Clarke and Beck use behavioural evidence to argue that approximate ratio computations are sufficient for claiming that the approximate number system represents the rationals, and the ANS does not represent the reals. We argue that pure behaviour is a poor litmus test for this problem, and that we should trust the psychophysical models that place ANS representations within the reals.

Kotek et al. argue on the basis of novel experimental evidence that sentences like ‘Most of the dots are blue’ are ambiguous, i.e. have two distinct truth conditions. Kotek et al. furthermore suggest that when their results are taken together with those of earlier work by Lidz et al., the overall picture that emerges casts doubt on the conclusions that Lidz et al. drew from their earlier results. We disagree with this characterization of the relationship between the two studies. Our (...) main aim in this reply is to clarify the relationship as we see it. In our view, Kotek et al.’s central claims are simply logically independent of those of Lidz et al.: the former concern which truth condition a certain kind of sentence has, while the latter concern the procedures that speakers choose for the purposes of determining whether a particular truth condition is satisfied in various scenes. The appearance of a conflict between the two studies stems from inattention to the distinction between questions about truth conditions and questions about verification procedures. (shrink)