proposition

(redirected from propositions)
Also found in: Dictionary, Thesaurus, Medical, Legal.
Related to propositions: prepositions

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 ?
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.
Bertha, the slim, fair-haired girl, whose present thoughts and emotions were an enigma to me amidst the fatiguing obviousness of the other minds around me, was as absorbing to me as a single unknown to-day--as a single hypothetic proposition to remain problematic till sunset; and all the cramped, hemmed-in belief and disbelief, trust and distrust, of my nature, welled out in this one narrow channel.
He always shied at propositions based on gentlemen's agreements, and a man who ventured his honor as a gentleman, in dealing with Daylight, inevitably was treated to an unpleasant time.
This lesser Prince de Wagram of the administration, to whom the duty of gathering opinions and ideas and making verbal reports thereon was entrusted, knew all the secrets of parliamentary politics; dragged in the lukewarm, fetched, carried, and buried propositions, said the Yes and the No that the ministers dared not say for themselves.
These unmeaning propositions are hardly suspected to be a caricature of a great theory of knowledge, which Plato in various ways and under many figures of speech is seeking to unfold.
These propositions will be most readily understood by looking to our domestic races.
Yes, Cleitophon, but he also said that justice is the interest of the stronger, and, while admitting both these propositions, he further acknowledged that the stronger may command the weaker who are his subjects to do what is not for his own interest; whence follows that justice is the injury quite as much as the interest of the stronger.
That all men are mortal," "that Columbus discovered America," "that Charles I died in his bed," "that all philosophers are wise," are propositions.
But general propositions as to feeding on meal and on grass were doubtful and obscure.
All these propositions being overruled, it was concluded, at last, to bind him in his chair, and the word was passed for Dennis.
Idiotic propositions of a parallel nature have been freely offered for my acceptance, and I have been called upon to admit that I would give Poor Law relief to anybody, anywhere, anyhow.
Later it was confirmed and solidified when Wilson proposed that out of courtesy to the strangers the usual topics be put aside and the hour be devoted to conversation upon ordinary subjects and the cultivation of friendly relations and good-fellowship--a proposition which was put to vote and carried.