Definition:Statement

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Definition

A statement is a sentence which has objective and logical meaning.


Also defined as

In a non-mathematical / logical context, the term statement has a wider and looser meaning than this.


In the field of computer science, where it is more usual to encounter commands and questions, the term statement is generally used to encompass all types of sentence; what we refer to as a statement tends to be given the term assertion.


In other fields of science, the term statement is usually tacitly understood as being a true statement, and in such a context such statements can be referred to as laws of asserted statements.


Some sources, in their definition of statement, specifically invoke Law of Excluded Middle and Principle of Non-Contradiction, and word the definition as:

A statement (or proposition) is a sentence which is either true or false and cannot be both true and false.

However, it needs to be understood that this definition restricts discussion to Aristotelian logic and does not encompass logic of the intuitionist school.


Also known as

Equivalent terms for statement are:

  • Assertion
  • Declarative sentence
  • Indicative sentence
  • Declaration
  • Expression (used in a wider context, and has a less precise interpretation)
  • Boolean expression (used in the specific context of mathematical logic)


The term proposition is often seen for statement, but modern usage prefers to reserve the term proposition for something more specific.


Some sources use the word sentence, but that word is considered nowadays to have too wide a range of meanings to be precise enough in this context.


The term relation can sometimes be seen, to be used to mean a statement composed of mathematical signs and objects, but this usage of the word relation is not endorsed on $\mathsf{Pr} \infty \mathsf{fWiki}$.


Some sources, not having developed the necessary linguistic terms as successfully as the mathematical ideas behind them, use vague terms like sentence of English, which fails on multiple levels.


Examples

Example: $3 \times 4 = 11$

$3 \times 4 = 11$ is an example of a false statement.


Example: $2^{19 \,937} - 1$ is Prime

$2^{19 \,937} - 1$ is a prime number

is an example of a true statement.


Also see


In the various branches of symbolic logic, statements are assigned symbols:


During the course of an argument, statements perform different tasks. In this context, a statement is given a name according to what task it is doing, as follows:

  • Definition:Hypothesis: sometimes used to mean either assumption or premise, but this tends nowadays to mean a statement whose truth is suspected, but has not actually been proven to be true.



Other types of sentence

There are other types of sentences which may be encountered, for example:

  • Questions: for example:
"What do you get if you multiply six by nine?"
  • Commands: for example:
"Multiply six by nine."


Other types of sentence which are also technically commands are:

  • Instructions:
"In order to solve this problem, you need to multiply six by nine."
  • Requests:
"Would you please kindly multiply six by nine, if it's not too much trouble?"
"Why don't you just sit right down there and multiply six by nine?"
  • Exhortations:
"May the powers that be strike me down here and now if six multiplied by nine isn't forty-two in base thirteen!"


Sources

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