Distribution and Immediate Inference
Distribution and immediate inference test whether you can move from one categorical proposition to another without a second premise. The exam expects the distribution table, the square of opposition, and the operations of conversion, obversion and contraposition.
Core rules
- A term is distributed when the proposition says something about every member of its class. In A, the subject is distributed. In E, both terms are distributed. In I, neither term is distributed. In O, the predicate is distributed.
- Conversion swaps subject and predicate. E and I convert simply; A converts per accidens only if existence is assumed; O cannot be converted.
- Obversion changes quality and replaces the predicate with its complement; it is valid for A, E, I and O.
- Contraposition replaces subject and predicate by their complements and swaps them. It is valid for A and O in traditional logic; E and I do not contrapose validly.
Worked example
All dogs are animals is A. Dogs is distributed; animals is undistributed. Obversion gives No dogs are non-animals. Simple conversion gives All animals are dogs, which is invalid because animals is undistributed in the original. Contraposition gives All non-animals are non-dogs, which is valid for A.
Traps
The commonest error is converting an A proposition simply. Do not confuse obversion with conversion. In contraposition, complement both terms, not one. Do not apply distribution to the copula or quantifier. Check whether your course uses existential import before accepting conversion per accidens.