Inference by Added Determinants

In one line

Inference by added determinants adds the same qualifying word to both the subject and the predicate of a proposition.

In the wording a student can write in an examination: an inference by added determinants is one in which the same determinant, that is, the same qualifying term, is attached to both the subject and the predicate of the given proposition, the quality and quantity remaining unchanged.

The form

"A horse is an animal" gives "A white horse is a white animal."

"A partner is an agent of the firm" gives "A sleeping partner is a sleeping agent of the firm."

"A judge is a public servant" gives "A retired judge is a retired public servant."

The determinant is the added word: white, sleeping, retired. It is added to both terms, and nothing else is altered.

When it holds

The inference is sound when the determinant means the same thing applied to the subject as it means applied to the predicate.

"White" applied to a horse and "white" applied to an animal mean the same colour, so the inference goes through. "Retired" applied to a judge and to a public servant means the same withdrawal from office, so that goes through too.

The rule in one line: the determinant must be absolute and univocal, that is, it must have a fixed meaning that does not shift with the class it qualifies.

When it fails, and the three ways it does

One: the determinant is relative. This is the classical failure and it is the one to have ready.

"An elephant is an animal" gives, by added determinants, "A small elephant is a small animal." That is false. A small elephant is a very large animal, because "small" means small for an elephant in the first place and small for an animal in the second, and those are different standards.

Every comparative word behaves this way: small, large, heavy, quick, expensive, young. A relative determinant takes its standard from the class it qualifies, so attaching it to two different classes attaches two different meanings.

Two: the determinant is evaluative. "Good", "bad", "competent", "reliable" are relative in a further way: they carry a standard drawn from a purpose.

"A surgeon is a man" gives "A good surgeon is a good man." Plainly false. Good as a surgeon is skill at surgery; good as a man is something else entirely, and the two need not go together.

This failure matters in law more than the first. "A director is a person" does not give "a negligent director is a negligent person", and "an advocate is an agent" does not give "a diligent advocate is a diligent agent", because diligence as an advocate is measured against professional standards and diligence as an agent against the ordinary duty of an agent.