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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.
An open-ended question is a question that cannot be answered with a "yes" or "no" response, or with a static response. Open-ended questions are phrased as a statement which requires a longer answer. They can be compared to closed questions which demand a “yes”/“no” or short answer. [1]
In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water is boiling." expresses a proposition since it can be true or false. The sentences "Is the water boiling?" or "Boil the water!", on the other hand, express no propositions since they are neither true nor false.
Without the benefit of a lie detector or Pinocchio’s growing nose, some sentences can leave you stumped. There are some facts that sound so outlandish, you immediately think they are false ...
a meaningful declarative sentence that is true or false, [citation needed] or; a proposition. Which is the assertion that is made by (i.e., the meaning of) a true or false declarative sentence. [1] [2] In the latter case, a (declarative) sentence is just one way of expressing an underlying statement.
A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one another. In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic or syntactic structure and by the placement of logical constants.
is true while "Mary believes that the moon is made of green cheese" is false. In both cases, each component sentence (i.e. "Al Gore was president of the USA on April 20, 2000" and "the moon is made of green cheese") is false, but each compound sentence formed by prefixing the phrase "Mary believes that" differs in truth-value
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