Bristol-Leuven Workshop 1, 27 January 2015
Venue: Arts Reception Room, first floor of 43 Woodland Rd.
9.00-9.30: Coffee and workshop introduction
9.30-10.30: Mona Simion, Function Talk in Epistemology
11.00-12.00: Sam Roberts, Structural reflection
12.15-13.15: Markus Eronen, Levels of Organization and Ubiquitous Downward Causation
15:00-16.00: Sam Pollock, Mathematical Concepts and Uniqueness
16.15-17.15: Stefan Buijsman, The content of mathematical testimony
After workshop: Pub and Dinner.
Title: Function Talk in Epistemology
Abstract: Several people in recent literature attempt to naturalize epistemic normativity by making use of an etiological account of functions (EF). This paper aims to show that, even in their most modest incarnation, etiological functions fail to explain epistemic normativity. It is argued that 1) in order to be relevant to epistemic normativity, the positive feedback mechanism which figures as an essential component of all EF accounts needs be domain specific, and 2) as a result, contra EF, the function of the mechanism at stake cannot figure in the explanation of its continuous existence. Furthermore, I offer reasons to believe that this result generalizes outside epistemology, and thus the employability of EF accounts is restricted to explaining biological functions.
Title: Structural reflection
Abstract: Set-theoretic reflection principles seem to be an attractive way of effecting reductions in incompleteness. They face a number of problems, however. Chief among them is a form of bad company; some reflection principles are outright inconsistent. The challenge is to provide a general and informative notion of reflection which avoids the inconsistent principles. In this talk I will propose a notion of structural reflection which seems to do just this.
Title: Levels of Organization and Ubiquitous Downward Causation
Abstract: The idea of ‘levels of organization’ plays a central role in the philosophy of the life sciences, particularly in debates on mechanistic explanation, reduction, and downward causation. I argue that the most state-of-the-art and scientifically plausible account of levels of organization, the account of levels of mechanism proposed by Bechtel and Craver, is fundamentally problematic. I also examine the explanatory goals that have motivated accounts of levels of organization and show that these goals can be reached by appealing to more well-defined and fundamental notions, such as scale and composition, making any further account of levels redundant. One outcome of this is that the problem of downward causation can be explained away, and downward causation turns out to be a ubiquitous and unproblematic phenomenon.
Title: Mathematical Concepts and Uniqueness
Abstract: Pre-formally, most of us think that we can be guaranteed of understanding each other when we talk about arithmetic and real analysis to the extent that we all have the same (or, equivalent) subject matters in mind. Dedekind's categoricity theorems seem to ensure this for (implicitly) second-order versions of the the theories, but we might have good reason to want to retain the uniqueness of the naturals and reals without going second-order. Likewise, we might have reason to want to extend uniqueness to set theory, where no full formal categoricity theorem exists. There are lots of things to consider in each case, not least the nature of mathematical concepts and their properties. I look at some attempts to bestow uniqueness in the absence of, or at least distinctly from, a formal categoricity theorem and suggest that informal routes are potentially of much more philosophical importance than Dedekind's formal theorems.
Title: The content of mathematical testimony
Abstract: Any philosophy of mathematics needs to specify what the content of mathematical statements looks like. In general, this is easy for platonist theories and quite a lot harder, due to the unavailability of mathematical facts or objects, for nominalist positions. I first survey the various accounts that are held by people form the three main traditions (platonism, constructivism, nominalism) to then see how well their notions of content hold up in the case of testimonial knowledge of mathematical statements. Since this kind of knowledge is something that even children posses, it rules out the more conceptually elaborate conceptions of content. The end result will be that constructivism as construed so far, and some forms of nominalism fail to give a satisfactory account of the content of mathematical statements.