![\"samuel-becketts-bookshelf\"](\"https:\/\/www.3ammagazine.com\/3am\/\/wp-content\/uploads\/2012\/01\/samuel-becketts-bookshelf.jpg\" "\\"samuel-becketts-bookshelf\\"")
<\/div>\nIn a paper presented in 2011, Jean-Michel Rabat \u00e9<\/a> discusses a divergence between Beckett<\/strong>‘s and Bataille<\/strong>‘s treatment of “\u2026 an experience of impotence, dispossession and unknowing\u2026” in terms of “\u2026 the different libraries they bring to bear on these issues.” The impact of these different libraries is immense: from his library Beckett writes his plays and novels; from his, Bataille develops his system of thought “\u2026 in which waste and excess are crucial notions.” Mauss, Hegel and Nietzsche are the representative luminaries of Bataille’s library; Spinoza, Geulinincx and Democritus those for Beckett.<\/p>\n This essay extends the implicit idea that interpretation is not always library neutral. A concern is that much Beckett scholarship that has wanted to develop philosophical connections has used a library containing what has been crudely and erroneously labelled ‘Continental philosophy’ and ignored an alternative one, equally crudely, equally erroneously, labelled the ‘Analytic philosophy’ library. The one library includes the likes of Badiou, Critchley<\/a>, Derrida, Lacan, Bataille, Zeno, Deleuze, Clemente, Blanchot, MacIntyre, Hegel, Heidegger, Ardorno, Zizek, Guattari, Foucault, Nietzsche, Lyotard, Cavell, Rorty, and Rabat \u00e9 himself. It is a rich library.<\/p>\n The second library includes Williamson<\/a>, Sorensen, Priest, Sellars, Fodor, Lewis, Sosa, Russell, Quine, Frege, Wittgenstein, Kuhn, McDowell, Unger, van Frassen, Carnap, Grice, Putnam, Dummett, Davidson, Rosenberg<\/a>, Leiter, Schwitzgebel<\/a>, Parfitt, Chalmers and it is immediately clear that there are philosophers, such as McDowell or Wittgenstein, who can be found in either or both. Recently there has been little ecumenical exchange between denizens of the two libraries, although Rorty and Cavell are perhaps exceptions to this.<\/p>\n But anyway, it’s stupid to have two libraries. It’s better to think that there’s just the one, with all sorts of possible reading lists and reference points. The naturalist philosopher Brian Leiter<\/a> has done much to insist that there is nothing principled about the existence of these two libraries, even though he takes a distinctive philosophical position and finds some philosophical positions jejune and some writers bogus. He condemns the arguments and styles of those he dislikes because they are all in the same library and so he believes they should adhere to common standards of excellence.<\/p>\n In particular, Leieter insists that there are no actual Analytic or Continental traditions to underwrite the notion of the two libraries. \u2018Analytic’ picks out a style of doing philosophy that looks to be clear and precise, logical and leans more towards the sciences and maths than the humanities, whereas \u2018Continental’ tends to pick out a more literary, a more culturally and politically orientated style, one with a greater focus on the human condition and meaningfulness than the Analytic. Perhaps the most interesting difference in focus is that continental philosophers tends to always wear an historical overcoat. The historicist bent frames much of its philosophy, but it’s not mandatory, nor is it mandatorily absent in the work of analytic philosophers.<\/p>\n Leiter makes it clear that actually there is a great deal of overlap both in style of approach and substantive commitments up until the twentieth century. And he also points out that under both headings are philosophers who have almost nothing in common with each other. If there is something that helps us recognise the Analytic approach to philosophy it is what Leiter describes as \u2018its adoption of the research paradigm common to the natural sciences, a paradigm in which numerous individual researchers make small contributions to the solution of a set of generally recognised problems.’ He goes on that, \u2018[t]his is true, interestingly, of even the best work by Anglophone philosophers about so-called \u201cContinental” philosophy: researchers debate and work out the details of the readings of Hegel by Brandom, Forster, Pippin, and Wood, or the readings of Foucault by Dreyfus and Rabinow, Gutting, and Pile.<\/p>\n The staring-at-trees-rather-than-forests aspect of this approach has its critics, but Nietzsche, in discussing the philologists of his day, is quoted by Leiter as arguing that this condemned approach is necessary if it is to bring rewards:<\/p>\n \u2018Almost always the books of scholars are somehow oppressive, oppressed: the “specialist” emerges somewhere\u2014his zeal, his seriousness, his fury, his overestimation of the nook in which he sits and spins, his hunched back; every specialist has his hunched back. Every scholarly book also mirrors a soul that has become crooked; every craft makes crooked.\u2026Nothing can be done about that. Let nobody suppose that one could possibly avoid such crippling by some artifice of education. On this earth one pays dearly for every kind of mastery.\u2026For having a specialty one pays by also being the victim of this specialty. But you would have it otherwise \u2014 cheaper and fairer and above all more comfortable \u2014 isn’t that right, my dear contemporaries. Well then, but in that case you also immediately get something else: instead of the craftsman and master, the “man of letters,” the dexterous, “polydexterous” man of letters who, to be sure, lacks the hunched back \u2014 not counting the posture he assumes before you, being the salesman of the spirit and the “carrier” of culture \u2014 the man of letters who really is nothing but “represents” almost everything, playing and “substituting” for the expert, and taking it upon himself in all modesty to get himself paid, honored, and celebrated in place of the expert.<\/p>\n No, my scholarly friends, I bless you even for your hunched back. And for despising, as I do, the “men of letters” and culture parasites. And for not knowing how to make a business of the spirit. And for having opinions that cannot be translated into financial values. And for not representing anything that you are not. And because your sole aim is to become masters of your craft, with reverence for every kind of mastery and competence, and with uncompromising opposition to everything that is semblance, half-genuine, dressed up, virtuosolike, demagogical, or histrionic in litteris et artibus<\/em> \u2014 to everything that cannot prove to you its unconditional probity in discipline and prior training (The Gay Science<\/a><\/em>, sec. 366).<\/p><\/blockquote>\n So this kind of work tends to lead to very detailed, very cleverly argued miniatures. Synoptic visioning they are not. This is work that tends to demand knowing everything about a little. For a grand vision you need to know a lot about a lot, and much of the grand synoptic visioning in philosophy has been in writers like Nietzsche, Hegel, Marx done before the explosion of specialist knowledge. \u2018Semblance, half-genuine, dressed up’ is the accusation thrown back at attempts at grand visioning without the requisite specialised knowledge. So this isn’t a question of traditions, it’s a question of intellectual honesty and quality of thought and nothing else. (Certainly not geography.)<\/p>\n In this spirit I approach some philosophical queries about Beckett. I have noted that many writers examining Beckett and his interest in philosophy tend not to use the analytic library. But if the walls between the two libraries is conventional and arbitrary then there’s no good reason for this to continue. As an example of what bringing the libraries together I will argue that insights from recent work in the so-called analytic philosophy ibrary into vagueness offer new readings to the Beckett canon.<\/p>\n Beckett writes that he wanted to write impossibility, in order to disrupt those who want to merely enjoy art rather than become enlightened by it. Beckett makes this clear in his essay La peinture de van Velde ou le Monde et le Pantalon<\/em>, where he writes: “For it is not question here of the grotesque and despicable animal whose specter haunts artists’ studios, like the tapirs one is likely to find in the dorms of the Normaliens, but of the inoffensive barmy one who rushes, as other people go to the movies, into galleries and even into churches, seized by the hope – listen carefully now – of enjoying himself (de jouir). He doesn’t want to be taught, the pig, or become better. He only thinks of his pleasure. He is the one who justifies the existence of painting as a public thing. I dedicate to him these remarks, all made to make him even dizzier. He only wants to enjoy. The impossible is made to prevent him from enjoying.” It is this dedication to the \u2018impossible’ that is striking here.<\/p>\n Beckett announces this programme in his famous letter to Kaun<\/strong> in the 1930s: “It is to be hoped the time will come, thank God, in some circles it already has, when language is best used where it is most efficiently abused. Since we cannot dismiss it all at once, at least we do not want to leave anything undone that may contribute to its disrepute. To drill one hole after another into it until that which lurks behind, be it something or nothing, starts seeping through – I cannot imagine a higher goal for a writer today.”