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