Clarke and Beck import certain assumptions about the nature of numbers. Although these are widespread within research on number cognition, they are highly contentious among philosophers of mathematics. In this commentary, we isolate and critically evaluate one core assumption: the identity thesis.

"Like Dewey, he has revolted against the empiricist dogma and the Kantian dualisms which have compartmentalized philosophical thought.... Unlike Dewey, he has provided detailed incisive argumentation, and has shown just where the dogmas and dualisms break down." --Richard Rorty, _The Yale Review_.

Clarke and Beck argue that the approximate number system represents rational numbers, like 1/3 or 3.5. I think this claim is not supported by the evidence. Rather, I argue, ANS should be interpreted as representing natural numbers and ratios among them; and we should view the contents of these representations are genuinely approximate.

Despite the considerable attention that the systematicity argument has enjoyed, it is worthwhile examining the argument within the context of similar explanatory arguments from the history of science. This kind of analysis helps show that Connectionism, qua Connectionism, really does not have an explanation of systematicity. Second, and more surprisingly, one finds that the systematicity argument sets such a high explanatory standard that not even Classicism can explain the systematicity of thought.

Many authors have posited an “object file” system, which underlies perceptual selection and tracking of objects. Several have proposed that this system internalizes principles specifying what counts as an object and relies on them during tracking. Here I consider a popular view on which the object file system is tuned to entities that satisfy principles of three-dimensionality, cohesion, and boundedness. I argue that the evidence gathered in support of this view is consistent with a more permissive view on which object (...) files select and track according to well-known perceptual organization criteria. Further evidence supplies positive support for the permissive view. (shrink)