<\/p>\n So Beckett writes to create the impossible in order to prevent art being just enjoyed. Beckett’s art aims to be disreputable, to work like a drill, and the vivid image of ‘that which lurks behind’ language is sinister, threatening, suggesting the eerie loathsome monstrousness worthy of Lovecraft<\/strong> or M.R. James<\/strong>.<\/p>\n One of his efforts to create such lurking impossibility was to draw on his knowledge of pre-Socratic philosophers and their discovery of various paradoxes to embed them into the fabric of the worlds he presents. These impossibilities worked as the drill holes he writes of in the Kaun letter. But thanks to work done in recent years in the analytic library, it is clear that he makes a mistake. He truly adds an impossibility in the form of an ancient Greek paradox, but mistakes it for a different puzzle. The mistaken identity means that he was deluded about the nature of the particular hole he was drilling. But he got lucky, because the one he actually uses is better than the one he thought he had.<\/p>\n Matthew Feldman<\/strong>‘s essay linking Beckett to the Presocratics called for a ‘genetic scholarship’, “\u2026that is, to conclude with the finished text by way of a scholarly inquiry into how it was composed. By this I mean that only turning to extant manuscripts, to the influences and ‘work in progress’ of literary creation, are scholars able to establish readings that can be ‘falsifiable’ – to \u2026 appropriate Karl Popper’s sense of the term – that is to say, arguments that can be shown through documentation to have been an actual stimulus in the act of artistic construction, and therefore a provable influence upon the artist’s imagination rather than a product of the critic’s imagination.”<\/p>\n This exercise of genetic scholarship is now well established following the Knowlson biography<\/a> of 1996. But such an approach brings intriguing dilemmas for scholars and critics as a consequence of discovering that Beckett’s own scholarship and philosophical argumentation are flawed and that these mistakes are embedded in his resulting texts. What happens when errors are embedded into the texts so that intended authorial meanings are absent, replaced by unintended ones? Do the known and explicit author’s intentions override what he actually writes, inviting critical discretion and a license to restore by invention those meanings? Or rather, are critics to ignore the intended meanings and work with the actual achieved ones in the text, even if these contradict what the author was wanting to express, completing the process of discovery in the spirit of genetic scholarship?<\/p>\n For a writer of Beckett’s stature, and in the light of the type of critical scrutiny to which his texts have been subjected, that likes to emphasise the ideas and often buckles the structure of the texts to their content, Beckett’s scholarly and philosophical errors may signal a greater crisis than would be the case for writers whose ideas and outlook is taken less seriously. The publication of the second volume of his letters<\/a>, already panning out as one the most significant literary projects of genetic scholarship ever, underlines this point.<\/p>\n Beckett draws wrong conclusions from the material he uses largely because his scholarship muddles up two different puzzles. What Beckett thinks he is presenting is not in fact what he presents. Critics who have followed Beckett’s intentions and read them into the texts have therefore written about what isn’t there. Where an author’s intentions and what is actually written come apart there is a crisis for critical interpretation.<\/p>\n Beckett drills a hole using a heap paradox. This he uses in non-trivial ways. It is referred to by Hamm at the start of Endgame<\/a><\/em> to set the metaphysical mise-en-sc\u00c3\u00a8ne for the whole play, and Happy Days<\/a><\/em> is dominated by its corrosive image. But it seems that Beckett didn’t grasp the threat of this puzzle, mistaking it for a less dangerous one that the mathematician Cantor tamed at the beginning of the last century. Beckett, by accidentally using a much more toxic puzzle, adds to the ferocity of his artistic project. The lurking presence he intends to drill through to and have seep out is more terrifying than he thought it was. Given that his aim was to make the pigs who want art to be merely fun squeal, this would have been a happy revelation for him.<\/p>\n What’s the evidence for this being the case? In replying to Alan Schneider<\/strong>‘s letter of 21 November 1957 on the direction of Endgame<\/em>, Beckett writes in No Author Better Served: The Correspondence of Samuel Beckett and Alan Schneider<\/em><\/a>:<\/p>\n Old Greek: I can’t find my notes on the pre-Socratics. The arguments of the Heap and the Bald Head (which hair falling produces baldness) were used by all the Sophists and I think have been variously attributed to one or the other. They disprove the reality of mass in the same way and by means of the same fallacy as the arguments of the Arrow and Achilles and the Tortoise, invented a century earlier by Zeno the Eleatic, disprove the reality of movement. The leading Sophist, against whom Plato wrote his Dialogue<\/em>, was Protagoras and he is probably the “old Greek” whose name Hamm can’t remember. One purpose of the image throughout the play is to suggest the impossibility logically, i.e. eristically, of the “thing” ever coming to an end.<\/p><\/blockquote>\n So in this letter we have the evidence that Beckett is unclear about who is the old Greek who is the source of the puzzles of the heap and the bald head. His reference to his lost notes suggests that he did at one time know but he has forgotten. He is certainly uncertain, quite rightly, that Protagoras is the man he’s looking for, because he isn’t. But he is specific about the inferences he draws from the puzzles. He takes them to show that mass doesn’t exist for the same reason that Zeno shows that movement is impossible. So he thinks that he is presenting one of Zeno’s paradoxes about infinity. But here’s his mistake. What he’s actually presenting is a different paradox, one that recent philosophical work shows to be about the indeterminacies of borderlines. Philosophers in the analytic library have labelled this puzzle one of vagueness. Zeno’s infinity puzzles and the puzzles of the heap (\u2018sorites<\/em>‘ in Greek) are therefore not the same puzzle.<\/p>\n Mind you, Zeno does have a puzzle involving a heap. It’s just not the sorites puzzle though. Zeno’s millet seed puzzle is not a sorites puzzle. So by mistake vagueness structures several of his texts, most obviously Endgame<\/em>, Mercier and Camier<\/em><\/a> and Happy Days<\/em>, the latter being less an assertion of a puzzle than a display of one, like Escher’s print Belvedere<\/em> and the language of a zombie.<\/p>\n The misidentified source material is the sorites puzzle. Clov at the beginning of Endgame<\/em> comments, “Finished, it’s finished, nearly finished, it must be nearly finished. Grain upon grain, one by one, and one day, suddenly, there’s a heap, a little heap, the impossible heap. I can’t be punished any more. I’ll go now to my kitchen, ten feet by ten feet by ten feet, and wait for him to whistle me. Nice dimensions, nice proportions, I’ll lean on the table, and look at the wall, and wait for him to whistle me.” In Ackerley and Gontarski’s Faber Companion to Beckett<\/a><\/em> Beckett speaks of “Zeno’s grains, a logician’s jest” but we also learn that he “\u2026told O’Brien that the allusion was not to Zeno but to a philosopher he no longer recalled.” Beckett’s philosophical source, Windelband, rightly identifies Aristotle’s contemporary Eubilides of Miletus as presenting the puzzle but wrongly claims that it was “retraceable to Zeno”. Modern scholars dispute this, although the misattribution is understandable. Zeno of Elea, a century earlier than Eubilides, was the originator of a puzzle involving millet seed, but not the puzzle, and at a twist it might be reformulated as a sorites puzzle.<\/p>\n Beckett relied on Windelband for his knowledge of the pre-Socratics, and it is only relatively recently that philosophers have got to grips with vagueness and made it clear that Zeno wasn’t working at the same puzzle as the sorites. Timothy Williamson<\/a> wrote the classic text about vagueness in 1994 and made this clear. Of course, Beckett would not have had access to the scholarship of this formidable logician and so his mistake is understandable. But here’s a case of work being done in the analytic library directly bringing fruits to bear on Beckett scholarship. Thanks to Williamson and others working on vagueness a new dimension of what Beckett’s texts mean is revealed, a meaning that eluded even Beckett.<\/p>\n Zeno’s seed paradox, as reported by Wiliamson, goes: “If the fall of a seed to the ground were completely silent, so would be the fall of a bushel of seed, which it is not.; thus each seed must make a noise when it falls to the ground.” Reformulated as a forced sorites, it becomes; ‘Does one seed make a noise when it falls to the ground? Do two seeds? Three?…’ But Williamson, author of Vagueness<\/em><\/a>, the classic modern text on the sorites, is careful to distinguish Zeno’s puzzle from that of the later Eubilides, writing that “Zeno seems to have based his puzzle on something much more specific: a principle that the noise made when some grains fall to the ground is proportional to their weight.” Williamson is clear that Eubilides is the guy who discovered the proper sorites. And it’s likely that that Beckett once knew this. What he didn’t realise was what Eubilides’ puzzle was about.