**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.