Wittgenstein (early): Sliding Down the Sky Rope

Wittgenstein (early) Sliding Down the Sky Rope J.D. Casten Chapter from book forthcoming in 2012, Cybernetic Revelation. (Click here to go to J.D. Casten's Website) (click here for easy to read & print .pdf version) OVERVIEW Ludwig Wittgenstein’s Tractatus Logico-Philsophicus, as it is named, is a logical philosophical tract— a course to follow, to logically identify some fundamental aspects of logic including its representational and linguistic character, ontological substantiation, self-referential nature, and limit at “my” world of experience. Wittgenstein had training as an engineer, and the Tractatus looks somewhat prophetically (it first appeared in 1921) like a computer program of numbered concise logical statements. Yet, unlike a computer program, which is composed largely of commands, the Tractatus is descriptive. And it is not necessarily argumentative—no doubt one may take issue with the Tractatus, as I will, but Wittgenstein’s intent seems to be expository—he does not engage much in conflicting points of view (e.g. Frege and Russell), as Plato’s does in his dialogues—what Wittgenstein is concerned with here is the logical point of view, as he saw it. It is in this way that we can see Wittgenstein’s project here as related to Kant’s Critique of Pure Reason, where Kant tried to establish the faculties necessary for logical judgments (Apperception, Understanding, Imagination, etc.): Kant’s Robot, if you will, seems to be a shot at the apparatus of subjective experience and judgment. Now, while Hegel tries to frame the being of consciousness within that robot (pure ego framed by a world of things, other people, social history, etc.), Wittgenstein tries to refine the logical apparatus of that “robot perspective.” (I call it a “robot” because, by discussing such a perspective and representing it, we create a model that is not quite the flesh and blood of a real subjective experience: it is a replica of functional essentials.) There are seven major divisions in the numbering of the Tractatus, with each major division (save the last) having subdivided numbering (and, the first division having a total of seven divisions itself). The number seven is symbolically significant—the Sun having been considered the seventh orb in the heavens, and also the source of en-light-ened Reason found outside of Plato’s cave. Roughly the seven major divisions concern the following: 1: The world as logical facts (being is composed of the consistently related) 2: A state of affairs of things, & our ability to picture them (division of the objective world, and “subjective” ability to represent it) 3: A shift from pictures to propositions (linguistic ability to think (not about, but of) the objective world) 4: Truth possibilities of propositions (sense of language given by relation to objective world) 5: Truth functions, operations, and their limits (related propositions in a self-referential and descriptive “system”) 6: Generation of numbers, mathematics, laws and their limits (Pressing logic up to the world of “geometrical” experience) 7: The absolute limit (Can’t speak of that beyond (or “tangential” to?) experiential surface) PERCEIVING REALITY THROUGH PICTORIAL FORM In his Tractatus, Wittgenstein uses pictures to represent a distinction between perceptual thinking, and “reality:” (Kantian) “representation” identified as actual representation. Throughout the Tractatus, Wittgenstein shifts the meaning of “picturing reality,” from a mirroring of reproduced concrete sensation to a denoting of abstracted logical form essentials—picturing becomes both a starting point, and a metaphor for logical representation: a representation of representation. We will briefly now plot out the course of that metamorphic journey in order to elucidate the running thread of a problem. Just as the word “reflection” can mean “thinking,” and given that early modern philosophers like John Locke, wrote of “reflection” to describe how “ideas,” from the outside world are internalized, Wittgenstein is concerned with “pictures” that represent “the state of affairs.” One should note that for Wittgenstein, “the world,” or “the case,” is made up of “facts,” all being composed of “the states of affairs,” which in turn are made of up combined things, the entirety of which comprise “reality.” This terminology and hair-splitting used by Wittgenstein to re-describe what we take for granted as our world with consistently related objects sets a stage of a more precise logical space. Now, within that logical space, as a part of it, we can have “pictures” that represent their own world with consistently related objects; and the pictures may or may not map to reality via “pictorial form.” In 2.15 Wittgenstein claims: “The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way. Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture.” (Tractatus, 2.15) It is not clear to me if there is some odd reversal here, were pictorial form precedes the ability to distinguish objects in a state of affairs—but at any rate, there is a proposed correspondence between pictures and objects. FROM VIRTUAL REALITIES TO PROPOSITIONS To take Wittgenstein’s approach a step further, using a more modern technological analogy, imagine that you have been hooked up to sophisticated virtual reality gear, possibly with video goggles, a tactile suit, headphones— and that this virtual reality simulation is giving you a live sensory feed from a sensory robot in a white cubical room, with a table in the center, and an apple on it. In this case, there is a reality: the actual room, table, and apple; and there is a representation of it being displayed directly to your sense organs, so realistic that you might not be able to tell that it was not real (you might have also been placed in a sensory deprivation tank, with computers hooked up to your very nervous system with a similar sensory feed). Here we would no doubt say that the reproduction was a “picture” that shared a very minutely detailed pictorial form with reality—again, so much so that you might not be able to distinguish the two—the pictorial form would be nearly identical to the form of reality which is the logical form (2.18). Whereas pictorial form is purely representational, logical form need not be. Logical form concerns the identity of what is pictured. This can be illustrated in a range of representations, from the virtual reality; to a holographic representation of the apple on the table; a photograph of it; a hyper-realistic painting; an impressionistic painting; a more abstract painting (a red circle with a line/stem on a crude stick figure table); a hieroglyph depicting a red circle on a square; and in turn simply an “O” representing the apple, an “N” representing the relation of “this on top of that,” and a “T” representing “table,” we might have the highly abstract, and linguistic picture that looked like this: ONT (as in ontology). Following Wittgenstein, I would suggest that while more perceptual pictorial form fades into the background with our abstract progression, logical form involved with thinking comes to the fore: perceptual mirroring gives way to logical identity (although Wittgenstein rarely uses the words “mirror” nor “identity.”) Wittgenstein does, however, claim that there is continuity from the pictorial to the propositional (ONT, like aRb, may be an elementary proposition), along the lines of hieroglyphics and sign language—where logical form is maintained well into phonetic notation and visual picturing is absent. Along with propositions come representational truth values. Wittgenstein claims that sense of propositions come from their logical correspondence with reality. If the proposition says “the apple is on the table,” and the apple is on the table, the sentence is true (and even if the apple was not on the table, the very possibility of an apple on a table would give the proposition “the apple is on the table” sense). PARALLEL HISTORIES OF PICTORIAL AND LOGICAL FORM However, there is definitely a problem for Wittgenstein trying to maintain that propositions are representational due to their speculated “evolution” (my word). Was there not a point in history, or in our example, where convention enters the picture, when hieroglyphs metaphorically shift due to a context