<\/p>\n Eubilides invented seven famous puzzles, two of which were the sorites and \u2018phalakros<\/em>‘, similar in respect of their being ‘little by little’ arguments. The sorites and the phalakros are puzzles of vagueness. The sorites (heap) and phalakros (bald) were in antiquity formulated as a series of questions. ‘Does one grain of sand make a heap? Two? Three?…’ Similarly with the bald man; ‘Is a man with one hair on his head bald? Two? Three?…’ and so on. Eventually there comes a figure where it becomes doubtful as to what the right answer is. And this period of doubt continues for some time until another figure is reached where a right answer seems clear again.<\/p>\n This is the puzzle that Clov recognises in Endgame<\/em> and to which Beckett refers in his Riverside Notebook<\/em> when he writes, “C perplexed. All seemingly in order, yet a change. Fatal grain added to form impossible heap. Ratio ruentis acetvi<\/em>.” This appeal to the sorites puzzle suggests that his mania for minimalism rests on more than just Adolf Loos’ injunction, ‘ornament is a crime’ and Mies van der Rohe’s ‘less is more’. It also adds reason for his ‘Process of Elimination’ in the What Where<\/a><\/em> notebook (Theatrical II 437) where every little change adds up to impossible change. It also adds to what he says in his lecture on Racine<\/strong>, where he talks about the monologue within the dialogue, where several voices add up, little by little, echo by echo, fragment by fragment, until they form a unity. The notebook for Tritte<\/em> – Footfalls<\/em> – contains a discussion of voices which Gontarski glosses: “In the dialogue within the monologues (parts II and III), for example, the Mother’s “What do you mean, May, not enough” of part II should be echoed by the voice of Mrs. W’s in part III, “What do you mean, Amy, to put it mildly,” according to Beckett. “Same style for both relationships,” he notes” (IV 337). Understanding the sorites brings a new resource for freshly understanding all this.<\/p>\n Beckett’s art drills the blindspot of the sorites. The non-heap impossibly becomes a heap. The bald man becomes non-bald. Clov sees this when he mutters, scared as hell, ‘suddenly’ and names his horror, ‘the impossible heap.’ In Mercier and Camier<\/em> there’s a reference to “every millet grain that falls”, suggesting Zeno rather than the Eubilides, but vaguely conceived as a sorites, and so deliciously vaguely vague. In Malone Dies<\/a><\/em> we are given “fun and games with the cones and cylinders, the millet grains beloved of birds and other panics” which picks up the anxiety and terror of the sorites that Clov registers in the later work. In Malone<\/em> we also have Big Lambert’s wife having two heaps of lentils on her table, the smaller getting bigger and the big one smaller. Beckett here presents the embedded logical contradiction of the sorites as a display, as with Happy Days<\/em>.<\/p>\n Winnie in Happy Days<\/em>, buried in ‘the impossible heap’ that so terrifies Clov in Endgame<\/em>, trapped in the impossible, encroaching end where suddenly, one day, at some point, a threshold will be reached, a line will be crossed, but unknowably\u2026 What did Beckett think was going to happen? There’s evidence that by taking the problem as a question of infinity, Beckett has been taken to be presenting in many of his texts an unending process rather than any completion to zero, so his voices dwindle and reduce to minima just above ending, as if an ending was impossible, and that the torture of existence continued remorselessly. But if the issue is not infinity but vagueness then these readings may require revision.<\/p>\n <\/p>\n Eubilides worked in the 4th century BC. His puzzle was popularised by Diodorus Cronus who like Eubilides had “\u2026sophistical leanings, \u2026 flamboyancy and \u2026 love of showmanship” according to Sedley but who, supposedly, died of shame when he couldn’t solve a puzzle set by some other philosopher in front of the King of Egypt. The sorites became a chief weapon between two schools of philosophy, the Stoa and the Academy. Plato led the Academy in attacking the dogmatism of the Stoa. The sorites was the master puzzle against which the Stoics seemed defeated. The catastrophic power of the puzzle was recognized by Academicians after 273 when Arcesilaus adopted Diodorus’ sorites’ reasoning.<\/p>\n The Stoic reasoner argued for something similar to Descartes’ clear and certain impression. Knowledge was certain clarity. These impressions were considered as having propositional content. The Stoa believed that they were able to pick out truth with complete accuracy. The catastrophe threatened by the sorites is clear: a clear impression can be nibbled away by imperceptibly small subtractions until the certain impression is lost. So far, so Beckettian.<\/p>\n The Stoic response emphasised Beckettian ignorance. Chryssipus became head of the Stoics in about 232 according to Williamson. Chryssipus was considered by the Ancients as the greatest logician of them all according to Barnes. “Unfortunately the two volumes (i.e. scrolls of papyrus) he is known to have written On the Little By Little Argument do not survive; nor do his three volumes On Sorites Arguments Against Words. There are only fragments and reports,” reports Williamson.<\/p>\n Yet what has been reconstructed from these fragments suggests that Chrysippus understood the problem of the borderline in terms of our ignorance, rather than anything about the heap itself. A sequence of questions and answers presumed a monotonic sequence (so no answer of ‘no’ fell between answers of ‘yes’, and vice versa) and the Stoic presumed a principle of bivalence. Logically, there has to be a grain the removal of which turns a heap into a non-heap and a non-heap into a heap. However, for whatever reason, we cannot discriminate in enough fine-grained detail to ever know which grain it is. Even were we to pick out the correct grain we couldn’t know it because the grain next to it would seem just as clear to us as the actual one. We would just have been lucky.<\/p>\n The pattern of responses in the typical sorites shows certainty moving through a smeared zone of uncertainty back towards certainty again. The issue the Stoics had to face was how to respond in the smeary zone. The crisp sharp borderline they knew existed in there somewhere was forever hidden. Chryssipus recommended a strategy of silence. Upon approaching the smear and doubt, his guiding principle was, ‘where knowledge is uncertain, no answer should be given’.<\/p>\n Silence here is not merely ‘not saying’. It is also about ‘not believing’. Beckett inherits this idea about silence. It is linked to what his characters are able to believe. The Stoics held that one should believe only what one knows is correct. The wise person trains her discriminatory powers so she is fooled less than ordinary thinkers. But the sorites confronts even her with indiscriminable impressions that training cannot annihilate. In these cases, judgment must be suspended. She may try acting on plausible assumptions without believing the truth of them in such cases. She is not omniscient but she is infallible, in that, like the Cartesian, her impressions are her own even if they are unbelievable. But Stoics doubted the existence of such wise people. They were an ideal.<\/p>\n As Williamson<\/a> explains, in order to avoid error of thought and speech Chryssipus recommended that “\u2026 at some point in the sorites interrogation one should fall silent and withhold assent\u2026 If the source of the puzzle is just that one does not know whether \u2018yes’ or \u2018no’ is the right answer to some of the questions, it turns out to be on a level with other matters of which one is simply ignorant\u2026 Why should such an honest admission of ignorance not completely dissolve the puzzle.” The profound silence of Chryssipus is the silence of fallibility, of ignorance, of the futility of going on and trying to answer something that is unknown. Beckett’s silence is a Chryssipean inheritance.<\/p>\n But an explanatory step is missing in this analysis. Why does Chryssipus recommend silence rather than the admission ‘I don’t know.’ It is because of a crucial feature of the structure of vagueness. Not only is it unclear where the actual sharp borderline between heap and non-heap lies, it is also unclear where the sharp borderline between clear and unclear is as well. In other words, not only don’t we know where the last grain of a heap is, nor do we know where the last grain we are certain is a heap is either. The borderline of the smeary borderline is susceptible to the same troubling reasoning faced trying to locate the original borderline. ‘Heap’ is sorites susceptible, and so is ‘clear heap’. And so is ‘clearly clearly heap’. The iteration threatens to stretch out infinitely. Philosophers have labelled this feature ‘higher order vagueness’.