Reduction of Sentences to Their Logical Forms

The rule in one line: "only S is P" becomes "all P is S". The same holds for "none but", "no one except" and "alone".

"All except" and "all but". "All the defendants except the third were served." Two propositions are being asserted at once, and both must be written: All the defendants other than the third are persons who were served, and The third defendant is not a person who was served. An answer that gives only the first has dropped half of what the sentence says.

Exclusive propositions using "the only". "The only remedy is an injunction." Reduce: All remedies available here are injunctions.

Numerical and quasi-numerical quantity. "Most of the witnesses were unreliable", "a few sections apply", "several documents were produced". All of these are particular in logic: they say something about part of the class and not the whole. Reduce with "some". "Most witnesses were unreliable" becomes Some witnesses are persons who were unreliable. Note what is lost: logic's "some" cannot express "most", and the traditional scheme has no way to record it. That loss is one of the failures of the traditional classification, at sequence 320.

Singular propositions. "Ravi is a minor." The subject class has one member and the whole of it is spoken about, so the proposition is universal. Reduce: All persons identical with Ravi are minors, in strict form, or simply treat it as an A proposition and say so. The strict form looks laboured and is needed only when an operation such as conversion has to be carried out on it.

Negative words other than in the copula. "No document was produced" is already E in shape. But "Documents were not produced" may be E or O depending on the sense, and "Not all documents were produced" is O and not E: it denies the universal and asserts only that at least one was not. "Not all S is P" reduces to "Some S is not P". This is the second most examined trap in the topic.

Sentences whose grammatical subject is not the logical subject. "There are agreements which are void." Reduce: Some agreements are void. I form. The word "there" is doing grammatical work only.

Interrogative and exclamatory forms. A rhetorical question is reduced to the proposition it asserts, as at sequence 240. A genuine question is not a proposition and cannot be reduced at all, and saying so is the correct answer.

Sentences containing "few" and "a few". "Few sections apply" suggests a negative: it means that not many do, and it is usually reduced as Some sections are not sections which apply. "A few sections apply" is affirmative: Some sections are sections which apply. The article changes the quality, which is a real feature of English and a favourite of examiners.

Adverbs of time and place. "He always pays late" reduces to All occasions of his paying are occasions of late payment. "He never appeared" reduces to No occasion of the hearing is an occasion on which he appeared. The trick is to make the class a class of occasions, times or places, and it is the standard method for any sentence about frequency.

A worked example: a statutory sentence

Section 91(1)(b) of the Code of Civil Procedure 1908 permits a suit in the case of a public nuisance to be instituted, with the leave of the Court, by two or more persons, even though no special damage has been caused to such persons by reason of such public nuisance.

Find the propositions. There are two, and the second is the one carried by "even though".

First: with leave, two or more persons may institute such a suit. Reduce: All cases of a suit under this clause by two or more persons with leave are cases of a permitted suit. A form.

Second: the absence of special damage is no bar. This is a negative and it must be got into the copula. Reduce: No case of such a suit is a case barred by the absence of special damage to the plaintiffs. E form.

What reduction reveals. The words "even though" carry a whole proposition, and it is a negative universal excluding a defence. A reader who did not reduce would very likely read "even though" as an aside rather than as an enactment, and would miss that the clause abolishes a requirement which the general law of tort otherwise imposes.

That is the practical value of the topic. Reduction is not an exercise in tidiness. It makes a reader count the propositions in a sentence, and legislative sentences routinely carry more than one.

Distinctions that carry marks

What this does not mean

Reduction does not improve the sentence. If the original asserts something doubtful, the reduced form asserts the same doubtful thing.

"Only" does not simply mean "all". It reverses the terms, and reading it as an ordinary universal is the single commonest error in this topic.

"Not all" is not "none". It is an O proposition, and treating it as E turns a modest denial into a sweeping one.

Reduction is not always possible. A genuine question, a command or an exclamation expresses no proposition and cannot be reduced. Saying so is the right answer, not a failure.

Quick revision

Target form: quantifier, subject, copula, predicate. Quality lives in the copula.

Procedure: predicate, subject, quantity, quality, write out.

"Only S is P" becomes "all P is S". Same for "none but", "no one except", "alone".

"All except" carries two propositions and both must be written.

"Not all S is P" is O, not E.

"Few" is negative, "a few" is affirmative.

Most, many, several, a majority: all reduce to "some", and the extra information is simply lost.

Singular propositions are universal, A or E.

Frequency and place are handled by making the class a class of occasions.

Test yourself

1. What is reduction to logical form, and what are its three governing rules?

It is the rewriting of an ordinary sentence as a standard categorical proposition in the order quantifier, subject, copula, predicate. The rules are: change nothing that is asserted, since reduction is translation and not improvement; make the quantifier explicit, since ordinary sentences often omit it; and put the quality into the copula rather than leaving a negative floating in the predicate.

2. Reduce "Only registered documents are admissible" and explain the trap.

It reduces to "All admissible documents are registered documents", an A proposition with the terms reversed from where the sentence places them. The trap is to read it as "all registered documents are admissible", which asserts something quite different and much stronger. The rule is that "only S is P" becomes "all P is S", and the same applies to "none but", "no one except" and "alone".

3. Reduce "All the defendants except the second were served."

Two propositions are asserted and both must be written. First, an A proposition: "All defendants other than the second are persons who were served." Second, an E proposition about the exception: "The second defendant is not a person who was served." An answer that gives only the first has dropped half of what the sentence says, and in a pleading that half is usually the important one.

4. Distinguish the reduction of "Few witnesses were reliable" from "A few witnesses were reliable".

"Few" carries a negative sense, meaning that not many were, and it reduces to the O proposition "Some witnesses are not reliable witnesses". "A few" is affirmative, meaning that some were, and it reduces to the I proposition "Some witnesses are reliable witnesses". The article changes the quality of the proposition, which is a genuine feature of English usage and a favourite examination point.

5. How are propositions about frequency reduced?

By making the subject a class of occasions, times or places. "He always pays late" becomes "All occasions of his paying are occasions of late payment", an A proposition. "He never appeared" becomes "No occasion of the hearing is an occasion on which he appeared", an E proposition. Without this device such sentences have no obvious subject term and cannot be fitted into the standard forms at all.

6. Why does reduction matter when reading a statute?

Because it forces a reader to count the propositions in a sentence, and legislative sentences routinely carry more than one. Words such as "even though", "except" and "provided that" each introduce a further proposition, often a negative universal excluding a defence or a requirement. A reader who does not reduce is likely to treat such words as asides, and so to miss part of what the section enacts.