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Definition:
Implication is a general concept describing the relationship between statements in which the
truth of a single statement or even a group of statements ensures the truth of a later
statement. Logic usually distinguishes between several different types of implication:
Material Implication: A conditional statement of the type "If P, then Q" where the truth of P ensure that Q must also be true. It is possible for a statement of "material implication" to be false if it happens that P is true and Q is false after all.
Strict Implication: It is logically impossible for P to be true and Q to be false.
Entailment: The statement P is said to entail Q if Q can be logically deduced from P.
The term implication is obviously used differently in logic than in casual conversation where "implication" is usually used to refer to some idea which is being communicated in an implicit manner. For example, in casual conversation, "His latest essay managed to be very coherent" implies that other essay are usually incoherent - even though that isn't stated explicitly.
In logic, the term "implicature" is commonly used for this type of implication. Coined by H.P. Grice, implicature generally refers to any sort of proposition which is not specifically stated, but which must be logically intended and believed by the speaker on the assumption that they are attempting to engage in cooperative communication. The above statement, for example, makes little sense unless the speaker believes that past essays were incoherent or is trying to deceive people into adopting that belief.
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Related Resources:
What is the Logic and the Philosophy of Language?
The two fields Logic and the Philosophy of Language are often treated separately, but they are nevertheless close enough that they are presented together here. Logic is the study of methods of reasoning and argumentation, both proper and improper. The Philosophy of Language, on the other hand, involves the study of how our language interacts with our thinking.What is Philosophy?
What is philosophy? Is there any point in studying philosophy, or is it a useless subject? What are the different branches of philosophy - what's the difference between aestheitcs and ethics? What's the difference between metaphysics and epistemology?