<\/p>\n Chryssipus is ignorant of the borderline of his ignorance, and ignorant of the borderline of the borderline of that ignorance. This ‘higher order’ iteration is echoed throughout Beckett. On the principle that we should assert nothing false, his silence preserved this principle. Silence didn’t assert knowledge of ignorance, it asserted nothing. Indeed, to ensure that the principle of refusing to assert what is not clear, Chryssipus recommends that silence begin at a place before certain uncertainty. This squeezes the scope of certainty, reducing it. The more maniacally followed, the recommendation makes ever less assertible. The complexity of the sorites threatens to erode, little by little, what can be thought, what can be said. The delicacy of the situation, its precariousness, results in an expanding blindspot.<\/p>\n The sceptic Carneades thought Chyrissipus’ strategy no better than a refusal to play the next move in a game, or like falling to sleep. ‘Why should your pursuer care whether he traps you silent or speaking?’ he asks. Beckett’s texts speak to the contempt of the sceptic; the wreckage of humanity is working perfectly and yet cannot speak into the vagueness not even Beckett fully understands if, as is likely, he didn’t understand the implications of the sorites. As Gontarski notes, “Clov’s opening speech is motivated by some barely perceptible change that he perceives while inspecting his environment. In the Riverside<\/em> notebook Beckett writes: ‘C perplexed. All seemingly in order, yet a change'”. And it helps explain the sequential patterning that is essential to Beckett’s aesthetic.<\/p>\n The precariousness of Chryssipus’ position is in answering the sceptic who wonders why she might not then suspend judgment over all cases, clear and unclear. Chryssipus is, as Williamson neatly puts it, “in a very delicate position. He stops at clear cases, avoiding the risk of giving answers that are not clearly correct only at the cost of failing to give answers that are clearly correct (in the Stoic sense).”<\/p>\n Carneades argues against the existence of Stoic Gods using a little by little argument that patterns itself differently from the classic formula but is still nevertheless recognisably a sorites. “If Zeus is a God\u2026 Poseidon too, being his brother, will be a God. But if Poseidon (the sea) is a God, the (river) Achelous too will be a God. And if Anchelous is, so is the Nile. If the Nile is, so are all rivers. If all rivers are, streams too would be Gods. If streams were, torrents would be. But streams are not. Therefore Zeus is not a God either. But if there were Gods, Zeus too would be a God. Therefore there are no Gods.” Silence in the face of this fierce reasoning against Stoic rational theology is inadequate to resist non-arbitrarily any step of the argument.<\/p>\n The problem is conceived in terms of disputations about the premises of the argument, rather than the argument form itself, which was regarded as being valid. The sorites became a focus of dispute between Dogmatic\/rationalist doctors and Empiricist ones. How many observations were enough to make it reasonable to suppose a certain cure? The sorites threatened the common-sense idea of ‘enough’. Galen and the Empiricist doctors reasoned that the sorites would dispute the existence of flocks, herds, nations, crowds, boyhood and seasons. They argued that something was wrong with the sorites argument, although they didn’t know what.<\/p>\n Beckett’s familiarity with the sorites was such that he knew of samples outside of philosophy. Horace<\/strong> defends young poets using sorites against the idea of ‘old poets’ in the Epistle to Augustine<\/em> (II.i, 47). The attraction of Horace for Beckett lay in his timidity at Philippi, and, according to Ackerley “\u2026by what Lempriere regrets, licentious expressions and indelicate thoughts.” Horace’s ratio ruentis acetvi<\/em>, Clov’s ‘impossible heap’, emanates from the ‘amiable madness’ he references in his study of Proust<\/strong> from Schopenhauer.<\/p>\n My claim, however, is more than that Beckett drew on elements of the sorites puzzle. He presents the sorites in terms of a theory-particular answer to the puzzle rather than in general terms. In Watt<\/a><\/em> there is a sustained passage where the sorites characterised as an ‘epistemic’ solution to vagueness makes better sense of the passage than all other attempts to characterise it. Consider this: “The sun on the wall, since I was looking at the sun at the wall at the time, underwent an instantaneous and I venture a radical change of appearance. It was the same sun and the same wall, or so a little older that the difference may safely be disregarded, but so changed that I felt I had been transported, without my having remarked it, to some quite different yard, and to some quite different season, in an unfamiliar country\u2026”<\/p>\n Notice that the change is ‘instantaneous’ rather than a gradual transformation. The epistemic conception of the sorites is precisely that there is, in fact, an exact and precise borderline, contrary to everything that seems to be the case. So ignorance of the truth causes the problem, not absence of borderlines or ideterministic language or thought. A commitment to bivalence, the principle that every proposition is either true or false, is at the heart of classical logic and the epistemic approach preserves classical logic and thus this commitment. That Beckett presents the mystical experience described here in Watt<\/em> as ‘instantaneous’ suggests that he wasn’t presenting a deviant logic to the situation but was rather holding on to the classical in order to dramatise the absurdity of the truth. He punches through to the other side of the sorites blindspot and introspects the unintrospectable transition. This accounts for the mystical feel.<\/p>\n Given that Beckett misidentified what the sorites was a puzzle about he was in a sense writing blind. But Watt<\/em> can now be read in terms of its solution given in terms of our ignorance of the actual sharp borderlines that our thought and language cannot discover. The madness of the scene is one that reveals a character knowing the unknowable. The hole he drills reveals that strange absolute changed sameness which baffles coherence and us with the vertiginous sensation of borderless transition characteristic of vagueness.<\/p>\n Other theories of vagueness reject sharp boundaries. Deviant logics have been applied to the sorites. Many valued logicians and fuzzy logics argue that if a two value logic claiming that every proposition is either true or false can’t handle the situation, then introduce more values. But the philosopher Mark Sainsbury remarks that “you do not improve a bad idea by iterating it.” The approach fails to handle thoughts such as hedging which allows us to hover between being decisive because each disjunct is assigned equal value. Yet asserting equal disjuncts should increase the truth value of the statement, but many valued logic can’t register this because it only assigns its truth value to the most probable claim. Equal disjuncts don’t increase the assigned value.<\/p>\n Supervaluationists such as Kit Fine argue that the statements in the smeary borderline lack truth values. This position therefore proposes that there is a truth-value gap at the point where Chryssipus falls silent. Fine and David Lewis conceive of vagueness in terms of a massive hyper-ambiguity. The claim is that there is no settled agreement about which language is being used and so tiny differences between languages sets up the indeterminism in the borderline cases. Roy Sorensen summarises the position: “Instead of there being one vague concept, there are many precise concepts that closely resemble each other. \u2018Child’ can mean a human being at most one day old or mean a human being at most two days old or mean a human being at most three days old \u2026. Thus the logic of vagueness is a logic for equivocators.” Propositions that are considered true on all disambiguations are true. But as Michael Tye argues, disambiguation is usually done before assessing the truth value of any proposition. How else do you know whether what is being said is true or not if you haven’t decided yet what is being said? Mixed interpretations is a feature of ambiguity but not vagueness.<\/p>\n Supervaluation approaches retain an appearance of bivalence because it can say that every proposition must be true or false. But by reversing the order of disambiguation (doing it after assigning truth values) the claim is a non-substantive one for any borderline case. And other features of the classical logic repertoire are lost. Tarski’s Convention T makes truth disquotational, which is the claim that states that “a statement S is true iff S”. So, for example, ‘A thousand grains of sand make a heap’ is true if and only if a thousand grains of sand make a heap. Supervaluationists think that truth is ‘true under all precisifications’ and they call this ‘supertrue.’ But if they accepted Convention T then supertrue would be disquotational. Williamson argues that the supervaluationist would be committed to saying P is either supertrue or not-P is supertrue, which in turn would commit them to either P is true or Not P is true. Supervaluationists would have then lost their truth-value gap.<\/p>\n Sorensen, who is with Williamson the leading philosopher arguing that vagueness is about our ignorance of the sharp borderlines rather than any fault in our language, accuses the supervaluationist of ontological dishonesty. As part of his solution to the sorites paradox, the supervaluationist will assert, ‘There is a human being who was a child when n days old but not when n + 1 days old’. For this statement comes out true under all admissible precisifications of ‘child’. However, when pressed the supervaluationist will add an unofficial clarification: ‘Oh, of course I do not mean that there really is a sharp threshold for childhood’. For Sorensen the dishonesty runs deep: the supervaluationist position hides nihilism.<\/p>\n Peter Unger in 1979 argued that the sorites dissolved the coherence of all vague terms. Given that nearly everything is sorites susceptible, the position resulted in the rejection of more or less everything. The corrosive force of this position is where one might expect Beckett’s sympathies to lie. The nihilist sorites denies the base step of the argument. If reason can show that a single grain is a heap and also prove it isn’t then there is something inherently absurd in the very idea of a heap. The nihilist courageously faces the consequences of the extreme position and the world is annihilated. All that is left is at best an ‘as if’ universe. For pragmatic reasons we may continue to talk as if heaps and bald men exist but it is merely a convention to retain a thread.<\/p>\n But vagueness is vague. The nihilist proves that vagueness doesn’t exist. Therefore an argument depending on it can’t exist either. The nihilist is a self-defeater. If vagueness exists then it cannot. But perhaps the self-defeater is an argument for the impossibility of asserting the nihilist position, and perhaps this is what Beckett anticipates will come oozing through the hole he is drilling through language. The seminal work of Roy Sorensen from his 1988 classic study of Blindspots<\/a><\/em> have drawn attention to the varieties of this phenomenon where truth is inaccessible, even unknowable.<\/p>\n An important moment in revitalising interest in this phenomenon was in the discovery of a type of sentence discovered by G.E. Moore, one of the founders of Analytic philosophy, at about the same time Beckett was writing Murphy<\/a><\/em> and Watt<\/em>. “It is raining but I do not believe it,” is the sentence of 1943. It is an example of a sentence that is quite possibly true, is grammatical, logical but, nevertheless, unassertable. Fitch proved that there are unknowable truths in 1963. Williamson thinks of this discovery as an embarrassment not a paradox.<\/p>\n Moore was the March Hare in the John Tenniel<\/strong> depiction of The Mad Hatter’s Tea Party (J.M.E. McTaggert was the dormouse, Bertrand Russell the Mad Hatter) and the threesome were known as the Mad Tea Party of Trinity according to Wiener. His strange sentence is only strange given current background assumptions brought about by a critique of Hegelian idealism led by Moore and others. Idealism denies unthinkable truths. The sentence was the one discovery that impressed Ludwig Wittgenstein and brooding on it helped formulate the extreme positivism of the Tractatus.<\/p>\n The sentence is an example of a pragmatic paradox philosophers label the counterprivate. They link it to the introspective turn in philosophy that is associated immediately with Descartes but is perhaps first elaborated in Augustine who wrote, “I am not at all afraid of the Academicians, who say What if you are deceived? For if I am deceived I am. For he who is not, cannot be deceived, by this same token I am. And since I am if I am deceived, how am I deceived in believing that I am? For it is certain that I am if I am deceived. Since, therefore, I, the person deceived, should be, even if I were deceived, certainly I am not deceived in this knowledge that I am. And consequently, neither am I deceived in knowing that I know. For, as I know that I am, so I know this also, that I know.” Beckett’s interest in the Cartesian introspective project is well-documented.<\/p>\n Sorensen draws out the closeness of the Augustinean and the Cartesian project. He writes about Descartes in opposition to Descartes’ own self-representation. Descartes thought of himself as a revolutionary, breaking away from his Catholic background and education. Sorenson argues that Descartes was actually continuing in the introspective tradition of Augustine. He endorses Miles Burnyeat’s contention that Augustine was the first philosopher to make the subjective\u2013objective distinction. For Beckett, the introspective writer par excellence, this genealogy is pertinent.<\/p>\n The linguistic nihilist presumes all vague terms are merely pseudo-terms. They are self-defeaters. The metaphysical nihilist assumes that all vague predicates exist but are empty. ‘Heap’ is like ’empty full’. There is a third option but it has never been taken, which is to apply vague predicates to everything. Nihilist incoherence requires no drilling. The epistemic approach does.<\/p>\n Alternatively, maybe Beckett is appealing to a form of contextualism. Indexicality is the culprit (e.g. ‘I am always here’ etc). The influence of the Heraclitean thesis that ‘all is flux’ is important to Beckett elsewhere. Beckett read Heraclitus in the 1930s and is suggested by Estragon’s contention that ‘everything oozes’ and in Murphy<\/em> where the line from his Windelband volume is raised where according to Gontarski the short circuit of love requited confutes the Heraclitean principle of “\u2026the circuit completed by matter of its successive changes in the universe” (quoting from Windelband). Just as each assertion on separate days that “tomorrow Godot will come” is not identical with any of the other assertions, the uniformity of the sentence used to make the assertion may fool the unwary or novice language user. Contextualists may insist on the truth of each inductive step whilst equivocating as to whether what each step means is identical with its predecessor or successor. In this way the sorites series is reduced to a series of indexicals that denies that any induction step can ever be falsified.<\/p>\n Scott Soames argues that all vague terms are indexical and Hans Kamp argues that vague words work like satellites orbiting the store of the linguistic commitments of the sorites-monger. Diane Raffman argues that sorites work using a gestalt psychology, so sorites series are triggered shifts between look-alikes. Stewart Shapiro takes a notion prevalent in legal debates, developed from Waissman and popularised by H.L.A. Hart, of ‘open texture’. Language is open textured in that “every description stretches, as it were, into a horizon of open possibilities: However far I go, I shall always carry this horizon with me.” This position is used to justify discretion when judging borderline cases. Delia Graff relativises to an American pragmaticism. Practical interest relativises meanings and produces enough shiftiness to prevent a sorites series.<\/p>\n Sorensen complains that contextualists end up with too much shiftiness. “Analogy: hydrologists agree there is much hidden water but all hydrologists are scientifically committed to denying Thales’ claim that all is water,” he says. He also argues that some sorites are just too damn complex for the sort of homespun equivocation contextualism deals in. A billion, billion, billion iterations of Godot may be embedded in a sorites that never could generate the required context shifts. Sorenson remorselessly drills home his complaint: “More fancifully, there could be a vague predicate that instantly kills anyone who thinks about it.”<\/p>\n Beckett did indeed have doubts about the stabilising anaphoric resources of language. He did feel the existential unease of both the nihilist and the Heraclitean, where his sympathy is with Holderlin’s lines, “\u2026suffering humanity perishes and falls blindly from one hour to the other, like water dashed from crag to crag year after year, down into the unknown.” But it is through the resources of classical logic that the sorites has been understood as a problem of ignorance, and human fallibility. Beckett takes ignorance to be an essential aspect of the human condition. He gropes blindly towards the epistemic solution to the sorites rather than via deviant logics, nihilism or contextualism.<\/p>\n Beckett shows the madness of classically behaving language. The epistemic solution is the only approach to the sorites which assumes classical bivalence \u2013 the principle that a proposition is either true or false \u2013 in a way that the unavoidable incredulity of the solution is fully grasped. As we’ve seen, supervaluation does so but only by assigning truth values before deciding which particular language they’re speaking. The epistemic solution decides which language its speaking and then commits to bivalence. So there has to be a sharp cut off point, and so the fault lies in us. We are absolutely ignorant of where the sharp cut-off point is. The solution is rightly greeted with incredulity by competent language users because it seems to violate a tautology but is actually a blindspot.<\/p>\n Remember that Beckett didn’t know that this was what he was introducing into his texts because, by following Windelband’s lead, he misidentified the paradox’s nature. Had Beckett been reading contemporary philosophers of his time then he might have picked up some of this stuff. But given that from what we know he was reading overviews, summaries and classics, it is unlikely that a non-specialist would have had contact with this material. So although the philosophical analysis of the sorites has been a central concern for analytic philosophers throughout the last century, and in particular since the mid 1970s following Michael Dummett’s seminal paper, Wang’s Paradox<\/em>, Beckett didn’t know anything about it.