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Categorical proposition

- asserts that either all or part of the class denoted by the subject term is include or excluded from the class denoted by the predicate term


Standard form categorical proposition

1) quantifier -> all, no, some
2) subject term -> "members of the AMA" (before copula)
3) copula -> are and are not
4) predicate term -> "people holding degrees from recognized academic institutions" (after copula)



1) All S are P (A) ....Universal.....Affirmative
2) No S are P (E).....Universal..... Negative
3) Some S are P (I)...Particular .. Affirmative
4) Some S are not P (O).. Particular ... Negative


Existential Fallacy

- invalid merely because the premise does not exist
- Boolean standpoint (modern square)
- only used in contrary, subcontrary and subalternation (traditional) -> when universal goes to particular


Boolean stand point

- recognizes that particular statements make a positive assertion about existence


Venn Diagrams

A) shade S side
E) shade middle
I) x in the middle
O) x in S side


Modern Square of Opposition

- Boolean standpoint

Logically undetermined-> has truth value can't determine what it is

Contradictory -> opposite truth values


Testing immediate inferences

- one premise and one conclusion
- plug premise into modern square of opposition
- if it works then it's unconditionally valid regardless of existential fallacy
- illicit contrary, illicit subcontrary, illicit subalternation, illicit contraposition, illicit conversion


1) Conversion
2) illicit conversion

1) switch subject and predicate terms
2) E,I -> same truth value.
A,O -> undetermined truth value



- change the quality
- replace predicate term with compliment (non P)
- all true


1) Contraposition
2) illicit contraposition

1) switch subject and predicate terms
- replace subject and predicate term with compliments

2) E,I -> undetermined truth value.
A,O -> determined truth value


Traditional Square of opposition

- contradictory -> opposite truth value
- contrary -> at least one is false (not both true). ... If a is true e is false. But if a is false e is either false or true
- subcontrary -> at least one is true (not both false)... If I is false O is true but if I is true A could be true or false
- subalternation -> truth flows downward, falsity flows upward