Those of you who read Leiter's blog are no doubt familiar with the series of philosophical texts being published in the NYT's 'Opinionator' section. The series is called 'The Stone', and it is under the direction of Simon Critchley (to Leiter's horror). For the most part, the 'The Stone' texts have been widely criticized for a variety of reasons. For example, one of the recent installments is a piece which diagnoses Wittgenstein as autistic, suggests that there is an inherent connection between being autistic (referred to as being 'mind-blind', following a terminology introduced by S. Baron-Cohen) and doing philosophy, and further conjectures that this may be the reason why there is such a poor gender balance in philosophy (given the much higher incidence of autism among men). The piece was rightly torn to pieces at several places (here and here, for example).
This week, however, The Stone has a piece by the Prince of Darkness (that's his name in the Logician's Liberation League) Graham Priest, unsurprisingly on the topic of dialethia and true contradictions. Graham did a good job at explaining in more or less accessible terms what a paradox is, why it is important for philosophy, and the two basic approaches to a paradox: either accept the initially implausible conclusion, or go back in your inferential steps to figure out where you went 'wrong'.
Generally, I think that the first approach, what we could call the 'bite-the-bullet' approach, is not often enough taken in philosophy. Graham's example is Cantor on the notion of infinity: Cantor made the bold move of accepting that, yes, the set of the natural numbers and the set of even numbers are of the same size, as implausible as it might seem given that the set of natural numbers has elements that the set of even numbers does not have (namely, all those odd numbers). Much progress has ensued in our understanding of the concept of infinity and many other mathematical subjects from this 'bullet-biting'.
Now, as I have suggested before, I think that many currently widespread versions of philosophical methodology tend to be overly conservative: we are encouraged to reject outright seemingly counter-intuitive conclusions and thus to take the second approach as described by Graham. In such cases, either one must reject one of the premises that led to the counter-intuitive conclusion, or one must show which inferential step within the reasoning is incorrect. We thereby seek to maintain the status quo of our prior beliefs for as much as possible, which also means that we are not likely to discover truly novel facts.
Graham is a courageous bullet-biter: his bullet is the thesis that there are true contradictions, propositions that are both true and false. While I may not agree with all his positions, I think his general attitude should be more often emulated in philosophy: when hitting upon a seemingly implausible conclusion, rather than immediately ditching it, first give it a chance to see whether other interesting, non-trivial discoveries and conclusions can follow from it. It may turn out to be sheer madness after all, but it may also turn out to be a truly novel insight, and an overly conservative methodology cannot make this distinction.
(Also, it is rather amusing to read the many, many comments to Graham's piece by the NYT readers!)
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