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Concept# Atomic sentence

Summary

In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences. For example, "The dog ran" is an atomic sentence in natural language, whereas "The dog ran and the cat hid" is a molecular sentence in natural language.
From a logical analysis point of view, the truth or falsity of sentences in general is determined by only two things: the logical form of the sentence and the truth or falsity of its simple sentences. This is to say, for example, that the truth of the sentence "John is Greek and John is happy" is a function of the meaning of "and", and the truth values of the atomic sentences "John is Greek" and "John is happy". However, the truth or falsity of an atomic sentence is not a matter that is within the scope of logic itself, but rather whatever art or science the content of the atomic sentence happens to be talking about.
Logic has developed artificial languages, for example sentential calculus and predicate calculus, partly with the purpose of revealing the underlying logic of natural-language statements, the surface grammar of which may conceal the underlying logical structure. In these artificial languages an atomic sentence is a string of symbols which can represent an elementary sentence in a natural language, and it can be defined as follows. In a formal language, a well-formed formula (or wff) is a string of symbols constituted in accordance with the rules of syntax of the language. A term is a variable, an individual constant or an n-place function letter followed by n terms. An atomic formula is a wff consisting of either a sentential letter or an n-place predicate letter followed by n terms. A sentence is a wff in which any variables are bound. An atomic sentence is an atomic formula containing no variables. It follows that an atomic sentence contains no logical connectives, variables, or quantifiers.

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Atomic sentence

In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences. For example, "The dog ran" is an atomic sentence in natural language, whereas "The dog ran and the cat hid" is a molecular sentence in natural language. From a logical analysis point of view, the truth or falsity of sentences in general is determined by only two things: the logical form of the sentence and the truth or falsity of its simple sentences.

Sentence (mathematical logic)

In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values: as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.

Truth-bearer

A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of opinion on the matter, the term truth-bearer is used to be neutral among the various theories.