<\/p>\n And it’s likely that he only touched on it through the originators because of his interest in the PreSocratics. Throughout the medieval period little was written about the sorites. It did reappear in the Renaissance in the guise of the literary pursuit of humanist rhetoric. The Roman Epicurean-Christian humanist Lorenzo Valla was a key figure in reconstituting the sorites as a valid form of argument. But sorites puzzles were relatively unimportant, although Leibniz referred to both the heap and the bald man in arguing with Locke in the seventeenth century.<\/p>\n The rejection of Hegelian idealism and consequently the rejection of its rejection of the law of the excluded middle at the end of the nineteenth century was supported by the development of logic by Frege and Russell. Logic, like science and maths, required precision. Consequently, as Williamson vividly puts it, “vagueness, like madness, must be mentioned in order to be excluded.” Russell and Peirce produced theories of vagueness and the value of precision was developed as a key value. Natural language was presented by Frege as deficient. Frege conceived of vagueness as incomplete definition. But if Beckett’s reading remained influenced by Hegelianism then it is unlikely that he could have even considered vagueness in the terms now considered fruitful by contemporary philosophers.<\/p>\n The recent work, by Williamson and Sorensen in particular, has reclaimed some of the original ideas about the sorites found in Chryssipus, that vagueness is ignorance of sharp borderlines, not absence of sharp borderlines through incomplete, faulty or for some other reason indeterminate language and thought. Of course, the claim that Chryssipus was an epistemicist is not uncontested. Susanne Bobzien has recently argued in particular against Williamson’s conclusion about the Stoic, suggesting that he was more of a supervaluationist than Williamson accepts. And Roy Sorensen would probably argue that Williamson is more of a supervaluationist than he would accept.<\/p>\n But given Beckett’s conception of his creative process as one of impotence and ignorance \u2013 whereby the impotence is harnessed to the ignorance – the sorites is being approached as a vehicle for his ignorance-based impotence. It is an idea that in turn buckles the sorites puzzle to his ethic of ignorance derived from his study of Arnoldus Geulincx, the seventeenth century Flemish metaphysician and philosopher. In Murphy<\/em> there is a reference to the “beautiful Belgian-Latin” of Geulincx’s “Where you are worth nothing, there you should want nothing”. What better than a puzzle whose solution renounces knowledge and insists on unbelievability. As a principle organising the “stains on the silence” that he considered his texts to be, this blindspot approach would have immense appeal to the writer who saw artistic calling in terms of efficient disobedience.<\/p>\n <\/p>\n Ignorance plays a significant role in Beckett’s self-contrast with Joyce<\/strong>: in the James Knowlson biography we hear Beckett saying, “I realized that Joyce had gone as far as one could in the direction of knowing more, in control of one’s material. He was always adding to it; you only have to look at his proofs to see that. I realised that my own way was impoverishment, in lack of knowledge and in taking away, subtracting rather than adding… But I do remember speaking about Joyce’s heroic achievement. I had a great admiration for him. That’s what it was: epic, heroic, what he achieved. I realized that I couldn’t go down that same road.”<\/p>\n The sorites raises blindspots about borderlines. “A million grains is a heap. If so, then so is a million minus one grain. Therefore one grain is a heap.” If we want to deny the induction step, we are committed to saying there is a grain the removal of which turns a heap into a non-heap. Language and thought doesn’t seem capable of such a fine grained distinction but that’s because the border is a blindspot.<\/p>\n The species of the blindspot extends to Ekbom’s prediction paradoxes: “Students know that there will be a surprise exam in the next week. They know it can’t take place on the last day. If they know it can’t be given on day n then they know it can’t be given on day n-1. Therefore they know the test cannot be given.” But the teacher can still give a surprise test and so there is a paradox.<\/p>\n The super-game puzzles involve iterated prisoner’s dilemma puzzles: in a one-off prisoners dilemma competitive behaviour dominates cooperation. It might be supposed that in a sequence of 100 games, for example, this behaviour polarity would reverse. Yet if on the last play they will revert to competitive domination, then if at n the players know they will compete then at n-1 they know they will compete. Therefore they will compete in every game.<\/p>\n Beckett’s trapped characters and tightly orchestrated scenarios track the dilemmas of this species of absurdity. In Sorensen’s classic text on this blindspot phenomenon he writes a wintry Beckettian comment: “Since the best we can count on is an indifferent universe, we are left with the conclusion that some truths may well have been placed out of reach by the rules of representation .”<\/p>\n This approach adds to our understanding of what Belacqua’s ‘dark gulf’ is in Dream Of Fair To Middling Women<\/a><\/em> (p. 120) “\u2026 akin to the incoherent continuum explored by the greatest artists, Beethoven, Holderlin, Rembrandt and Rimbaud” (p. 138). It extends the scope of blindspot significance, and identifies the ‘incoherent continuum’ as a token sample of it.<\/p>\n In the lecture notes produced by Grace McKinley<\/strong> in 1931 Beckett discusses Racine in terms of that same incoherent continuum pictured as a terrible walking on the spot. So we have: “Berenive: conclusion of the play is an intensification not modification of the opening. Unbearable clarity. \u2018Dark with excessive light.’ Movement without a pietinement sur place [a marching on the spot]. Gradual conquest of character by light of her own character” (Beckett Remembering: Remembering Beckett<\/a><\/em>). Earlier, he comments that Racine’s Andromaque<\/em><\/a> ends “[W]hen the mind has an integral awareness of the facts as opposed to a fragmentary consciousness. To explain:- the dialogue is really a monologue. It is the exp[pression] of a fragmentary consciousness.” Further on McKinley notes: “Pylade etc. are the fragments of the divided minds of Orestes etc. Their function is to express the vision in the minds of their protagonists. It is when these fragments are blended into a whole that the play comes to an end, e.g. when Hermione realises after Pyrrus has been murdered that her love for him is the greatest thing, and not the soothing of her vanity \u2013out she passes \u2013 suicide.” The unified thought annihilates what introspection hoped to disinter.<\/p>\n Racine remained important to Beckett. Introducing the McKinley notes, James Knowlson writes: “For if the impact and the influence of Racine on Beckett began when he was a student and can be seen in allusions to \u2026. all \u2026 the \u2026plays on which he lectured in his first novel, Dream Of Fair to Middling Women<\/em> (written just after he quit his lecturship), it extended well into his middle period as a dramatist, when he reread the entire theatre of Racine in the early 1960s, relating them directly to \u2018the chances of the theatre today’.<\/p>\n Knowlson suggests that from Racine Beckett took his “focus on inner worlds,” “the monologue,” “‘the psychological oppositions and their physical manifestations in the stage lighting that he saw in Phedre<\/em>,” and “his fascination with the tradition of spotlight painting in art.” But Knowlson remarks that “\u2026 above all\u2026 he was impressed \u2026 Racine could depict over-all mental as well as physical stasis.” He cites Beckett from McKinley’s notes: “The precipitation of the mind towards a point where there is no longer more than one consideration, a precipitation towards a stasis. In this act the minds of all the characters make a leap toward this stasis” (Knowlson et al<\/em> 2006, p. 306).<\/p>\n The terrible “walking on the spot”, “I can’t go on, I’ll go on” etc, etc is the Beckettian routine. A sublime anti-Racinean Racinean, his novels and plays present introspected fragments of consciousness. In seeking unity the texts are similar to assertions like ‘I know that perpetual motion machines are impossible but I shall strive to build one nevertheless.’ As when told the immovable meets the irresistible, we should deny the possibility. Yet Beckett’s texts drill past the injunction. The sorites gives Beckett further artillery to batter at impossibility, even though he smuggled it in under his own nose, disguised as something else, like a Trojan’s Horse. Or like the peculiar impossibility of the instruction: “Don’t think about Godot.” The instruction triggers its own defeat.<\/p>\n Beckett’s anxiety can be framed by this conversion of Racinean theatre into vague sorites. His increasingly pressurised, miniaturised fragmentary texts witness to blindspotted blindspots. Beckett’s texts are diagrammatical and work like maps of disintegration. They are presented as patterned and choreographed, obsessed with time periods and shapes. Beckett was maniacally concerned to produce synchronised voice, movement, silence, light and dark. His texts are like prototypes of experiments in consciousness, anti-holistic, atomised and differentiated. How is unity possible? The philosopher Jesse Prinz argues that attention creates unity. Unity is explained in terms of synchronised neural states. Different sensory areas are phase locked and patterns are correlated so that unified consciousness is presented. There is good evidence that oscillation patterns have a systematic relationship like this.