The Failure of the Traditional Classification
Chapter Thirty-Two
Syllabus topic 2.5, "Failure of Traditional classification propositions."
Pages 154 to 158 of 334
In one line
The traditional classification fails because it forces every proposition into a subject-predicate mould, and a great many propositions do not fit it.
In the wording a student can write in an examination: the fourfold classification assumes that every proposition consists of two terms joined by a copula, and that its quantity and quality exhaust its logical form. Relational propositions, propositions of existence, compound propositions and propositions with more than one quantifier cannot be accommodated on that assumption, and the scheme's treatment of existential import produces results that cannot be sustained.
The assumption being attacked
Traditional logic holds that every proposition has this shape: a subject term, a copula, a predicate term, with a quantifier in front. Classify by quantity and by quality, and you have said everything there is to say about its form.
That assumption is not obviously wrong. It handles "all contracts are agreements" perfectly. It is wrong nevertheless, and the failures below are the standard list.
Failure one: relational propositions
"Bombay is larger than Pune."
What is the subject and what is the predicate? If the subject is "Bombay", the predicate must be "larger than Pune", which treats a relation between two things as a quality of one of them. That is not merely inelegant. It makes the inference to "Pune is smaller than Bombay" invisible, because the two propositions now share no term at all.
The point is general. Relations are two-ended and the subject-predicate form has only one end. Almost every proposition in the law of obligations is relational: A owes B money; X is the tenant of Y; the mortgagor redeemed from the mortgagee. Traditional logic can record them and cannot reason with them.
Worse still are relations among three or more: "A paid B on behalf of C." The scheme has nowhere to put a third party at all.
Failure two: existential import
This is the failure that produces MU's own topic 2.9 and it is the most examined of the group.
Traditional logic takes a universal affirmative to imply that its subject exists. From "all contracts are agreements" it allows the inference to "some contracts are agreements", which asserts that there is at least one contract. That inference is called subalternation and it is part of the square of opposition at sequence 410.
Now consider "All trespassers will be prosecuted." On the traditional reading this implies that there are trespassers. The notice on a gate implies nothing of the kind; it is a warning, and it is not falsified by the absence of trespassers.
Consider a statutory example. A section provides that all persons convicted under a repealed provision shall be entitled to a refund. Read traditionally, the section asserts that such persons exist. It does no such thing: it provides for them if there are any.
The Failure of the Traditional Classification
The scheme cannot distinguish between a universal that carries a commitment to the existence of its subject and one that does not, because it treats them all alike. That is the failure, and the modern classification's answer is to deny existential import to universals altogether, which is topic 2.9.
Failure three: compound propositions
The traditional scheme puts hypothetical and disjunctive propositions into a separate class called conditional and then does very little with them. It has no systematic account of how their truth depends on the truth of their parts, and therefore no way of testing an argument built out of them.
That is a large gap. Statutes are written in compounds, as sequence 290 showed, and the traditional scheme offers no equivalent of a truth table.
Conjunction is worse off still. "The notice was served and the rent was unpaid" is a compound proposition with two components, and traditional logic has no class for it at all: it is not categorical, since it is not one subject and one predicate, and it is not conditional. In practice the scheme simply treats it as two propositions, which is right in this case and cannot be generalised.
Failure four: multiple quantifiers
"Every creditor has some remedy."
There are two quantifiers here and the traditional form allows only one. Worse, the sentence is ambiguous in a way the scheme cannot even express: it may mean that for each creditor there is some remedy or other, or that there is one remedy available to every creditor. Those are different propositions with different truth conditions, and the difference matters enormously in law.
The traditional scheme has no apparatus for the distinction. The modern one has, and its ability to handle it is one of the main reasons the modern scheme exists.
Failure five: existence and the copula
"Ghosts do not exist." What is being denied of what? If "ghosts" is the subject, the proposition says of ghosts that they lack existence, which requires there to be ghosts for the denial to be about. The subject-predicate form treats existence as a quality on a level with being white or being enforceable, and it does not behave like one.
"There is no contract between the parties" raises the same difficulty in a legal setting, and it is not academic: whether such a plea denies a quality of a thing or denies that there is any such thing decides what has to be pleaded and proved.
Failure six: what "some" loses
As sequence 300 showed, "most witnesses were unreliable", "a majority of the sections apply" and "two of the three defendants were served" all reduce to "some". The scheme has one particular quantifier and it means "at least one". Everything more precise is discarded in the reduction.
The Failure of the Traditional Classification
This is a genuine loss for a lawyer, since proportions and numbers are the ordinary currency of proof.
Failure seven: tense and modality
The copula is "is" or "are", and it is timeless. "The notice was served", "the notice will be served" and "the notice must be served" differ in ways the scheme cannot record, and the third of them, which is the ordinary form of a legal obligation, is not a matter of quantity or quality at all.
Traditional logic handles tense by the device of sequence 300, turning the proposition into one about occasions. It has no comparable device for "must", "may" and "shall", which is why the logic of obligation and permission had to be developed separately and much later.
