philosophy unit 4

Universal Affirmative S distributed P undistributed

A proposition

Universal Negative S and P distributed

E proposition

Particular Affirmative S and P undistributed

I proposition

Particular negative S undistributed P distributed

O proposition

quantifiers

“all” “none” and “some”

copula

“are” and “are not”

quality

either affirmative or negative depending on whether it confirms or denies class membership

quantitity

either universal or particular depending on whether the statement makes a claim about every member or just some member of the class

existential import

way to interpret a universal proposition, whether it implies the actual existence of the subject

boolean standpoint

no universal propositions have existential imports, such statements never imply the existence of the things talked about

aristotelian standpoint

universal propositions about existing things have existential import, such statements imply the existence of the things mentioned, “open to existence”

contradictory

necessarily have opposite truth value (A and O, E and I)

Vacuosly true

truth value results solely from fact that subject class is empty, the truth value of these propositions does not violate the “logically undetermined rlation” because it results not from any relation (ex. flying zebras)

unconditionally valid

arguments that are valid from the Boolean standpoint because they are valid regardless of whether their terms refer to existing things

existential fallacy (boolean)

formal fallacy that occurs whenever an argument is invalid merely becasue the premise lacks existential support, always has universal premise and a particular conclusion, attempts to get a conclusion having existential import from a premise that lacks it

existential fallacy inference form

All A are B. Therefore some A are B

existential fallacy inference form

it is false that some a are not b. therefore it is false that no a are b

existential fallacy inference form

no a are b. therefore, it is false that all a are b

existential fallacy inference form

it is false that some a are b. therefore, some a are not b

conversion

switch subject term with predicate term (A and O undetermined, E and I equivalent)

valid conversion form

no a are b. therefore no b are a

valid conversion form

some a are b. therefore, some b are a

illicit conversion form

all a are b. therefore, all b are a

illicit conversion form

some a are not b. therefore some b are not a

observion

change quality and replace the predicate with its term complement (all equivalent)

contraposition

switch subject and predicate and replace the subject and predicate terms with their term complements (A and O equivalent, E and I undetermined)

valid contraposition forms

all a are b. therefore all non-b are non-a

valid contraposition forms

some a are not b. therefore, some non-b are non-a

illicit contraposition forms

some a are b. therefore some non-b are non-a

illicit contraposition forms

no a are b. therefore, no non-b are non-a

contradictory relation

opposite truth value (A and O) (E and I)

Contrary relation

at least one is false (A and E)

Subcontrary relation

at least one true (I and O)

subalternation relation

truth value flows down and falsity flows up (A and I) (E and O)

illicit contrary forms

it is false that all a are b. therefore, no a are b

illicit contrary forms

it is false that no a are b. therefore, all a are b

illicit subcontrary forms

some a are b. therefore, it is false that some a are not b

illicit subcontrary forms

some a are not b. therefore, some a are b

illicit subcontrary forms

some a are b. therefore, some a are not b

illicit subalternation forms

some a are not b. therefore no a are b

illicit subalternation forms

it is false that all a are b. therefore, it is false that some a are b

illicit subalternation forms

it is false that no a are b. therefore it is false that some a are not b

existential fallacy (aristotelian)

when contrary, sub-contrary, and subalternation are used to draw a conclusion from a premise about things that do not exist, begin with universal proposition and conclude with particular proposition

conditionally valid

inference after Aristotelian standpoint has been adopted and we are not certain if the subject term of premise denotes actually existing things (ex. students who failed the test)