19 Mar 2012

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Chapter 3 Categorical Logic

3.1 Categorical syllogism

- An inference from two categorical premises.

- Categorical statements; are the logic from which arguments are constructed.

- Subject term, tells us which things the statement is about.

- Predicate term, characterizes the members of the subject term.

- Scope word, tells us how many members of the subject term we’re talking about.

- Copula, is what joins the subject to predicate.

- Universal affirmation makes a positive statement about all members of the subject class.

- Particular affirmation, it is about some particular members of the subject class.

3.2 Distributed and undistributed terms

- Distributed term makes a claim about all members of the class that it names.

- Undistributed term makes a claim about some but not all of the members of the class that it names.

3.3 Distribution of subject terms

- Subject terms in universal statements are distributed

- Subject terms in particular statements are undistributed.

3.4 Distribution of predicate terms

- Predicate terms in affirmative statements are undistributed.

- Predicate terms in negative statements are distributed.

3.5 Counter examples

- Finding a counter example to a proposition means finding some case that would prove the proposition false.

3.6 Truth value

- You know the truth-value of a proposition when you know whether that proposition is true or false.

3.7 Conversion

- Exchange subject and predicate terms.

- Conversion is valid for E and I statements only

- So S are P No P are S, No Women are fathers, no Fathers are women.

- Some S are P, some P are S. Some plants are carnivores, some carnivores are plants.

3.8 Complements

- The complements of a class are made up of everything that falls outside of that class.