One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important part of mathematics, namely mathematics (...) as it is exercised by ordinary people. I do so by looking at the different theories that have been put forward in the recent debate, and showing for each of these that they are unable to account for the mathematical practices of ordinary people. In order to show that these practices do need to be accounted for, I also argue that ordinary people are doing mathematics, i.e. that they engage in properly mathematical practices. Because these practices are properly mathematical, they should be accounted for by any philosophy of mathematics. The conclusion of my thesis, then, is that current theories fail to do something that they should do, while remaining neutral on how well they perform when it comes to accounting for the practices of professional mathematicians. (shrink)

In the target article, Crespi & Badcock (C&B) propose a novel hypothesis based on observations that a large set of phenotypic traits exhibit diametrically opposite phenotypes in autism-spectrum versus psychotic-spectrum conditions. They propose that development of these conditions is mediated in part by alterations in This hypothesis is based on the model of the Prader-Willi and Angelman syndromes. The authors have produced a masterful discussion of the differences between psychosis and autism. Of course, another article could be written on the (...) similarities. (shrink)

Recent years have seen enticing empirical approaches to solving the epistemological problem of the theory-ladenness of observation. I group these approaches in two categories according to their method of choice: testing and refereeing. I argue that none deliver what friends of theory-neutrality want them to. Testing does not work because both evidence from cognitive neuroscience and perceptual pluralism independently invalidate the existence of a common observation core. Refereeing does not work because it treats theory-ladenness as a kind of superficial, removable (...) bias. Even if such treatment is plausible, there is likely no method to ascertain that effects of this bias are not present. More importantly, evidence from cognitive neuroscience suggests that a deeper, likely irremovable kind of theory-ladenness lies within the perceptual modules. (shrink)