The Traditional Classification: Categorical and Conditional

By modality: how the predicate is said to belong to the subject. This is the basis the other three chapters do not touch, and it has three members.

Apodictic, or necessary: "every contract must have consideration". The predicate is asserted to belong necessarily.

Assertoric, or actual: "this contract has consideration". The predicate is asserted simply to belong, as a matter of fact.

Problematic, or possible: "this agreement may be a contract". The predicate is asserted only to be possible.

Why modality was dropped by modern logic, and where it went. The three modal forms are not truth-functional, since knowing whether p is true does not settle whether p is necessary, so no truth table can reach them. Modern logic accordingly left them out of the propositional calculus and they became the subject of a separate modal logic, developed much later. That is the same fate as the tenses at sequence 390, and for the same reason.

Why it matters to a lawyer. Because legal language is saturated with modality and the three forms have entirely different effects: "shall" is apodictic, "is" is assertoric, and "may" is problematic. A provision saying the Court shall admit the document, one saying it admits the document and one saying it may admit it are three different rules, and the difference is a difference of modality and of nothing else.

Analytic and synthetic propositions

Added after the past-paper check, since MU asks for these by name with an example.

An analytic proposition is one whose predicate is already contained in the connotation of its subject, so that denying it produces a contradiction and no observation is needed to establish it. "A contract is an agreement" is analytic, because being an agreement is part of what "contract" means. So is "a bachelor is unmarried".

A synthetic proposition is one whose predicate adds something the connotation of the subject does not contain, so that denying it produces no contradiction and observation or evidence is needed. "This contract is in writing" is synthetic, and so is "most contracts are performed".

The test. Ask whether the proposition can be shown true by examining the meaning of the subject term alone. If it can, it is analytic; if the world has to be consulted, it is synthetic. The distinction is Kant's and it is the ancestor of the modern distinction between what is true by definition and what is true as a matter of fact.

Where a lawyer meets it, and this is the useful part. A definition clause makes propositions analytic within its own Act. Once an Act provides that "vehicle" means a conveyance used for the carriage of persons or goods, the proposition "every vehicle under this Act is used for the carriage of persons or goods" is analytic: it cannot be disproved by evidence, because it follows from the definition. Whether a particular object is a vehicle remains synthetic and is proved by evidence.

The practical rule that comes out of it. Evidence is relevant to synthetic propositions and irrelevant to analytic ones. A party who leads evidence to show that some vehicles are not used for carriage has misunderstood what a definition clause does, and this is a real and frequent error.

Categorical propositions

Every categorical proposition has four parts, and naming them is examinable in its own right.

The quantity word, or quantifier: "all", "no", "some". It says how much of the subject is being spoken about.

The subject term: what is being spoken about.

The copula: "is", "are", "is not", "are not". It joins subject to predicate and carries the quality, affirmative or negative. MU sets it as a topic of its own at 2.10.

The predicate term: what is being said about the subject.

Every categorical proposition can be forced into this shape, and forcing it there is the exercise called reduction to logical form, at sequence 300.

Conditional propositions, named here and taken at sequence 290

Traditional logic divides conditionals into two.

Hypothetical, of the form "if p then q". The first part is the antecedent and the second the consequent.

Disjunctive, of the form "either p or q". Each part is called an alternative.

Some books add a third, the conjunctive proposition of the form "not both p and q", though most treat it as a disjunctive in disguise. MU's syllabus does not name it separately and neither does this book, beyond this line.

Where the law puts each

This is worth a paragraph, because it explains the shape of every statute a student will read.

Definition clauses are categorical. "'Immoveable property' includes land, benefits to arise out of land, and things attached to the earth." The assertion is flat.

Operative provisions are conditional, almost without exception. "Where a person, being under no obligation to do so, lawfully does anything for another person, and such other person enjoys the benefit thereof, the latter is bound to make compensation." That is "if p and q then r", and the section asserts nothing about whether anybody has done anything.

A statute is therefore mostly a set of conditionals whose antecedents are questions of fact. The trial establishes the antecedents; the section supplies the consequents. That is the judicial syllogism of sequence 100 seen from the drafting side, and it is why the conditional is the characteristic form of legal language.

A worked example

Classify each of the following.

"Every agreement enforceable by law is a contract." Categorical. Quantity "every", subject "agreement enforceable by law", copula "is", predicate "a contract". The qualification "enforceable by law" is a constituent of the subject term and does not make the proposition conditional, which is the trap in this example.

"If an agreement is enforceable by law, it is a contract." Conditional, hypothetical. Antecedent "an agreement is enforceable by law", consequent "it is a contract". Nothing is asserted about any agreement.

"No agreement made by a minor is enforceable." Categorical and negative. Quantity "no", and the copula carries the negative quality.

"Either the notice was served or the suit is premature." Conditional, disjunctive. Two alternatives, neither asserted by itself.

Compare the first two. They look almost identical and behave differently. The categorical version, combined with "this agreement is enforceable by law", yields "this agreement is a contract" immediately. The conditional version yields the same conclusion, but only after the antecedent has been affirmed, and the affirming is a separate step that somebody has to take and prove. In an examination the difference between a proposition whose qualification sits inside the subject term and one whose qualification is an antecedent is exactly what is being tested.

