Proposition
Propositions are the meanings of declarative sentences, objects of beliefs, and bearers of truth values. They explain how different sentences, like 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's 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. 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.
Types
Various types of propositions are distinguished based on the kind and domain of information they convey and how they assert it. Many of the distinctions overlap and can be combined to form more specific subtypes. For example, a universal proposition can be either affirmative or negative. Affirmative propositions state that something is the case, such as "the tree is green". They contrast with negative propositions, which deny that something is the case, like "the tree is not green". In classical logic, a proposition with a double negation, such as "the tree is not not green", is equivalent to an affirmative proposition. In some cases, roughly the same information can be expressed with and without negations, as in "he is not happy" and "he is sad". This raises the question of whether being affirmative or negative is an essential feature of propositions at the level of content rather than a linguistic artifact at the level of expression. A closely related distinction is between true and false propositions: a true proposition accurately represents reality, while a false proposition misrepresents it. If an affirmative proposition is true, then the corresponding negative proposition is false, and vice versa.Universal propositions assert that something is the case for all entities in a domain, as in "all humans are mortal". They contrast with existential propositions, which state that something is the case for at least one entity in a domain, such as "some humans are left-handed". Both universal and existential propositions make general statements. Unlike them, singular propositions are about one specific entity, as in "Socrates is wise". Philosophers discuss various problems associated with the nature and existence of singular propositions, like how to understand propositions about non-existing entities, as in "Santa Claus has a beard".
Another distinction is between categorical and conditional propositions. Categorical propositions assert how things are, independently of other statements or assumptions. Conditional or hypothetical propositions link two simpler propositions, typically expressed as an "if-then" sentence. They hold that the then-statement, called consequent, is true in case the if-statement, called antecedent, is true, as in "if it rains, then the ground gets wet". Conditional propositions are compound propositions since they have components that are themselves propositions. Other compound propositions include conjunctive and disjunctive propositions. Conjunctive propositions claim that all their component statements are true, typically expressed as an "and" sentence, such as "the tree is green and the sky is blue". Disjunctive propositions assert that one of their component statements is true, typically expressed as an "or" sentence, as in "it is windy or it is rainy". For inclusive disjunctive propositions, at least one but possibly both component statements are true, while for exclusive disjunctive propositions, exactly one component statement is true and the other is false.
The difference between analytic and synthetic propositions depends on the source of their truth. The truth of analytic propositions is determined only by the meanings of concepts, independent of the actual state of the world. For example, the proposition "all bachelors are unmarried" is analytically true because the concept "bachelor" already includes the meaning of "unmarried". The truth of synthetic propositions, such as "snow is white", depends on the state of the world. A similar distinction, based on the source of knowledge rather than truth, is between a priori and a posteriori propositions. A priori propositions can be known through pure reasoning alone, such as "", while a posteriori propositions describe empirical facts knowable through sensory experience, like "the sun is shining".
Modal propositions express what is possible, necessary, or impossible. Rather than asserting how the world is, they describe how it could or could not have been, as in "it is possible that I will win the lottery" and "it is impossible to travel faster than light". Logicians examine the relation between different modal propositions. For example, classical modal logic states that a proposition is necessarily true if it is impossible that it is false. There are different types of modality. Alethic modality is about what is possible or necessary relative to the laws of nature, metaphysics, or logic. It contrasts with epistemic modality, which concerns what may or must be the case relative to someone's knowledge or evidence, as in "the butler cannot be the killer". Similarly, deterministic propositions express certain information, while probabilistic propositions indicate degrees of uncertainty.
Normative propositions express what ought to be the case, like "you should not drink and drive". They include permissions, requirements, and prohibitions. Moral propositions are normative propositions that assert moral principles or judgments, such as "you should keep promises". Normative propositions contrast with descriptive propositions, which express what is rather than what ought to be. The schools of cognitivism and non-cognitivism debate the existence of normative propositions. Non-cognitivism argues that normative sentences are neither true nor false and do not express propositions, for example, because they convey emotions rather than propositions.
A gappy proposition, also called an incomplete or unfilled proposition, is a statement whose subject matter is not properly specified, which results in an incomplete meaning. This can happen when the proposition involves an empty name, which does not refer to any real entity, such as the name Pegasus. Given the difficulties in assigning truth values to gappy propositions, philosophers debate whether they are propositions in the strict sense rather than other meaning contents. Temporal propositions, another type, are statements that refer to specific times, such as "the Berlin Wall fell in 1989". Propositions are also classified by the domain or field of inquiry to which they belong, such as mathematical, scientific, metaphysical, and theological propositions.