WAB: "Fragments" | Original publication on WAB's website (2005.1.14, last revision 2006.4.3).

Cameron McEwen: The digital Wittgenstein

Keywords: Wittgenstein, Tractatus, Beckett, Heidegger, analog, digital, difference


The fundamental difference between analog and digital systems may be understood as underlying philosophical discourse since the Greeks. In this initial chapter of an extended project to explicate Wittgenstein from this vantage, texts from Beckett and Heidegger are cited in an attempt to throw new light on the introductory remarks to the Tractatus.

The digital Wittgenstein

For first principles are not sought, since they are present and to hand; and if what is present is sought for, it becomes hidden and lost. (al Ghazali)

Αρμονίη άφανής φανερής κρείσσων (Herakleitos, DK 54)1
Wittgenstein’s nephew2, Heinz von Foerster (1911-2002), was founder and director of the Biological Computer Lab at the University of Illinois. He led the annual Cybernetics Conference sponsored by the Macy Foundation in the years from 1949 to 1953 and edited the five volumes of their proceedings3. In the 1950 conference (volume 2 of the original edition), Ralph Gerard presented a paper on "Some of the Problems Concerning Digital Notions in the Central Nervous System" where he gives the following entirely unremarkable definitions: "an analogical system is one in which one of two variables is continuous on the other, while in a digital system the variable is discontinuous and quantized."4

Everyone is familiar with analog and digital technologies in watches, music recordings and televisions. But analog and digital systems play a remarkable role (sometimes alone, sometimes in combination) also in philosophy and in all thinking and experience, where they function, though seldom explicitly, as first principles (ie, as fundamental architectures or archetypes of thought).

The properties of analogical and digital systems as first principles of thought may be set out as follows:

  • "an analogical system is one in which one of two variables is continuous on the other" and in which one of the two is necessarily derivative of the other. ‘Necessarily derivative’ because if the two were equally real, ie, equally present as first principle, the system would be originally plural, therefore originally "discontinuous and quantized", therefore "a digital system" and not "an analogical system" at all. By definition, an analogical system must be singular at origin and must admit difference only secondarily (where ‘secondarily’ has both logical and temporal implication). An analogical system is therefore "continuous" both in that difference is not fundamental to it and in that its complexity is a factor of linear time.

  • "in a digital system the variable is discontinuous and quantized." As first principle, such a system must be plural (otherwise it would be analogical) and difference must be principial to it (where ‘principial’ has both logical and temporal implication). A digital system is therefore discontinuous in that difference is fundamental to it (enabling plurality and discrete or quantized definition) and in that its complexity is an essential characteristic of it independent of linear time.
The notion of original difference which is inherent to a digital system is difficult in a variety of ways. It is incompatible with those linear and progressive (ie, analogical) systems of thinking, education and information storage with which the western world has functioned (with varying degrees of coverage and with varying degrees of success) for a millennium or two. In this sense, it offends a deeply established sense of identity and order. Second, it is difficult conceptually to do with an absence which is deeper than any presence. If a digital system is discontinuous as first principle, the border between the quantized or discrete variables must be inexplicable in terms of them (alone or together). Were it explicable from them, it would be derivative and the system would be analogical, not digital (since difference, hence also plurality, would be secondary, and this, the secondary status of difference and plurality, is exactly what it means for a system to be analogical). Third, it is difficult existentially to allow for a fundamental absence which would be deeper than any possible presence giving personal meaning or consolation.

Samuel Beckett may be read as formulating these multiple difficulties. When the composer Morton Feldman asked him in 1976 for "the quintessence"5 of his work, Beckett gave him (at first verbally, later written out with some small corrections as follows):

TO AND FRO in shadow from inner to outer shadow
from impenetrable self to impenetrable nonself by way of neither
as between two lit refuges whose doors once neared gently close,
once turned away from gently part again
beckoned back and forth and turned away
heedless of the way, intent on the one gleam or the other
unheard footfalls only sound
till at last halt for good, absent for good from self and other
then no sound
then gently light unfading on that unheeded neither
unspeakable home6

What Beckett calls "that unheeded neither", the "way of neither as between two", is the original "unspeakable" difference through which a digital system ("to and fro") functions (but which is fatal to any analogical system).

