I promised — foolishly, as I’m quite snowed under with other things too! — to introduce a paper of Neil Tennant’s on entailment and deducibility next week at our logic reading group. So as background I thought it might be of interest to take a trip down memory lane, and at the meeting today talk a little about discussions of entailment from Lewy and Smiley that were in the air when Tennant was first tackling entailment. I dashed off some notes today before the reading group: those who don’t know or don’t remember what those Cambridge heroes were up to might be interested in this (necessarily brief and partial) nostalgia trip: ‘Entailment, with nods to Lewy and Smiley‘. [Nov. 20: further slight tidying up.]
3 thoughts on “Entailment – a blast from the past”
Minor typo in P4 on page 2: “We define ‘strict implication’ be saying …” should be “We define ‘strict implication’ by saying …” (ie, replace “be” with “by”).
It’s a very interesting discussion, but I’m not sure I find the “In Rome” example and associated arguments convincing.
For a start, I’m not convinced that P5 is right. Sure, it’s true that in a sense that “you will always in fact have B as well since it is necessary”, but that doesn’t mean B shouldn’t be stated in the argument. A doesn’t give you C on its own, I would say; it gives you C only with the help of B.
When premises or intermediate steps are “dropped”, it naturally becomes less clear that the remaining premises guarantee the truth of the conclusion.
So Lewy may be pulling a fast one.
But also, I’m not sure that biting the bullet as in O’3 is so bad. Of course, if you just say “facts about speech habits in Rome can entail facts about numbers”, it does seem strange. (Though I’m not sure I’d say “absurd” or “intolerable”. I have to wonder how much work is being done by the rhetoric, both there and in referring to the facts about language as mere “habits”, but that’s an aside.)
I think the strangeness may be, at least partly, an illusion caused by ignoring a larger picture. For while it’s true that the facts about language are contingent, they’re not *arbitrary*. There are reasons why Italians say “Due pie due fa quattro”, rather than something else, and reasons why Italians think that’s true, rather than false. It’s at least not obvious to me that in this larger picture it would still seem strange that some necessary truths follow from everything that’s involved.
I’m not sure I need (or want?) this further point, but I’ll include it anyway: I might even call on something like P5 to suggest that people may be in the habit of implicitly dropping dropping necessary facts that are part of why they believe something is true. So even if it seems strange on general principles that we could infer a necessary fact from contingent ones, perhaps that’s not actually what we’re doing. Perhaps there are some necessary facts in there as well that we’re overlooking.
Excellent paper! I thoroughly enjoyed it and am recommending it as suggested reading to my students. I certainly hope that it also gets published soon, for it is such a neat little article imho.
Thanks for the nice comment (and the corrections!)