Proposition

Proposition is a term used in logic to describe the content of assertions. Assertions are non-linguistic abstractions from sentences and can be evaluated as either true or false. The nature of propositions is highly controversial amongst philosophers, many of whom are skeptical about the existence of propositions. Many logicians prefer to avoid use of the term proposition in favour of using sentences.

Different sentences may express the same proposition when they both have the same meaning. For example, Snow is white (in English) and Schnee ist weiss (in German) are different sentences, but both say the same thing, namely, that snow is white. Hence they express the same proposition. Two different sentences in the same language may also express the same proposition. For example, Tiny crystals of frozen water precipitation are white is in English, but is said to be the same proposition as snow is white by virtue of the definition of snow.

The usual convention for naming propositions is to create a noun phrase by prefixing the word that to any sentence which expresses the proposition in question. Thus, that Jones is a bachelor is the proposition expressed by the sentence Jones is a bachelor.

Two other logical uses bear note: In Aristotelian logic a proposition is a particular kind of sentence: one which affirms or denies a predicate of a subject. Aristotelian propositions take forms like All men are mortal and Socrates is a man. Propositional logic is so named because its atomic elements are the expressions of complete propositions; they are often simply called propositions. The sentence A and B expresses both proposition A and proposition B. Both of these uses treat a proposition simply as a sentence (albeit of a certain kind). This usage is increasingly non-standard, and will not be used in the rest of this article.

Often propositions are related to closed sentences, to distinguish them from what is expressed by an open sentence, or predicate. In this sense, propositions are statements that are either true or false. This conception of a proposition was supported by the philosophical school of logical positivism.

Some philosophers, such as John Searle, hold that other kinds of speech or actions also assert propositions. Yes-no questions are an inquiry into a proposition's truth value. Traffic signs express propositions without using speech or written language. It is also possible to use a declarative sentence to express a proposition without asserting it, as when a teacher asks a student to comment on a quote; the quote is a proposition (that is, it has a meaning) but the teacher is not asserting it. Snow is white expresses the proposition that snow is white without asserting it (i.e. claiming snow is white).

Propositions are usually spoken of as the content of beliefs and similar intentional attitudes such as desires, preferences, and hopes. For example, "I desire that I have a new car," or "I wonder whether it will snow" (or, whether it is the case that it will snow). Desire, belief, and so on, are thus called propositional attitudes when they take this sort of content.

Treatment in logic
In Aristotelian logic a proposition is a particular kind of sentence, one which affirms or denies a predicate of a subject. Aristotelian propositions take forms like All men are mortal and Socrates is a man.

Propositions are the elements in the domain of propositional logic. The sentence A and B expresses both proposition A and proposition B.

Propositions are what is expressed by predicate logic. (x)Fx is said to express a proposition. However, neither F nor x is a proposition itself. One early goal of predicate logic was to try and capture the structure of propositions independently of the sentences that express them; both the German and English versions of snow is white may be translated as Ws. By virtue of the definition of the object s (snow) this may be transformed into the more precise formulation of the proposition given above. Whether this translation can really be done is a matter of philosophical debate.

Modal operators like possibility or necessity have propositions as their subject (propositions are said to be in their scope). Modal logic has been similarly used in examining propositional attitudes like belief and desire, because the subjects of beliefs and desires are said to be propositions as well.

Objections to propositions
Many philosophers and linguists claim that the notion of a proposition is too vague or not useful. For them, it is just a misleading concept that should be removed from philosophy and semantics. W.V.O. Quine maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences.