Observations on Sick Mathematics
In Philosophical perspectives on mathematical practice, Bart Van Kerkhove, Jonas De Vuyst, & Jean Paul Van Bendegem, edd. (London: College Publications, 2010), pp. 269-300.
This paper argues that new light may be shed on mathematical reasoning in its non-pathological forms by careful... more This paper argues that new light may be shed on mathematical reasoning in its non-pathological forms by careful observation of its pathologies. The first section explores the application to mathematics of recent work on fallacy theory, specifically the concept of an ‘argumentation scheme’: a characteristic pattern under which many similar inferential steps may be subsumed. Fallacies may then be understood as argumentation schemes used inappropriately. The next section demonstrates how some specific mathematical fallacies may be characterized in terms of argumentation schemes. The third section considers the phenomenon of correct answers which result from incorrect methods. This turns out to pose some deep questions concerning the nature of mathematical knowledge. In particular, it is argued that a satisfactory epistemology for mathematical practice must address the role of luck.
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Seen by:Knowledge Under Threat
forthcoming in Philosophy and Phenomenological Research
Many contemporary epistemologists hold that a subject S’s true belief that p counts as knowledge only if S’s belief... more Many contemporary epistemologists hold that a subject S’s true belief that p counts as knowledge only if S’s belief that p is also, in some important sense, safe. I describe accounts of this safety condition from John Hawthorne, Duncan Pritchard, and Ernest Sosa. There have been three counterexamples to safety proposed in the recent literature, from Comesaña, Neta and Rohrbaugh, and Kelp. I explain why all three proposals fail: each moves fallaciously from the fact that S was at epistemic risk just before forming her belief to the conclusion that S’s belief was formed unsafely. In light of lessons from their failure, I provide a new and successful counterexample to the safety condition on knowledge. It follows, then, that knowledge need not be safe. Safety at a time depends counterfactually on what would likely happen at that time or soon after in a way that knowledge does not. I close by considering one objection concerning higher-order safety.
Could Reliability Naturally Imply Safety?
The aim of the present essay is to argue that robust virtue epistemology is correct. That is, a complete account of... more The aim of the present essay is to argue that robust virtue epistemology is correct. That is, a complete account of knowledge is not in need for an additional modal criterion in order to account for knowledge-undermining epistemic luck. I begin by presenting the problems facing robust virtue epistemology by examining two prominent counterexamples—the Barney and ‘epistemic twin earth’ cases. After proposing a way in which virtue epistemology can explain away these two problematic cases, thereby, implying that cognitive abilities are also safe, I offer a naturalistic explanation in support of this last claim, inspired by evolutionary epistemology. Finally, I argue that naturalized epistemology should not be thought of as being exclusively descriptive. On the contrary, the evolutionary story I offer in support of the claim that reliability implies safety can provide us with a plausible epistemic norm.
Believing Things Unknown
Forthcoming in Noûs. This is a pre-copyediting draft, so please ignore any (non-philosophical) mistakes.
Combating Anti Anti-Luck Epistemology
(2011) Australasian Journal of Philosophy 89 (1):47-58.
One thing nearly all epistemologists agree upon is that Gettier cases are decisive counterexamples to the tripartite... more
One thing nearly all epistemologists agree upon is that Gettier cases are decisive counterexamples to the tripartite analysis of knowledge; whatever else is true of knowledge, it is not merely belief that is both justified and true. They now agree that knowledge is not justified true belief because this is consistent with there being too much luck present in the cases, and that knowledge excludes such luck. This is to endorse what has become known as the 'anti-luck platitude'.
But what if generations of philosophers have been mistaken about this, blinded at least partially by a deeply entrenched professional bias? There has been another, albeit minority, response to Gettier: to deny that the cases are counterexamples at all. Stephen Hetherington, a principal and vocal proponent of this view, advances what he calls the 'Knowing Luckily Proposal'. If Hetherington is correct, this would call for a major re-evaluation and re-orientation of post-Gettier analytic epistemology, since much of it assumes the anti-luck platitude both in elucidating the concept of knowledge, and in the application of such accounts to central philosophical problems. It is therefore imperative that the Knowing Luckily Proposal be considered and evaluated in detail.
In this paper I critically assess the Knowing Luckily Proposal. I argue that while it draws our attention to certain important features of knowledge, ultimately it fails, and the anti-luck platitude emerges unscathed. Whatever else is true of knowledge, therefore, it is non-lucky true belief. For a proposition to count as knowledge, we cannot arrive at its truth accidentally or for the wrong reason.
