proposition


Also found in: Dictionary, Thesaurus, Medical, Legal, Wikipedia.

proposition

1. Philosophy
a. the content of a sentence that affirms or denies something and is capable of being true or false
b. the meaning of such a sentence: I am warm always expresses the same proposition whoever the speaker is
2. Maths a statement or theorem, usually containing its proof

Proposition

 

a declarative sentence which with its content (sense) is regarded as either true or false. Propositions thus conceived are usually contrasted to interrogative and imperative sentences and in general to any sentence in which an evaluation of truth is impossible. Examples of propositions are “Moscow is the capital,” “Five is less than three and greater than two,” and “All engineers have studied the resistance of materials.” Of these propositions, the first and third are true and the second is false. “Truth” and “falseness” are called truth values of a proposition (or values of its truthfulness). By definition, any proposition has grammatical and logical aspects. The grammatical aspect is expressed by a declarative proposition (simple or complex), and the logical aspect is expressed by its meaning and truth value. Propositions that vary as grammatical sentences (for example, belonging to different languages) can express one and the same meaning. This meaning, common to grammatically differing propositions, is the content or sense of a proposition; the meaning is often called a judgment. However, the terminology relating to propositions is not fixed, and the terms “proposition,” “sentence,” and “judgment” are sometimes used synonymously, or meanings other than those described above are attributed to these terms.

Various methods of using propositions are distinguished in linguistic practice. A proposition is said to be used affirmatively if it is used to affirm the truth of the thought it expresses. Affirmative usage of a proposition is most frequent; people expressing their own thoughts usually claim that they are true. (In logic, in order to distinguish a proposition as a statement which can be either true or false from one which is an affirmation of truth, the special sign ǀ— is applied in certain cases; ǀ— A means affirmation of the proposition A.)

In the case when the truth of a proposition’s content is not affirmed, there is nonaffirmative usage of a proposition (for example, in classroom dictation propositions are used nonaffirmatively). One of the methods of a proposition’s nonaffirmative usage is indirect usage. Its only purpose is transmitting content, rather than affirming that the sense is true. For example, the proposition “The orbits of planets have a circular form” is used thus as part of the proposition “Kepler thought that the orbits of planets have a circular form.” In affirming the latter, we do not at all mean to say that it is true that the orbits of planets have a circular form; we desire to communicate the proposition that Kepler affirmed, and this proposition in itself may be either true or false (in this instance, it is false). Reference to (citation of) propositions should be distinguished from their usage.

In logic propositions are used mainly in the application of logical calculations to any concrete field of objects. Variable propositions and forms (declarative forms) of propositions figure essentially in the formulas of so-called pure logical calculations. A variable proposition is not a proposition in the true sense; it is a variable of the proposition—that is, a variable for which concrete (“constant”) propositions (of a given type) or their names can be substituted. The form of a proposition is an expression containing the variables (possibly, in particular, the variables for the proposition) that become a proposition after the substitution of certain values—from appropriate admissible areas of values—instead of all variables entering into it. For example, the formula x + y > 2 is the form of a proposition: x and y are variables which acquire value from the field of real numbers; if x = 1 and y = 2, this formula becomes the true proposition 1 + 2 > 2.

REFERENCES

Tarski, A. Vvedenie v logiku i metodoligiiu deduktivnykh nauk. Moscow, 1948. (Translated from English.)
Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. (Translated from English.)

B. V. BIRIUKOV

In linguistics, a proposition is a unity of language communication. The segmentation of linguistic material by intonation and content leads to the communication units of speech sometimes called phrases. The segmentation of linguistic material by formal characteristics results in the syntactic units of language frequently called sentences. (Other correlative pairs of terms exist.) The sentence and the phrase are units of the same level (communicative), but they pertain to different aspects of linguistic material. The proposition as a real unit of intercourse is a synthesis of the correlative units of language and speech—sentences and phrases. In modern linguistics there are other interpretations of the concept of “proposition.”

REFERENCES

Vannikov, IU. V. “Vyskazyvanie kak sinteticheskaia edinitsa.” In Voprosy grammatiki i slovoobrazovaniia. Moscow, 1968.
Hausenblas, K. “On the Characterization and Classification of Discourses.” Travaux linguistiques de Prague, 1966, no. 1.

IU. V. VANNIKOV

proposition

[‚präp·ə′zish·ən]
(mathematics)
Any problem or theorem.
A statement that makes an assertion that is either false or true or has been designated as false or true.

proposition

(logic)
A statement in propositional logic which may be either true or false. Each proposition is typically represented by a letter in a formula such as "p => q", meaning proposition p implies proposition q.
References in classic literature ?
Keen and dispassionate, with a genius for mercilessly cutting to the marrow of a proposition, Hall has at the same time been a zealot for the improvement and extension of telephone service.
Descending from these general principles, we find the proposition that in legal contemplation the Union is perpetual confirmed by the history of the Union itself.
Madame de Villefort, in spite of all the remarks which she considered it her duty to make, secretly approved of the proposition, my father consented to it at her instigation, and it was only on account of my poor grandfather that I finally abandoned the project.
After some negotiation and delay, therefore, they declined the proposition that had been made to them, but subsequently despatched a party for the mouth of the Columbia, to establish a post there before any expedition sent out by Mr.
Perhaps this incredible proposition of his is only intended to mystify us," growled an apoplectic old admiral.
I have had a proposition made me concerning you," he said with an unnatural smile.
The girl put the question to Usanga, who, degraded, cunning, and entirely unprincipled, was always perfectly willing to promise anything whether he had any intentions of fulfilling his promises or not, and so immediately assented to the proposition.
Mine was a business proposition, not a marriage proposal," she interrupted, coldly angry.
It was life, and life was a savage proposition at best.
Then, if he says no to the proposition, I reckon I'll lose.
Between Barbicane's proposition and its realization no true Yankee would have allowed even the semblance of a difficulty to be possible.
They had the audacity to make such a proposition as that to me