where, had we not been present at the entire evolution of transformations, we never would have known that the abstract proposition did indeed connect with reality via its logical form? In other words, although we might be able to see a connection between the Latin usage of the word “video” to mean “I see,” and the latter use of “video” to mean “I understand,” what happens to the logical identity of the word, “video,” where there is a significant shift of denotation? Wouldn’t Wittgenstein have to claim that representations can be ambiguous and that their disambiguation, necessary for a sense with his use of the possibility of the representational truth or falsity of a proposition, would require a context that is part and parcel of the entire fabric of history a specific word’s, (“video”), evolution? For example, the proposition, “I see the central point of your picture,” differs in contexts such as (a) understanding the main meaning of a work of art, or (b) actually visually noticing a dot that is camouflaged among many off center dots. How does that example compare to a picture of an apple on a table being used in a multitude of situations—where the same logical form applies to different apples on tables? In each case the same representation or proposition can be used in different contexts; but in the latter, the logical form remains consistent, while in the former, the “pictorial form” of the proposition remains consistent, while the logical form differs. Although it would seem that logical form as thought is born of pictorial form, and hence that we might have a contradiction here, due to a deep schism between the two types of form, it might be resolved by noting that nowhere is there a hard and fast rule that pictorial form must always have only a one to one correspondence to a particular logical form—they need only have a connection. While the pictorial form is material, through and through, the logical form was always mental thought, or at least has its own material evolutionary history parallel to the history of the more apparently material pictorial form (e.g. something like a “meme” history—a cultural use that is communicated from brain to brain in parallel to the material signifier, or pictorial form—more on this later). SEVERANCE OF PERCEIVED AND LOGICAL REALITY Wittgenstein catches this parallel when switching his terminology to that of “signs” and “symbols” in division 3. Propositions are composed of physical signs, yet multiple propositional signs can refer to singular symbols (or expressed thoughts); and single propositions also have the ability to express multiple symbols. Yet, he does not go into much depth concerning propositions having a physical-representative connection to “physically perceived” reality, in contrast to these logical symbolic conveyances of the propositions that “represent” an abstract logical reality. There is a sort of “bait and switch” here. The intuitively sensible idea of a proposition picturing a sensible reality takes a relatively arbitrary relation to the idea of logical symbols of thought picturing logical objects of reality. Logical symbols could not really be said to “represent” logical objects in a pictorial way, as they have only correspondence of points of “logical thought” to points of “logical space” in reality. The connection between pictorial form and logical form in “logico-pictoral-form” (2.2) is severed; and there is the question of whether it really ever was there in the first place. CONSTRUCTING LOGICAL FUNCTIONS: GOD'S DICEY LOGIC Once Wittgenstein has his logical symbol/objects correspondence however, much of the logical core of the Tractatus falls into place: Elementary propositions, of the form “a is related to b by relation R - aRb” (much like our “ONT”), can range from tautologies at one extreme to contradictions at the other, with sensible true or false propositions in-between (and more complex propositions can be built out of these elementary propositions). To unfold three examples from the chart of division 5.101: 1234 (TTTT) (p, q) Tautology (if p then p and if q then q) (TTFT) (p, q) in words: if p then q (FFFF) (p, q) Contradiction (p and not p, and q and not q) Each column contains an outcome based on a relationship between p and q: In column 1: p:T, q:T; in column 2: p:F, q:T; column 3: p:T, q:F; column 4: p:F, q:F There are four sets of binaries: (a) Two proposition variables (p, q) (b) Two possible values for the first (p: T or p: F) (c) Two possible values for the second (q: T or q: F) (d) Two possible function output values (T or F) Now, Truth Functions present another monumental leap from one realm to another, with seemingly little connection: as with the leap from pictorial form to logical form, there is the leap from related elementary propositions (e.g. p, q) to the consequent complex proposition (e.g. if p then q): where logic holds by virtue of God! (5.123 – or “a god” rather). Interestingly, following Hume, Wittgenstein proximally makes the claim that: “Superstition is nothing but belief in the causal nexus.” (Tractatus, 5.1361) Temporal causality is “superstition,” while “a god” insures implication. The truth grounds (5.101) of the implication if p then q that make that proposition true are simply the truth possibilities of elementary propositions p and q that make if p then q true. This is a completely circular way of saying that what defines if p then q as true is a certain combination of truth values for p and q—in other words if p then q will be true by definition of (TTFT) (p, q). It is similar for every other truth function (i.e. “p v q”, “p . q”, “~p”, “~q”, etc.): the 16 total possible variations from (a) two variables (p, q) with (b) two possibilities for p (T, F) (c) two possibilities for q (T, F) (d) and two possible outcomes (T,F) [or (2 ^ 4)] defines all logical relations (prior to their being identified with logical operators). Although the binary division is the most elegant, one wonders: Why not a logic based on threes?: (True, False, or Maybe for each of p, q, r— would result in a table with 81 possible variations: would the “modal logic (with a maybe) and 'mediated comparison/connection' (3 variables)” given by those combinations be less valid?) Has Wittgenstein read too much into a set of binary possibilities, or is there something fundamental about the relationship between the binary and logic? How do we bridge the gap between a table of binary possibilities, and propositional logic? The real world application of each of these four binaries needs to be examined: (a) two propositions (p, q) — because at least two are needed for any comparison or connection; (b) & (c) two factual possibilities for two propositions (T, F)— because they independently may or may not represent a situation (more on this below) and (d) two possible results as the outcome for the relations of the two propositions (T, F)— because the comparison or connection of two true or false propositions will result in a true or false outcome. But there is definitely a problem with conflating the first (b & c -inputs) and second (d-output) types of truth and falsity. One type, for Wittgenstein, is either about representational (synthetic) truth or truth by definition (analytic)— while the other type is about the necessity of logical relationships: a sort of hyper-analytic (or a priori) hypothesis. I might call these first level truths (those of mirroring the world), and second level truths (those concerning relationships between mirror/propositions). No wonder a god is required here for Wittgenstein, for it must be some power exterior too his own observation (the first level truths) that would make the world's consistency deductively (by implication) absolute (the second level truths) rather than inductively “probable.” In other words, although induction may be a matter of probable certainty, the “hardness” of deduction is an unknowable faith. Maybe “God does not play dice with the universe,” to quote Einstein, but God is a matter of faith, not certitude. A little more on this is discussed below, concerning truth functions vs. operations. A serious question remains: what is the relationship between the analytic/synthetic truth of propositions, and an a priori structured truth of logical connections, and are the two incommensurable? Is implication ever