicians are not liars is a particular negative proposition. • It is written schematically as • Some S is not P • Says that at least one member of the class designated by the subject term S is excluded from the whole of the class designated by the predicate term P.

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