# Immediate Inference Cheat Sheet

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.

## 2 thoughts on “Immediate Inference Cheat Sheet”

1. Louise Withers says:

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.

2. 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.