Derrida, Badiou and the Formal Imperative by Christopher Norris

Author:Christopher Norris [Norris, Christopher]
Language: eng
Format: epub, pdf
Tags: Philosophy, Modern, History & Surveys
ISBN: 9781441193971
Publisher: Continuum
Published: 2012-08-02T00:00:00+00:00

VII

At this stage, it is worth noting that one major bone of contention between realists and anti-realists in philosophy of mathematics, logic and the formal sciences is the issue as to whether those disciplines have need of – or should properly find any place for – the classical axiom of double-negation-elimination. This is the principle commonly expressed as ‘two negatives make a positive’, or the jointly logical and grammatical rule that to insert two ‘nots’ or equivalent negating terms into any given sentence is to have them cancel out and thus restore the sentence to a straightforward assertion of whatever was originally stated or affirmed. It is the basis of arguments that work through reductio ad absurdum, that is, by means of a demonstrative (logical) sequence of reasoning to the effect that any denial or rejection of statement x has a plainly absurd or unacceptable consequence and hence (by double-negation-elimination) that x should be affirmed. Conversely it is maintained by those, like Dummett, who espouse an intuitionist or anti-realist approach to mathematics that the axiom need not and should not be upheld precisely on account of its conducing to a thesis which itself – in their view – goes against certain basic principles of right reason.99 Chief among them, as we have seen, is the intuitionist/anti-realist precept that truth cannot intelligibly be supposed to transcend or exceed the bounds of whatever can be known, discovered, formally proved, empirically established or otherwise borne out by the best investigative methods or techniques to hand. On this account, the process of enquiry should not be envisaged as exploring regions of objective, pre-existent though hitherto unexplored conceptual or natural-scientific terrain but rather as opening up new paths of thought that in turn open up – indeed which create – new landscapes for the inventive designer-explorer. In which case there is clearly no need or room for the objectivist idea that thinking can find out truths beyond its present-best knowledge by following out certain logical implications that hold good despite and against our current state of ignorance concerning them.

It is here, I submit, that Derrida’s work poses the greatest challenge to received ways of thinking in epistemology and philosophy of science. It is best seen as a form of highly detailed and sophisticated thought-experimental reasoning conducted in and through the encounter with texts which effectively constitute just such a challenge through their turning out to harbour unresolved problems, aporias or conceptual anomalies that act as a spur to otherwise strictly inconceivable advances in knowledge. Of course there has been much debate between those who affirm and those who deny that thought-experiments can deliver something more than purely analytic, that is, self-evident but wholly uninformative truths and can actually establish substantive theses with respect to various scientific and other regions of enquiry.100 Starting out with Kant’s arguments for the existence of synthetic a priori knowledge, this debate has typically swung back and forth between, on the one hand, assertions that such real-world applicable knowledge may indeed

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