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| Version française |
Briefly, it is always well to return to the springing of thought; in this case, a re-examination of Wittgenstein's *Tractatus Logico-Philosophicus* is in order, particularly in regard to the digital domain. The work relies on the Sheffer stroke* ("not both A and B") and its dual ("neither A nor B") to construct a logical picture of the world. General propositions are obtained "by taking any selection of atomic propositions, negating them all, then taking any selection of the set of propositions now obtained, together with any of the originals - and so on indefinitely. This is, he [Wittgenstein] says, the general truth-function and also the general form of proposition." (Russell introduction.) Certainly, the Sheffer stroke and its dual operate on a Boolean calculus with 0 and 1 values, a digital domain.
Two points are immediately evident: First, the domain is reminiscent of any digital construct, including ASCII, Mosaic decoding, Quick- Time, etc. Second, the Sheffer stroke and its dual both construe a negation which is ELSEWHERE; the instability of the stroke is bolstered by "neither A nor B," which, I have shown in other texts, implies a conceivably fissured and non-circumscribed domain. If the stroke itself is a phallic reordering of the propositional calculus into a singular basis, the negation is an opening beyond or elsewhere than the calculus. Nevertheless, both operations within a computer or networked domain imply, necessarily, recourse to the digital at every step; this is the effect of protocol, address, and recognition.
There is a shaky argument possible here. Consider the stroke operating on ASCII symbols themselves (the "monkeys typing Hamlet" thought-experiment); then all ASCII utterances, which are always already coded, are reproduced. Hence the *Tractatus* holds in this limited domain. The truth-table would simply be the existence of an ASCII string within a pre-inscribed framework. Within the frame of this essay, for example, the ASCII utterance "ASCII utterance" = 1 since it is present. It is clear that sets of potential utterances are subsets of others; the domain folds in upon itself.
It should be noted that, by Cantor's diagonal argument, it would never be possible to (re)produce, even theoretically on an aleph-null level, the set of all utterances. But this is not germane; what we are considering is the set of all utterances always already produced within a domain. The totality of Net utterances, for example, from 1990-1995, forms such a set. It is clear by the absurdity of this totality that the set is somewhat absurd and fuzzy, even within ASCII. Questions immediately arise concerning the epistemology of the Net; still, the principle is worth considering.
The digital domain is a frozen domain in the sense of acceptance of binary information; in this sense, a deeper (Sheffer and dual) construction, beyond ASCII, is envisioned. This construction is based only on distinction between 1 and 0, one and the other. (I have shown elsewhere ("Spew" etc. in Internet Text) that repeated dis- tinctions lead to peculiar symmetries. But 1/0 is dependent only upon concatenation at this point.)
Let us examine briefly the seven integral (1,2,3,4,5,6,7) sections of the *Tractatus* in light of all of this:
"1 The world is all that is the case." In German, "Die Welt is alles, was der Fall ist." and the comma-separation implies, as well, that the world is a totality. Consider the Internet as "that which is the case" - or any other digital domain. Then the case is defined by firewall, protocol, etc.
"2 What is the case - a fact - is the existence of states of affairs." To translate into digital communication: A fact is a concatenation or string of binary symbols (note that the symbols themselves are empty; one can use just as easily "3/4", "</>", etc.). This is evident from "2.01 A state of affairs (a state of things) is a combination of objects (things)."
"3 A logical picture of facts is a thought." This is followed by "3.01 The totality of true thoughts is a picture of the world." If "logical" is defined by "an instance of" - using the Sheffer stroke or its dual to produce concatenated binary symbols - this is clearly true, since the domain is compared to the set of concatenations. (Note that the domain may be considered to possess a "resonance" with itself; it is technically reflexive, a self-mapping.)
"4 A thought is a proposition with a sense." (German: "Der Gedanke ist der sinnvolle Satz." Note "sinnvolle.") And in "4.002 Man possesses the ability to construct languages capable of expressing every sense, without having any idea how each word has meaning or what its meaning is - just as people speak without knowing how the individual sounds are produced." This - and other statements within the section - argues for either a hierarchical or holarchic division of the domain, which is precisely what occurs in Net topography, or within a computer in the escalation from machine/assembly language through compilers/interpreters to higher-level programming. Wittgenstein goes on to say "Language disguises thought. So much so, that from the outward form of the clothing it is impossible to infer the form of the thought beneath it, because the outward form of the clothing is not designed to reveal the form of the body, but for entirely different purposes."
If the logicism of the *Tractatus* was faulted for its ultimate insistence on a metaphysical atomism, that atomism is clearly returning full-force within the digital domain. Obviously the domain ALWAYS operates within a specific bandwidth, but, by virtue of the gestural quality of non-distributive non-Boolean lattices/logics, the domain extends itself elsewhere or beyond the specificity. The return to the *Tractatus* and its argument is a return to the initial bandwidth; Wittgenstein in 4.002 is clearly aware of this. What is occurring here is a peculiar return to a 19th-century classicism, dream of an absolute. Ironically, it also becomes the dream of the future. Let us proceed.
