Reduction of Sentences to Their Logical Forms

In one line

To reduce a sentence to logical form is to rewrite it as a standard categorical proposition, quantifier first, then subject, then copula, then predicate.

In the wording a student can write in an examination: reduction is the process of restating an ordinary sentence in one of the four standard forms, A, E, I or O, so that its quantity and quality are explicit and its subject and predicate are separated, without altering what the sentence asserts.

The target

Every reduced proposition looks like this and nothing else:

Three rules govern the process and they are worth stating before any example.

Change nothing that is asserted. Reduction is translation, not improvement. If the original is ambiguous, the ambiguity must be resolved by a decision that is stated, not by a silent choice.

Make the quantifier explicit. Ordinary sentences frequently have none, and supplying it is the main work.

Put the quality in the copula. A negative must end up in the copula, not floating in the predicate, unless the predicate term is itself genuinely negative.

The procedure

Step one, find the predicate. What is being said? This is easier than finding the subject, and it is the reliable place to start.

Step two, find the subject. What is it being said about?

Step three, settle the quantity. How much of the subject is spoken of? All of it, or part of it?

Step four, settle the quality. Is the predicate affirmed or denied?

Step five, write it out in the standard order, adding "is" or "are" as the copula and turning the predicate into a noun phrase where necessary. "All swans are white" is preferred to "all swans are white things" in ordinary work, but where the predicate must be a class name for a later operation, as in conversion at sequence 450, it is written as a class: "All swans are white things."

The awkward forms, each worked

Sentences with no quantifier. "Contracts require consideration." Ordinary English leaves the quantifier out where the universal is meant. Reduce: All contracts are agreements requiring consideration. A form.

Indefinite sentences. "Men are mortal" is universal; "Men were waiting outside the court" is particular. The words are the same shape and the quantity differs, and only the sense decides. When a sentence is genuinely indefinite, say so and give the reading adopted.

"Only" and "none but". These reverse the terms, and this is the most examined trap in the topic. "Only graduates are eligible" does not mean all graduates are eligible; it means nobody else is. Reduce: All eligible persons are graduates. A form, with subject and predicate swapped from where the sentence puts them.