(Mathematical Logic:)
A well formed formula (wff) of predicate calculus with no free variables. Propositions are the sentences (or statements) of logic: a proposition is something to which a truth value can be attributed.

Examples of propositions are "2+2=4", "2+2=5", "for all positive integers x,y,z,n, if n>2 then xn+yn!=zn". "x2=2*y2" is not a proposition, as the variables x,y are free. "2+2", "2+, ")))x(+" aren't even formulae, hence not propositions.

Prop`o*si"tion (?), n. [L. propositio: cf. F. proposition. See Propound.]

1.

The act of setting or placing before; the act of offering.

"Oblations for the altar of proposition."

Jer. Taylor.

2.

That which is proposed; that which is offered, as for consideration, acceptance, or adoption; a proposal; as, the enemy made propositions of peace; his proposition was not accepted.

3.

A statement of religious doctrine; an article of faith; creed; as, the propositions of Wyclif and Huss.

Some persons . . . change their propositions according as their temporal necessities or advantages do turn. Jer. Taylor.

4. Gram. & Logic

A complete sentence, or part of a sentence consisting of a subject and predicate united by a copula; a thought expressed or propounded in language; a from of speech in which a predicate is affirmed or denied of a subject; as, snow is white.

5. Math.

A statement in terms of a truth to be demonstrated, or of an operation to be performed.

⇒ It is called a theorem when it is something to be proved, and a problem when it is something to be done.

6. Rhet.

That which is offered or affirmed as the subject of the discourse; anything stated or affirmed for discussion or illustration.

7. Poetry

The part of a poem in which the author states the subject or matter of it.

Leaves of proposition Jewish Antiq., the showbread.

Wyclif (Luke vi. 4).

Syn. -- Proposal; offer; statement; declaration. -- Proposition, Proposal. These words are both from the Latin verb proponere, to set forth, and as here compared they mark different forms or stages of a negotiation. A proposition is something presented for discussion or consideration; as, propositions of peace. A proposal is some definite thing offered by one party to be accepted or rejected by the other. If the proposition is favorably received, it is usually followed by proposals which complete the arrangement.

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