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Let a be a true sentence entailed by A but not by B. Let f be any falsehood entailed by A. Since A entails both a and f the conjunction, a&f is a falsehood entailed by A, and so part of A's falsity content.
PA never insists (proves) that a proof of A entails A's truth, unless it already has a proof of A to back up that claim.
For example, a definition of kind (a) entails that a proposition's being metaphysically necessary consists in its being epistemically necessitated by a certain class of propositions.
Sentence A entails sentence B if in all models in which the interpretation of A is true, also the interpretation of B is true.
For some, the settling condition implies belief: the sense in which I'm settled on A-ing when I intend to A entails that I believe that I will A (Harman 1976, Velleman 1989).
It is a matter of consensus in the philosophy of intention that intending to do A entails wanting to do A, in the motivational sense for which the 'primitive sign of wanting is trying to get' (Anscombe 1963, p. 68).
Similar(48)
We're always ready for a good story involving an entail!
Hitting a billiard ball with a cue entails both a cause and a location.
The boy inherited the estate through an entail.
At least where a breach entails a risk of personal information being extracted from compromised data.
Indeed, as \(\neg raven(a)\) entails \ raven(a) \rightarrow black(a)\), it can be shown that \(h\) is (directly) Hempel-confirmed by the observation of any object that is not a raven (an apple, a cat, a shoe, or whatever), apparently disclosing puzzling "prospects for indoor ornithology" (Goodman 1955, 71).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com