Equivalent Immediate Inferences of the four Categorical Statements:
All S is P
= No S is non-P (obverse)
= All non-P is non-S (contrapositive)
No S is P
= All S is non-P (obverse)
= No P is S (converse)
Some S is P
= Some S is not non-P (obverse)
= Some P is S (converse)
Some S is not P
= Some S is non-P (obverse)
= Some non-P is not non-S (contrapositive)
Immediate inferences work in reverse:
All S is non-P
= No S is P (obverse)
All non-S is non-P
= All P is S (contrapositive)
No S is non-P
= All S is P (obverse)
Some S is non-P
= Some S is not P (obverse)
Some S is not non-P
= Some S is P (obverse)
Some non-S is not non-P
= Some P is not S (contrapositive)
Immediate inferences can be combined:
No non-S is P
= No P is non-S = All P is S (converse, obverse)
Some non-S is P
= Some P is non-S = Some P is not S (converse, obverse)
Other translations:
All non-S is P
= All non-P is S (contrapositive)
No non-S is non-P
= All non-S is P (obverse)
Some non-S is not P
= Some non-P is not S (contrapositive)
Some non-S is non-P
= Some non-S is not P (obverse)
All of this and more is included in this complete Immediate Inference Chart.
Not sure if this is where I should ask my question, but it’s the only place I could find. Is there a reason why categorical statement form must use only nouns or noun phrases in the subject and predicates, or why they have to be in a form with “to be” verbs? Is it just a rule when they were set up, or is there a reason? Thanks so much.
Thank you for the good question. The primary purpose of limiting categorical form to [Quantifier][Subject noun][“to be” copula][Predicate noun] is to make analyzing categorical statements simpler. It allows us to use a standard form for the Square of Opposition, as well as standard schemas for categorical syllogisms. It is not given to teach students to speak in categorical form.
All S is P
= No S is non-P
= All non-P is non-S
Will it be correct to say that the above are examples of ‘A’ Proposition?
Or that the examples below are ‘O’ Propositions?
Some S is not P
= Some S is non-P
= Some non-P is not non-S
Just a little modification of my earlier questions.
All S is P, No S is non-P, All non-P is non-S. Will it be correct to say that the above are examples of ‘A’ Proposition? Or that the examples below are ‘O’ Propositions? Some S is not P, Some S is non-P, Some non-P is not non-S.