For Heidegger, similarly, difference is ineluctable, original and unspeakable: "Für uns ist die Sache des Denkens (…) das Sein hinsichtlich seiner Differenz zum Seienden. (…) Für uns ist die Sache des Denkens, vorläufig benannt, die Differenz als Differenz."7 Again: "[D]ie Unterscheidung sei der Steg, der uns überall in allem Verhalten und ständig in jeglicher Haltung vom Seienden zum Sein und vom Sein zum Seienden führte. Das ist im Bilde gesprochen und legt die Vorstellung nahe, als lägen und stünden Seiendes und Sein auf verschieden Ufern eines Stromes, den wir gar nicht benennen und vielleicht ...niemals benennen können. Denn worauf sollen wir uns dabei stützen, was soll noch als Strom zwischen dem Seienden und dem Sein strömen, was weder Seiendes ist noch zum Sein gehört?"8 Therefore: "In dieser Unklarheit des Unterschieds zwischen Seienden und dem Sein steht bis zur Stunde das ganze abendländische Denken."9

The works of Beckett and Heidegger are often said to be illogical and incomprehensible. And they certainly are illogical and incomprehensible if taken from an analogical perspective as analogical expressions. If, by fundamental contrast, their work is digital, the question arises as to how it can be appreciated as such. A series of extraordinary difficulties are knotted at this point.

The analog/digital difference is either continuous or discontinuous, ie, the analog/digital difference is self-referential (a key consideration in the work of Heinz von Foerster on, eg, the cybernetics of cybernetics10). It is therefore not possible ‘to move from the one to the other’ (a phrase with fundamentally different meaning depending upon its analog or digital context) without already instantiating one of them in doing so. Since it is exactly the point of Beckett and Heidegger to put forward the discontinuous, ie digital, thesis, any appreciation of their work must already be digital in order to achieve this possibility (a remarkable enough phrase and suggestion). The same is true of Wittgenstein.

Analogical perception is principially unable to understand the point at issue. As Wittgenstein puts the matter in the first line of his only published book, "Dieses Buch wird vielleicht nur der verstehen, der die Gedanken, die darin ausgedrückt sind - oder doch ähnliche Gedanken - schon selbst einmal gedacht hat."11

A ‘knot in time’ (T S Eliot) is implicated here. What is to be achieved – the understanding of an essential discontinuity – must already be in place in order to start to do this. Any sort of gradual process in this direction would be analogical and therefore essentially incapable of what is demanded. Indeed, contradictory to what is demanded. Thus Wittgenstein is speaking precisely when he says, immediately after the passage from the introductory remarks to the Tractatus just given: "Es ist also kein Lehrbuch." What is at stake cannot in principle be taught or learned (in the usual analog senses of these). Therefore Wittgenstein’s observation concerning Frege in the Tractatus (6.1271): "Aber es ist merkwürdig, daß ein so exakter Denker wie Frege sich auf den Grad des Einleuchtens als Kriterium des logischen Satzes berufen hat."

Since the ‘Grad’ (‘step’, ‘degree’) is necessarily analogical, philosophy as a digital enterprise cannot, in Wittgenstein’s view, be learned or otherwise grad-ually assimilated: "Die Philosophie ist keine Lehre, sondern eine Tätigkeit." (Tractatus 4.112)

In order to ‘come to’ an understanding of digital experience, a Kierkegaardian leap is required from one sort of fundamental system-structure to another: "In der Logik gibt es kein Nebeneinander" (5.454). This possibility is to be achieved - but not achieved through any sort of continuous or gradual process! Since such a leap is already digital, the only means to the end is the end itself…12

It follows, as Tractatus 5.555 has it: "… mit dem muß ich es zu tun haben, was es mir möglich macht, sie zu erfinden." Similarly, from Heidegger: "Weil es vordem das Seltsame gibt, damit wir es finden." (GA77, S 164)

There is no approach to a digital system through a gradual (ie, stepwise) process of, say, education or habituation, since, on the one hand, gradual process is by definition analogical and, on the other hand, digital expression (if it is at all) is always already there – like Athena from the head of Zeus.13

It may be that Wittgenstein’s later work is an effort to exercise and probe this ‘already there’ quality of digital logic and meaning. If the logic of human experience is digital (as the Tractatus argues), and if such logic is ‘already there’ but somehow fundamentally unknown (as the Tractatus also argues), it would be necessary to try to find a (necessarily peculiar) way to them, ie, to where we already are. An ever-renewed reconsideration of the existing practice of human beings in their language and action would be fitting to the thesis of the Tractatus that a kind of backwards leap is to be made (ever-renewed reconsideration and revision) to where we already are (of existing practice).

