The Two Classifications Compared
Chapter Thirty-Seven
Syllabus topic 2.8, "Comparative Study of Traditional and Modern Classification of Propositions."
Pages 180 to 183 of 334
In one line
Both schemes classify propositions, but they cut at different places, for different purposes, and the modern scheme covers a wider field.
In the wording a student can write in an examination: the traditional classification divides propositions by the manner of assertion and then by quantity and quality, taking the term as its unit; the modern classification divides them by structure, taking the whole proposition as its unit, and it reaches propositions the traditional scheme cannot represent.
How to answer a comparison question
Not by describing one scheme and then the other. A comparison is answered by naming the points of comparison and running both schemes past each of them. Six points cover the ground.
The basis of division. The unit of analysis. The classes produced. The method of testing. The coverage. The treatment of existence.
An answer built on those six, with a sentence on each for each scheme, is complete. What follows fills them in.
Point by point
Basis of division. Traditional logic divides by the manner of assertion: absolute or conditional; then by quantity and quality. Modern logic divides by structure: whether the proposition contains another proposition as a component.
Unit of analysis. Traditional logic's unit is the term. Its entire apparatus, distribution, conversion, obversion, works on subjects and predicates. Modern logic's unit is the whole proposition, which is why a simple proposition can be replaced by a single letter and nothing is lost.
Classes produced. Traditional: categorical, subdivided into A, E, I and O; and conditional, subdivided into hypothetical and disjunctive. Modern: simple, subdivided into subject-predicate and relational; and compound, subdivided by connective into negative, conjunctive, disjunctive, implicative and equivalent.
Method of testing. Traditional logic tests by rules stated in words: the rules of conversion, the rules of the syllogism, the square of opposition. Modern logic tests by computation: a truth table settles a compound, and the procedure exercises no judgment at all.
Coverage. Traditional logic reaches ordinary categorical statements. It does not reach relational propositions, multiple quantifiers, or conjunctions. Modern logic reaches all of them.
Existence. Traditional universals carry existential import; modern universals do not. This is topic 2.9 and is the subject of the next chapter.
Where the two agree
An answer that presents the two as enemies has overstated the case, and examiners notice. Three agreements are worth stating.
Every inference traditional logic licenses is still valid. Modern logic did not overturn a single valid syllogism or a single rule of eduction. What it did was extend the field.
Both are formal. Both study the form of a proposition and disregard its subject matter, which is what makes both of them logic rather than a branch of some other science.
The Two Classifications Compared
Both classifications intersect rather than compete. Every A, E, I and O proposition is a simple proposition in the modern scheme. Every traditional hypothetical is a modern implicative compound. The two schemes are two grids over one field, and the modern grid extends beyond the edges of the older one.
Where the modern scheme is better, and where it costs something
Better: coverage, mechanical testing, the handling of relations and quantifier scope, and honesty about existence.
The cost, and it is real. The modern scheme is further from ordinary language. Reading "all contracts are agreements" as "for anything whatever, if it is a contract then it is an agreement" is exact and unnatural, and material implication's odd rows are the price of truth-functionality, as sequence 350 admitted. A student who says the modern scheme is simply superior has not noticed that it buys its precision with a currency.
And a practical cost for a lawyer. Legal reasoning is largely conducted in the traditional vocabulary. Judgments speak of universals, particulars, exceptions and provisos, not of quantifier scope. A lawyer who can only think in the modern notation will find nothing to talk to.
A worked example
Take one proposition and put it through both schemes completely.
"No agreement made by a person of unsound mind is enforceable."
Traditional analysis. Categorical, since it asserts absolutely. Quantity universal, quality negative, so it is an E proposition. Subject term "agreement made by a person of unsound mind", predicate term "enforceable". Both terms distributed, by the rules at sequence 310. It converts simply to "no enforceable agreement is one made by a person of unsound mind", and it obverts to "all agreements made by a person of unsound mind are unenforceable".
Modern analysis. Simple, since it contains no component proposition. Written ∀x(Ux ⊃ ~Ex), where Ux is "x is an agreement made by a person of unsound mind" and Ex is "x is enforceable". It asserts nothing about whether any such agreements exist. It contains one quantifier and one conditional, and its negation is ∃x(Ux • Ex), which asserts that there is at least one such agreement which is enforceable.
What each analysis gives you. The traditional one gives you the immediate inferences: what else follows from this proposition alone, which is Module III's subject. The modern one gives you the truth conditions and the exact form of the denial, which is what a pleader needs when drafting a traverse. Both are useful and neither replaces the other, which is the fair conclusion to a comparison question.
