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I have a question:

Here are two English conditional sentences:

A) If I run, I'll throw up

B) If I move, I'll throw up

Does sentence A logically entail B or does B entail A? Why

Maybe they are logically equivalent? If so could you explain why this is.

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    Although running looks like a special case of moving, the terms in run-of-the-mill English are not that closely related. "Moving" in that context sounds more like a small movement (displacement) - like an abbreviated version of "move at all". – Lawrence Jul 11 '17 at 10:31
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    If you were so queasy that to move [at all] would cause you to throw up, then obviously running would also trigger this. As such, logically A would be true if B were true (but not vice versa, nor are they equivalent). Though as @Lawrence says, the terms are sufficiently different that I doubt you'd use the fact in practice. – TripeHound Jul 11 '17 at 11:14
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    You might want to wait a day or so before selecting an answer :-) You might get some better ones! By the way are you studying linguistics? – Araucaria Jul 11 '17 at 15:29
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    I'm voting to close this question as off-topic because it appears to be a matter of logic rather than language or usage. – Spagirl Jul 12 '17 at 13:16
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    @Spagirl Linguistic semantics necessarily involves logic. This particular topic has been discussed by many famous linguists: Angela Kratzer, Irene Heim, Sabine Iatridou and so forth. Maybe look a few of them up. This is a site for linguists after all! (and the specifics of this question will, rather surprisingly perhaps, not generalise to all languages. – Araucaria Jul 12 '17 at 15:08
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Short answer:

Although running entails moving, the Original Poster's sentence A), which involves running, does not entail sentence B), which involves moving. In other words sentence A being true does not guarantee that sentence B) is true. In fact the reverse holds.


Full answer:

Entailments and downward entailing environments

This question is far more interesting than it first appears. Under normal circumstances if A is a subset of B, A entails B. Running, of course, is a subset of the actions covered by the verb moving. For this reason the truth of sentence (1) below entails the truth of sentence (2):

  1. Bob ran.
  2. Bob moved.

So if we know that sentence (1) is true, we can be certain that sentence (2) is true. Of course, this will not work the other way round. Just knowing that Bob moved does not guarantee that he ran. Instead of running, Bob may have shambled, or danced, or writhed around on the floor. This relationship therefore does not run both ways. Sentence (1) entails sentence (2), but sentence (2) does not entail sentence (1).

Something interesting happens if we negate the sentence though:

  1. Bob didn't run.
  2. Bob didn't move.

Now the relationship seems to be reversed. Just because we know that (3) is true and that Bob did not run, it doesn't mean that we know that (4) is true. Bob may have been moving in all sorts of interesting ways without running. However, we can be absolutely certain that if Bob didn't move he didn't run! (This is because not moving describes a subset of the possible cases covered by not running.)

Environments which reverse the normal pattern of entailment, such as negative clauses, are called downwards entailing environments.

Now, conditional antecedents (the clauses in a conditional which follow the word if), are very similar in many ways to negative clauses. For example, they often take negative-polarity items. Consider the item at all in the following examples

  • *You like Bertha at all. (ungrammatical)
  • You don't like Bertha at all.
  • If you like Bertha at all, come to her leaving party.

From the examples above we can see that at all doesn't work well in a positive sentence but can be licensed by a negative clause or by a conditional antecedent.

A second weird property of conditional antecedents is that, like negative sentences, they are downward entailing environments:

  1. If Bob ran, his shoe fell off.
  2. If Bob moved, his shoe fell off.

Here we see that the although running entails moving, sentence (5) being true does not entail sentence (6) being true. It might easily be the case that if Bob ran, his shoe fell of, but that if he scratched his head it did not. However, if for some inexplicable reason Bob's shoe did fall of whenever he moved, then it was also the case that Bob's shoe fell off if he ran.

Notice that this only happens in the antecedent. This is not true of conditional consequents (the consequent is the main clause of the conditional):

  1. If the bell rang, Bob ran.
  2. If the bell rang, Bob moved.

Here we see the normal running-->moving entailment. If we know that (7) is true, then we know, of course, that (8) is also true.

The Original Poster's example

A. If I run, I'll vomit.

B. If I move, I'll vomit.

As with the conditionals (5) and (6), the verbs run and move occur in a conditional antecedent. For this reason although running involves moving, the truth of (9) does not necessarily mean that (10) is true. In fact we see the reverse situation. Sentence (10) being true necessarily guarantees the truth of (9).

  • Thanks for your answer, it is very detailed. So, is it correct to say that the context [If I ______, I will vomit] is in fact downwards-entailing? – Genki Jul 11 '17 at 15:30
  • @Genki To simplify, running entails moving, meaning if you are running, then you are moving. I think you're complicating the issue with the use of these two verbs in conditionals themselves. Or is how conditionals entail your primary concern? Also, what is 'downward-entailing'. Entailing is only one direction. – Mitch Jul 11 '17 at 15:58
  • @Genki Well the whole sentence [If A, B] is a conditional. We wouldn't want to say that conditionals are downward entailing. People normally say that conditional protases are downward entailing (or not), but they mean that when the clauses in two conditional protases entail each other we see the opposite entailment in the conditionals - or not. I have been a bit cheeky in my answer, by the way ... – Araucaria Jul 11 '17 at 16:11
  • @Genki .... the reason is that I've given you my view based on my work on my PhD. Many people believe that conditionals, even indicative ones are not downwards entailing. See some discussion in von Fintel 1999, for example. However, in order to have to make these kinds of arguments, they have to pansy around with future facing conditionals. If you stick them in the past tense then it's clear they are in fact, DE. But it all depends on when you think a conditional is true or false. – Araucaria Jul 11 '17 at 16:15
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    @JohnLawler Thanks for that, I've been looking for that sheet. ( - you've used it here before, of course). And, in fact, thanks for the NPI page too. Was trying to find a less hackneyed conditional NPI, and negative clause NPI, but being tired couldn't think of one. So, remembering your NPI page (which I've used as a go-to page many times) I googled "NPI Lawler". Bingo. Thank you ... – Araucaria Jul 11 '17 at 21:00

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