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A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary Truth-bearer of truth or falsity. Propositions are the Abstract object Denotation by declarative sentences; for example, "The sky is blue" expresses the proposition that the sky is blue. Unlike sentences, propositions are not Phrase, so the English language sentence "Snow is white" and the German language "Schnee ist weiß" denote the same proposition. Propositions also serve as the objects of belief and other propositional attitudes, such as when someone believes that the sky is blue.
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 if given the actual world as input, but would return if given some alternate world where the sky is green. 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". The term is often used broadly and has been used to refer to various related concepts.
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 mood, such as "Open the door!", which issue commands. Different declarative sentences can express the same idea, like the English language sentence "Snow is white" and the German language 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 objects 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 value. 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 language 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.
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 Disjunction 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 or 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 Scientific law, 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".
Normativity propositions express what ought to be the case, like "you should not drink and drive". They include permissions, requirements, and prohibitions. Morality 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 qualify as propositions in the strict sense. Alternative proposals suggest that they are another type of meaning content. 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.
Realism contrasts with anti-realism, which denies the existence of propositions. Anti-realists provide alternative explanations of proposition-related phenomena. For example, they may assert that other entities act as truth-bearers or propose ways to explain shared sentence meanings and belief contents that do not require propositions. Some anti-realists reject any talk of propositions, while others treat them as theoretically useful fictions that reveal patterns and simplify explanations but are not fundamental features of reality.
Various arguments for and against realism are discussed in the academic literature. Proponents hold that propositions are essential to the understanding of various phenomena: they explain how two sentences can mean the same thing, how a common content underlies cross-linguistic communication, and how people can share beliefs. Another line of argument appeals to linguistic evidence. For example, the sentence "the proposition that the earth is round is uncontroversial" explicitly refers to a proposition, thereby indicating its existence. Several types of expressions may designate propositions, including that-clauses, definite descriptions, and . Critics contend that these phenomena and linguistic devices can be explained without positing propositions, implying that propositions are methodologically unnecessary and ontologically redundant. Other objections focus on theoretical difficulties and paradoxes associated with propositions, such as the liar paradox.
One formal argument for the set-based conception of propositions, developed by David Lewis and Robert Stalnaker, assumes that propositions are properties of the possible worlds where they are true. If a property is identified with the set of entities to which it applies, it follows that propositions are sets of possible worlds. Other arguments for the possible worlds view point to its mathematical precision, formal simplicity, and explanatory power.
One difficulty for the possible worlds view comes from necessary propositions, such as "" and "there are infinitely many prime numbers". A proposition is necessary if it is true in all possible worlds, meaning that it is equivalent to the set of all possible worlds. As a result, all necessary propositions are identical since they all correspond to the same set, which implies that there is only a single necessary proposition. Opponents argue that this is false since different necessary propositions express distinct ideas. For example, a person may know one necessary proposition but be ignorant of another. Critics conclude that the possible worlds view is too coarse-grained to capture these distinctions. Other objections question the existence of possible worlds or hold that sets cannot perform the role of propositions since sets cannot be true or false.
Another set-based proposal relies on the concept of truthmakers rather than possible worlds. A truthmaker of a proposition is an entity that makes the proposition true: if the entity exists, then it is responsible for the proposition being true. On this view, a proposition is a set of possible truthmakers. The theory is based on the idea that truth conditions are essential to a proposition: the proposition describes the conditions of what the world is like, and it is true if the world fulfills those conditions. The set of possible truthmakers encodes the truth condition of the proposition. Unlike the possible worlds view, this approach can distinguish necessary propositions: even propositions that are true in all possible worlds can still have different truthmakers.
This idea is closely related to the principle of compositionality: the theory that the meaning of a compound expression is determined by the meanings of its parts and the way they are combined. According to this principle, one can understand the sentence "Tina is happy" by knowing English grammar and the meanings of the words "Tina", "is", and "happy", even if one has never encountered this specific combination of words before. The principle of compositionality explains how knowledge of a limited number of words and rules makes it possible to comprehend an infinite number of sentences.