<\/p>\n Beckett’s interest is the introspective inner consciousness. Prinz’s theory of consciousness explains why Beckett is presenting an area of our conscious experience that is unavailable to introspective investigation. The guiding metaphor Prinz uses to help us understand this is the refrigerator light model of unity. The light in the fridge goes on only when the door is opened. Fragmented conscious is never directly introspectable because introspection unifies. It’s like a child wanting to see what’s there when she’s not looking. Beckett is presenting us with known unknowability.<\/p>\n Beckett’s predicament appeals because the futilitarian humility in his work senses irremediable human vulnerability and powerlessness. Science endorses his view that intuitions of stability and permanence are not trustworthy. It sympathises with the epistemic hostility of the universe and human fallibility. Eyes are small. The universe is enormous. Electro-magnetic disturbances are of all different sizes, wavelengths, and most are beyond our limits. We can’t see physical reality’s deep fundamental structures. If we were built so that we could see the very small and the very fast we would confront fluctuations in the gluon fields that hold quarks and nuclei together. Reality would look like the inside of a larva lamp. Philosophising to middle-sized objects like people would be massively problematic from that perspective. Sight is the master sense. The limits of our eyes program our philosophical intuitions. Other senses are equally limited. Hearing limitations are geometrical. Touch is a combination of limited senses, a reading of temperature and air pressure subject to extreme geometric limits. Hearing misses high frequencies. Smell and taste are complex like touch. They have limited spatial range. They sample only a tiny part of the universe.<\/p>\n The eye samples three colour patterns. Taste samples twenty-nine tastes. The nose samples over nine hundred stinks. There are taste receptors on our lungs identical to those on our tongues. They are sensitive to bitterness and warn against toxins. Senses sense different shaped molecules that fit different receptors. Because light molecules are very similar in shape to smell and taste molecules, vision can taste and smell. Since Aristotle’s count of five senses, two new ones have been discovered. Balance\/kinesthesia allows us to sense movement through the ether and gives us a sense of acceleration. We also sense time and circadian rhythms. But our senses are very limited, very selective and miss both distant events in space and time and the deep structure of the world.<\/p>\n The scientist strives to defeat the fallibility. She enhances senses using instruments and minds. Minds translate distant things into meanings we can understand. The physicist believes the world is comprehensible. The important move is to resist natural intuitions about the world. The physicist Frank Wilczek argues that substituting sharp testable propositions for the imprecise folk ones was the great scientific revolution. Science eliminates ontological vagueness. Beckett drills through to its epistemic core.<\/p>\n Galileo replaced Aristotelian rationalism with precise tests. Removing vagueness so that tests could be falsifiable was a key to this scientific method. Karl Popper demanded falsifiability to ensure propositions were sharp. Wilszeck modifies this. Some beautiful and compelling propositions should be proved true on aesthetic grounds. The mystic strangeness of Paul Dirac supports this approach as Farmelo’s biography about him suggests. Some doubt there is a single scientific method, like the philosopher Craig Callender does.<\/p>\n Wilczek identifies three eras of this single scientific revolution: the ancient Greeks who developed sharp assertions about measuring and geometry; Newton’s seventeenth century discovery of laws of motion and finally the twentieth century period where biology and physics is developing a project of reductionism which moves from tracking how matter behaves to investigating what matter is. Scientists ask why there are chemical elements using a process of analysis and synthesis. Small objects seem to obey simple laws better than big ones. The physicist builds a theory of everything from these. Where reductionism stops there is emergence. The scientist wonders why this process works. It relies on facts about the physical world. It relies on uniform laws in space and time. But laws can be analysed locally and in isolation from all others. Strangely, these laws may be contingent, so worlds might have been different.<\/p>\n The scientist works to translate between five different languages. Experience is the brain translating senses using a deeper neural code inaccessible through introspection. Ordinary language conveys the world experienced like this. Ordinary mathematics describes this world. Computer language in turn translates this. The shorter the description given to the computer to describe our world, the better. Ernst Mach discussed the economy of science and the minimum description length for a computation, and Einstein cautioned that theories should be as minimal as possible but no more so. The basic laws of science are precise mathematical equations about the very lower tier of existence. As equations improve we expand our understanding of the world accordingly.<\/p>\n But despite all this, we can never know a blindspot. The ignorance of vagueness is a symmetrical blindspot, and as such it is absolutely unknowable. Contrast it with an assymetrical blindspot, such as G.E. Moore’s discovery of the peculiar form of sentence that cannot be asserted: ‘I went to the cinema on Tuesday but I don’t think I did.’ It is an assymetrical blindspot because it can’t be asserted in the first person but in a third person version of it can, as in, for example, ‘Moore went to the cinema on Tuesday but he doesn’t think he did.’ Roy Sorensen contrasts this approach with that of Williamson, who argues that the ignorance is relative to the medical limits of human discriminability. Sorensen proposes and defends reasons for thinking that species parochialism is not a relevant factor. So even when physics is complete, we cannot know everything knowable.<\/p>\n Sorensen has the recipe for this kind of epistemic blindspots, which he calls “mendacious mathematical inductions.” They are built out of generalisations with four properties: Firstly, the generalisation must be counter-example resistant. A sorites generalisation is absolutely counter-example resistant because the blindspot is symmetrical. Other generalisations may be relatively counter-example resistant because the blindspot is asymmetrical such as the Moorean sentence I gave an example of above or an adjective such as \u2018modest’ (no one can know they are modest, even though others can know this of someone else) or ‘Everyone knows Godot won’t appear, except Pozzo’. The resistance to counter-example requires force; the resistance must be strong enough to invite the acceptance of this counter example resistance. The generalization must present a serious obstacle for counter examples.<\/p>\n Secondly, the generalisation must appear non-vacuous. Base steps must appear true and substantial even if they are not. So, for example, prediction paradoxes have false base steps that appear true. In these paradoxes a teacher announces to her class that they will have a surprise test by the end of the week. The students think about this and begin by reasoning that if by the last day there has been no test then the test would have to be on the last day. However, they would know that and so there would be no surprise. Having reasoned so, they rule out the possibility of having the test on the last day. But then the same reasoning applies to the penultimate day. And by such reasoning they conclude that on no day can there be a surprise test. It is the granted opening concession in the prediction paradox that the surprise test cannot take place on the last day that leads to the induction step being taken seriously when actually it is merely a vacuous truth.<\/p>\n The convenience of mathematical induction needs a sequential arrangement of generalisations to be exploitable, as in the surprise test, as in the sorites. If we have all three of these properties then we have \u2018slippery generalisations’.<\/p>\n Sorensen calls them that, claiming that ‘the name is appropriate because sequential counter-example resistant generalisations that appear to be non-vacuous suffice for the construction of categorical slippery slope arguments.’ But we also need to distinguish good mathematical inductions from bad. If we have a generalization that is supported and non-vacuously true then we require that generalisation cloaks counter-examples.<\/p>\n There are different types of cloaking devices. Holistic blindspots cloak blindspots that are not co-accessible even though each one is separately accessible as in Moorean sentences. There the generalization is ‘someone believes that p then someone believes that someone believes that p.’ The counter-example is ‘someone believes that p but no one believes that someone believes that p’, so that each conjunct is believable but the conjunction isn’t.