A worked example
Take a single sentence from the law of contract and see how many of the failures it triggers.
"A minor's agreement is void, and every person who has received a benefit under it must restore it, unless the court otherwise directs."
Relational. "Received a benefit under it" relates a person to an agreement. Two ends, one place to put them.
Compound. The sentence has three components joined by "and" and "unless". The traditional scheme has no class for the whole.
Multiple quantifiers. "Every person who has received a benefit" quantifies over persons; "a benefit" quantifies over benefits. Read one way it is every person and every benefit; read another, every person and at least one benefit.
Modal. "Must restore" is an obligation, and neither quantity nor quality captures it.
Existential import. Does the sentence assert that anybody has received a benefit? Traditionally yes; obviously not.
The verdict. One ordinary legislative sentence, five failures. That is why the modern classification exists, and it is a better answer to the examination question than a list of abstract objections with no example attached.
Distinctions that carry marks
| Failure | What the scheme cannot do | Modern answer |
|---|---|---|
| Relational propositions | Represent a relation with two or more ends | Relations as predicates of two or more arguments |
| Existential import | Distinguish universals that assert existence from those that do not | Universals assert none |
| Compound propositions | Test them, or classify conjunctions at all | Truth-functional connectives and truth tables |
| Multiple quantifiers | Express the ambiguity, let alone resolve it | Quantifiers with scope |
| Existence | Treat existence as other than a quality | The existential quantifier |
| Numerical quantity | Say more than "at least one" | Numerical quantification |
| Tense and modality | Record them at all | Separate logics, later |
What this does not mean
The traditional scheme is not useless. It handles ordinary categorical statements well, and every valid inference it licenses is still valid. It is incomplete, not incorrect.
The Failure of the Traditional Classification
"Failure" does not mean the scheme produces wrong answers. It means it produces no answer where an answer is available, and this is worth saying explicitly, because "failure" sounds stronger than the criticism actually is.
The examination question is not an invitation to abuse the older logic. The marks are for naming the specific failures and illustrating them, not for saying that traditional logic is outdated.
Quick revision
The assumption attacked: every proposition is a subject, a copula and a predicate, and quantity and quality exhaust its form.
Seven failures: relational propositions; existential import; compound propositions; multiple quantifiers; existence as a predicate; the loss of numerical quantity in "some"; tense and modality.
The most examined: existential import, because it produces MU's own topic 2.9. "All trespassers will be prosecuted" does not assert that there are trespassers.
Relational failure matters most to a lawyer, since the vocabulary of obligations is relational throughout.
The right characterisation: incomplete, not incorrect. Every inference it licenses remains valid.
Test yourself
1. What assumption of the traditional classification is under attack, and why does it fail?
The assumption that every proposition consists of a subject term joined by a copula to a predicate term, with quantity and quality exhausting its logical form. It fails because a great many propositions do not have that shape: relational propositions have two or more ends, compound propositions are built out of whole propositions rather than terms, and propositions with more than one quantifier cannot be written in a form that has room for only one.
2. Explain the failure over relational propositions.
"Bombay is larger than Pune" can be forced into the scheme only by treating "larger than Pune" as a quality of Bombay, which conceals the fact that a relation between two things is involved. The consequence is that the obvious inference to "Pune is smaller than Bombay" becomes invisible, since the two propositions then share no term. Relations with three ends, such as "A paid B on behalf of C", cannot be represented at all.
3. What is the difficulty about existential import?
Traditional logic takes a universal affirmative to assert that its subject exists, allowing the inference from "all S is P" to "some S is P". But "all trespassers will be prosecuted" plainly does not assert that there are trespassers, and a section providing for all persons convicted under a repealed provision does not assert that any such persons exist. The scheme cannot distinguish universals that carry an existential commitment from those that do not, because it treats them all alike.
4. Why are compound propositions a problem for the traditional scheme?
The Failure of the Traditional Classification
Because it classes hypothetical and disjunctive propositions together as conditional and then supplies no systematic account of how their truth depends on the truth of their parts, so it offers no method of testing an argument built out of them. Conjunctions fare worse still: "p and q" is neither categorical nor conditional, and the scheme has no class for it, treating it in practice as two separate propositions.
5. Illustrate the difficulty with multiple quantifiers.
"Every creditor has some remedy" contains two quantifiers, and the traditional form has room for one. The sentence is also ambiguous between meaning that each creditor has some remedy or other and meaning that there is one remedy available to all creditors, which are different propositions with different truth conditions. Traditional logic cannot express the ambiguity, let alone resolve it, whereas the modern scheme does both by giving quantifiers a scope.
6. Is it right to say the traditional classification is wrong?
No, and the distinction matters for the answer. Every inference the traditional scheme licenses remains valid, and it handles ordinary categorical statements well. What it does is fail to reach a large class of propositions, so that it returns no answer where an answer is available. The correct description is that it is incomplete rather than incorrect, and the modern classification was built to cover what it leaves out.
The rest of this subject
These notes are cut from the University's printed syllabus. Open the syllabus itself, or the past papers, for the same subject.