Distinctions that carry marks

What this does not mean

A qualified subject does not make a proposition conditional. "All agreements enforceable by law are contracts" is categorical. The qualification is inside the subject term.

"Categorical" does not mean emphatic. In ordinary speech a categorical denial is a firm one. In logic it means unconditional, and a hesitant unconditional assertion is still categorical.

A conditional is not a weaker categorical. It is a different kind of proposition, with two components rather than two terms.

Quick revision

Basis of the division: the manner of assertion. MU also calls the traditional scheme Aristotle's classification.

Categorical: asserts absolutely. Four parts: quantifier, subject, copula, predicate.

Conditional: asserts a relation between propositions and asserts neither of them. Two kinds: hypothetical, if p then q, with antecedent and consequent; disjunctive, either p or q, with alternatives.

A conditional cannot support an inference by itself until the condition is settled, which is why it cannot be an argument on its own.

In law: definitions are categorical, operative provisions are conditional. A statute is largely a set of conditionals whose antecedents are questions of fact.

Four bases of classification: quantity, quality, relation and modality. The categorical and conditional division is the division by RELATION.

Modality: apodictic or necessary, assertoric or actual, problematic or possible. Not truth-functional, so modern logic left it to a separate modal logic. In law, "shall", "is" and "may" are the three modalities.

Analytic: the predicate is contained in the connotation of the subject, so denying it contradicts. Synthetic: the predicate adds something, so evidence is needed. A definition clause makes propositions analytic within its own Act, and evidence is irrelevant to them.

Trap: a qualification inside the subject term does not make a categorical proposition conditional.

Test yourself

1. On what basis does traditional logic divide propositions into categorical and conditional, and what does each mean?

The basis is the manner of assertion. A categorical proposition asserts its predicate of its subject absolutely, without attaching any condition, as in "all contracts are agreements". A conditional proposition asserts only a relation between two propositions and asserts neither of them, as in "if an agreement is enforceable by law it is a contract", which says nothing about whether any agreement is enforceable.

2. Name the four parts of a categorical proposition and identify them in an example.

The quantifier, the subject term, the copula and the predicate term. In "All contracts made by minors are void", "all" is the quantifier, "contracts made by minors" is the subject term, "are" is the copula, carrying affirmative quality, and "void" is the predicate term. Every categorical proposition can be put into this shape, and doing so is what reduction to logical form means.

3. Name the kinds of conditional proposition and their parts.

Hypothetical propositions, of the form "if p then q", whose parts are the antecedent and the consequent; and disjunctive propositions, of the form "either p or q", whose parts are called alternatives. Some writers add the conjunctive proposition, "not both p and q", though it is usually treated as a disjunctive in another form and MU's syllabus does not name it separately.

4. Why is the conditional the characteristic form of legal language?

Because an operative provision has to state what shall follow if certain facts exist, without asserting that they do. A section is therefore a conditional whose antecedent is a question of fact and whose consequent is a legal result, and the trial exists to establish the antecedent. This is the drafting side of the judicial syllogism: the statute supplies the major premise and the evidence supplies the minor.

5. Classify: "All agreements made without consideration are void" and "If an agreement is made without consideration, it is void". What difference does the classification make?

The first is categorical, the qualification "made without consideration" being part of the subject term. The second is hypothetical, with that qualification as the antecedent. The difference is what is needed to draw a conclusion about a particular agreement: from the categorical one, the additional premise that this agreement is of the described kind; from the conditional one, the affirmation of the antecedent as a separate step. In practice the two come to the same result, and only the categorical form asserts anything about a class of agreements outright.

7. On what four bases does traditional logic classify a proposition?

By quantity, universal or particular; by quality, affirmative or negative; by relation, categorical or conditional; and by modality, apodictic or necessary, assertoric or actual, and problematic or possible. The four are independent, so every proposition has an answer under each of them, and the division into categorical and conditional made in this chapter is the division by relation.

8. What is modality, and why did modern logic drop it?

Modality is the manner in which the predicate is said to belong to the subject: necessarily in an apodictic proposition, actually in an assertoric one, and possibly in a problematic one. Modern logic dropped it from the propositional calculus because modal propositions are not truth-functional: knowing whether a proposition is true does not settle whether it is necessary, so no truth table can reach it. Modality became the subject of a separate modal logic developed much later.

9. Distinguish analytic from synthetic propositions, and give the legal application.

An analytic proposition has a predicate already contained in the connotation of its subject, so that denying it is a contradiction and no evidence is needed: "a contract is an agreement". A synthetic proposition has a predicate that adds something the subject does not contain, so evidence is needed: "this contract is in writing". The legal application is that a definition clause makes propositions analytic within its own Act, so evidence directed against them is irrelevant, while whether a particular thing falls within the definition remains synthetic and is proved by evidence.

6. Does a qualification in the subject make a proposition conditional?

No. "All agreements enforceable by law are contracts" is categorical, because the qualification is a constituent of the subject term and nothing is held back. A proposition is conditional only when what it asserts is a relation between two propositions, neither of which is asserted on its own. Confusing a qualified subject with an antecedent is the commonest error in classifying propositions.