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This book suggests the cancellability test for distinguishing the logical consequence from conversational implicature of an assertion.

Examples

1a. You can have either soup or salad. 
1b. You cannot have both.
1c. You can have either soup or salad, and you can have both, if you want.

The book says 1b is an implicature of 1a, because the meaning of 1b would be cancelled without contradiction by furthur elaboration like 1c.

If the assertion of a sentence carries with it a suggestion that could be cancelled (without contradiction) by further elaboration by the speaker, then the suggestion is a conversational implicature, not part of the content of the original claim. (The same book, p.191)

However, with the cancellability test it's still elusive for me to tell implicature in the examples below.

2a. It was much colder than today.
2b. It was much colder than today last week.
2c. It was much colder than today, and the last week was not colder than today. (say, it = yesterday)

3a. This table is as wide as that table is.
3b. This table is as wide as that table is wide.
3c. This table is as wide as that table is tall, and this table isn't as wide as that table is wide.

so my question is,

  • Are examples 2b and 3b implicatures of 2a and 3a?
  • Can we say the cancellation test of 2c and 3c is legitimate? since 2c "It was much colder than today" isn't necessariliy the right interpretation of 2a. Because of deictic influence, the right interpretation of 2a could be 2b, then the elaboration of 2c would be no longer effective.
  • What's the difference between ambiguity and implicature? I'm suspecting I'm confused of these two concepts. Is it just because ambiguity where the interpretation of 2b and 3b comes from?
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  • I think the concept you're looking for is more vagueness than ambiguity... Jun 22 '16 at 2:36
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There is no point to quarreling over definitions. If you want to take cancellability as criterial for what you will call "conversational implicature", then go ahead and do that. Or, if you don't, then don't. One can ask for clarity, but there seems to be no empirical issue.

I find your examples obscure. What is "it" in 2b? It can't mean "yesterday", because *"Yesterday was much colder than today last week" is ungrammatical.

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  • Yes, "it" in 2b could be any time before "today". Therefore, 2a is an ambiguous sentence. it could be translated into "last week" in 2b or other possible times. That's why I thought the assertion 2a could be cancelled by 2b. (or this is wrong because "it" in 2a is uncertain so the cancellation is out of question. Therefore, 2b is not an implicature but merely one of possible interpretations of 2a. is it right?) I want to figure out difference between ambiguity and implicature. Sorry if my poor English confused you.
    – MJ Park
    Apr 24 '16 at 13:14
  • Your example 2a is vague because the subject "it" has many interpretations. I don't think 2b is a sense of 2a, however. An implicature is a sort of implication, but vague sentences don't imply their various interpretations, so the interpretations can't be implicatures.
    – Greg Lee
    Apr 24 '16 at 16:40

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