When subitizing, infants precisely discriminate collections containing three or fewer items, after which performance falls to chance. It remains unclear, however, why performance falls to chance given that infants approximately enumerate larger collections. This is the big-small problem. This paper clarifies the problem, notes that it is exacerbated by influential ways of thinking about numerical cognition and argues that existing "solutions" prove unsatisfactory. It then develops an improved solution, which turns on independently motivated claims about mental formats and infant working memory. This improved solution has ramifications for numerical architecture, the structure of perceptual representations, and the ways in which perceptual states refer.
When is it proper or acceptable for a speaker to presuppose a proposition in the course of performing a speech act? Taking Stalnaker's common ground model as my background, I argue that this is best framed as a matter of the conversational permissibility of the speaker's presupposition, and that we should not construe this permissibility in terms of the reasonableness of a speaker's presupposition. Instead, I propose that the permissibility of a speaker's presupposition is fixed by what is mutually conversationally salient to all participants, where this can in principle outstrip what any of the participants reasonably regards as mutually salient.
According to the rationality of perception thesis, perceptual processes and experiences can be rationally appraised. This thesis raises the questions of whether there can be norms of rationality for perception, and what they could be. Here, to answer these questions, we consider Bayesian norms as possible candidates. Analysing two Bayesian models of perceptual anomalies in schizophrenia, we argue that experience-forming processes can be rationally appraised according to probabilism. After suggesting that violations of probabilism in perception are accompanied by fragmented conscious experiences and can involve epistemic and practical costs, we clarify the implications of our contribution for the rationality of perception thesis and Bayesian approaches to perception.
Why do we find it easier to attribute knowledge than belief? A promising answer suggests that attributing belief requires representations with content that can come apart from reality, whereas attributing knowledge does not. However, this account fails to generalize to desire attribution. Like belief, desire can diverge from the world, yet research suggests that attributing desire is fast, easy, and early developing-much more like attributing knowledge than belief. I propose an alternative explanation, the efficient recovery account, which explains differences between knowledge, belief, and desire attribution in terms of processing efficiency rather than representational content.
Frances Egan argues for a deflationist view of intentionality, on which intentionality is merely part of a pragmatically motivated explanatory "gloss" on theories of mind and behavior. While sympathetic to the project, I worry that the view is inadvertently committed to genuine intentionality: For intentionality to be a mere pragmatically motivated gloss on our theories, theorists must accept theories with particular glosses and have other theory-directed attitudes, which seem to be genuinely intentional. I suggest that we adopt a restricted deflationism, accepting some instances of intentionality but not others. This view preserves the spirit, though not the letter, of Egan's.
