Monday, April 17, 2023

The paradox of the heap and the effect of the real


It is said that Chryssipus the Stoic held that there were, for all problems, true solutions. But he also held that at times, we can’t see them – and those times called for a morally disciplined silence. It is in this spirit he approached the paradox of the heap – the sorites. The paradox is as follows: if we construct a heap from seeds, say, we can, by adding seeds successively, reach a point where we might say that we have a heap, and identify that with the number of seeds we have used – say, 200. And yet, when we subtract one seed, we are disinclined to say that we no longer have a heap. Given that fact, we might play the game by claiming that we haven’t reached a heap no matter how many seeds we use in order to avoid identifying the heap with a certain number of seeds – but then, paradoxically, we will never achieve a heap. In fact, we don’t really seem to be able to quantify a thing like a heap; neither do we want to say that the heap is a quality when clearly it can be analyzed into its separate parts. To borrow a term from contemporary logic,  there is no “heapmaker” – so how can there be a heap? Chryssipus, according to Sextus Empiricus, recommended that “when the Sorites is being propounded one should, while the argument is proceeding, stop and suspend judgement to avoid falling into absurdity.”  Analytic philosophers, such as Mario Magnucci, who wrote a seminal paper on the stoic response to the sorites, have attempted to incorporate Chryssipus’s response into standard Western logic. To me, the stoic response is closer to the notion of Mu in Rinzai Zen. The famous Mu Koan goes like this: a disciple of Zhaozhou, a Chinese zen master, asked him if a dog has the Buddha nature. Zhaouzhou answered Wu – Mu in Japanese – which means no, empty, vacant, and – it is said – applies in different ways to the question: that there is no dog, that there is no Buddha nature, that the dog does not have Buddha nature, and so on. In other words, the answer is meant to break the mental habit of thinking that the way of assembly – where distinct parts are put together – and the way of disassembly, where distinct parts are separated, are grounded in the real. Indetermination is neither a fact of the real nor not a fact of the real.


I believe the sorites paradox shows us something interesting, maybe deep, about the boundary between logic and structure. Structure, of course, is assemblage, inevitably, even as it pops out from various compositions in terms of motif, pattern, point of view. Logic deals with the structure of propositions, and in particular, the structure of variables and substitutions, but it cannot explain that structure. What substitution is cannot be explained by the logical use of substitution.

And, in turn, structure falls down helpless before the detail. What Barthes meant by the Reality effect concerns this moment.

“However, it seems that if analysis intends to be exhaustive (and what value could a method have that could not account for the completeness of its object, or in other words, here, the complete surface of the narrative text?) in looking to reach to the absolute detail, the indivisible unit, the fugitive transition,  in order to assign it to a place in the structure,  it must fatally encounter notations that no function (even indirectly) can  justify: these notations are scandalous (from the point of view of structure) or, what is still more disquieting, they seem to be accorded by a sort of narrative luxury, prodigal to the point of dispersing “useless” details and thus elevating the cost of narrative information.”

Barthes’ point is one that no reader of a text in a foreign language does not know well: the word – for me, in French or German, the languages I read in other than English – that I have to look up. Or skip looking up. Often, of course, skipping makes no difference – and here we are amidst luxury indeed.

Substitution – that unplumbed dimension of modernity!



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