Distinctions that carry marks
| Point of comparison | Traditional | Modern |
|---|---|---|
| Basis of division | Manner of assertion, then quantity and quality | Structure: does it contain a component proposition? |
| Unit of analysis | The term | The whole proposition |
| First cut | Categorical and conditional | Simple and compound |
| Subclasses | A, E, I, O; hypothetical, disjunctive | Subject-predicate, relational; negative, conjunctive, disjunctive, implicative, equivalent |
| Method of test | Rules stated in words | Truth tables, mechanical |
| Relational propositions | Cannot represent | Ordinary members |
| Conjunctions | No class for them | A class of compound |
| Multiple quantifiers | Cannot express | Handled by scope |
| Existential import of universals | Carried | Denied |
| Closeness to ordinary language | Close | Distant |
The Two Classifications Compared
| Both schemes | ||
|---|---|---|
| Are formal | Yes | Both disregard subject matter |
| Overlap | Yes | Every A, E, I, O proposition is simple in the modern scheme |
| Conflict on validity | No | Every traditionally valid inference remains valid |
What this does not mean
The modern scheme did not refute the traditional one. It extended the field and revised one doctrine, existential import. Nothing else was withdrawn.
A comparison question is not an invitation to praise one scheme. The marks are for points of comparison, and an answer that runs both past six named points beats an answer that argues for a winner.
"Traditional" does not mean obsolete. The vocabulary of legal reasoning is traditional, and the whole of Module III is traditional logic.
Quick revision
Six points of comparison: basis of division, unit of analysis, classes produced, method of testing, coverage, treatment of existence.
Traditional: manner of assertion; the term; categorical and conditional; rules in words; ordinary categoricals only; universals carry existential import.
Modern: structure; the whole proposition; simple and compound; truth tables; relations, conjunctions and quantifier scope included; universals carry no existential import.
Three agreements: every traditionally valid inference remains valid; both are formal; the classifications intersect, since every A, E, I and O proposition is simple.
The cost of the modern scheme: distance from ordinary language, and material implication's odd rows.
Test yourself
1. On what points should the two classifications be compared?
On the basis of division, the unit of analysis, the classes each produces, the method by which each tests an inference, the range of propositions each can represent, and the treatment of existential import. An answer built on these six points, taking each scheme past each of them, is a comparison; an answer that describes one scheme and then the other is two descriptions.
2. State the basis of division and the unit of analysis in each scheme.
The traditional scheme divides by the manner of assertion, absolute or conditional, and then by quantity and quality, and its unit is the term, since distribution, conversion and obversion all operate on subjects and predicates. The modern scheme divides by structure, asking whether a proposition contains another proposition as a component, and its unit is the whole proposition, which is why a simple proposition can be replaced by a single letter.
The Two Classifications Compared
3. Give three respects in which the modern scheme has wider coverage.
It represents relational propositions, treating the relation as a predicate with two or more arguments, where the traditional subject-predicate form has only one place. It gives conjunctions a class, which the traditional scheme does not have at all. And it handles propositions with more than one quantifier by giving quantifiers a scope, so that the two readings of "every creditor has some remedy" can be distinguished and written down.
4. In what respects do the two schemes agree?
Every inference the traditional scheme licenses remains valid under the modern one, so there is no conflict about results. Both are formal, studying the shape of propositions and disregarding their subject matter. And the two classifications intersect rather than compete: every A, E, I and O proposition is a simple proposition in the modern scheme, and every traditional hypothetical is a modern implicative compound.
5. What does the modern scheme cost?
Distance from ordinary language. Reading "all contracts are agreements" as a quantified conditional is exact and unnatural, and material implication's treatment of a false antecedent is accepted as the price of truth-functionality rather than defended as an account of "if". There is also a practical cost for a lawyer, since judgments and statutes are written in the traditional vocabulary of universals, exceptions and provisos, and not in quantifier notation.
6. Analyse "No agreement made by a person of unsound mind is enforceable" in both schemes.
Traditionally it is a categorical proposition, universal in quantity and negative in quality, so an E proposition, with both terms distributed; it converts simply and obverts to a universal affirmative with a negative predicate. In the modern scheme it is a simple proposition, written ∀x(Ux ⊃ ~Ex), asserting nothing about whether any such agreements exist, and its denial is ∃x(Ux • Ex). The first analysis yields the immediate inferences, the second the truth conditions and the exact form of the traverse.
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.