A recollection of Heinz von Foerster from around 1919 (when Wittgenstein was 30) captures the point at issue: "Und einmal hat er [= der Onkel, LW] mich gefragt: 'Sag, Heinz, was möchtest du denn gerne werden?' Ich war damals sieben Jahre alt und habe geantwortet: 'Ich möchte gerne Naturforscher werden.' - 'Dann musst du aber doch sehr viel wissen.' Da habe ich gesagt: 'Aber ich weiß sehr viel!' Darauf hat er entgegnet: 'Ja, aber du weißt eines nicht - wie recht du hast!'"14

Compare Heidegger: "Wir wollen jedoch nicht weiterkommen. Wir möchten nur erst einmal eigens dorthin gelangen, wo wir uns schon aufhalten."15 "Die verweilende Rückkehr da-hin, wo wir schon sind, ist unendlich schwerer als die eiligen Fahrten dorthin, wo wir noch nicht sind und nie sein werden."16 "Seltsamer Sprung, der uns vermutlich den Einblick erbringt, daß wir uns noch nicht genügend dort aufhalten, wo wir eigentlich schon sind."17

In Vermischte Bemerkungen, Wittgenstein makes the same point in near identical words: "Wenn der Ort, zu dem ich gelangen will, nur auf einer Leiter zu ersteigen wäre, gäbe ich es auf, dahin zu gelangen. Denn dort, wo ich wirklich hin muß, dort muß ich eigentlich schon sein."18

What is at stake here concerns the entire way in which a person is in the world, what Heidegger calls "wo wir uns schon aufhalten", "wo wir schon sind". The claim is that there is a kind of Archimedean lever whereby world can not only be moved, but utterly transformed.19 This lever is the relation of subject to object, or of person to world, whose transformative power is located in the fundamental difference between analog and digital systems. The difference between these modes of system turns on the nature of ‘relation’ itself: is relation primary or secondary, discontinuous or continuous, synchronic or diachronic, etc? And what is at stake between them is nothing less than the nature of world.

Now Wittgenstein and Heidegger were born in 1889, Beckett in 1906 and von Foerster in 1911. It might therefore seem that the idea of digital and analogical systems as rival fundaments to human experience is a new suggestion and, like digital technology, very modern. In fact, however, the idea is as old as philosophy itself (and may be much older20). In his Sophist, Plato sets out the following ‘battle’ over the question of ‘true reality’:

What we shall see is something like a battle of gods and giants going on between them over their quarrel about reality [γιγαντομαχία περì της ουσίας] ....One party is trying to drag everything down to earth out of heaven and the unseen, literally grasping rocks and trees in their hands, for they lay hold upon every stock and stone and strenuously affirm that real existence belongs only to that which can be handled and offers resistance to the touch. They define reality as the same thing as body, and as soon as one of the opposite party asserts that anything without a body is real, they are utterly contemptuous and will not listen to another word. (…) Their adversaries are very wary in defending their position somewhere in the heights of the unseen, maintaining with all their force that true reality [την αληθινήν ουσίαν] consists in certain intelligible and bodiless forms. In the clash of argument they shatter and pulverize those bodies which their opponents wield, and what those others allege to be true reality they call, not real being, but a sort of moving process of becoming. On this issue an interminable battle is always going on between the two camps [εν μέσω δε περι ταυτα απλετος αμφοτέρων μάχη τις (…) αει συνέστηκεν]. (…) It seems that only one course is open to the philosopher who values knowledge and truth above all else. He must refuse to accept from the champions of the forms the doctrine that all reality is changeless [and exclusively immaterial], and he must turn a deaf ear to the other party who represent reality as everywhere changing [and as only material]. Like a child begging for 'both', he must declare that reality or the sum of things is both at once [το όν τε και το παν συναμφότερα] (Sophist 246a-249d)21.
The gods and the giants in Plato’s battle present two varieties of the analog position. Each believes that ‘true reality’ is singular, that "real existence belongs only to" one side or other of competing possibilities. For them, difference and complexity are secondary and, as secondary, deficient in respect to truth, reality and being (την αληθινήν ουσίαν, το όν τε και το παν). Difference and complexity are therefore matters of "interminable battle" whose intended end for each is, and must be (given their shared analogical logic), only to eradicate the other.22 The philosophical child, by contrast, holds to ‘both’ and therefore represents the digital position where the differentiated two yet belong originally together. Here difference, complexity and systematicity are primary and exemplary.

