Skepticism About Mathematics
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My original honours topic:
In epistemology, two areas are consistently set aside as special, generally because they are seen as more likely to yield knowledge (indeed, they are often viewed as paradigm cases for what it means to have knowledge). The first area is the set of results of first-person introspective investigation (e.g. my knowledge that I am in pain gained through my introspective awareness of that pain); the second area is mathematics. But how immune are results in each of these areas to the claims of the sceptic? If one agrees that these areas offer the best chance of achieving certain knowledge, then the answer to this question will provide an upper limit for the level of certainty that can be expected for claims to knowledge made in other areas and via other means.
In my project I would like to focus on the area of mathematics, tracing the interactions of various models for mathematical activity with the claims of the sceptic. This investigation would likely involve three parts: firstly, an overview of the possible models for mathematical activity together with a theoretical framework that will allow comparisons to be made between them (e.g. a listing of the general questions a model of mathematical activity needs to answer ’ models could then be compared in terms of the answers they provide to these questions [or why they deem some of them to be irrelevant]); secondly, an exhaustive listing of the possible sceptical criticisms that can be made with regard to mathematical activity; finally, a detailed analysis of the ways in which the previously discussed models for mathematical activity are affected by these sceptical claims, coupled with a more general discussion of the ways in which these claims interact with the theoretical framework that the models have been situated within.
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More recent concerns
- Where does this project now sit in virtue of the subject-first direction I’ve been heading in? Does skepticism in this form still make sense?
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