The Two Classifications Compared

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.