It is an unfailing mark of the greatest thinkers of the tradition, like Plato, that they recognize the digital possibility and therefore recognize the principial difference of it from analog possibilities. From an analog position, by contrast, the digital possibility either does not exist at all or exists only in secondary fashion which is, therefore, deficient and demanding of analysis (in the etymological sense of ‘breaking up’ into its supposedly more basic components).

One of the recurrent problems addressed by thinkers of the first sort is how to speak to those of the second sort without fundamental distortion. The recurrent ambition of ‘thinkers’ of the second sort is the impossible construction of digital realities as analogical systems: Heidegger’s "die eiligen Fahrten dorthin, wo wir noch nicht sind und nie sein werden"23. The former problem is rooted in the latter ambition.

On the basis of this background, the Tractatus Logico-Philosophicus may be read as setting out the foundations or (in Wittgenstein’s terms) the logic of digital systematicity.

The first paragraph of Wittgenstein’s introductory remarks to the Tractatus has already been cited: "Dieses Buch wird vielleicht nur der verstehen, der die Gedanken, die darin ausgedrückt sind - oder doch ähnliche Gedanken - schon selbst einmal gedacht hat." There is no gradual way to these thoughts because they are already here, indeed, already so well known by us that we exercise them in all that we do and say. Still, we are somehow confused about them and this confusion then breeds philosophical and other problems. The second paragraph therefore reads (to be echoed in the final lines of the work): "Das Buch behandelt die philosophischen Probleme und zeigt - wie ich glaube -, daß die Fragestellung dieser Probleme auf dem Mißverständnis der Logik unserer Sprache beruht. Man könnte den ganzen Sinn des Buches etwa in die Worte fassen: Was sich überhaupt sagen läßt, läßt sich klar sagen; und wovon man nicht reden kann, darüber muß man schweigen."

Language (and therefore the logic of language) is already used by us and, indeed, properly used: "Alle Sätze unserer Umgangssprache sind tatsächlich, so wie sie sind, logisch vollkommen geordnet" (Tractatus 5.5563). Compare: before the advent of chemistry, humans metabolized oxygen with chemical exactitude. We don’t have to understand what we are doing in order to do it correctly. We can even misunderstand what we are doing and still do it correctly (as the oxygen example shows). However, such misunderstanding can have important consequences. It is Wittgenstein’s contention that our misunderstanding of language provides the motivating context ("die Fragestellung") for philosophical problems24. Proper use, we might say, is not known in its propriety: "du weißt eines nicht - wie recht du hast!"

This misunderstanding of language, hence of the logic of language, is said, in turn, to rest on a lack of knowledge concerning what can and cannot be said, between what is naturally or fundamentally clear ("läßt sich klar sagen") and what is naturally or fundamentally opaque ("wovon man nicht reden kann").

In the terms of Plato’s γιγαντομαχία, the giants, as children of Earth and denizens of the underworld, are champions of the dark: they are the "party [which] is trying to drag everything down to earth out of heaven". By contrast, the Olympic gods, "defending their position somewhere in the heights", are champions of the light. Each maintains that the fundamental relation of the light and the dark is such that only one or the other is "real existence" or "true reality". Both fail to heed another possibility which is exemplified in their existing activity of fighting with one another. This is an activity which takes place at first principle [περι της ουσίας] and is, as Plato says, "always going on" [αει συνέστηκεν].

It is this third fundamental possibility, Beckett’s "unheeded neither", Heidegger’s "Unterscheidung", which the philosophical child sees in the γιγαντομαχία. Plato explicitly connects what is always going on between the gods and giants – εν μέσω δε (…) αμφοτέρων (246c) – with what the philosophical child discerns about reality itself: το όν τε και το παν συναμφότερα (249d). In doing so, the child recognizes a transitive border between the warring champions of the light and of the dark which at once allows their discrete (or quantified) delimitation and their systematic connection: "Like a child begging for 'both', he must declare that reality or the sum of things is both at once."

Now the darkness of this border is of a different order from the dark championed by Plato’s giants. It is the darkness of that original difference which grounds digital systematicity and which first enables, in such a system, the relation of light-dark variables within it. Since this border is deeper than any of the discrete relata held together by it, it is unfathomable and silent by definition. Any attempt to indicate it or to say it (other than allowing it to function in a digital system) unavoidably makes the fundamental error of turning it into exactly what it is not, ie, into analogical difference which is ultimately unipolar.

Beckett treats this second dark in his 1958 play Krapp’s Last Tape:

…clear to me at last that the dark I have always struggled to keep under is in reality my most - (KRAPP curses, switches off, winds tape forward, [mechanical with gabble, 3 seconds], switches on again) - unshatterable association until my dissolution of storm and night with the light of the understanding and the fire.
This moment (which may have had some rough equivalent in Beckett’s life) records the differentiation of the analogical "dark I have always struggled to keep under", where either the dark or the light is necessarily more real than the other, from that digital dark of fundamental difference ("in reality my most"), which first allows the formerly only opposed light and dark variables to be seen in their systematic connection ("unshatterable association… of storm and night with the light of the understanding and the fire"25). Beckett uses the device of the tape recorder with its wind forward feature to show how the switch from analogical to digital perception is no gradual transition, but an "unspeakable" leap between modes of experience. Beckett’s language is explicitly digital here: "switches off…switches on". The whole passsage is a careful and exact construction where even the brackets work to show the essential break which is at stake both in the leap between analog/digital modes of perception and within the digital system itself: "(KRAPP curses, switches off, winds tape forward, [mechanical with gabble, 3 seconds], switches on again)". The stage description, "mechanical with gabble", is a remarkable dramatization of the "unspeakable" nature of the border which is crossed here.

Heidegger described this second dark in his 1957 Freiburger lecture series as follows:

Der Herkunft der Grundsätze des Denkens, der Ort des Denkens, das diese Sätze setzt, das Wesen des hier genannten Ortes und seiner Ortschaft, all dieses bleibt für uns in ein Dunkel gehüllt. Diese Dunkelheit ist vielleicht bei allem Denken jederzeit im Spiel. Der Mensch kann sie nicht beiseitigen. Er muß vielmehr lernen, das Dunkel als das Unumgängliche anzuerkennen und von ihm jene Vorurteile fernzuhalten, die das hohe Walten des Dunklen zerstören. So hält sich das Dunkle geschieden von der Finsternis als der bloßen und völligen Abwesenheit von Licht. Das Dunkle aber ist das Geheimnis des Lichten. Das Dunkel behält das Lichte bei sich. Dieses gehört zu jenem.26
Wittgenstein appears to make a similar point in his 1937 diary when he writes (Denkbewegungen, Part 2, p. 223):

Aber mein Glaube morgen kann lichter (oder dunkler) sein als mein Glaube heute. Hilf & Erleuchte! & möge kein Dunkel über mich kommen!
Ich bitte, & ich hab’s schon so, wie ich’s haben will: nämlich halb Himmel, halb Hölle!
If "Himmel" and "Hölle" may be equated with the light and the dark earlier in the passage, it would seem that Wittgenstein is differentiating between a dark that he wants ("wie ich’s haben will"), one that is compatible with the light ("nämlich halb Himmel, halb Hölle"), and a dark which he doesn't want and is incompatible with the light ("Hilf & Erleuchte! & möge kein Dunkel über mich kommen!").

The entry which immediately follows seems to confirm this reading:

Die Sonne geht um ca ½ 2 unter geht aber dann dem Rand des Berges so entlang daß man noch längere Zeit ihren äußersten Rand wahrnimmt. Es ist herrlich! Sie ist also doch nicht eigentlich untergegangen. –
What Wittgenstein terms "herrlich" is the sight of the rim of the sun just above the mountain (so a sun which can partially be seen, one that is half light, half dark) which he contrasts to the dark of the sun which has fully set ("eigentlich untergegangen"). The difference appears to be just that described by Heidegger between "Dunkel" and "Finsternis": "So hält sich das Dunkle geschieden von der Finsternis als der bloßen und völligen Abwesenheit von Licht." What is different between the two darks is their compatibility or incompatibility with the light, therefore the existence or non-existence of an inclusive border between the two.27

Such a transitive, yet abysmal, border is Beckett’s "unspeakable home", Heidegger’s Strom "den wir gar nicht benennen und vielleicht (...) niemals benennen können". Similarly, Tractatus 6.522: "Es gibt allerdings Unaussprechliches."28

Like Beckett and Heidegger, indeed like Plato, Kant and Hegel, Wittgenstein locates that of which "man nicht reden kann" in the original border which is fundamental to digital systematicity. The next sentence of his introductory remarks therefore specifies: "Das Buch will also dem Denken eine Grenze29 ziehen…"30

