A proposition is a statement that can be either true or false.
It is a central concept in the philosophy of language, semantics, logic, and related fields. 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.
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.
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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