“This sentence is meaningless because it is self-referential.”
— Douglas Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid p. 495
In many of his works, in particular his landmark 1966 essay “Structure, Sign and Play in the Discourse of the Human Sciences,” Jacques Derrida calls into question not only the tenets of the Structuralist school of literary criticism popular at the time, but also all of “western science and western philosophy,” the concept of meaning, and the idea of human consciousness. His numerous reasons for this tremendous inquisition of essential concepts center around his belief that meaning, language and thought have no substance beyond that of the symbols and formal systems that are allegedly used to access or reference some deeper, fundamental meaning. Words and symbols can only lead to other words and more symbols, never a true definition or meaning. Some years later, in 1979, Douglas Hofstadter published his influential book Gödel, Escher, Bach: An Eternal Golden Braid. In this book he confronts the same ideas as did Derrida, but concludes that it is exactly the self-referencing quality of formal systems such as language that gives their components their meaning. Especially given their wildly different academic backgrounds and interests, it is astounding that two such highly esteemed scholars could consider the problems of meaning, language and consciousness, independently decide that these problems hinge on the idea of recursion and self-reference, and then arrive at directly opposite conclusions.
Derrida’s “Structure, Sign and Play” on Meaning, Language and Consciousness
“Structure, Sign and Play in the Discourse of the Human Sciences” was originally distributed at a 1966 conference at Johns Hopkins University, called “The Languages of Criticism and the Sciences of Man.” The main point of this conference was to bring the ideas of Structuralist thinkers to a United States audience; Derrida’s paper was in opposition to these ideas. Regarding language, Structuralism asserts that idea/meaning and symbol/word are inextricably linked. One of the founders of Structuralism, Ferdinand de Saussure, stated this concept thus:
Psychologically our thought—apart from its expression in words—is only a shapeless and indistinct mass. Philosophers and linguists have always agreed in recognizing that without the help of signs we would be unable to make a clear-cut, consistent distinction between two ideas. Without language, thought is a vague, uncharted nebula. There are no pre-existing ideas, and nothing is distinct before the appearance of language. Against the floating realm of thought, would sounds by themselves yield predelimited identities? No more so than thought.1
From this point of view, it is easy to explain the existence of meaning—simply because meaning has been rendered inseparable from its symbols. If one cannot confront meaning without its symbols, nor symbols without meanings, and those symbols are clearly observed to exist, then meaning clearly exists—it is evidenced by its symbols. Assuredly, the “existence of meaning” might have been taken for granted by the founders of Structuralism, but that does not justify or ameliorate this argument’s disturbing air of inconsistency and circular reason.
To refute this point of view, Derrida begins by discussing how symbol and meaning were viewed prior to the advent of Structuralism, and examines the interest in structure that gave rise to Structuralist ideas. Prior to Structuralism, Derrida argues, structure was not thought of for its own sake, although there has been awareness of structure as long as there has been Western thought. Instead, centers were used to correlate elements of structure (symbols / words / language / ideas / consciousness) with one another in broad enough groups such that they appeared to be symbolizing genuine gestalts and irreducible truths. A center, in Derrida’s nomenclature, is the intersection of meaning in a group of related symbols, “the point at which the substitution of contents, elements, or terms is no longer possible.”2 Centers enabled flexibility in the range of system elements that could be referenced by other system elements, while defining that range narrowly enough to create the impression of categories of meaning. Derrida called this quality of relation with flexibility “play.”
The problem with centers was that they, themselves, had no location in the groups of system elements which they associated. The center itself cannot be within the group of system elements which it bundles together, or it loses its ability and authority to associate those elements. Thus, while they enabled play by forming groups of symbols, they also made play impossible by making the groups within which play occurs inherently ill-defined, indeed paradoxical.
