A professor announces: 'Some students will find this exam difficult.' A student infers she means 'not all students will find it difficult.' What generates this inference?
AThe word 'some' is defined to mean 'not all' — it semantically excludes the possibility that all students will struggle
BThe maxim of quantity: if the professor knew all students would struggle, she would have said 'all'; by using the weaker term, she implicates she cannot assert the stronger one
CThe student is making a logical error — 'some' is compatible with 'all' and the inference is unwarranted
DThe inference is a presupposition triggered by 'some,' not an implicature generated by conversational norms
The inference is a scalar implicature arising from the Horn scale ⟨some, all⟩. 'All' entails 'some' but not vice versa — 'some' is weaker. By the maxim of quantity, a cooperative speaker who knew all students would struggle would have said 'all.' Using the weaker 'some' implicates that the stronger term doesn't apply. Option A is the classic misconception: 'some' does not semantically mean 'not all' — it is logically compatible with 'all.' The inference is pragmatic, not semantic.
Question 2 Multiple Choice
A student claims: 'Some students passed' and 'Not all students passed' convey the same information, so there's no meaningful distinction. What is the key flaw in this reasoning?
AThe sentences are different only in register — 'some passed' is informal, 'not all passed' is formal
B'Some students passed' has 'not all' as a cancellable pragmatic implicature; 'Not all students passed' semantically asserts the exclusion and cannot be cancelled
C'Not all passed' is a stronger claim that entails 'some passed,' while 'some passed' does not entail 'not all passed'
DThere is no meaningful distinction — both sentences convey identical information in context
The implicature from 'some' can be cancelled: 'Some students passed — in fact, all of them did' is perfectly coherent. No contradiction arises because 'not all' was only implicated, not asserted. But 'Not all students passed — in fact, all of them did' is a contradiction because 'not all' is semantically asserted and cannot be cancelled. This cancellability test is the diagnostic proof that scalar implicatures are pragmatic inferences, not semantic content. The student's mistake is treating what is communicated as the same as what is literally said.
Question 3 True / False
'Some of the students attended the meeting — in fact, all of them did' is not a contradiction, which demonstrates that the inference from 'some' to 'not all' is a pragmatic implicature rather than part of the sentence's semantic meaning.
TTrue
FFalse
Answer: True
Cancellability is the definitive test for implicature. An implicature is cancelled when a subsequent clause explicitly asserts what the implicature denied, and no contradiction results. Here, the scalar implicature ('not all attended') is cancelled by 'in fact, all of them did,' and the sentence is simply informative rather than self-contradictory. If 'some' semantically meant 'not all,' the sentence would be a contradiction — like 'The number is even and it is not even.' The coherence of the cancellation proves the 'not all' was implicated, not semantically encoded.
Question 4 True / False
Scalar implicatures, like semantic entailments, are fixed inferences that can seldom be cancelled without contradiction.
TTrue
FFalse
Answer: False
Cancellability is precisely what distinguishes scalar implicatures from entailments. Entailments are part of a sentence's semantic content and cannot be cancelled: 'Mary is married' entails 'Mary is not a bachelor' — you cannot coherently add 'in fact, she is a bachelor.' But scalar implicatures can be cancelled: 'Some students passed — in fact, all of them did' eliminates the 'not all' implicature without contradiction. This difference is not incidental: it defines the boundary between semantics (what sentences mean) and pragmatics (what utterances communicate in context).
Question 5 Short Answer
Explain why the cancellability of scalar implicatures is evidence that they are pragmatic inferences rather than part of the literal semantic meaning of a sentence.
Think about your answer, then reveal below.
Model answer: Semantic entailments are baked into a sentence's meaning — they cannot be overridden without contradiction. If 'some' semantically meant 'not all,' then 'Some attended, in fact all did' would be self-contradictory. But it is not — you can cancel the inference without logical absurdity. This shows that 'not all' was never part of what the sentence said; it was an inference the listener drew from the assumption that the speaker is being maximally informative (Grice's maxim of quantity). Because implicatures arise from pragmatic reasoning about the speaker's choices, they can be undone when the context shows that reasoning was unwarranted. Cancellability reveals the line between what language encodes and what communication conveys.
The deeper significance is that cancellability distinguishes two entirely different kinds of meaning: semantic content (truth-conditionally encoded in the sentence, speaker-independent) and pragmatic implicature (context-dependent inference from assumed speaker cooperation). Scalar implicatures like 'not all' feel so natural and automatic that they seem semantic — but the cancellation test reveals their true status as pragmatic. This matters for understanding how much interpretive work listeners do beyond decoding literal content.