Search results
Results from the WOW.Com Content Network
The fifth and sixth examples are meaningful declarative sentences, but are not statements but rather matters of opinion or taste. Whether or not the sentence "Pegasus exists." is a statement is a subject of debate among philosophers. Bertrand Russell held that it is a (false) statement. [citation needed] Strawson held it is not a statement at all.
Compound statements may contain (sequences of) statements, nestable to any reasonable depth, and generally involve tests to decide whether or not to obey or repeat these contained statements. Notation for the following examples: <statement> is any single statement (could be simple or compound). <sequence> is any sequence of zero or more ...
Propositional logic deals with statements, which are defined as declarative sentences having truth value. [29] [1] Examples of statements might include: Wikipedia is a free online encyclopedia that anyone can edit. London is the capital of England. All Wikipedia editors speak at least three languages.
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
In philosophy, an explanation is a set of statements that renders understandable the existence or occurrence of an object, event, or state of affairs. Among its most common forms are: Causal explanation; Deductive-nomological explanation, involves subsuming the explanandum under a generalization from which it may be derived in a deductive ...
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements.For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.
Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other than its logical constants).