1"The harmony which cannot be perceived is superior to the one which can." Heidegger variously translates as "Fügung unscheinbare über das zum Vorschein drängende Gefüge edel." (GA55:142) and as "Einklang, der verborgen bleibt im Unscheinbaren nämlich, vermag Höheres als ein äußerlich aufgemachtes Zusammenrichten." (GA16:437). Other translations are: "The hidden harmony is better than the visible" (G.W.T. Patrick) and "The hidden attunement is better than the open" (Burnet).
2Foerster (originally, Förster) was not the son of one of Wittgenstein’s sisters (nor, of course, of his brothers), although he seems to have been a distant relation. In ‘Metaphysics of an Experimental Epistemologist’ (1995), he speaks of "a cousin of mine, a nephew of ‘uncle Ludwig’, Paul Wittgenstein". This Paul Wittgenstein (1907-1979) was the son Wittgenstein’s cousin, Karl (Carletto) Wittgenstein, and the grandchild of Wittgenstein’s uncle, Paul Wittgenstein (1842-1928). Foerster was therefore Wittgenstein’s ‘nephew’ only in the broad sense of being a member of the next generation in the extended family.
3Currently being reissued as Cybernetics/Kybernetik. Die Macy-Konferenzen 1946-1953, 2 Bde, edited by Claus Pias, diaphanes Verlag (Berlin) 2003/4.
4‘Quantized’ (Latin ‘quantus’ = ‘how much’) means ‘discrete’, something which is separate and therefore quantifiable. ‘Discrete’ derives from Latin, ‘discernere‘ (dis + cernere, pp cretus) meaning ‘discern’, ‘distinguish’, ‘separate’, ‘sift out’, ‘determine’. ‘Cernere’ is cognate with Latin, Celtic and Germanic words for ‘seive’ and with the Greek ‘krinein’, which we retain in ‘crisis‘, ‘critic’, ‘critique’, etc. This etymology points to the deep background of the question of essential difference in many fields: medicine (where the ‘crisis’ determines the direction of the ‘turn’ back to life or to death), tragedy (where the ‘crisis’ determines the potentially fatal ‘turn’ of events), politics (where the governor or governing body must ‘decree’ [<de-cernere] laws and decisions regarding peace and war), philosophy (where proper ‘judgement’, ie krinein, is the great question and where Kritik is therefore required between the types of judgements made by humans).
5Feldman is quoted by Knowlson (Damned to Fame: The Life of Samuel Beckett, 1996) as saying to Beckett: "I said that I was looking for the quintessence, something that just hovered." (97) Beckett himself is recorded as observing to Martin Esslin, "I take away all the accidentals because I want to come down to the bedrock of the essentials, the archetypal." (Beckett Remembering / Remembering Beckett, ed James and Elizabeth Knowlson, New York, 2006, 47-49)
6"Neither’, from Samuel Beckett: The Complete Short Prose, 1929-1989, ed S E Gontarski, 1996. The original draft (which Beckett wrote for Feldman in the middle of their conversation) began: "To and fro in shadow, from outer shadow to inner shadow. To and fro, between unattainable self and unattainable non-self." (Damned to Fame, 98).
7'Die onto-theo-logische Verfassung der Metaphysik', in Identität und Differenz, 1957, S 36-37.
8GA48, S 322. Heidegger's use of 'weder....noch' here ("was weder Seiendes ist noch zum Sein gehört") is very common in his texts from first to last. Weder/Noch is the title given to the German translation of Beckett's Neither.
9GA50, S 129
10Cybernetics of Cybernetics, Biological Computer Laboratory, University of Illinois, Urbana Illinois, 1974; 2nd edition: Future Systems, Minneapolis Minnesota, 1996.
11The first sentence of the introductory remarks to the Tractatus.
12Although Kierkegaard is often thought to have originated consideration of the leap, the fundamental difference between analog and digital systems was clear to Leibniz (who was delighted to find the latter in the I Ching). Not without influence from Leibniz, Kant specified the critical role of fundamentally different types of experience for philosophy and, indeed, for all human behavior, especially ethical behavior. Such a leap is implicated in the Wahl seen by Fichte, following Kant, which the philosopher must ‘always already’ have made in going about her business. Hegel then specifies this leap at the heart of reality itself and, subsequently, at the heart of that peculiar sort of reality which is human experience (including the human experience of speculating about the heart of reality itself). At the same time in England, but again in the footsteps of Kant, Wordsworth and Coleridge were attempting to specify the digital/analogical contrast and its implications. Wittgenstein, like Heidegger, must be read as belonging to this tradition, but only after an unprecidented war had revealed both the stakes, and the futility, of it. Beckett, in turn, writes after a second world war which had (as if this were necessary) served to reiterate the point.
