Definition:Entailment/Historical Note
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Historical Note on Entailment
The concept of entailment was contrived as an attempt to define a logical connective which avoids the Paradoxes of Material Implication and the Paradoxes of Strict Implication.
It does this by insisting that, before $p$ can imply $q$, it must be relevant to and actually used in the definition of $q$.
Hence the Disjunctive Syllogism:
- $\neg p, p \lor q \vdash p \implies q$
is rejected.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): implication: 3. (entailment)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): implication: 3. (entailment)