Bertrand Russell formulated an influential view of structured propositions. He argued that propositions like "Jason loves Patty" are made up of the individuals they refer to (Jason and Patty) and the properties or relations they instantiate (love). A slightly different proposal by Gottlob Frege distinguishes between individuals and the way they are presented. According to this view, modes of presentation rather than individuals make up propositions. For Frege, the sentences "the morning star is a planet" and "the evening star is a planet" express two different propositions, whereas for Russell, they express the same proposition. The difference lies in the fact that morning star and evening star are different ways of presenting the same individual: the planet Venus. Other approaches to the internal structure of propositions have been suggested, including the idea that they are built up from functions.
A central topic for structured proposition views is the problem of unity: showing how the parts of propositions fuse together into a single entity that represents the world and can be true or false. A related difficulty is to explain how different propositions can have the same constituents, such as the contrast between "Jason loves Patty" and "Patty loves Jason". Instrumentalism about structured propositions is a view that seeks to bypass difficulties of the structured proposition view. It asserts that structural analysis is a useful theoretical tool for understanding certain aspects of propositions but does not reveal their intrinsic nature.
A similar approach characterizes propositions as a special type of relation. Relations are ways of how entities stand to each other. The relation is larger than is a two-place relation since it connects two entities, a larger one and a smaller one. If one of its positions is fixed, as in is larger than the Moon, it becomes a one-place relation or a property. If the other position is also fixed, as in Jupiter is larger than the Moon, it becomes a zero-place relation without any open positions. The relation-based view argues that simple propositions are zero-place relations, meaning that propositions are fully saturated relational states that either obtain or fail to obtain. A related suggestion identifies true propositions with facts or states of affairs. According to this view, sentences and beliefs represent reality, and propositions are what is represented, meaning that propositions are not themselves representations in a strict sense.
Another discussion concerns the ontological domain to which propositions belong. Following the Platonist ideas of Bernard Bolzano and Gottlob Frege, propositions have often been treated as abstract objects that have no causal effects and exist outside space and time. According to this view, propositions like "there are rocks" exist independently of any mental activity and would be true even if there were no humans. However, theoretical difficulties associated with abstract objects, such as the problem of explaining how knowledge of abstract objects is possible, have prompted philosophers to seek alternative conceptions. In response, naturalist theories have characterized propositions as mental or linguistic entities.
One approach of this form defines propositions in relation to psychological activities that represent the world, such as perceptions and judgments. It distinguishes between individual mental acts and general types that apply to several acts, identifying propositions with those types. For example, if two persons judge the same proposition to be true, then their mental states belong to the same act type corresponding to this proposition. This view argues that mental states have conditions of satisfaction that determine their accuracy, with truth corresponding to accurate psychological representation. Fictionalism, another theory, treats propositions as useful inventions that exist as aspects of linguistic frameworks. According to this view, propositions depend on language and have no independent existence.
Abundant conceptions of propositions assert that all well-formed declarative sentences express propositions. Sparse conceptions suggest that this may not be generally the case. For example, Non-cognitivism accept a sparse conception, arguing that some moral statements do not express propositions since they are neither true nor false.
Hyperintensional theories introduce fine-grained distinctions between propositions. For them, two propositions can have different truth values even when they are made up of necessarily equivalent parts. For example, the propositions "he has a 40% chance of succeeding" and "he has a 60% chance of failing" are necessarily equivalent. However, a person may believe one and not the other, indicating a difference in meaning. One approach to hyperintensionality, called two-dimensional semantics, associates two distinct propositions with the same declarative sentence corresponding to different ways of how it can be interpreted.
