A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity.
Formally, propositions are often modeled as functions which map a possible world to a truth value.
For instance, the proposition that the sky is blue can be modeled as a function which would return the truth value
However, a number of alternative formalizations have been proposed, notably the structured propositions view.
Propositions have played a large role throughout the history of logic, linguistics, philosophy of language, and related disciplines.
Some researchers have doubted whether a consistent definition of propositionhood is possible, David Lewis even remarking that "the conception we associate with the word ‘proposition’ may be something of a jumble of conflicting desiderata".
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.
In modern logic, propositions are standardly understood semantically as indicator functions that take a possible world and return a truth value.
For example, "Snow is white" (in English) and "Schnee ist weiß" (in German) are different sentences, but they say the same thing, so they express the same proposition.
[citation needed] The above definitions can result in two identical sentences/sentence-tokens appearing to have the same meaning, and thus expressing the same proposition and yet having different truth-values, as in "I am Spartacus" said by Spartacus and said by John Smith, and "It is Wednesday" said on a Wednesday and on a Thursday.
These examples reflect the problem of ambiguity in common language, resulting in a mistaken equivalence of the statements.
A related problem is when identical sentences have the same truth-value, yet express different propositions.
In other words, the example problems can be averted if sentences are formulated with precision such that their terms have unambiguous meanings.
W. V. Quine, who granted the existence of sets in mathematics,[11] maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences.
Aristotelian logic identifies a categorical proposition as a sentence which affirms or denies a predicate of a subject, optionally with the help of a copula.
Some philosophers argue that some (or all) kinds of speech or actions besides the declarative ones also have propositional content.
Propositions are also spoken of as the content of beliefs and similar intentional attitudes, such as desires, preferences, and hopes.
Desire, belief, doubt, and so on, are thus called propositional attitudes when they take this sort of content.
[9] Bertrand Russell held that propositions were structured entities with objects and properties as constituents.