A highly emblematic paradigm in experimental pragmatics consists in presenting participants with an existentially quantified sentence of the form Some X are Y in a context in which all X are obviously Y. Participants who reject such sentences as false or infelicitous are said to adopt a ‘pragmatic’ instead of a ‘logical’ reading of some, and to derive the scalar implicature Some, but not all X are Y. Although there are several competing accounts of scalar implicatures, virtually all of them assume that a participant who responds pragmatically to an under-informative some-sentence mentally entertains a linguistic representation of the negation of a stronger alternative (All X are Y). Yet, there is no evidence that judging an under-informative some-sentence false or infelicitous actually involves the derivation of the some, but not all scalar implicature. We report three experiments consisting of a sentence-picture verification task followed by a forced choice between two paraphrases of the sentence initially assessed. These experiments robustly show that hearers who reject an under-informative some-sentence do so without explicitly entertaining a some, but not all implicature. Our results represent a strong challenge for grammatical accounts of scalar implicature, which all presuppose a mechanism of negation of stronger alternatives, and force a drastic reinterpretation of processing data on scalar implicatures. More generally, our findings show that one should not conflate psychological models of pragmatic processing with a reconstructed link between sentences and their potential meanings. •Traditional studies on scalar implicatures assume the Explicit Derivation Hypothesis.•This hypothesis is that pragmatic responses correspond to scalar implicatures.•In Phase 1, we use the same tasks that routinely feature in the relevant literature.•But, additionally, in Phase 2 we prompt participants to reflect on their judgement.•There is no congruence between pragmatic responses and implicature derivation.•A central assumption of experimental pragmatics lacks empirical grounds.