Explaining the relation of propositions to the mind is especially difficult for non-mentalist views of propositions, such as those of the logical positivists and Russell described above, and Gottlob Frege's view that propositions are Platonist entities, that is, existing in an abstract, non-physical realm. So some recent views of propositions have taken them to be mental. Although propositions cannot be particular thoughts since those are not shareable, they could be types of cognitive events or properties of thoughts (which could be the same across different thinkers).
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. For more, see the entry on internalism and externalism in philosophy of mind.
Numerous refinements and alternative notions of proposition-hood have been proposed including inquisitive propositions and structured propositions. (2025). 9780198814795, Oxford University Press. ISBN 9780198814795 Propositions are called structured propositions if they have constituents, in some broad sense. Assuming a structured view of propositions, one can distinguish between singular propositions (also Russellian propositions, named after Bertrand Russell) which are about a particular individual, general propositions, which are not about any particular individual, and particularized propositions, which are about a particular individual but do not contain that individual as a constituent.
Two meaningful declarative sentences express the same proposition, if and only if they mean the same thing.which defines proposition in terms of synonymity. 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. Another definition of proposition is:
Two meaningful declarative sentence-tokens express the same proposition, if and only if they mean the same thing.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. "I am Spartacus" spoken by Spartacus is the declaration that the individual speaking is called Spartacus and it is true. When spoken by John Smith, it is a declaration about a different speaker and it is false. The term "I" means different things, so "I am Spartacus" means different things.
A related problem is when identical sentences have the same truth-value, yet express different propositions. The sentence "I am a philosopher" could have been spoken by both Socrates and Plato. In both instances, the statement is true, but means something different.
These problems are addressed in predicate logic by using a variable for the problematic term, so that "X is a philosopher" can have Socrates or Plato substituted for X, illustrating that "Socrates is a philosopher" and "Plato is a philosopher" are different propositions. Similarly, "I am Spartacus" becomes "X is Spartacus", where X is replaced with terms representing the individuals Spartacus and John Smith.
In other words, the example problems can be averted if sentences are formulated with precision such that their terms have unambiguous meanings.
A number of philosophers and linguists claim that all definitions of a proposition are too vague to be useful. For them, it is just a misleading concept that should be removed from philosophy and semantics. W. V. Quine, who granted the existence of sets in mathematics, maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences.
Philosopher of language Peter Strawson (1919–2006) advocated the use of the term "statement" in sense (2) in preference to proposition. Strawson used the term "statement" to make the point that two declarative sentences can make the same statement if they say the same thing in different ways. Thus, in the usage advocated by Strawson, "All men are mortal." and "Every man is mortal." are two different sentences that make the same statement.
In either case, a statement is viewed as a truthbearer.
Examples of sentences that are (or make) true statements:
Examples of sentences that are also statements, even though they aren't true:
Examples of sentences that are not (or do not make) statements:
The first two examples are not declarative sentences and therefore are not (or do not make) statements. The third and fourth are declarative sentences but, lacking meaning, are neither true nor false and therefore are not (or do not make) statements. The fifth and sixth examples are meaningful declarative sentences, but are not statements but rather matters of opinion or taste. Whether or not the sentence "Pegasus exists." is a statement is a subject of debate among philosophers. Bertrand Russell held that it is a (false) statement. Strawson held it is not a statement at all.
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. An Aristotelian proposition may take the form of "All men are mortal" or "Socrates is a man." In the first example, the subject is "men", predicate is "mortal" and copula is "are", while in the second example, the subject is "Socrates", the predicate is "a man" and copula is "is".
Some philosophers argue that some (or all) kinds of speech or actions besides the declarative ones also have propositional content. For example, yes–no questions present propositions, being inquiries into the truth value of them. On the other hand, some Semiotics can be declarative assertions of propositions, without forming a sentence nor even being linguistic (e.g. traffic signs convey definite meaning which is either true or false).
Propositions are also spoken of as the content of 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, doubt, and so on, are thus called propositional attitudes when they take this sort of content.
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