Proposition

Template:Short description Template:More citations needed 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. Propositions are the objects denoted by declarative sentences; for example, "The sky is blue" expresses the proposition that the sky is blue. Unlike sentences, propositions are not linguistic expressions, so the English sentence "Snow is white" and the German "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 $T$ if given the actual world as input, but would return $F$ 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.

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.Template:Efn Instead, they reflect the information content of sentences and track cross-linguistic sameness. The terms "proposition" and "statement" are sometimes used as synonyms.Template:Efn 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 , meaning Template:Gloss. Through its past participle , it gave rise to the Latin terms and and the Old French term . 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.Template:Efn 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 "$2+2=4$", 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".

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 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.

Relation to the mind

In relation to the mind, propositions are discussed primarily 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.

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.

In modern logic

In modern logic, propositions are standardly defined as functions which take a possible world and return a truth value. For example, the proposition that the sky is blue could be represented as a function notated as $f$. Then if there is a possible world $w$ where the sky is blue and another world $v$ where it is not, we would have that $f(w)=T$ and $f(v)=F$. Via the notion of a characteristic set, propositions can be modeled equivalently as a set of possible worlds, namely those where the proposition is true. For instance, if $w$ and $w^{\prime }$ are the only worlds in which the sky is blue, the proposition that the sky is blue could be modeled as the set $\{w,w^{\prime }\}$.

Numerous refinements and alternative notions of proposition-hood have been proposed including inquisitive propositions and structured propositions. 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.

Objections to propositions

Attempts to provide a workable definition of proposition include the following:

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.

Statements

In logic and semantics, the term statement is variously understood to mean either:

1. A meaningful declarative sentence that is true or false, or
2. a proposition. Which is the assertion that is made by (i.e., the meaning of) a true or false declarative sentence.

In the latter case, a (declarative) sentence is just one way of expressing an underlying statement. A statement is what a sentence means, it is the notion or idea that a sentence expresses, i.e., what it represents. For example, it could be said that "2 + 2 = 4" and "two plus two equals four" are two different sentences expressing the same statement. As another example, consider that the Arabic numeral '7', the Roman numeral 'VII', and the English word 'seven' are all distinct from the underlying number.Template:Sfn

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 truth bearer.

Examples of sentences that are (or make) true statements:

• "Socrates is a man."
• "A triangle has three sides."
• "Madrid is the capital of Spain."

Examples of sentences that are also statements, even though they aren't true:

• "All toasters are made of solid gold."
• "Two plus two equals five."

Examples of sentences that are not (or do not make) statements:

1. "Who are you?"
2. "Run!"
3. "Greenness perambulates."
4. "I had one grunch but the eggplant over there."
5. "King Charles III is wise."
6. "Broccoli tastes good."
7. "Pegasus exists."

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.

As an abstract entity

In some treatments, "statement" is introduced in order to distinguish a sentence from its informational content. A statement is regarded as the information content of an information-bearing sentence. Thus, a sentence is related to the statement it bears like a numeral to the number it refers to. Statements are abstract logical entities, while sentences are grammatical entities.Template:SfnTemplate:Sfn

Historical usage

By Aristotle

In Aristotelian logic a proposition was defined as a particular kind of sentence (a declarative sentence) that affirms or denies a predicate of a subject, optionally with the help of a copula. Aristotelian propositions take forms like "All men are mortal" and "Socrates is a man."

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".

By the logical positivists

Often, propositions are related to closed formulae (or logical sentence) to distinguish them from what is expressed by an open formula. In this sense, propositions are "statements" that are truth-bearers. This conception of a proposition was supported by the philosophical school of logical positivism.

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 signs 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 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, doubt, and so on, are thus called propositional attitudes when they take this sort of content.

By Russell

Bertrand Russell held that propositions were structured entities with objects and properties as constituents. One important difference between Ludwig Wittgenstein's view (according to which a proposition is the set of possible worlds/states of affairs in which it is true) 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 "two plus two equals four" is distinct on a Russellian account from the proposition "three plus three equals six". If propositions are sets of possible worlds, however, then all mathematical truths (and all other necessary truths) are the same set (the set of all possible worlds).

See also

• Belief
  • Doxastic logic
• Categorical proposition
• Concept
• Probabilistic proposition
• Sentence (mathematical logic)
• Truthbearer - statements

References

Sources

• Template:Cite dictionary
• Template:Cite books

Further reading

• A. G. Hamilton, Logic for Mathematicians, Cambridge University Press, 1980, Template:ISBN.
• P. F. Strawson, "On Referring" in Mind, Vol 59 No 235 (Jul 1950)

External links

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