Realism, Tolerance and the Paradox of Independent Reality
The notion of tolerance toward beliefs not our own is often linked with a sort of fundamental pluralism or relativism regarding those beliefs. By fundamental pluralism or relativism, I mean a position that ties what is true to what we believe is true and also acknowledges (in one way or another) many beliefs and, by virtue of the link between beliefs and truth, many truths. By contrast, tolerance is not often associated with the notion that there is one truth or one fixed determinate 'way things are', independent of us and our beliefs. This paper explores one way in which tolerance sits naturally with the latter notion, arising from a tension between confidence and humility. A paradox underpinning that tension is explored and its presence identified as central to the preservation and growth of tolerance. It is argued that the paradox is also present in most epistemologies, from realism to modern 'descriptive', or internalist accounts of knowledge, and so is not only present in religious belief, but is a fundamental phenomena underpinning knowledge generally. Given its dual instructive role, a position acknowledging and exploring the paradox is advocated over positions that attempt to resolve it.
Independence and Inter-translatability
Mathematical realism, without its claim that mathematical reality is real and independent, is in many key respects indistinguishable from central versions of mathematical anti-realism; but, the addition of such a claim itself does little to set mathematical realism apart as an interestingly distinct position, so long as that claim is simply stipulated and its role and significance in the overall account left unexplained. In such a case, what ought to be the core of a mathematical realist account: the independence of mathematical reality; becomes a somewhat ad hoc addition to what remains - in all essential respects - an account inter-translatable with anti-realism.
This paper will explore the idea that this is just what happens when mathematical realist accounts deny or all-too-effectively overcome Benacerraf's access problem. The interest and strength in mathematical realism is also precisely its greatest challenge: the 'gap' between, or differentiation of what independently is and what we understand, even know it to be. This is what gives realism its intuitive appeal and its ability to accommodate the most robust conception of the objectivity and certainty of mathematical truth.
Accounts that close this gap, or 'solve' the access problem without retaining its two elements (independent reality and our conceptual grasp of it) as distinct elements risk losing what literally distinguishes realism from its alternatives.