Logical Implication (Noun)
Meaning
A logical relation between propositions p and q of the form `if p then q'; if p is true then q cannot be false.
Classification
Nouns denoting relations between people or things or ideas.
Examples
- In classical logic, logical implication is a relation between two statements where one statement is a prerequisite for the other to be true.
- The law of contrapositive formulates that the conditional logical implication 'if p then q' is logically equivalent to 'not q then not p'.
- Logical implication is a closely related concept to causality, but it is not the same, as one does not necessarily imply the other.
- Logicians understand that a logical implication can be true even when its components are not necessarily true on their own, as long as the premise is not denied the conclusion.
- According to Aristotle, in the valid syllogism form of modus ponens, if p implies q and p is true, then q must be true, demonstrating a fundamental principle of logical implication.