Propositions and Classification
What this domain tests
The difference between a sentence and a proposition, the quality/quantity classification, and the naming and distribution pattern of the four categorical forms A, E, I and O. This unit supplies the vocabulary used by every later unit.
Propositions
A proposition is what a declarative sentence asserts; it is either true or false. Questions, commands and exclamations are not propositions. The same proposition may be expressed by different sentences, and one sentence may express different propositions if it is ambiguous.
Types of proposition
- Categorical: asserts a relation between two classes ("All S are P").
- Hypothetical (conditional): "If p then q" - antecedent and consequent.
- Disjunctive: "Either p or q".
- Conjunctive: "p and q".
Categorical structure
Quantity is universal or particular; quality is affirmative or negative.
- A: All S are P - universal affirmative
- E: No S are P - universal negative
- I: Some S are P - particular affirmative
- O: Some S are not P - particular negative
Distribution: A distributes S; E distributes S and P; I distributes neither; O distributes P.
Worked example
"No mammals are cold-blooded." Quantity: universal. Quality: negative. Form: E. Both "mammals" and "cold-blooded" are distributed, so simple conversion is legitimate: "No cold-blooded things are mammals."
Traps that cost marks
Treating singular propositions like "Socrates is mortal" as particular - the tradition treats them as universal; misclassifying "Few students passed", which is logically an I or an O; reading "not all S are P" as E when it is O.