13Heidegger concludes Sein und Zeit by noting that it has been underway to where it would start: "Und am Ende läßt er sich nicht ‘vom Zaun brechen’, sondern das Entfachen des Streites [= die Gigantomachie] bedarf schon eine Zurüstung. Hierzu allein ist die vorliegende Untersuchung unterwegs." (SZ, S 437 = GA2, S 577)
14FAZ-Magazin H461, 20.12.1988 (available at http://home.snafu.de/pedasy/hvf-int.htm). This meeting with Wittgenstein took place at the home of Margaret Stonborough, Wittgenstein’s sister and a friend of Foerster’s mother.
15‘Die Sprache’, Unterwegs zur Sprache, 1959, S 12
16‘Das Wesen der Sprache’, US, S 190
17Identität und Differenz, S 21
18S 31 (1994 edition), Nachlass Item 109, Page 207.
19Between worlds there is no world. Therefore the attention given to ‘nothing’ by Heidegger and Beckett. This point will be taken up later in the project in regard to Weininger’s influence on Wittgenstein and in regard to Wittgenstein’s notion of ethics. It is into this ‘nothing’ that Wittgenstein‘s ladder leads (Tractatus 6.54).
20Plurality at first principle is the essence of the digital system. Presumably its roots may be traced back thousands of years before the advent of philosophy in polytheistic mythologies with their wars between rival gods. Where gods – ie, the original powers - are discrete enough to battle each other, without this concluding in some monotheistic victory, a digital system is already in place. Cf, Tractatus 5.4541 "Die Menschen haben immer geahnt, daß es ein Gebiet von Fragen geben müsse, deren Antworten - a priori - symmetrisch, und zu einem abgeschlossenen, regelmäßigen Gebilde vereint liegen." It was Plato’s genius to see that a γιγαντομαχία implicates digital systematicity and therefore also the principial difference between it and analog systematicity.
21Heidegger brackets the whole of Sein und Zeit (1927) between references to Plato’s ontological battle. The book opens by noting "Die genannte Frage [die Frage nach dem Sein] ist heute in Vergessenheit gekommen, obzwar unsere Zeit sich als Fortschritt rechnet, die "Metaphysik" wieder zu bejahen. Gleichwohl hält man sich der Anstrengungen einer neu zu entfachenden γιγαντομαχία περι της ουσίας für enthoben." On its last page he notes: "Der Streit bezüglich der Interpretation des Seins [d.h., γιγαντομαχία περι της ουσίας] kann nicht geschlichtet werden, weil er noch nicht einmal entfacht ist." In his next book, Kant und das Problem der Metaphysik (1929), he then observes: "Die fundamentalontologische Grundlegung der Metaphysik in Sein und Zeit muß sich als Wiederholung verstehen. Die Stelle aus Platons Sophistes, die die Betrachtung eröffnet, dient nicht zur Dekoration, sondern als Hinweis darauf, daß in der antiken Metaphysik die Gigantomachie über das Sein des Seienden entbrannt ist. In diesem Kampf muß schon - mag die Seinsfrage dort noch so allgemein und vieldeutig gestellt sein - sichtbar werden, in welcher Weise hier das Sein als solches verstanden wird." (§ 44 = GA3, S 239-240).
22Cf Heidegger: "Das einzige Gesetz der Verwüstung ist, daß das Nötige das Nötigste und das allein Nötige sei." (GA77, S236)
23Text given in full above, reference in note 15. Heidegger’s point concerning "die eiligen Fahrten" repeats Hegel’s charge against Fichte and Schelling that their thought proceeds "wie aus der Pistole"  (Vorrede, Phänomenologie des Geistes). Hegel’s critique is that Fichte and Schelling can account for identity (aka, ‘the absolute’) only arbitrarily, since the quest for identity in an analog system contradicts its need for difference in order to be a system at all. All Fichte and Schelling can do, therefore, is shoot identity out of their systems. By contrast, Hegel and Wittgenstein share the (digital) conviction that everything which can be said, can be said clearly and definitively: "Erst was vollkommen bestimmt ist, ist zugleich exoterisch, begreiflich und fähig, gelernt und das Eigentum aller zu sein. Die verständige Form der Wissenschaft ist der allen dargebotene und für alle gleichgemachte Weg zu ihr…" (Vorrede, Phänomenologie des Geistes). Similarly in Wittgenstein: "In logic nothing is hidden. (…) What is difficult is to make the rules explicit" (Wittgenstein’s Lectures 1930-1932, p 3). Thus: "Was sich überhaupt sagen läßt, läßt sich klar sagen" and "Die Grenzen meiner Sprache bedeuten die Grenzen meiner Welt" (5.6). For a digital system, nothing is esoteric and mysterious - except the existence of the explanitory (ie, explanation enabling) digital system itself: "Nicht wie die Welt ist, ist das Mystische, sondern daß sie ist" (6.44).