more than a highly certain induction? An induction that in circular fashion, is deeply intertwined and based on implication itself (If something happens regularly, then it may happen again)? No doubt, the binary logic here tied to a minimum of comparing and connecting two independent statements, and their truth or falsity, ties into representation: propositions may or may not represent reality, and hence are true or false. The whole notion of truth and falsity is “illustrated” by the notion of pictorial form corresponding to a perceived reality of logical form—but do we perceive a reality of logical form? When the complex of a picture that completely maps a reality is simplified towards hieroglyphics and propositions on the one hand; and objects are singled out in a visual field on the other—what maintains a connection between the signs of the picture and the logical object in reality? A logical symbol? Where did that come from? If propositions do not indeed represent reality, absolutely, as I am suggesting, then basing logic on truth values of propositions as representations is suspect. A logical symbol may connect to reality—but does it represent it? And if not, what is the nature of truth and falsity, other than a coherence of logical symbols associated with other logical symbols that have a consistent relation to logical objects associated with other logical objects. Wouldn't there be a sort of “indeterminate translation” between the realm of logical symbols and logical objects? In other words, might there be idiosyncratic logical symbols for each person (remember, logical symbols are not tied to logical objects via pictorial representation) in such a way that each person’s understanding of a proposition would be slightly skewed from every other person: making logic a matter of “statistical convergence,” among populations rather than absolute identity? Each person has their own experiences that are shared with others only in part: Language is indeed public, yet every person’s use of it is semi-private, given their personal idiosyncratic histories. The “logical identity” of public “objects” (which may only exist in the minds of individuals—more on this later) might simply be as sort of holographic chimera projected by individual (human) cells. (A hologram not perceived by a who, but an ideal that has no real existence). THE DIFFERENTIATING SHEFFER STROKE Strategically, Wittgenstein discusses implication, both absolute (if p then q) and probable (prior evidence of p with q may mean p if q is given) before moving on to truth operations. A truth function relates only to the (VVVV) (p, q) parts of the chart (where “V” = “T” or “F”); but operations, such as “or - v” and “not - ~” are added and discussed later. The distinction is important, for Wittgenstein implies that truth operations (e.g. p v ~q) are “semi-arbitrary” (my words) in relation to truth functions. We could have an indefinite number of truth operations with a given truth function (Given (p, q) of various combinations, and (VVVV)). The truth function—which gives the truth value of a representational propositional relation—is primary, while the truth operation—a sort of propositional logical equation—is somewhat derivative and can take a number of forms: much as single symbolic logical expressions can find form in a multitude of material sign propositions, single truth functions can find expression in a number of truth operation notations. However, it is through truth operations that more complex truth functions are constructed. Wittgenstein’s notation for generating propositions is an expansion of his elementary truth functions, where beyond the simple (FFFT) (p, q) which indicates “neither p nor q “(or “p\|q” from which all other truth functions may be derived by use of recursive truth functions) we have (-----T) (ξ,…) (hereafter I will alter the notation from “ξ” to “E”) where “E….,” or “Ē” is a set of propositions, and hence (-----T)(Ē) or N(Ē) is the negation of all values of the indicated propositions— and the possibility of deriving, or generating, generalized propositions. N(Ē) is like a super Sheffer stroked (“\|”) series of propositions, which stroke itself visually illustrates the boundary between elements—differentiates them—and can act like a law of non-contradiction where we cannot have both p and ~p. IDENTITY OF SIGN AND SYMBOL? Now in (5.526) Wittgenstein claims: “We can describe the world completely by means of fully generalized propositions, i.e. without first correlating any name with a particular object. Then, in order to arrive at the customary mode of expression, we simply need to add, after an expression like, ‘There is one and only one x such that…’, the words, ‘and that x is a’.” (Tractatus, 5.526) Interestingly, he soon adds, (5.53): “Identity of object I express by the identity of sign, and not by using a sign for identity. Difference of objects I express by difference of signs.” (Tractatus, 5.53) Wittgenstein clearly identifies his two logical spheres in these quotes; and although one realm (symbolic propositions) might map the other (logical objects), in its entirety, or at any single point, once he says “x is a” or rather “name x is object a,” or “‘Fido’ is Fido,” he is speaking of the logical identity of name and object. Maybe he could have said, “‘Fido’ represents Fido,” and maybe that’s what “x is a” means, but then we’re back to the problem of just how a logical symbolic proposition can represent or picture a logical object. Following Richard Rorty, we might claim that a symbolic proposition is “about” the world it is connected to. Either that, or “represents” means something radically other than “picturing.” All this logical “representation” takes place in a phenomenological world—where “my” body is in “my” world that is completely intertwined with logic and language; but which is observed from solipsistic subject perspective that is the philosophical self at the limit of said world. CLIMBING THE LADDER What sorts of aspects of the world does the logical self find? And what can it do with logic? Using N(Ē), they can generate propositions. As we discovered when examining the truth grounds of implication, “The propositions of logic are tautologies” (6.1), which are to be distinguished from being merely general—and create a purely self-referential system of analytic propositions. Similarly, with mathematics, which Wittgenstein calls “a method of logic,” we have equations which resemble tautologies, and we can prove its propositions without recourse to facts of the world—following intuition with calculation and substituting one expression for another. Moving now, from the general function of proposition generation, through the tautologies of logic, towards the more “worldly” realms of mathematics (at least with geometry) we pass on to the realm of “laws.” Laws, by their very nature are more “specific” than logic itself (which is beyond being general, and is transcendental); laws sync up with the structures of the world, and with particular mechanical generalizing systems, describe the world completely (with some systems being more elegant than others). Some laws refer to systems of laws, and not the world, and mechanical laws will never point to a specific object. In fact, many candidates for laws don’t wash up completely, like causality, and induction. And, aspects like the will, ethics, death, and god are literally out of this world. Answers to questions about these later issues are lacking (as they are not scientific questions of logical description). Even the Tractatus itself, leads the way to “transcendental logic,” where the reader “must transcend these propositions,” and “throw away the ladder after he has climbed up it” (6.54). SLIDING DOWN THE SKY ROPE But slipping back through the cracks of the sky, as it were, we might return to earth again with a clamorous electrical storm of the nervous system— as we gently slide down a rope from the sky of logic and see if we can touch ground. For, as we saw earlier, Wittgenstein has problems grounding his logic in the representations of the world. He climbs the ladder of pictorial representation, only to throw it away in favor of logical symbols. His notion of truth or falsity rests on this representational non-ground (truth or falsity is defined in relation to depicting a possible world); and hence his truth functions rest on an illusion as well. The entire house of cards may fall. His logical symbols may mirror his logical world of objects, but both, as described, may be conjured out of thin air—the former as simply a mirror of smoke invented to suit the needs of “representing” the latter—the latter being a possible “continuum” not sliced up into logical objects in the first place. But we can use logical propositions, such as “the cat is on the mat,” so this must be explained. What follows is an abbreviated alternative to Wittgenstein’s phenomenological-representational foundations. UNCONSCIOUS BIO-LOGICAL DICTIONARY Reversing through the Tractatus, we 21st century philosophers can hardly ignore cognitive science – taking Wittgenstein near to his word, we might try to address the scientific question of logic. First, it might be noted that our ability to think is not constrained so much by logic, as by the structure of the brain itself. The brain is composed of a chemical, electrical, and structural system—a structure of interconnected nodes. These nodes activate in parallel sequence in partly genetically grown, partly conditioned, neural pathways; pathways that are often “self-referential,” but also that open out to the world via the senses and motor actions. This is a mechanical system, operated by laws, which itself is flexible enough to understand logic—and imagine what is beyond it. This is the embodied brain as conscious agent with a robust ability to reason intelligently, where intelligence might be defined as the ability to model the world, and make connections among its various parts that work to accomplish diverse purposes. What Wittgenstein contrasts with symbolic logical thought, propositional signs, and the objects of the world, may indeed exist: but all materially, and differently than envisioned by him. One can only speculate on the first type of full conceptual language used by humans, if there was one—I would hazard the sign language used by some apes as a candidate; but even insects have signaling powers—and hence the genealogical ancestry of language may lead back to the origins of life itself. Yet, we do have denotative powers: as much as language may change, much seems to remain constant, not only for dictionaries to remain somewhat consistent during a lifetime, but also for the etymological ability to trace “meanings” of words back to the beginnings of writing, and speculatively, before (e.g. with the reconstruction of a proto-language). Although the signs have changed, some symbols, no doubt altered in some ways by changing context, may retain some of their original character. Along with the evolution of language, has come an evolution of cultural practices—which might survive based on their aptness in the human milieu and environment: memes. It is a matter for research to determine which aspects of language and cultural practices are genetic (ala Chomsky), which culturally indoctrinated (and possibly very old), and which freely learned. HIGHLIGHTING PERCEPTION FOCI Now, in contrast to the genealogy of language, we also have a phenomenology of linguistic perception: when the human body confronts an environment of objects, most likely there is in interaction between the brain and the stimuli of the environment, which might not yet be differentiated into specific objects yet. The activity of the brain, would neither passively receive “object” images (the visual field, for example, might only experience patches of hue, luminosity, and texture passively), nor would it completely hallucinate an object (there does seem to be a consistent world “out there” that we all share). This brain activity might rather highlight “objects” in the environment. This highlighting might occur when environmental stimuli activate parts of the brain that have prior experience with similar stimuli. The brain may focus on the familiar aspects of a possible “object” by automatic reflex, or consciously, and “identify” the object by a processing of a “cluster of stimuli cues” that activate a cluster of neurons associated with that stimuli cluster; which cluster of neurons in turn feedback to allow concentration on the relevant stimuli and differentiate an object from its milieu (a pattern may have various ways of being interpreted, but the brain may identify certain sub-patterns as relevant, and hence distinguish them as identifiable objects). Expectation from prior experience and novel stimuli would feedback with each other, as the object would become clear. Moreover, the clusters of stimulated neurons could be associated with words and propositions (among many other associations), and hence an instance of a cat on a mat, could be associated with the term “a cat on a mat.” This use of words would constitute the intersection of the genealogical history of language itself, and the phenomenological epistemology of the perceiving brain and subject. IDIOSYNCRASY AND FOCAL LOGIC Every person has their own idiosyncratic history of experiences, experiences that may color the various uses of words, and make language semi-private and semi-public. These experiences would color the symbolic propositions, and not the material propositional signs (not as much at least). The symbolic propositions would, as sentences and words (and a variety of other uses), be instantiated in the brain, as cross-referenced by the various witnessed usages of certain signs (hence a central concept, or symbol, might have several ways of being named or described; and a single sign could bring to mind several different concepts or symbols). Indeterminate translation is not a problem, as each person may have a consistent internal language that syncs up with a parallel consistent public language—enough for the principle of charity, where everyone can communicate effectively, but nobody means exactly the same thing by what they say. For many symbols, there would be a one-to-one correspondence to a focal public sign (word or proposition), but each would be situated in the entire fabric of an individual’s private vernacular. Most likely, due to the robust over-determination and over-lapping cross-references of public discourse, private languages would remain only semi-private. ”Family resemblances” among concepts need not multiply indefinitely until there is no longer an identifiable family (as some philosophers have critiqued the later Wittgenstein), but would have strong focal clusters, that have associations among themselves that are stronger than their associations with other families (although certain concepts and practices would belong to several families, they would not belong to every family—”six degrees of separation connecting every node” does not mean that we cannot distinguish network hubs). It follows from this that logic may have fuzzy boundaries: some propositional and cultural practice relations would hold strong and fast, possibly being genetic in origin, (Quine might say they are towards the center of a network of associated knowledge—Donald Davidson might suggest such are the core elements involved with the principle of charity); while other propositional relations would be quite contingent (on the periphery of knowledge). Yet, for me, “logical knowledge” is not simply a matter of statistical coherence of propositions among themselves—and coherence with the world’s connections to which they stand in relation; for there also appears to be a logical structure to representing the world: representing can actually model (partly publicly, partly idiosyncratically) the world, by deconstructing it (meant here to designate the projection of a structure onto a structure that provides the material for the projection: turning a structure on itself), singling out a few of many possible interpretations: hence Derrida’s claim that the copy precedes the original (we see through the copy or representation that structures the original). Of course, logic seems to limn the edge of neuro-biology, so thinking outside of logic—a logic which is flexible enough to imagine the false, and the fuzzy—and the breakdown of identity and consistency—a logic of probability and statistical foci rather than a strict Sheffer stroked identity— such a logic is framed by the general usage of propositions which can point beyond themselves to the (im)possible.

Wittgenstein (early)
Sliding Down the Sky Rope
J.D. Casten

Chapter from book forthcoming in 2012, Cybernetic Revelation.

(Click here to go to J.D. Casten's Website)

(click here for easy to read & print .pdf version)

OVERVIEW

Ludwig Wittgenstein’s Tractatus Logico-Philsophicus, as it is named, is a logical philosophical tract— a course to follow, to logically identify some fundamental aspects of logic including its representational and linguistic character, ontological substantiation, self-referential nature, and limit at “my” world of experience. Wittgenstein had training as an engineer, and the Tractatus looks somewhat prophetically (it first appeared in 1921) like a computer program of numbered concise logical statements. Yet, unlike a computer program, which is composed largely of commands, the Tractatus is descriptive. And it is not necessarily argumentative—no doubt one may take issue with the Tractatus, as I will, but Wittgenstein’s intent seems to be expository—he does not engage much in conflicting points of view (e.g. Frege and Russell), as Plato’s does in his dialogues—what Wittgenstein is concerned with here is the logical point of view, as he saw it.

It is in this way that we can see Wittgenstein’s project here as related to Kant’s Critique of Pure Reason, where Kant tried to establish the faculties necessary for logical judgments (Apperception, Understanding, Imagination, etc.): Kant’s Robot, if you will, seems to be a shot at the apparatus of subjective experience and judgment. Now, while Hegel tries to frame the being of consciousness within that robot (pure ego framed by a world of things, other people, social history, etc.), Wittgenstein tries to refine the logical apparatus of that “robot perspective.” (I call it a “robot” because, by discussing such a perspective and representing it, we create a model that is not quite the flesh and blood of a real subjective experience: it is a replica of functional essentials.)

There are seven major divisions in the numbering of the Tractatus, with each major division (save the last) having subdivided numbering (and, the first division having a total of seven divisions itself). The number seven is symbolically significant—the Sun having been considered the seventh orb in the heavens, and also the source of en-light-ened Reason found outside of Plato’s cave. Roughly the seven major divisions concern the following:

1: The world as logical facts

(being is composed of the consistently related)

2: A state of affairs of things, & our ability to picture them

(division of the objective world, and “subjective” ability to represent it)

3: A shift from pictures to propositions

(linguistic ability to think (not about, but of) the objective world)

4: Truth possibilities of propositions

(sense of language given by relation to objective world)

5: Truth functions, operations, and their limits

(related propositions in a self-referential and descriptive “system”)

6: Generation of numbers, mathematics, laws and their limits

(Pressing logic up to the world of “geometrical” experience)

7: The absolute limit

(Can’t speak of that beyond (or “tangential” to?) experiential surface)

PERCEIVING REALITY THROUGH PICTORIAL FORM

In his Tractatus, Wittgenstein uses pictures to represent a distinction between perceptual thinking, and “reality:” (Kantian) “representation” identified as actual representation. Throughout the Tractatus, Wittgenstein shifts the meaning of “picturing reality,” from a mirroring of reproduced concrete sensation to a denoting of abstracted logical form essentials—picturing becomes both a starting point, and a metaphor for logical representation: a representation of representation. We will briefly now plot out the course of that metamorphic journey in order to elucidate the running thread of a problem.

Just as the word “reflection” can mean “thinking,” and given that early modern philosophers like John Locke, wrote of “reflection” to describe how “ideas,” from the outside world are internalized, Wittgenstein is concerned with “pictures” that represent “the state of affairs.” One should note that for Wittgenstein, “the world,” or “the case,” is made up of “facts,” all being composed of “the states of affairs,” which in turn are made of up combined things, the entirety of which comprise “reality.” This terminology and hair-splitting used by Wittgenstein to re-describe what we take for granted as our world with consistently related objects sets a stage of a more precise logical space.

Now, within that logical space, as a part of it, we can have “pictures” that represent their own world with consistently related objects; and the pictures may or may not map to reality via “pictorial form.” In 2.15 Wittgenstein claims:

“The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way.

Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture.”

(Tractatus, 2.15)

It is not clear to me if there is some odd reversal here, were pictorial form precedes the ability to distinguish objects in a state of affairs—but at any rate, there is a proposed correspondence between pictures and objects.

FROM VIRTUAL REALITIES TO PROPOSITIONS

To take Wittgenstein’s approach a step further, using a more modern technological analogy, imagine that you have been hooked up to sophisticated virtual reality gear, possibly with video goggles, a tactile suit, headphones— and that this virtual reality simulation is giving you a live sensory feed from a sensory robot in a white cubical room, with a table in the center, and an apple on it. In this case, there is a reality: the actual room, table, and apple; and there is a representation of it being displayed directly to your sense organs, so realistic that you might not be able to tell that it was not real (you might have also been placed in a sensory deprivation tank, with computers hooked up to your very nervous system with a similar sensory feed). Here we would no doubt say that the reproduction was a “picture” that shared a very minutely detailed pictorial form with reality—again, so much so that you might not be able to distinguish the two—the pictorial form would be nearly identical to the form of reality which is the logical form (2.18).

Whereas pictorial form is purely representational, logical form need not be. Logical form concerns the identity of what is pictured. This can be illustrated in a range of representations, from the virtual reality; to a holographic representation of the apple on the table; a photograph of it; a hyper-realistic painting; an impressionistic painting; a more abstract painting (a red circle with a line/stem on a crude stick figure table); a hieroglyph depicting a red circle on a square; and in turn simply an “O” representing the apple, an “N” representing the relation of “this on top of that,” and a “T” representing “table,” we might have the highly abstract, and linguistic picture that looked like this: ONT (as in ontology). Following Wittgenstein, I would suggest that while more perceptual pictorial form fades into the background with our abstract progression, logical form involved with thinking comes to the fore: perceptual mirroring gives way to logical identity (although Wittgenstein rarely uses the words “mirror” nor “identity.”) Wittgenstein does, however, claim that there is continuity from the pictorial to the propositional (ONT, like aRb, may be an elementary proposition), along the lines of hieroglyphics and sign language—where logical form is maintained well into phonetic notation and visual picturing is absent.

Along with propositions come representational truth values. Wittgenstein claims that sense of propositions come from their logical correspondence with reality. If the proposition says “the apple is on the table,” and the apple is on the table, the sentence is true (and even if the apple was not on the table, the very possibility of an apple on a table would give the proposition “the apple is on the table” sense).

PARALLEL HISTORIES OF PICTORIAL AND LOGICAL FORM

However, there is definitely a problem for Wittgenstein trying to maintain that propositions are representational due to their speculated “evolution” (my word). Was there not a point in history, or in our example, where convention enters the picture, when hieroglyphs metaphorically shift due to a context where, had we not been present at the entire evolution of transformations, we never would have known that the abstract proposition did indeed connect with reality via its logical form? In other words, although we might be able to see a connection between the Latin usage of the word “video” to mean “I see,” and the latter use of “video” to mean “I understand,” what happens to the logical identity of the word, “video,” where there is a significant shift of denotation? Wouldn’t Wittgenstein have to claim that representations can be ambiguous and that their disambiguation, necessary for a sense with his use of the possibility of the representational truth or falsity of a proposition, would require a context that is part and parcel of the entire fabric of history a specific word’s, (“video”), evolution? For example, the proposition, “I see the central point of your picture,” differs in contexts such as (a) understanding the main meaning of a work of art, or (b) actually visually noticing a dot that is camouflaged among many off center dots. How does that example compare to a picture of an apple on a table being used in a multitude of situations—where the same logical form applies to different apples on tables? In each case the same representation or proposition can be used in different contexts; but in the latter, the logical form remains consistent, while in the former, the “pictorial form” of the proposition remains consistent, while the logical form differs.

Although it would seem that logical form as thought is born of pictorial form, and hence that we might have a contradiction here, due to a deep schism between the two types of form, it might be resolved by noting that nowhere is there a hard and fast rule that pictorial form must always have only a one to one correspondence to a particular logical form—they need only have a connection. While the pictorial form is material, through and through, the logical form was always mental thought, or at least has its own material evolutionary history parallel to the history of the more apparently material pictorial form (e.g. something like a “meme” history—a cultural use that is communicated from brain to brain in parallel to the material signifier, or pictorial form—more on this later).

SEVERANCE OF PERCEIVED AND LOGICAL REALITY

Wittgenstein catches this parallel when switching his terminology to that of “signs” and “symbols” in division 3. Propositions are composed of physical signs, yet multiple propositional signs can refer to singular symbols (or expressed thoughts); and single propositions also have the ability to express multiple symbols. Yet, he does not go into much depth concerning propositions having a physical-representative connection to “physically perceived” reality, in contrast to these logical symbolic conveyances of the propositions that “represent” an abstract logical reality. There is a sort of “bait and switch” here. The intuitively sensible idea of a proposition picturing a sensible reality takes a relatively arbitrary relation to the idea of logical symbols of thought picturing logical objects of reality. Logical symbols could not really be said to “represent” logical objects in a pictorial way, as they have only correspondence of points of “logical thought” to points of “logical space” in reality. The connection between pictorial form and logical form in “logico-pictoral-form” (2.2) is severed; and there is the question of whether it really ever was there in the first place.

CONSTRUCTING LOGICAL FUNCTIONS: GOD'S DICEY LOGIC

Once Wittgenstein has his logical symbol/objects correspondence however, much of the logical core of the Tractatus falls into place: Elementary propositions, of the form “a is related to b by relation R - aRb” (much like our “ONT”), can range from tautologies at one extreme to contradictions at the other, with sensible true or false propositions in-between (and more complex propositions can be built out of these elementary propositions). To unfold three examples from the chart of division 5.101:

1234

(TTTT) (p, q) Tautology (if p then p and if q then q)

(TTFT) (p, q) in words: if p then q

(FFFF) (p, q) Contradiction (p and not p, and q and not q)

Each column contains an outcome based on a relationship between p and q:

In column 1: p:T, q:T; in column 2: p:F, q:T; column 3: p:T, q:F; column 4: p:F, q:F

There are four sets of binaries:

(a) Two proposition variables (p, q)

(b) Two possible values for the first (p: T or p: F)

(d) Two possible function output values (T or F)

Now, Truth Functions present another monumental leap from one realm to another, with seemingly little connection: as with the leap from pictorial form to logical form, there is the leap from related elementary propositions (e.g. p, q) to the consequent complex proposition (e.g. if p then q): where logic holds by virtue of God! (5.123 – or “a god” rather). Interestingly, following Hume, Wittgenstein proximally makes the claim that:

“Superstition is nothing but belief in the causal nexus.”

(Tractatus, 5.1361)

Temporal causality is “superstition,” while “a god” insures implication. The truth grounds (5.101) of the implication if p then q that make that proposition true are simply the truth possibilities of elementary propositions p and q that make if p then q true. This is a completely circular way of saying that what defines if p then q as true is a certain combination of truth values for p and q—in other words if p then q will be true by definition of (TTFT) (p, q). It is similar for every other truth function (i.e. “p v q”, “p . q”, “~p”, “~q”, etc.): the 16 total possible variations from (a) two variables (p, q) with (b) two possibilities for p (T, F) (c) two possibilities for q (T, F) (d) and two possible outcomes (T,F) [or (2 ^ 4)] defines all logical relations (prior to their being identified with logical operators). Although the binary division is the most elegant, one wonders: Why not a logic based on threes?: (True, False, or Maybe for each of p, q, r— would result in a table with 81 possible variations: would the “modal logic (with a maybe) and 'mediated comparison/connection' (3 variables)” given by those combinations be less valid?)

Has Wittgenstein read too much into a set of binary possibilities, or is there something fundamental about the relationship between the binary and logic? How do we bridge the gap between a table of binary possibilities, and propositional logic? The real world application of each of these four binaries needs to be examined: (a) two propositions (p, q) — because at least two are needed for any comparison or connection; (b) & (c) two factual possibilities for two propositions (T, F)— because they independently may or may not represent a situation (more on this below) and (d) two possible results as the outcome for the relations of the two propositions (T, F)— because the comparison or connection of two true or false propositions will result in a true or false outcome. But there is definitely a problem with conflating the first (b & c -inputs) and second (d-output) types of truth and falsity. One type, for Wittgenstein, is either about representational (synthetic) truth or truth by definition (analytic)— while the other type is about the necessity of logical relationships: a sort of hyper-analytic (or a priori) hypothesis. I might call these first level truths (those of mirroring the world), and second level truths (those concerning relationships between mirror/propositions). No wonder a god is required here for Wittgenstein, for it must be some power exterior too his own observation (the first level truths) that would make the world's consistency deductively (by implication) absolute (the second level truths) rather than inductively “probable.” In other words, although induction may be a matter of probable certainty, the “hardness” of deduction is an unknowable faith. Maybe “God does not play dice with the universe,” to quote Einstein, but God is a matter of faith, not certitude. A little more on this is discussed below, concerning truth functions vs. operations. A serious question remains: what is the relationship between the analytic/synthetic truth of propositions, and an a priori structured truth of logical connections, and are the two incommensurable? Is implication ever more than a highly certain induction? An induction that in circular fashion, is deeply intertwined and based on implication itself (If something happens regularly, then it may happen again)?

No doubt, the binary logic here tied to a minimum of comparing and connecting two independent statements, and their truth or falsity, ties into representation: propositions may or may not represent reality, and hence are true or false. The whole notion of truth and falsity is “illustrated” by the notion of pictorial form corresponding to a perceived reality of logical form—but do we perceive a reality of logical form? When the complex of a picture that completely maps a reality is simplified towards hieroglyphics and propositions on the one hand; and objects are singled out in a visual field on the other—what maintains a connection between the signs of the picture and the logical object in reality? A logical symbol? Where did that come from? If propositions do not indeed represent reality, absolutely, as I am suggesting, then basing logic on truth values of propositions as representations is suspect. A logical symbol may connect to reality—but does it represent it? And if not, what is the nature of truth and falsity, other than a coherence of logical symbols associated with other logical symbols that have a consistent relation to logical objects associated with other logical objects. Wouldn't there be a sort of “indeterminate translation” between the realm of logical symbols and logical objects? In other words, might there be idiosyncratic logical symbols for each person (remember, logical symbols are not tied to logical objects via pictorial representation) in such a way that each person’s understanding of a proposition would be slightly skewed from every other person: making logic a matter of “statistical convergence,” among populations rather than absolute identity? Each person has their own experiences that are shared with others only in part: Language is indeed public, yet every person’s use of it is semi-private, given their personal idiosyncratic histories. The “logical identity” of public “objects” (which may only exist in the minds of individuals—more on this later) might simply be as sort of holographic chimera projected by individual (human) cells. (A hologram not perceived by a who, but an ideal that has no real existence).

THE DIFFERENTIATING SHEFFER STROKE

Strategically, Wittgenstein discusses implication, both absolute (if p then q) and probable (prior evidence of p with q may mean p if q is given) before moving on to truth operations. A truth function relates only to the (VVVV) (p, q) parts of the chart (where “V” = “T” or “F”); but operations, such as “or - v” and “not - ~” are added and discussed later. The distinction is important, for Wittgenstein implies that truth operations (e.g. p v ~q) are “semi-arbitrary” (my words) in relation to truth functions. We could have an indefinite number of truth operations with a given truth function (Given (p, q) of various combinations, and (VVVV)). The truth function—which gives the truth value of a representational propositional relation—is primary, while the truth operation—a sort of propositional logical equation—is somewhat derivative and can take a number of forms: much as single symbolic logical expressions can find form in a multitude of material sign propositions, single truth functions can find expression in a number of truth operation notations. However, it is through truth operations that more complex truth functions are constructed. Wittgenstein’s notation for generating propositions is an expansion of his elementary truth functions, where beyond the simple (FFFT) (p, q) which indicates “neither p nor q “(or “p|q” from which all other truth functions may be derived by use of recursive truth functions) we have (-----T) (ξ,…) (hereafter I will alter the notation from “ξ” to “E”) where “E….,” or “Ē” is a set of propositions, and hence (-----T)(Ē) or N(Ē) is the negation of all values of the indicated propositions— and the possibility of deriving, or generating, generalized propositions. N(Ē) is like a super Sheffer stroked (“|”) series of propositions, which stroke itself visually illustrates the boundary between elements—differentiates them—and can act like a law of non-contradiction where we cannot have both p and ~p.

IDENTITY OF SIGN AND SYMBOL?

Now in (5.526) Wittgenstein claims:

“We can describe the world completely by means of fully generalized propositions, i.e. without first correlating any name with a particular object.

Then, in order to arrive at the customary mode of expression, we simply need to add, after an expression like, ‘There is one and only one x such that…’, the words, ‘and that x is a’.”

(Tractatus, 5.526)

Interestingly, he soon adds, (5.53):

“Identity of object I express by the identity of sign, and not by using a sign for identity. Difference of objects I express by difference of signs.”

(Tractatus, 5.53)

Wittgenstein clearly identifies his two logical spheres in these quotes; and although one realm (symbolic propositions) might map the other (logical objects), in its entirety, or at any single point, once he says “x is a” or rather “name x is object a,” or “‘Fido’ is Fido,” he is speaking of the logical identity of name and object. Maybe he could have said, “‘Fido’ represents Fido,” and maybe that’s what “x is a” means, but then we’re back to the problem of just how a logical symbolic proposition can represent or picture a logical object. Following Richard Rorty, we might claim that a symbolic proposition is “about” the world it is connected to. Either that, or “represents” means something radically other than “picturing.”

All this logical “representation” takes place in a phenomenological world—where “my” body is in “my” world that is completely intertwined with logic and language; but which is observed from solipsistic subject perspective that is the philosophical self at the limit of said world.

CLIMBING THE LADDER

What sorts of aspects of the world does the logical self find? And what can it do with logic? Using N(Ē), they can generate propositions. As we discovered when examining the truth grounds of implication, “The propositions of logic are tautologies” (6.1), which are to be distinguished from being merely general—and create a purely self-referential system of analytic propositions. Similarly, with mathematics, which Wittgenstein calls “a method of logic,” we have equations which resemble tautologies, and we can prove its propositions without recourse to facts of the world—following intuition with calculation and substituting one expression for another. Moving now, from the general function of proposition generation, through the tautologies of logic, towards the more “worldly” realms of mathematics (at least with geometry) we pass on to the realm of “laws.” Laws, by their very nature are more “specific” than logic itself (which is beyond being general, and is transcendental); laws sync up with the structures of the world, and with particular mechanical generalizing systems, describe the world completely (with some systems being more elegant than others). Some laws refer to systems of laws, and not the world, and mechanical laws will never point to a specific object. In fact, many candidates for laws don’t wash up completely, like causality, and induction. And, aspects like the will, ethics, death, and god are literally out of this world. Answers to questions about these later issues are lacking (as they are not scientific questions of logical description). Even the Tractatus itself, leads the way to “transcendental logic,” where the reader “must transcend these propositions,” and “throw away the ladder after he has climbed up it” (6.54).

SLIDING DOWN THE SKY ROPE

But slipping back through the cracks of the sky, as it were, we might return to earth again with a clamorous electrical storm of the nervous system— as we gently slide down a rope from the sky of logic and see if we can touch ground.

For, as we saw earlier, Wittgenstein has problems grounding his logic in the representations of the world. He climbs the ladder of pictorial representation, only to throw it away in favor of logical symbols. His notion of truth or falsity rests on this representational non-ground (truth or falsity is defined in relation to depicting a possible world); and hence his truth functions rest on an illusion as well. The entire house of cards may fall. His logical symbols may mirror his logical world of objects, but both, as described, may be conjured out of thin air—the former as simply a mirror of smoke invented to suit the needs of “representing” the latter—the latter being a possible “continuum” not sliced up into logical objects in the first place.

But we can use logical propositions, such as “the cat is on the mat,” so this must be explained. What follows is an abbreviated alternative to Wittgenstein’s phenomenological-representational foundations.

UNCONSCIOUS BIO-LOGICAL DICTIONARY

Reversing through the Tractatus, we 21st century philosophers can hardly ignore cognitive science – taking Wittgenstein near to his word, we might try to address the scientific question of logic. First, it might be noted that our ability to think is not constrained so much by logic, as by the structure of the brain itself. The brain is composed of a chemical, electrical, and structural system—a structure of interconnected nodes. These nodes activate in parallel sequence in partly genetically grown, partly conditioned, neural pathways; pathways that are often “self-referential,” but also that open out to the world via the senses and motor actions. This is a mechanical system, operated by laws, which itself is flexible enough to understand logic—and imagine what is beyond it.

This is the embodied brain as conscious agent with a robust ability to reason intelligently, where intelligence might be defined as the ability to model the world, and make connections among its various parts that work to accomplish diverse purposes. What Wittgenstein contrasts with symbolic logical thought, propositional signs, and the objects of the world, may indeed exist: but all materially, and differently than envisioned by him. One can only speculate on the first type of full conceptual language used by humans, if there was one—I would hazard the sign language used by some apes as a candidate; but even insects have signaling powers—and hence the genealogical ancestry of language may lead back to the origins of life itself. Yet, we do have denotative powers: as much as language may change, much seems to remain constant, not only for dictionaries to remain somewhat consistent during a lifetime, but also for the etymological ability to trace “meanings” of words back to the beginnings of writing, and speculatively, before (e.g. with the reconstruction of a proto-language). Although the signs have changed, some symbols, no doubt altered in some ways by changing context, may retain some of their original character. Along with the evolution of language, has come an evolution of cultural practices—which might survive based on their aptness in the human milieu and environment: memes.

It is a matter for research to determine which aspects of language and cultural practices are genetic (ala Chomsky), which culturally indoctrinated (and possibly very old), and which freely learned.

HIGHLIGHTING PERCEPTION FOCI

Now, in contrast to the genealogy of language, we also have a phenomenology of linguistic perception: when the human body confronts an environment of objects, most likely there is in interaction between the brain and the stimuli of the environment, which might not yet be differentiated into specific objects yet. The activity of the brain, would neither passively receive “object” images (the visual field, for example, might only experience patches of hue, luminosity, and texture passively), nor would it completely hallucinate an object (there does seem to be a consistent world “out there” that we all share). This brain activity might rather highlight “objects” in the environment. This highlighting might occur when environmental stimuli activate parts of the brain that have prior experience with similar stimuli. The brain may focus on the familiar aspects of a possible “object” by automatic reflex, or consciously, and “identify” the object by a processing of a “cluster of stimuli cues” that activate a cluster of neurons associated with that stimuli cluster; which cluster of neurons in turn feedback to allow concentration on the relevant stimuli and differentiate an object from its milieu (a pattern may have various ways of being interpreted, but the brain may identify certain sub-patterns as relevant, and hence distinguish them as identifiable objects). Expectation from prior experience and novel stimuli would feedback with each other, as the object would become clear. Moreover, the clusters of stimulated neurons could be associated with words and propositions (among many other associations), and hence an instance of a cat on a mat, could be associated with the term “a cat on a mat.” This use of words would constitute the intersection of the genealogical history of language itself, and the phenomenological epistemology of the perceiving brain and subject.

IDIOSYNCRASY AND FOCAL LOGIC

Every person has their own idiosyncratic history of experiences, experiences that may color the various uses of words, and make language semi-private and semi-public. These experiences would color the symbolic propositions, and not the material propositional signs (not as much at least). The symbolic propositions would, as sentences and words (and a variety of other uses), be instantiated in the brain, as cross-referenced by the various witnessed usages of certain signs (hence a central concept, or symbol, might have several ways of being named or described; and a single sign could bring to mind several different concepts or symbols). Indeterminate translation is not a problem, as each person may have a consistent internal language that syncs up with a parallel consistent public language—enough for the principle of charity, where everyone can communicate effectively, but nobody means exactly the same thing by what they say. For many symbols, there would be a one-to-one correspondence to a focal public sign (word or proposition), but each would be situated in the entire fabric of an individual’s private vernacular. Most likely, due to the robust over-determination and over-lapping cross-references of public discourse, private languages would remain only semi-private.

”Family resemblances” among concepts need not multiply indefinitely until there is no longer an identifiable family (as some philosophers have critiqued the later Wittgenstein), but would have strong focal clusters, that have associations among themselves that are stronger than their associations with other families (although certain concepts and practices would belong to several families, they would not belong to every family—”six degrees of separation connecting every node” does not mean that we cannot distinguish network hubs). It follows from this that logic may have fuzzy boundaries: some propositional and cultural practice relations would hold strong and fast, possibly being genetic in origin, (Quine might say they are towards the center of a network of associated knowledge—Donald Davidson might suggest such are the core elements involved with the principle of charity); while other propositional relations would be quite contingent (on the periphery of knowledge). Yet, for me, “logical knowledge” is not simply a matter of statistical coherence of propositions among themselves—and coherence with the world’s connections to which they stand in relation; for there also appears to be a logical structure to representing the world: representing can actually model (partly publicly, partly idiosyncratically) the world, by deconstructing it (meant here to designate the projection of a structure onto a structure that provides the material for the projection: turning a structure on itself), singling out a few of many possible interpretations: hence Derrida’s claim that the copy precedes the original (we see through the copy or representation that structures the original). Of course, logic seems to limn the edge of neuro-biology, so thinking outside of logic—a logic which is flexible enough to imagine the false, and the fuzzy—and the breakdown of identity and consistency—a logic of probability and statistical foci rather than a strict Sheffer stroked identity— such a logic is framed by the general usage of propositions which can point beyond themselves to the (im)possible.