What a Proposition Is

In one line

A proposition is what a sentence says when the sentence is capable of being true or false.

In the wording a student can write in an examination: a proposition is the meaning expressed by a declarative sentence, and it is the unit that bears truth and falsity. The sentence is the form of words; the proposition is what those words assert.

Why the distinction is the first thing in Module II

Because the whole module is about classifying propositions, and it cannot be done on sentences. Sentences differ from one another in ways that make no logical difference at all, and treating them as the unit produces a classification of grammar rather than of thought.

Three facts make the point, and every one of them is asked.

One proposition, many sentences. "Ravi paid the money", "The money was paid by Ravi" and "It was Ravi who paid the money" are three sentences, differing in voice and in emphasis. They assert the same thing, and any one of them is true exactly when the others are. There is one proposition here and three sentences.

One proposition, many languages. A sentence in English and its correct translation into Marathi are two sentences and one proposition. If propositions were sentences, translation would be impossible in principle, and the fact that a witness may be examined through an interpreter would be inexplicable.

One sentence, many propositions. "I was there yesterday" expresses a different proposition every time a different person says it, and a different one again on a different day. The sentence is the same. What it asserts is not.

Which sentences express propositions

Grammar recognises four kinds of sentence and only one of them expresses a proposition.

Declarative sentences assert something and express propositions: "The notice was served."

Interrogative sentences ask: "Was the notice served?" Nothing is asserted, so nothing is true or false.

Imperative sentences command or request: "Serve the notice." Again nothing is asserted.

Exclamatory sentences express feeling: "How careless!"

Only the first can be a premise or a conclusion, which is the rule already used at sequence 30. This is not a grammatical nicety; it is why a plaint contains statements and a prayer clause, and why only the statements can be traversed in a written statement.

Two cautions. A sentence in the interrogative form may nevertheless assert something: a rhetorical question is an assertion wearing a question mark, and it is treated as the proposition it asserts. And a sentence in the declarative form may assert nothing determinate, as vague and ambiguous sentences do, which is the subject of the reduction chapter at sequence 300.

Proposition and statement

Some books use "statement" where this book uses "proposition", and MU's own reading list contains both usages. Nothing turns on it for this paper. Where a distinction is drawn, "statement" is the act of stating and "proposition" is what is stated, which parallels the distinction between judgment and proposition in the next chapter.