24Understanding language, ie, understanding the logic of language, would therefore not solve these problems but, rather, by removing their ‘Fragestellung’ – their motivating context, the place defining them as questions – dissolve them.
25With Beckett’s "unshatterable association (…) of storm and night with the light of the understanding and the fire", compare Heidegger’s "das Entfachen des Streites" (cited in note 13 above), "neu zu entfachenden", "entfacht" and "entbrannt" (in note 20 above). Gadamer reports that Heidegger, on the occasion of his leaving Freiburg for Marburg in 1923, gave a talk in Todtnauberg on ‘Wachsein am Feuer der Nacht’. The image of the fire in the night is, of course, already central to Plato’s allegory of the cave. The illuminating fire belongs together with the night because (digital) insight is implicated upon abysmal original difference.
26GA79, S 93, emphasis added.
27Just as there are two darks, so, correspondingly, there are two lights. Thus Beckett locates his "unheeded neither" "between two lit refuges", between "the one gleam or the other". But, surprisingly perhaps, the result is to expose "gently light unfading". These lights of the "refuges" of self and nonself, on the one hand, and of an "unspeakable home", on the other, are fundamentally different. They are differentiated by their relation to the dark and to plurality. The lights of the "refuges" want to be singular and alone, i.e., analog: "intent on the one gleam or the other". Although ineluctably involved with the dark way between them, "beckoned back and forth", they are "heedless of the way". Plurality is accidental and, as such, to be overcome or ignored. By contrast, the "light unfading on that unheeded neither" is the light exactly of the dark: "TO AND FRO in shadow (...) between two lit refuges". Here plurality, and especially the plurality of light and dark, is primary and exemplary, i.e., digital.
28Wittgenstein continues this paragraph at Tractatus 6.522 as follows: "Es gibt allerdings Unaussprechliches. Dies zeigt sich, es ist das Mystische." Compare a note from Kant’s Nachlass: "Das größte und einzig-practische aller Geheimnisse ist die Wiedergeburt wodurch er den Leib dieses Todes ablegt und in einem neuen Leben zu wandeln anhebt. Dies Mysterium deckt uns kein Hierophant auf sondern der Geist des Menschen selbst der den todten Buchstaben des Gesetzes verläßt und den Göttlichen Sinn desselben erfaßt sich aber diese Umwandelung selbst nicht erklären kann." (AA Bd.XXIII.437)
29The essential difference between analog and digital systematicity may be specified in terms of the place of the Grenze (border). In an analog system, the border comes at the end, either of an individual component or of a series of components. Beyond the border lies the undefined. Over there, beyond the border, lies what the component or series is not. In a digital system, the border is situated in the middle, enabling definition and specification on its basis. A great many confusions in philosophy, not least in the reading of Wittgenstein, arise from the confusion of these two fundamentally different sorts of border. The two correspond to the two darks discussed above.
30Emphasis added. For Hegel, this unspeakable border is death, ‘absolute Zerrissenheit’, but it is the death of God (where the genitive is both objective and subjective): "Aber ein wesentliches Moment ist dies Geschiedene, Unwirkliche selbst; denn nur darum, daß das Konkrete sich scheidet und zum Unwirklichen macht, ist es das sich Bewegende. Die Tätigkeit des Scheidens ist die Kraft und Arbeit des Verstandes, der verwundersamsten und größten oder vielmehr der absoluten Macht. (…) Der Tod, wenn wir jene Unwirklichkeit so nennen wollen, ist das Furchtbarste, und das Tote festzuhalten das, was die größte Kraft erfordert. (…) Aber nicht das Leben, das sich vor dem Tode scheut und von der Verwüstung rein bewahrt, sondern das ihn erträgt und in ihm sich erhält, ist das Leben des Geistes. Er gewinnt seine Wahrheit nur, indem er in der absoluten Zerrissenheit sich selbst findet." (Vorrede, Phänomenologie des Geistes)