Traditional and Modern General Propositions Distinguished
Chapter Thirty-Eight
Syllabus topic 2.9, "Distinction between the traditional and modern general propositions."
Pages 184 to 187 of 334
In one line
A traditional universal proposition asserts that its subject class has members; a modern one does not.
In the wording a student can write in an examination: on the traditional view, "all S is P" implies "some S is P", and therefore asserts that at least one S exists. On the modern view, "all S is P" is a conditional about anything whatever, is true when there are no S at all, and carries no such implication.
The one difference, and everything that follows from it
The whole distinction is a single disagreement, and it is worth isolating before anything else.
Traditional: a universal proposition asserts existence.
Modern: a universal proposition does not.
That is called existential import, and the two schemes answer the question differently. Particular propositions are not in dispute: both schemes agree that "some S is P" asserts that an S exists.
Why the traditional scheme says one thing
Because of the square of opposition, at sequence 410. Traditional logic holds that from A one may infer I, which is called subalternation: from "all contracts are agreements" it infers "some contracts are agreements". Since I asserts existence, A must assert it too, or the inference would take you from a true premise to a false conclusion.
So existential import is not an eccentric add-on to the traditional scheme. It is forced by an inference the scheme relies on, and abandoning it means abandoning subalternation, which is exactly what the modern scheme does.
Why the modern scheme says the other
Because of the symbolisation at sequence 360. "All S is P" is ∀x(Sx ⊃ Px). If nothing is S, then Sx is false for everything, so the conditional is true for everything, so the universal is true.
A universal proposition with an empty subject class is therefore true, and it says nothing about existence at all. That is not a decision taken for convenience; it falls out of the analysis, and any other analysis would produce the defects shown at sequence 360.
The four propositions in the two schemes
| Traditional reading | Modern reading | Asserts existence of S | |
|---|---|---|---|
| A: All S is P | There are S, and every one is P | If anything is S, it is P | Traditional yes, modern no |
| E: No S is P | There are S, and none is P | If anything is S, it is not P | Traditional yes, modern no |
| I: Some S is P | There is an S which is P | There is an S which is P | Both yes |
| O: Some S is not P | There is an S which is not P | There is an S which is not P | Both yes |
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