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Рroposition

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Propositions show up in formal logic as objects of a formal language. A formal language begins with different types of symbols. These types can include variables, operators, function symbols, predicate (or relation) symbols, quantifiers, and propositional constants

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2013-11-22

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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. The meaning of a proposition includes having the quality or property of being either true or false

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.

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."

Propositions show up in formal logic as objects of a formal language. A formal language begins with different types of symbols. These types can include variables, operators, function symbols, predicate (or relation) symbols, quantifiers, and propositional constants. (Grouping symbols are often added for convenience in using the language but do not play a logical role.) Symbols are concatenated together according to recursive rules in order to construct strings to which truth-values will be assigned. The rules specify how the operators, function and predicate symbols, and quantifiers are to be concatenated with other strings. A proposition is then a string with a specific form. The form that a proposition takes depends on the type of logic.

The type of logic called propositional, sentential, or statement logic includes only operators and propositional constants as symbols in its language. The propositions in this language are propositional constants, which are considered atomic propositions, and composite propositions, which are composed by recursively applying operators to propositions. Application here is simply a short way of saying that the corresponding concatenation rule has been applied.

The types of logics called predicate, quantificational, or n-order logic include variables, operators, predicate and function symbols, and quantifiers as symbols in their languages. The propositions in these logics are more complex. First, terms must be defined. A term is (i) a variable or (ii) a function symbol applied to the number of terms required by the function symbol's arity. For example, if + is a binary function symbol and x, y, and z are variables, then x+(y+z) is a term, which might be written with the symbols in various orders. A proposition is (i) a predicate symbol applied to the number of terms required by its arity, (ii) an operator applied to the number of propositions required by its arity, or (iii) a quantifier applied to a proposition. For example, if = is a binary predicate symbol and is a quantifier, then x,y,z [(x = y) → (x+z = y+z)] is a proposition. This more complex structure of propositions allows these logics to make finer distinctions between inferences, i.e., to have greater expressive power.

In this context, propositions are also called sentences, statements, statement forms, formulas, and well-formed formulas, though these terms are usually not synonymous within a single text. This definition treats propositions as syntactic objects, as opposed to semantic or mental objects. That is, propositions in this sense are meaningless, formal, abstract objects. They are assigned meaning and truth-values by mappings called interpretations and valuations, respectively.

Types of predicate:

Predicates may be classified in 2 ways, one of which is based on their structure (simple or compound), and the other on their morphological characteristics (verbal or nominal).

Structural classification: 

  1.  simple predicate (verbal and nominal)
  2.  compound predicate (verbaland nominal

Morphological classification: 

  1.  verbal predicate (simple and compound)
  2.  nominal predicate(simple and compound)

The simple nominal predicate – a predicate consisting merely of a noun or an adjective, without a link verb, is rare in English, but it is nevertheless a living type and must be recognized as such.

Only 2 spheres of its use: 

  1.  In sentences where the immediate neighborhood of the subject noun and the predicate noun or adjective is used to suggest the impossibility or absurdity of the idea that they might be connected. Sentences with this kind of simple nominal predicate are always exclamatory, e.g. My ideas obsolete!!!!!!! It would not do to call such sentences elliptical since the link verb cannot be added without completely changing the meaning of the sentence.
  2.  In the sentences un which the predicative comes first, the subject next, and no link verb is either used or possible. Such sentences seem to occur chiefly in colloquial style, e.g. “Splendid game, cricket”, remarked MR Barbecue-Smith heartily to no one in particular; “so thoroughly English”.

The compound nominal predicate is always consists of a link verb and a predicative, which may be expressed by various parts of speech, usually a noun, an adjective, also a stative, or an adverb.

Link verb – the idea of link suggests that its function is to connect the predicative with the subject. It is not correct. The true function of a link verb is not a connecting function. It expresses the tense and the mod in the predicate (to be also expresses number and person).

There are sentences in which the finite verb is a predicate itself, i.e. it contains some information about the subject which may be taken separately, but at the same time the verb is followed by a predicative and is in so far a link verb. He came home tired - the finite verb in such sentences conveys a meaning of its own, but the main point of the sentence lies in the information conveyed by the predicative noun or adjective. The finite verb performs the function of a link verb.

Since such sentences have both a simple verbal predicate and a compound nominal predicate, they form a special or mixed type: double predicates.