# proposition

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Related to propositional: propositional logic

## 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.
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