"5 A proposition is a truth-function of elementary propositions. (An elementary proposition is a truth-function of itself.)" The first part of 5 argues for compound or concatenated elementary propositions; we have seen this in the initial formulation cited above. The second part argues for a resonance or self-reflexivity of any statement; we have also found this correct. These considerations are clear in computer languages themselves; for a program to "run" in QBasic, concatenation symbols ("AND" in certain cases and ":" in others) are used. Consider the proposition in QBasic "X = X + 1." This is true; it will "run" within a program, if X is either undefined or defined as a number. But "X + 1 = X" will not run; the assignment is unclear. One can say, using a metaphysics of "run/not-run," that an elementary proposition is true of itself if it "runs" and not true ("false") of itself if it does not run. This eliminates the problematic ontological leap from tautology to substance that otherwise might be encountered. Another method of elimination is to consider the basic symbol set itself (0/1, etc.) as elementary propositions.
"6 The general form of a truth-function is [*p,*E,N(*E)]. This is the general form of a proposition." The expression is translated into ASCII; "E" and "N" are Greek letters, and "*X" means that "X" is over-lined. In Russell's description, "*p stands for all atomic [i.e. binary - A.S.] propositions"; the second expression "stands for any set of propositions"; and the third "stands for the negation of all the propositions making up *E." This returns to the considerations at the beginning of the essay.
The following earlier propositions are also immediately applicable:
"5.632 The subject does not belong to the world: rather, it is a limit of the world." "5.641 Thus there really is a sense in which philosophy can talk about the self in a non-psychological way. What brings the self into philosophy is the fact that the world is my world. The philosophical self is not the human being, not the human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of the world - not a part of it." The digital domain has an INTERIOR - the hierarchical/holarchic ordering, and an EXTERIOR - which is always already elsewhere, the metaphysical subject propelling the semantics of the domain.
While the domain is granular, the subject is not. But the explication of the subject approaches granularity, just as virtual reality achieves finer and finer rasters. There is no "ultimate" here.
"6.5 When the answer cannot be put into words, neither can the question be put into words. The riddle does not exist. If a question can be framed at all, it is also possible to answer it." A question that can be answered is a question that is FORMATTED. To FORMAT a question is to WRITE it in order to RUN it.
The representation of the metaphysical subject is always a REWRITE within the digital domain.
The existence of the representation is a RUN REWRITE.
"7 What we cannot speak about we must pass over in silence." The older translation: "we must consign to silence." German: "Wovon man nicht sprechen kann, darueber muss man schweigen." This has been subject to considerable interpretation ranging from the limitation of the domain of facticity to the problematic representation of ethics; certainly, the latter sections of the *Tractatus* tends towards ethos. Reverting momentarily to a Kripkean semantics, what is passed over is never a natural kind, nor a rigid designator; naming HOLDS within the world of pictures, facts, and propositions. Here, the silence is that of the exteriority of the metaphysical subject, whose real-life semantics are not reducible to codification (single, double, or triple). But the digital domain is manipulated and to some extent ulterior, even in virtual reality; codification is always present (just as codification is necessary in any definition of life, artificial or otherwise).
The digital domain, however defined, is therefore a construct amenable to an analytical treatment based on the *Tractatus* and other similar texts. The descriptive aphoristic of the later Wittgenstein, particularly *Philosophical Investigations* then becomes, not a questioning of the ontological status of the *Tractatus,* but an account of a fuzzy and irregular epistemology applied on the level of the semantics of the metaphysical subject. The earlier/later work is paralleled by interior/exterior; at the beginning of the third millennium, the increased raster of the digital (increased bandwidth) parallels the increased articulation of the exterior FROM the interior. Hence the necessity for a return, however undesirable, to the earlier Wittgenstein, even to a Hertzian mechanics. I see the resulting and necessary SPLIT (*SPALTUNG*) OF THE SUBJECT as unavoidable; on one hand, the horizon of perfect control and description, and, on the other, the postmodern fragmentation of the totality of the real world on every level, from that of the nation-state, to that of mathematics or even the closed dominion of the digital.
In other words, it is not that the torsion occurs only within a postmodernism of congealed and dispersed subjectivity, but also withouta digital articulation in which a remnant of 19th-century classicism is buried - and absolutely necessary for any form of digital communication or "reality" whatsoever.
*The Sheffer stroke and its dual are "elementary operations" out of which it is possible to construct the complete syntax of propositional logic. Nicod's single axiom basis utilizes the stroke.
Alain Sondheim
Moderator of the lists Cybermind, Image and Fiction-of-Philosophy, member of Spoons Collective
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