<\/p>\n Super blindspot resistance comes in two forms. One is where the antecedent is always a sub-blindspot. For example, ‘If everyone shares n permanent beliefs, then everyone shares n+1 permanent beliefs.’ To refute the generalisations we must find antecedents that are true and a consequence that is false. Where the antecedents are all blindspots counter-examples are impossible to find.<\/p>\n So cloaked but true generalisations have only potential counter-examples because a true generalisation has only false counter examples. The true counter examples are cloaked, as in the sorites. A cloaked generalization can’t rule out the possibility that the counter-example resistance is falsidical.<\/p>\n Slippery slope fallacies use a mendacious induction step. A mendacious induction step has three properties typically: it is apparently non-vacuous, it is sequential and it is either false or a cloaking generalisation.<\/p>\n It can therefore be sound argument. Sorensen gives examples, such as The second step is a cloaking generalisation. Its negation is a blindspot. We can only know that the consequent is false if we know how long any object has got and we are limited in our knowledge of the universe to know such things. The generalisation may be false, so it is weak.<\/p>\n Strong puzzles are when the generalisation couldn’t be false. Semantic anti-realists can’t allow these to exist for they disbelieve in unknowable truths. The sorites is a strong puzzle. This raises difficulties for those critics who want to interpret Beckett in terms of a theory of semantic anti-realism, such as Derrida.<\/p>\n Given that Beckett’s fictions are spectacular science fiction and slightly cluttered thought experiments this argument against parochialism is appealing. It smashes the hubristic assertion of the extreme naturalist who proposes that only things known scientifically are real. Beckett’s artistic assault violates the naturalist’s self-confidence.<\/p>\n In the PreSocratic Eubilides and Chryssipus we find a direct line from their puzzle of the heap to a silence that devours knowledge even of its own ignorance, and answers the specific question Beckett puts to Kaun in the famous letter cited earlier: “Is there any reason why that terrifyingly arbitrary materiality of the word surface should not be dissolved, as for example the sound surface of Beethoven’s Seventh Symphony is devoured by huge black pauses, so that for pages on end we cannot perceive it as other than a dizzying path of sounds connecting unfathomable chasms of silence?” This reads as a vivid and dramatic intuition of the sorites puzzle, and is more remarkably apt when we remember that Beckett didn’t know what the sorites actually implied. He just got lucky with this error.<\/p>\n It is a delicate and hard business to explain Beckett’s strange texts without explaining away their strangeness. The epistemic theory of vagueness is a perfect foil to Beckett’s strain of weird because it presents a simple, logical proof for the existence of necessarily unbelievable things. That these are linguistic things makes the business even more apposite for a writer who understood his calling as something like ‘word-storming in the name of beauty’.<\/p>\n In the course of working on the meta-sorites problem of incredulity Sorensen contrasts the ease we have in acquiring language with developing an understanding of how we do it. The ease with which we acquire language makes us over-opinionated about how it is done. Theories of language contradict the logical proof of the existence of sharp boundaries for vague terms. Theories positing a radical indeterminacy of language are directly challenged by conclusions drawn from analysis of the sorites. Theories embedding voluntarism, the theory that meaning is chosen, that beliefs can be a matter of will, are also severely tested by this approach. Various ideas of conventionalism find the sorites solution fatal to their approach. Phenomenological readings ditto.<\/p>\n Finding the sorites in Beckett, seeing the puzzle as an inadvertent but happily apposite explosion of irresolvable ignorance at the heart of all knowing subjects, even a God, and doing so through a method of genetic scholarship, gives critics new resources for thinking about Beckett’s use of time, silence, subtraction, everything. The sorites asks that these be considered in terms of a puzzle about their borderlines not infinity. Always in Beckett the question of when life begins and when it ends looms. Ditto meaning to meaningless. Presence to absence. Noise to abate. The sorites raises questions about their borderlines.<\/p>\n We can now see that Beckett’s texts offer ruminations on slippery slopes. Slippery slopes prototypically end with bad bottoms. “For want of a nail the kingdom was lost” is an example. Evaluating the badness of the bottom can be where iconoclasts make their mischief. De Quincy<\/strong>‘s playfully example in 1863 of such a slope seems to perversely invert values: “For, if once a man indulges himself in murder, very soon he comes to think little of robbing, and from robbing he comes next to drinking and Sabbath-breaking, and from that to incivility and procrastination. Once begin upon this downward path, and you never know where you are to stop. Many a man dated his ruin from some murder or other that perhaps he thought little of at the time.” De Quincy’s is a strange case where we start at a bad bottom (murder) and end with something not as bad (procrastination). De Quincy can be read as deliberately asking questions about received wisdoms in the spirit of Swiftean satire. Or again, perhaps it is just play.<\/p>\n Beckett’s slippery slopes are peculiar in a different way. If De Quincy’s slippery slope strikes us as a satirical inversion of values where the peak becomes the pit, Beckett’s seems involved with his minimalism, understood as a process of subtraction. Is Beckett presenting us with worlds crossing from non-zero to zero or else instead presenting a world of infinite process, a world of the ‘unnullable least’ where we are always approaching the zero limit but never reaching it. So we might ask of Beckett’s texts: is there always something rather than nothing? The sorites suggests that Beckett didn’t deny zero, he just denied knowing when it begins.<\/p>\n Beckett’s universe is even stranger than we thought, tougher, more fierce, more utterly disturbing. The clear evidence that the sorites is included in it should make critics draw inferences even Beckett missed. It suggests new avenues for critical investigation and imaginative response. But to return to the point at the start of this essay, the scholarship that disinters the sorites is likely to be found in the library Beckett scholars don’t access enough. And to miss this stuff does Beckett studies \u2013 and literary studies generally – a disservice. So we would do well to stop thinking in those terms. We’ve got one vast library with many rooms, levels, anti-chambers and corridors. In a letter written on the 14th November 1936 in Hamburg Beckett described it: “Through the walls come female Danish voices, two Jutland tarts in colloquy. Pure chirping. They should be on a funeral urn, in the Genesiacal period. Now I know how Ophelia should speak the flower speech. And that Hamlet was mad. He is buried in no fewer than 54 Jutlandish localities. All the lavatory men say Heil Hitler. The best pictures are in the cellar.”<\/p>\n In December that same year, in Wolfenbuttel, Beckett couldn’t fully understand why a certain reserve led the Cartesian mind of Lessing to “so thoroughly misunderstood the mind of Descartes.” We contemporary Beckettians are similarly in danger of misunderstanding Beckett, being too reserved to find the uncanny epistemologists of vagueness, perhaps because they don’t look up from their zeal, seriousness and fury, who no doubt overestimate the nook in which they sit and spin with their hunched backs and scholarly books that mirror souls that have become crooked – because every craft makes the soul crooked and on this earth, as Nietzsche says, one pays dearly for every kind of mastery. But we are too reserved, and so we don’t go into these strange rooms. Who knows what else we might find if we did?<\/p>\n![\"beckett\"](\"https:\/\/www.3ammagazine.com\/3am\/\/wp-content\/uploads\/2011\/11\/beckett.jpg\" "\\"beckett\\"")
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\n1. Some object has endured for a year
\n2. If some object has endured for n years then some object will have endured for n+1 years.
\n3. Therefore no object is oldest.<\/p>\n![\"caldermarshall\"](\"https:\/\/www.3ammagazine.com\/3am\/\/wp-content\/uploads\/2012\/01\/caldermarshall.jpg\" "\\"caldermarshall\\"")
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Beckett did indeed have doubts about the stabilising anaphoric resources of language. He did feel the existential unease of both the nihilist and the Heraclitean, where his sympathy is with Holderlin’s lines, “\u2026suffering humanity perishes and falls blindly from one hour to the other, like water dashed from crag to crag year after year, down into the unknown.” But it is through the resources of classical logic that the sorites has been understood as a problem of ignorance, and human fallibility. Beckett takes ignorance to be an essential aspect of the human condition. He gropes blindly towards the epistemic solution to the sorites rather than via deviant logics, nihilism or contextualism.<\/p>\n