Logic > Umar Shahzada

PROPOSITION Historical Usage Usage in Aristotle: Aristotelian logic It Identifies a proposition as a sentence which affirms or denies the predicate of a subject. An Aristotelian proposition may take the form All men are mortal or Socrates is a man. Such propositions comprise the atomic elements in Propositional logic. The sentence A and B expresses both proposition A and proposition B. Both treat the proposition as a sentence having the aforementioned form. Such usage is increasingly non-standard, and will not be used henceforth in this article.

Usage by the Logical Positivists: Often propositions are related to closed sentences, to distinguish them from what is expressed by an open sentence, or predicate. In this sense, propositions are statements that are either true or false. This conception of a proposition was supported by the philosophical school of logical positivism. Some philosophers, such as John Searle, hold that other kinds of speech or actions also assert propositions. Yes-no questions are an inquiry into a proposition's truth value. Traffic signs express propositions without using speech or written language. It is also possible to use a declarative sentence to express a proposition without asserting it, as when a teacher asks a student to comment on a quote; the quote is a proposition (that is, it has a meaning) but the teacher is not asserting it. Snow is white expresses the proposition that snow is white without asserting it (i.e. claiming snow is white). 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 in 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).

Singular Propositions Singular propositions (also called ‘Russellian propositions’) are propositions that are about a particular object or individual in virtue of having the object or individual as a constituent of the proposition. Alleged examples of singular propositions are the propositions that Mont Blanc is more than 4,000 meters high, that Socrates was wise, and that she [pointing to someone] lives in New York. Singular propositions are to be contrasted with general propositions and (what we can call) particularized propositions. The former are propositions that are not about any particular item (as opposed to a class or kind of item) and the latter are propositions that are about particulars or individuals but do not contain those individuals as constituents. Examples of the former are the propositions that most Americans favor a tax cut and that some music is great; examples of the latter are the propositions that the inventor of bifocals was bald and that the tallest spy is a man. The acceptance or rejection of singular propositions lies at the center of many issues in semantics, the philosophy of language, and metaphysics.

Structured Propositions It is a truism that two speakers can say the same thing by uttering different sentences, whether in the same or different languages. For example, when a German speaker utters the sentence ‘Schnee ist weiss’ and an English speaker utters the sentence ‘Snow is white’, they have said the same thing by uttering the sentences they did. Proponents of propositions hold that, speaking strictly, when speakers say the same thing by means of different declarative sentences, there is some (non-linguistic) thing, a proposition, that each has said. This proposition is said to be expressed by both of the sentences uttered (taken in the contexts of utterance -- to accommodate contextually sensitive expressions) by the speakers, and can be thought of as the information content of the sentences (taken in those contexts). The proposition is taken to be the thing that is in the first instance true or false. A declarative sentence is true or false derivatively, in virtue of expressing (in the context in which it is uttered -- I shall henceforth ignore contextual sensitivity and so dispense with qualifications of this sort) a true or false proposition. •

Propositions are thought to perform a number of other functions in addition to being the primary bearers of truth and falsity and the things expressed by declarative sentences. When a German and English speaker believe the same thing, say that the earth is round, the thing they both believe is not a sentence but a proposition. For the English speaker would express her belief by means of the

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sentence ‘The earth is round’ and the German speaker would express her belief by means of the different sentence ‘Die Erde ist rund’.

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