Opposition of Singular Propositions

The test settles it. Contraries may both be false. Can "Ravi is a minor" and "Ravi is not a minor" both be false? They cannot: Ravi is either a minor or he is not, by the law of excluded middle at sequence 160. So whatever corner they are placed in for other purposes, their actual relation is contradiction.

The lesson is a general one about classification, and it is worth stating because Module IV returns to it: a classification made for one purpose does not answer every question about its members. Treating a singular as universal is a device, and reading a device as a discovery is how errors are made.

Where a lawyer meets this

Constantly, because most propositions in a case are singular. "The notice was served on 4 April." "The defendant is a partner in the firm." "This document is the original."

The practical consequence is the pleading rule of sequence 410, and here it is simpler. Against a singular proposition there is one denial and it is complete. To deny "the defendant is a partner in the firm" is to assert "the defendant is not a partner in the firm", and nothing more is available or needed. There is no weaker denial and no stronger one.

Contrast a general proposition, where the choice between the contradictory and the contrary is a real tactical choice with a real cost. That choice does not arise for singulars, which is why a traverse of a specific allegation is a much simpler thing to draft than a traverse of a general one.

One caution. A proposition that looks singular may not be. "The goods were defective" is about a consignment and is general in disguise, and its denial is subject to everything at sequence 420, as the worked example there showed. The test is whether the subject names one individual or a class, and "the goods" is a class.

A worked example

A plaint alleges: "The suit notice was served on the defendant on 4 April 2024."

Is the proposition singular? Yes. The subject is one identified document served on one identified person on one identified date.

What are the possible denials?

The contradictory: the suit notice was not served on the defendant on 4 April 2024. That is complete, and there is nothing else.

Is there a contrary? No. There is no proposition standing to this one as "no S is P" stands to "all S is P", because there is no class to quantify over.

Now a trap. Consider the plea: "the suit notice was served on the defendant on 6 April 2024." Is that the contradictory? No. It is a different proposition with a different predicate, and it is not an opposition at all in the technical sense, because opposition requires the same subject and the same predicate. It happens to be inconsistent with the plaint on the facts, since one document cannot be served on one person on two different days, but that inconsistency comes from the facts about service and not from the relations of the square.

Why the distinction matters in the pleading. A defendant who pleads service on 6 April has not traversed the allegation of service on 4 April; he has raised a positive case. Under the ordinary rules of pleading an allegation not traversed may be taken as admitted, so the defendant must both deny the 4 April service and plead the 6 April service. Reading a positive inconsistent case as a denial is a real drafting error, and the logic of opposition is what shows that they are two different things.

Distinctions that carry marks

What this does not mean

Treating a singular as universal is not a contradiction of this chapter. It is a device for one purpose, and it does not carry over to the relations of opposition.

A proposition about a named thing is not always singular. "The goods were defective" names a consignment and quantifies over its members.

Two inconsistent positive cases are not contradictories. Opposition requires the same predicate, and pleading a different date is a positive case that must be pleaded as well as, not instead of, a denial.

Quick revision

A singular proposition has one opposite only: its contradictory.

Reason: quantity cannot vary where the subject class has one member, so only quality remains.

Contrariety, subcontrariety and subalternation all require a class with a middle case, and a single individual has none.

The classification of singulars as universal, at sequence 280, is a device for other purposes and does not govern opposition.

In pleading: a singular allegation has exactly one denial, which is complete. A general allegation offers a choice between contradictory and contrary.

Trap: a positive inconsistent case, such as service on a different date, is not a denial and must be pleaded in addition to one.

Test yourself

1. How many relations of opposition does a singular proposition admit, and which?

One, contradiction. "Ravi is a minor" and "Ravi is not a minor" differ in quality alone; exactly one of them is true and they cannot both be false. No other relation is available, because there is no third proposition with the same subject and predicate for the pair to stand in any further relation to.

2. Why do contrariety, subcontrariety and subalternation fail for singular propositions?

All three depend on the subject class having more than one member. Contraries can both be false only where some members have the predicate and some do not; subcontraries can both be true for the same reason; and subalternation relates a universal to a particular with the same terms, which requires a class that can be partly spoken of. A subject with one member offers no middle case and no particular counterpart.

3. Traditional logic treats a singular proposition as universal. Does that make "Ravi is a minor" and "Ravi is not a minor" contraries?

No. The classification of singulars as universal is a device adopted so that singular propositions can serve as premises where a universal is required; it is not a claim that they behave like universals in every respect. The test settles the matter: contraries may both be false, and these two cannot both be false, since by the law of excluded middle Ravi either is or is not a minor.

4. What is the practical consequence for pleading?

That a singular allegation has exactly one denial and it is complete, so no tactical choice arises. Against a general allegation a pleader must choose between the contradictory, which is cheap and sufficient, and the contrary, which is heavier and riskier. Against a singular allegation there is nothing to choose: the denial is the contradictory, and there is no stronger or weaker form of it.

5. Is "the goods were defective" a singular proposition?

No. Although "the goods" looks like a definite description of one thing, it names a consignment consisting of many items, and the proposition quantifies over them. It is a general proposition in disguise, so all four relations of opposition apply to it and its denial must be analysed as at sequence 420. The test is whether the subject names one individual or a class.

6. A plaint alleges service on 4 April and the written statement pleads service on 6 April. Has the allegation been traversed?

No. Opposition requires the same subject and the same predicate, and service on 6 April is a different predicate, so the plea is a positive case and not a denial. It is inconsistent with the plaint as a matter of fact, since one notice cannot be served on one person on two days, but that inconsistency arises from the facts and not from the square. The defendant must deny the allegation as well as plead his own case, or risk the allegation being taken as admitted.