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Proposition
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This article is about the term proposition in logic and philosophy; for other uses see Proposition
In logic and philosophy, proposition refers to either (a) the "content" or "meaning" of a meaningful declarative sentence or (b) the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence. Propositions in either case are intended to be truth-bearers, that is, they are either true or false.
The existence of propositions in the former sense, as well as the existence of "meanings", is disputed by some philosophers.
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Encyclopedia
This article is about the term proposition in logic and philosophy; for other uses see Proposition
In logic and philosophy, proposition refers to either (a) the "content" or "meaning" of a meaningful declarative sentence or (b) the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence. Propositions in either case are intended to be truth-bearers, that is, they are either true or false.
The existence of propositions in the former sense, as well as the existence of "meanings", is disputed by some philosophers. Where the concept of a "meaning" is admitted, its nature is controversial. In earlier texts writers have not always made it sufficiently clear whether they are using the term proposition in sense of the words or the "meaning" expressed by the words. To avoid the controversies and ontological implications, the term sentence is often now used instead of proposition to refer to just those strings of symbols that are truth-bearers, being either true or false under an interpretation. Strawson advocated the use of the term "statement".
Historical usage
Usage in Aristotle
Aristotelian logic identifies a proposition as a sentence which affirms or denies a predicate of a subject. An Aristotelian proposition may take the form "All men are mortal" or "Socrates is a man." In the first example the subject is "men" and the predicate "are mortal". In the second example the subject is "Socrates" and the predicate is "is a man".
Usage by the Logical Positivists
Often propositions are related to closed sentences to distinguish them from what is expressed by an open sentence. 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, and so on, are thus called propositional attitudes when they take this sort of content.
Usage by Russell
Bertrand Russell held that propositions were structured entities with objects and properties as constituents. Others have held that a proposition is the set of possible worlds/states of affairs in which it is true. One important difference between these views 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 that two plus two equals four is distinct on a Russellian account from three plus three equals six. If propositions are sets of possible worlds, however, then all mathematical truths are the same set (the set of all possible worlds).
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. 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 (see the entry on internalism and externalism in philosophy of mind).
Treatment in logic
As noted above, in Aristotelian logic a proposition is a particular kind of sentence, one which affirms or denies a predicate of a subject. Aristotelian propositions take forms like "All men are mortal" and "Socrates is a man."
In mathematical logic, propositions, also called "propositional formulas" or "statement forms", are statements that do not contain quantifiers. They are composed of well-formed formulas consisting entirely of atomic formulas, the five logical connective, and symbols of grouping. Propositional logic is one of the few areas of mathematics that is totally solved, in the sense that it has been proven internally consistent, every theorem is true, and every true statement can be proved. (From this fact, and Gödel's Theorem, it is easy to see that propositional logic is not sufficient to construct the set of integers.) The most common extension of propositional logic is called predicate logic, which adds variables and quantifiers.
Objections to propositions
Attempts to provide a workable definition of proposition include
Two meaningful declarative sentences express the same proposition if and only if they mean the same thing.
thus defining 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.
Two meaningful declarative sentence-tokens express the same proposition if and only if they mean the same thing.
Unfortunately, the above definition has the result that two sentences/sentence-tokens which have the same meaning and thus express the same proposition, could have different truth-values, e.g "I am Spartacus" said by Spartacus and said by John Smith; and e.g. "It is Wednesday" said on a Wednesday and on a Thursday.
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 maintained that the indeterminacy of translation prevented any meaningful discussion of propositions, and that they should be discarded in favor of sentences. Strawson advocated the use of the term "statement".
See also
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