Entailment [logical implication] vs material implication

The difference between material implication and entailment is that they apply in different contexts. The first is a statement of logic, the second of metalogic. If p and q are two sentences then the difference between “p implies q” and “p is a proof of q” is that the first is a statement within formal logic, the second is a statement about it. Entailment is a concept of proof theory, whereas material implication is the mechanics of a proof.

— Wikipedia on Entailment

2012.09.03 Monday ACHK