The Modern Classification: What It Is For

In one line

The modern classification divides propositions by their structure rather than by their subject and predicate, so that the parts which decide an inference are the parts the classification names.

In the wording a student can write in an examination: the aim of the modern classification is to divide propositions in a way that reflects the features on which their logical behaviour depends. It therefore asks first whether a proposition contains another proposition as a part, dividing propositions into simple and compound, instead of asking about quantity and quality.

The aim, stated properly

MU asks for the aim and not for the kinds, so the aim has to be answerable on its own. It has four parts.

To classify by what matters to inference. Quantity and quality are real features, but they are not the only ones that decide what follows from what. Whether a proposition is compound decides it too, and the traditional scheme never asked.

To reach the propositions the older scheme could not. Relational propositions, compounds, and propositions with more than one quantifier: the seven failures of the last chapter are the specification the modern classification was built against.

To make the test mechanical. Once propositions are classified by structure and the connectives are defined truth-functionally, whether a compound is true can be computed rather than argued about. That is what a truth table is, and it is possible only because of the way the classification is drawn.

To separate form from content completely. The traditional scheme keeps the subject and predicate in view, which keeps the subject matter in view. The modern scheme replaces a whole simple proposition with a single letter, so nothing of the content survives into the analysis at all.

The first cut: simple and compound

The modern classification's first question is the one prepared at sequence 260.

A simple proposition contains no other proposition as a component. It has constituents only. "The notice was served."

A compound proposition contains at least one component, that is, at least one part which is itself a proposition. "The notice was served and the rent was unpaid."

This single cut is what makes the rest possible. A simple proposition is written as a single letter, p, q, r, because there is nothing inside it that a truth table needs to see. A compound proposition is written as its components joined by connectives, and the truth table then works on the components.

Notice the contrast with the traditional first cut. Traditional logic asks whether the proposition asserts absolutely or conditionally, which puts hypotheticals in one box and everything else in another. Modern logic asks whether the proposition has propositional parts, which puts hypotheticals, disjunctions and conjunctions together in one box, since they behave alike, and leaves the categoricals in the other.