Proposition

Propositions are the meanings of declarative sentences, objects of beliefs, and bearers of truth values. They explain how different sentences, such as the English "Snow is white" and the German "Schnee ist weiß", can have identical meaning by expressing the same proposition. Similarly, they ground the fact that different people can share a belief by being directed at the same content. True propositions describe the world as it is, while false ones fail to do so. Researchers distinguish types of propositions by their informational content and mode of assertion, such as the contrasts between affirmative and negative propositions, between universal and existential propositions, and between categorical and conditional propositions. Many theories of the nature and roles of propositions have been proposed. Realists argue that propositions form part of reality, a view rejected by anti-realists. Non-reductive realists understand propositions as a unique kind of entity, whereas reductive realists analyze them in terms of other entities. One proposal sees them as sets of possible worlds, reflecting the idea that understanding a proposition involves grasping the circumstances under which it would be true. A different suggestion focuses on the individuals and concepts to which a proposition refers, defining propositions as structured entities composed of these constituents. Other accounts characterize propositions as specific kinds of properties, relations, or states of affairs. Philosophers also debate whether propositions are abstract objects outside space and time, psychological entities dependent on mental activity, or linguistic entities grounded in language. Paradoxes challenge the different theories of propositions, such as the liar paradox. The study of propositions has its roots in ancient philosophy, with influential contributions from Aristotle and the Stoics, and later from William of Ockham, Gottlob Frege, and Bertrand Russell. Propositions are relevant to many fields. Logicians examine their logical form and inferential patterns as the premises and conclusions of arguments. Linguists investigate propositions as the meanings of declarative sentences and explore how natural language encodes this information, including the issues of ambiguity, vagueness, and context sensitivity. In psychology and philosophy of mind, researchers analyze how the mind deals with propositions, studying propositional attitudes such as belief, desire, and intention.

Definition and roles

Propositions are typically characterized in terms of three interlocking roles: as the meanings of declarative sentences, as the contents of psychological attitudes like beliefs, and as the bearers of truth values. Philosophers debate the relations between these characterizations, questioning whether one is more fundamental than the others and whether they all describe the same class of entities. In their role as the meanings of declarative sentences, propositions are the ideas or semantic contents expressed by assertions such as "The door is open". Declarative sentences express what is the case. They contrast with interrogative sentences, like "Is the door open?", which request information, and imperative sentences, such as "Open the door!", which issue commands. Different declarative sentences can express the same idea, like the English sentence "Snow is white" and the German sentence "Schnee ist weiß". Accordingly, propositions are not identical to individual sentences and do not belong to any particular language. Instead, they reflect the information content of sentences and track cross-linguistic sameness. The terms "proposition" and "statement" are sometimes used as synonyms. However, the word "statement" is ambiguous since it can also refer to declarative sentences themselves rather than their meanings. The term proposition also overlaps with the term judgment, with one difference being that judgments are more closely associated with mental processes that affirm or deny the truth of a content. Propositions are further characterized as the contents or objects of psychological attitudes like beliefs. For example, if Leila believes that the train will be delayed, then she has a mental state, called a propositional attitude, directed at the proposition that the train will be delayed. There are many propositional attitudes besides beliefs, such as desires, hopes, and fears, like when Leila fears that the train will be delayed. The contents of propositional attitudes are shareable: different persons can have the same beliefs or fears, like when Diego also fears that the train will be delayed. Accordingly, propositions are not identical to individual beliefs or desires since the same proposition can underlie many individual mental states. Traditionally, propositions have been understood as non-mental or abstract entities, though alternative proposals see them as general types of mental entities. Propositional attitudes are typically expressed through that-clauses to link a psychological attitude to a proposition, as in "she believes that it will rain". For this reason, propositions are also characterized as the referents of that-clauses. Propositions are additionally treated as bearers of truth values. This means that each proposition is either true or false. The truth value of a proposition depends on its accuracy: true propositions describe the world as it is while false propositions fail to do so. Propositions are not the only entities that have truth values. Other truth-bearers include declarative sentences and beliefs, raising the question of how these truth-bearers relate to each other. According to one proposal, propositions are the primary truth-bearers, meaning that declarative sentences and beliefs are true or false in a derivative sense by being about true or false propositions. Propositions are also discussed as bearers of modal properties: a proposition can be possible, impossible, or necessary, depending on whether it is logically compatible with coherent scenarios, or in some sense conceivable or contradictory. The word proposition originates from the Latin term proponere, meaning 'to set forth or propose'. Through its past participle propositus, it gave rise to the Latin terms propositio and proposition and the Old French term proposition. The word entered the English language as a borrowing from Latin and French during the Middle English period, with its first known use in Wycliffe's Bible in 1382.

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