[This is my answer to Homework #1. If you have any questions or ideas arising out of this exercise, please don’t hesitate to bring them to me and/or Raj via email or in person. – Kai.]

Gamut actually comment on this issue briefly (on p. 208). They discuss the sentence “A or B” (with the understanding that “or” is inclusive disjunction) and the competing stronger statement “A” (of which “A or B” is a logical consequence). If “A or B” was correctly used, then S believes that L does not believe that “A or B” is true. Now, they say that it follows that S believes that L does not believe that “A” is true (and thus that (ii) can’t be the reason why “A” wasn’t uttered instead of “A or B”). The reason is this: ‘if L were to believe that “A” is true, then L would also believe that “A or B” is true, since this is a simple logical consequence of “A”.’

In general, one might argue that it can’t be that L believes a strong statement “B” and at the same time does not believe a weaker statement “A” which is entailed by “B”, since L will of course draw the inference from “B” to “A”. And thus, it shouldn’t be possible that the reason S chooses to assert the weaker “A” is that S believes that L already believes the stronger “B” (which logically entails “A”).

But one could object to this line of reasoning: it isn’t always so that a person believes all the logical consequences of one of their beliefs, especially if the logic leading to the entailed proposition is circuitous. This may be why Gamut point to the fact that “A or B” is a simple logical consequence of “A”.

So, unless we operate with the idealization that L is a perfectly logical believer, there might be circumstances where one should choose to assert a weaker statement “A” because one thinks that while L already believes the stronger and relevant statement “B”, L hasn’t drawn the inference to “A”.

Q: Can anyone construct a natural scenario that would support this prediction?

Conclusion: the Claim as stated in the Homework is not quite right.

Nevertheless, for the kinds of scalar implicatures that we have been discussing, the claim is probably right, since they all involve simple logical consequences.

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There are some other things one might say about Condition (ii). In particular, there seem to be natural speech acts where we assert “A” while not being convinced that L doesn’t already believe it, or even while being convinced that L does already believe it. Reminders are a case in point where one asserts something that L already believes. Another kind of case is where one asserts “A” to let L know than one has noticed “A”: “You got a new haircut!”.

We could fiddle with Gamut’s definition. Perhaps, one could replace (ii) with “S believes that it is not already common ground between S and L that A is true”, using the notion of “common ground” which we will discuss soon in the unit on presupposition.

Another possibility is to say that the speech acts I just mentioned are not assertions in the strict sense and thus should not be covered by Gamut’s definition. [But don’t scalar implicatures arise in those kinds of speech acts as well?] It is interesting to note that such non-standard assertions are sometimes marked with special speech act markers. The haircut example, for example, would naturally be marked with “ja” in German. One crude approximation to the meaning of “ja” is that it marks propositions that for all the speaker knows are already known to the hearer.