Derrida states that once the center-based structure itself was discussed within this system of centers, a “repetition” or self-reference took place which spawned a rupture, an “event,” a new problem of thought. The attempt to create a center for the concept of centers revealed the inherent problems with that system. “Successively, and in a regulated fashion, the center receives different forms or names…It could be shown that all the names related to fundamentals, to principles, or to the center have always designated an invariable presence—eidos, arche, telos, energia, ousia (essence, existence, substance, subject) alethia, transcendentality, consciousness, God, man, and so forth.”3 These listed words all seem to have a clear relationship to one another, but identifying that relationship by a definition gives only another word which must be added to the pile—no word can serve as the center around which all these symbols gather. For example, Derrida is calling them “names for the center,” so perhaps the word “center” should be added to the list—but that would rob it of its useful illusion of being a center.
“Henceforth,” he continues, “it became necessary to begin thinking that there was no center, that the center could not be thought in the form of a present-being, that the center had no natural site, that it was not a fixed locus but a function, a sort of nonlocus in which an infinite number of sign-substitutions came into play.”4 This is Structuralism, the system of thought which Derrida set out to criticize.
This position results in paradox. For Derrida, self-reference and recursion invalidate reason and consciousness; since language has no inherent meaning, thought, the relation of meanings to one another, cannot exist. Even symbol is destroyed—the very nature of a symbol is to reference something which it does not itself constitute, and this “something” has been shown not to exist. But for symbols, there is no alternative: “As I suggested a moment ago, as soon as one seeks to demonstrate in this way that there is no transcendental or privileged signified (center) and that the domain or play of signification has no limit, one must reject even the concept and word “sign” itself—which is precisely what cannot be done.”5 Rejection of sign is a rejection of language; even if one were inclined to do this, one would need words to articulate this decision—making the decision impossible. Here he stops: having concluded that language itself is paradoxical, there is literally nothing more to say on the subject. Derrida invalidated Structuralism’s easy definition of meaning, but did not give any substitute.
Though he would not have made a clear statement of purpose in “Structure, Sign and Play,” (as in this text he avoids, as far as possible, giving the impression of any certain center or underlying meaning) Derrida states this point uncharacteristically briefly and clearly in his 1967 book Of Grammatology: “There is nothing outside the text.”6
Hofstadter’s Gödel, Escher, Bach on Meaning, Language, and Consciousness
The sheer scope of Gödel, Escher, Bach: An Eternal Golden Braid can make it difficult, on first reading, to determine what (if any single thing) is the overarching point of the book. Some of its topics include music, logic, number theory, genetics, computer programming, Zen Buddhism, visual art, and artificial intelligence; its style and genre swing wildly between pure academic discussion and entertaining fantastic dialogue. The one thing that clearly ties the book together is its constant references to recursion. For this reason, Douglas Hofstadter took advantage of the book’s 20th anniversary edition to clarify its subject and message in a new preface, in which he states, “A crucial part of my book’s argument rests on the idea that meaning cannot be kept out of formal systems when sufficiently complex isomorphisms arise. Meaning comes in despite one’s best efforts to keep symbols meaningless!”7
Since an isomorphism is a mapping of elements in a system onto other elements in systems, in this context isomorphism is broadly a type of self-reference (the act of mapping symbols onto symbols). How different from Derrida’s conclusion that symbols that can only reference other symbols dissolve into meaninglessness! Hofstadter is actually saying that without referencing any kind of “deeper” symbol-less meaning, but only by referencing other symbols, systems of symbols acquire inherent meaning of their own.
Hofstadter begins establishing this point by identifying a strong relationship between consciousness/self-awareness and meaning in symbols. Still in the preface, he says, “Selves and semantics—in other words, me’s and meanings—do spring from the same source.” By this he asserts that the human self, complete with its knowledge of its own existence and its ability to receive and respond to meanings, is itself made solely of the same kind of information as the symbols it receives:
There is no reason to expect that “I,” or “the self”, should not be represented by a symbol. In fact, the symbol for the self is probably the most complex of all the symbols in the brain. For this reason, I call it a subsystem, rather than a symbol. To be precise, by “subsystem,” I mean a constellation of symbols, each of which can be separately activated under the control of the subsystem itself…Thus, there is no strict level distinction between symbols and subsystems.8
He then goes on to investigate and speculate on the nature of that “subsystem” that constitutes the “I”. According to Hofstadter, self-awareness, the quality of having a “soul,” a “self,” an “I,” is itself the result of a particular kind of self-reference in the “programming” of the human mind. This special self-reference, which he calls the “Strange Loop,” is information that references itself, but in such a way as to bring in new information before referencing itself again. Hofstadter says that one of the most powerful Strange Loops is of the “Gödelian” variety, which derives its name from Kurt Gödel’s famous 1931 proof of the incompleteness of formal systems. These Gödelian Strange Loops are statements which, if true, necessitate their own falsehood, showing the imperfections of the system upon which they are predicated. In fact, a good deal of Hofstadter’s book consists of demonstrating Gödel’s theorem by constructing a system of “Typographical Number Theory,” or TNT, simply in order to eventually disprove its completeness by deriving the sentence “G”, one of the interpretations of which is “‘G’ is not a theorem of TNT.” (In referencing itself by the name “G,” this sentence becomes a Strange Loop.) The question to ask is then “Is ‘G’ true or false?”—which clearly cannot be answered, thus showing that TNT is an incomplete system. There will always be statements outside its logical grasp.
“It is as if the sentence’s hidden Gödelian meaning had some kind of power over the vacuous symbol-shunting, meaning-impervious rules of the system… Something very strange thus emerges from the Gödelian loop: the revelation of the causal power of meaning in a rule-bound but meaning-free universe,”9 says Hofstadter about sentences such as “G.” This is the reason Strange Loops are so powerful: they actually affect from within the way formal systems can work. Every (sufficiently complex) system of rules has the capability to form statements equivalent to “G”, which although they are totally within their systems, have inherent meaning in that they have an effect over a formal system (their own): they point out those systems’ incompleteness. “In a sense it would not be going too far to say that by virtue of having such a loop, a formal system acquires a self (emphasis original),”10 he concludes. Although this “self” is minuscule (Hofstadter is quite willing to differentiate between the “sizes” or consciousness capabilities of souls11), it points the way to the conclusion that human minds, in all their adaptability and consciousness, are composed of innumerable Strange Loops upon Strange Loops. In fact, if any system possesses the ability to define itself or some part of itself in terms of itself, that ability is the quality of self-awareness and meaning, if only to a minute extent. Self-reference in itself is the basis of the soul; human ability to adapt and respond to meaningful symbol stimuli is a result of recursion. Hofstadter himself says it best, in his later book I Am a Strange Loop: “In the end, we self-perceiving, self-inventing, locked-in mirages are little miracles of self-reference.”12
By defining the self as a system of self-referencing symbols, Hofstadter segues neatly into the task of establishing a definition for “meaning”. If “self” in its most general sense is simply another word for “formal symbol system capable of self-reference,” human selves simply being massively complex systems of this variety, then “meaning” occurs whenever a symbol (such as a word) from outside the system in question effects or calls up a consistent, particular pattern or behavior in the formal system (such as a thought, in the human mind)13. To be sure, the problem of infinite regress rears its ugly head here as well, but Hofstadter averts it: “Actually, a recursive definition (when properly formulated) never leads to infinite regress or paradox. This is because a recursive definition never defines something in terms of itself, but always in terms of simpler versions of itself."14 These “simpler versions” beneath the word are a huge mass of verbal equivalencies and definitions, which themselves can be defined in terms of simpler words or fragments of words, until finally the “definition” and meaning of the word is carried out: a particular group of neurons is triggered in the brain. No infinite regress is possible, because relating the problem of definition to the physical realm means that “the infinite” is simply not going to get done.
The essence of Hofstadter’s book is a resounding affirmation of the existence of mind, consciousness and meaning, defined as being founded on self-reference and recursion. By defining “meaning” as the collected relationship between symbols and the system with which they communicate, Hofstadter demystifies the concept and makes it tractable and defensible.
Some Stylistic Comparison of Derrida and Hofstadter
Before delving into the deep and fundamental relationship between these two works, it is interesting to briefly compare some of their more superficial, stylistic similarities. Quite apparent is the two authors’ shared love for wordplay and penchant for creating new terms. Derrida, in particular, renames his idea of “center” many times in the course of “Structure, Sign and Play,” referring to it as “origin,” “subject,” “arche,” and “privileged signified”—not including the list of terms he says have represented the idea throughout history. Likewise, Hofstadter’s use of words such as “fugue” and “theorem” (which already have conventional definitions) is often extremely idiosyncratic and dependant on context.
Both works have a similar universality. Derrida, while writing roughly within the genre of literary criticism, maintains that “all is text;” thus, he extends the fields to which his opinions apply to every discipline that involves language—that is, all of them. Hofstadter goes even further—rather than discuss ideas alone, he investigates the relationship of meaning to recursion in so many different areas that the book almost seems scatterbrained (though many readers count this as one of its unique charms).
Most prominently, both works also share a powerful tendency to apply to themselves the very ideas they discuss. For example, in “Structure, Sign and Play,” the only example Derrida gives of his concept of “center” is the particular center that tries to define other centers. Moreover, it is sometimes said that the reason for Derrida’s dense and cryptic style is that he tries to convey the disappearance and invalidation of the center without the use of a center. But according to Derrida’s (roundabout) definition of center, center is essential to making any argument; it is the “core idea” of any statement—so of course, this is inherently a lost cause, but Derrida had to attempt it in order to remain true to his assertions. On Hofstadter’s side, the extreme recursion in Gödel, Escher, Bach is one of the book’s stylistic hallmarks. Particularly in the book’s dialogues, in which the concepts of the more strictly didactic chapters are played out in a fictional setting, Hofstadter even uses self-reference to discuss and explain self-reference—with remarkably successful results. (The dialogue “Six-Part Ricercar” at the book’s end is a crowning example of this; it is too long to quote here, but entirely enjoyable and worthwhile reading.) Perhaps self-reference upon self-reference is an unavoidable attribute of writing about meaning and recursion; perhaps this topic naturally induces similar quirks of style even in writers who could not be more different. Whatever the cause, the stylistically similar elements are a powerful clue to the true relationship between these two works.
Comparison of Derrida and Hofstadter on Meaning and Consciousness
Hofstadter confirms meaning while Derrida objects that it is a paradox. This begs the question of whether Hofstadter is then a Structuralist. If this were the case, it would be simple to identify the nature of their disagreement. But Structuralism affirms meaning by rendering it indivisible from symbol, while Hofstadter defines meaning as a symbol-triggered action taking place in the brain.
Derrida describes the beginning of Structuralism as an “event,” a “rupture and a redoubling.” Obviously, this “redoubling” is a recursion, which is similar to Hofstadter’s arguments in that it relates the concept of self-reference to that of meaning, but the nature of this particular recursion is much more important than it may at first appear: On close examination, it becomes clear that the Structuralist “event” that Derrida describes is actually the Strange Loop of Gödelian self-reference.
This is because the concept of “center” is a formal system, a set of rules that performs a task. The task of center is to organize symbols into loose groups. One of the rules of this formal system is that although they represent ideas around which other ideas gather, they cannot themselves be part of the group they define, as this would necessitate a new center. For example, the words “frankness,” “integrity,” “sincerity,” and “truthfulness,” as well as a great many others, all share the same center. But attempting to identify that center, perhaps calling it “honesty,” produces only another word which must be said to belong to the list of words surrounding the true center. Thus, if the system of centers is allowed to reference itself, it tries to produce a center of centers, itself requiring a center. But this cannot be done, not only because this does not define “center” in terms of simpler versions of itself, but also because of the rule that the center must be outside the group it categorizes. Since center both must and cannot be outside of itself, a center of centers is paradoxical and impossible in the same way as are sentences such as “G” described above, or the declaration “This sentence is false.” This is a classic example of a Strange Loop.
The consequence of this, for Derrida, is that the entire system of centers (along with the facile Structuralist solution that centers should simply be ignored and incorporated into the notion of “word”) is invalid and must be rejected, regardless of the consequences of that rejection. But Hofstadter has a quite different opinion of recursion than Derrida, viewing it as a potentially meaning-creating quality rather than a meaning-destroying one. According to Hofstadter, the fact that a system is capable of producing Strange Loops does not invalidate the entire system. In fact, all systems that use sets of rules capable of being used to draw conclusions have the inherent capability to draw conclusions about themselves. Gödel’s theorem shows that this capability means that all systems powerful enough to give meaning (or its illusion, depending on one’s approach) must also be powerful enough to give total nonsense and lack of meaning (of the variety of sentence “G”). Kurt Gödel devised his theorem to show that in mathematics, perhaps the single best example of a formal system, there are statements for which it is impossible to decide whether they are true or false.15 Yet mathematics, like all sufficiently powerful formal systems, remains able to produce conclusions. So the fact that a system contains self-reference is the hallmark of systems able to produce meaning, which implies that the existence of a Strange Loop within the system known as “language” actually validates its status as a formal system sufficiently powerful to produce meaningful conclusions. Thus, according to Hofstadter’s approach to systems, it is acceptable that there are statements within the system of centers that are undecideable. Meaning as defined by centers may still exist, regardless of whether or not it is possible to decide on the meaning or center of “center” itself.
Still, this is not the route that Hofstadter takes in his attempt to define meaning. Instead, he proposes that “meaning” be defined solely as the interaction between symbols and systems. In this system, it is not even problematic or “loopy” that centers cannot be defined in terms of other centers; the relation between centers and neurons is sufficient to define them (and every other symbol in the system of language). Neurons serve the same purpose here that centers do in Derrida’s view of meaning: they are the “underliers” of symbols.
This fact reveals a critical difference. To Derrida, “center” represents the idea that there should be some essential, independent meaning underlying symbol. But to Hofstadter, “meaning” is a mechanical action that symbols have on systems. There is no “true,” ultimate meaning behind a symbol beyond the action it triggers in the brain. Seeing that this is what Hofstadter means when he says that “meaning creeps in everywhere” reveals that, although Derrida seems a bit dismal when he concludes that meaning and consciousness are paradoxes whose existence cannot be firmly established or denied, Derrida does at least argue from the point of view that they ought to exist on some level other than that of the physical or the symbol. When Derrida states that “center” and meaning does not exist, he is not saying that it is inconceivable that certain words should consistently lead to particular neural behaviors—he is saying that it is impossible to access any kind of definition that hints at existence of truths independent of language, mind and humanity. It is in the attempted defense of this definition of meaning that Derrida arrives at paradox.
This sort of independent meaning is as impossible to Hofstadter as it is to Derrida. Hofstadter, however blissfully meaningful he seems, is actually reducing this almost spiritual concept of “meaning” to pure software/hardware interaction: the idea that in human language, symbols successful in conveying meaning are those that end up causing a particular group of cells to behave a certain way. There is no inherent difference between that ability and the ability of a string of machine code to cause an action in a computer. So in order to take advantage of the abundance of meaning in Hofstadter’s philosophy, one must give up any mysticism or spiritualism surrounding the notion of self and being; you have to be willing to see your soul and brain as entirely material entities in which “thought,” “meaning,” and indeed “self” have only a physical basis.
What this implies is that in acknowledging the unavoidable self-reference in systems of symbols, one must choose to prioritize soul or to prioritize meaning. Derrida, beginning from what Hofstadter calls the “soulist” idea that there is supposed to be some deeper, non-symbolic level of meaning below the symbol and underlying consciousness, investigates self-reference and, seeing that it is unavoidable, concludes that meaning may well be an illusion, and formal systems really signify nothing. The soulist point of view, demanding meaning on the level of the soul, results in sacrificing meaning: contradiction and an ocean of paradox.
Hofstadter, beginning from the “non-soulist” point of view, preserves the validity of the concept of “meaning” by defining it as the responses that formal systems make to particular symbols. So although in language those responses are formed from other symbols, the infinitely many unique relationships between those symbols and the systems are consistent—constituting the meaning. Hofstadter himself acknowledges that the implications this has for the human self are not terribly comfortable, but he adopts this standpoint in order to explain meaning and consciousness:
Of course, a “soulist” would…merely assert that the perceiver of all this neural action is the soul, which cannot be described in physical terms, and that is that. However, we shall try to give a “non-soulist” explanation of where consciousness arises.
Our alternative to the soulist explanation—and a disconcerting one it is, too—is to stop at the symbol level and say, “This is it—this is what consciousness is. Consciousness is that property of a system that arises wherever there exist symbols in the system which obey triggering patterns somewhat like the ones described in the past several sections.”16 (The previous sections are a discussion of symbols within systems that cause responses within those systems; that is, self-reference within formal systems.)
Conclusion
Although both Derrida and Hofstadter present compelling arguments for their positions, ultimately it is still necessary to make an individual decision in order to make any definitive statement on the nature of meaning and consciousness. Since, as both Hofstadter and Derrida would say, we cannot separate ourselves from thought, it is probably impossible to tell which viewpoint is “correct”—perhaps both or neither of them are. Nevertheless, the simple fact that Derrida’s and Hofstadter’s works independently determine that self-reference is at the core of meaning and consciousness gives that statement great plausibility. Thus, although the ultimate statement defining meaning and consciousness has yet to be made, Hofstadter and Derrida have tremendously enlightening views on this necessarily cloudy topic.
References:
1. De Saussure, Ferdinand. “Course in General Linguistics.” Critical Theory Since Plato. Ed. Adams, Hazard and Searle, Leroy. Boston: Thomson Wadsworth, 2005, p.789.
2. Derrida, Jacques. “Structure, Sign and Play in the Discourse of the Human Sciences.” Critical Theory Since Plato. Ed. Adams, Hazard and Searle, Leroy. Boston: Thomson Wadsworth, 2005, p. 1206.
3. Ibid., p. 1207.
4. Ibid., p. 1207.
5. Ibid., p. 1207.
6. Derrida, Jacques. Of Grammatology. Baltimore: Johns Hopkins University Press, 1998, p. 158.
7. Hofstadter, Douglas. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books, 1999, p. P-3.
8. Ibid., p. 385.
9. Ibid., p. P-6.
10. Ibid., p. P-3.
11. Ibid., p. P-7
12. Hofstadter, Douglas. I Am a Strange Loop. New York: Basic Books, 2008, p. 363.
13. “The meaning which you attribute to any passive symbol, such as a word on a page, actually derives from the meaning which is carried out by corresponding active symbols in your brain. So that the meaning of passive symbols can only be properly understood when it is related to the meaning of active symbols.” — Hofstadter, Douglas. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Basic Books, 1999, p. 325
14. Ibid., p. 127
15. Hofstadter paraphrases Gödel’s theorem thus: “All consistent axiomatic formulations of number theory include undecideable propositions.” Ibid., p. 17
16. Ibid., p. 385
Node your homework.
2018: I was an undergrad who didn't understand Derrida at all when I wrote this, but despite my errors I still like this essay.