Proposition

proposition is a statement expressing certain relationship between two or more terms

In common philosophical language, a proposition is the content of an assertion, that is, it is true-or-false and defined by the meaning of a particular piece of language. The proposition is independent of the medium of communication.

Since the definition of "proposition" is such a crucial matter to various topics in philosophy, the nature of propositions is highly controversial. Even the existence of propositions is sometimes called into question and, as a result, the term is widely used, even when the term is not itself explicitly defined and therefore confusion, in regard to "meaning", may arise.

Common usage
Different sentences 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.

Usage in Aristotle
Aristotelian logic identifies a proposition as a sentence which affirms or denies the predicate of a subject. An Aristotelian proposition may take the form All men are mortal or Socrates is a man. Such propositions comprise the atomic elements in Propositional logic. The sentence A and B expresses both proposition A and proposition B. Both treat the proposition as a sentence having the aforementioned form. Such usage is increasingly non-standard.

Usage by the Logical Positivists
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 also 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.

Usage in Russell
Bertrand Russell held that propositions were structured entities with objects and properties as constituents. Others have held that a proposition is the set of possible worlds/states of affairs in which it is true. One important difference between these views is that on the Russellian account, two propositions that are true in all the same states of affairs can still be differentiated. For instance, the proposition that two plus two equals four is distinct on a Russellian account from three plus three equals six. If propositions are sets of possible worlds, however, then all mathematical truths are the same set (the set of all possible worlds).

Relation to the mind
Propositions are primarily discussed in relation to the mind as they fit into propositional attitudes. Propositional attitudes are simply attitudes characteristic of folk psychology (belief, desire, etc.) that one can take toward a proposition (e.g. 'it is raining', 'snow is white', etc.). In English, propositions usually follow folk psychological attitudes by a "that clause" (e.g. 'Jane believes that it is raining). In philosophy of mind and psychology, mental states are often taken to primarily consist in propositional attitudes. The propositions are usually said to be the mental content of the attitude. For example, if Jane has a mental state of believing that it is raining, her mental content is the proposition 'it is raining'. Furthermore, since such mental states are about something (namely propositions), they are said to be intentional mental states. Philosophical debates surrounding propositions as they relate to propositional attitudes have also recently centered on whether they are internal or external to the agent or whether they are mind-dependent or mind-independent entities (see the entry on internalism and externalism in philosophy of mind).

Treatment in logic
As noted above, 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.

Objections to propositions
A number of 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. Quine maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences.