Gödel, Hofstadter, & the Self: A Critical Review of Douglas Hofstadter’s I Am a Strange Loop — Adam Westra

Adam Westra

It’s a huge pleasure to introduce Adam Westra to Numéro Cinq readers. Adam is a philosopher and translator and he happens to be studying Kant. This amazing essay proves that good writing exists in many forms and many arenas, that there is beauty in clarity, that vigorous, surprising prose is not just the province of the novelist and memoirist. Adam grew up in Calgary, with a year-long interlude in southern France at the age of seven, after which he went to a French Lycée, then Western Canada High School. He escaped to the Netherlands for a year before heading to the University of British Columbia, where he did a B.A. in Honours Philosophy (2003-2007). Thence to Montreal to do a Master’s in Philosophy at the Université de Montréal (2007-2009; thesis title: La Critique de la raison pure, une oeuvre inachevée). Now working on his Ph.D. in Philosophy in Montreal and Berlin on the role of analogy in philosophical thinking, with a particular emphasis on Kant.

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Douglas Hofstadter is an author worth reading: he has something to say, and he says it well. This fact jumped off the page with the 1979 publication of his brilliant, Pulitzer-Prize-winning book, Gödel, Escher, Bach: An Eternal Golden Braid (GEB). This eccentric, eclectic and electrifying book fascinated all kinds of readers for all kinds of reasons, and its audacious young author was instantly hailed as a one-of-a-kind, ‘geeky genius’. {{1}}[[1]]If I permit myself this expression, it’s only because I have the feeling that Hofstadter himself wouldn’t be insulted by this appellation, and might even be pleased by it.[[1]]  The irony, as Hofstadter himself points out, in both the Preface to the 20th anniversary edition of GEB (1999) and again, in the Preface to his most recent work, I Am A Strange Loop{{2}}[[2]]Douglas Hofstadter, I Am A Strange Loop, New York: Basic Books, 2007. 412 pages. Henceforth abbreviated as SL. All italics in quoted passages are Hofstadter’s.[[2]] (2007), is that while his first book’s success allowed him to capture the attention of a wide audience, as well as to secure an exceptionally free and well-supported academic position (notably the ‘Fluid Analogies Research Group’ at the University of Indiana) for pursuing his ideas, the most central – and original – insight contained in GEB, namely, “the parallel between Gödel’s miraculous manufacture of self-reference out of a substrate of meaningless symbols and the miraculous appearance of selves and souls in substrates consisting of inanimate matter” seems nevertheless to have gone unheard, like “a shout into a chasm” (SL, xiii). His goal in Strange Loop is therefore to reformulate, re-explain, and also to explore new aspects of this very insight – and this time, with “maximal clarity” (SL, xvii). {{3}}[[3]]While he does intend to contribute to the philosophical debate on the nature of mind and self, Hofstadter explicitly forswears attempting to prove his point of view, finding the typical ‘proofs’ that philosophers tend to give of their theories to be ultimately futile. His primary purpose is not to convince, but to communicate, and only thereby to change his readers’ way of looking at things (in this case, at them-selves).[[3]]

Indeed, one of the very first, and most significant, points that Hofstadter makes in this work is that what he says and how he says it, (and also that it is he who’s saying it), are inextricably bound together. In particular, Hofstadter takes analogy “very seriously”, having spent the greater part of his career studying its role in human thought:

“[…] I specialize in thinking about thinking. Indeed […] this topic has fueled my fire ever since I was a teen-ager. And one of my firmest conclusions is that we always think by seeking and drawing parallels to things we know from our past, and that we therefore communicate best when we exploit examples, analogies, and metaphors galore, when we avoid abstract generalities, when we use very down-to-earth, concrete, and simple language, and when we talk directly about our own experiences” (SL, xv).

And virtually all of the points, major and minor, that are made in the subsequent 350 pages are accordingly expressed by means of more-or-less explicit analogies (the formulations “just as … so”, “similarly”, “by contrast”, etc., are ubiquitous) and an amazing variety of concrete imagery, often drawn from everyday life.{{4}}[[4]]In the Index, under the heading “analogies, serious examples of”, Hofstadter lists close to one hundred entries! Some examples: “between the author’s mind and others’ minds”; “between dog looking at pixels and Russell looking at Gödel’s formula”; “between gems in Caspian Sea  and powers in Fibonacci sequence”; “between mosquito and flush toilet”; “between self-symbol and video feedback”.[[4]] Now, in both this important descriptive claim about the analogical/metaphorical nature of human cognition (“we always think”), as well as the consequent normative claim regarding the optimal form of conceptualization and reasoning (“we therefore communicate best”), Hofstadter’s starting-point and consequent approach to the study of the mind differ fundamentally from the “Snow is white” propositional model of human language and thought that is often used as a paradigm in contemporary analytic philosophy. In fact, this view of his actually comes much closer to that of the emerging “embodied cognition” movement – despite the curious fact that he never mentions the latter specifically – whose representatives, such as Mark Johnson and George Lakoff, argue – like Hofstadter, on the basis of neuroscientific research, and, again like Hofstadter, to a relatively wide audience – that all human thinking, including philosophical reflection, emerges from the body via a metaphorically-mediated process of abstraction. In any case, Hofstadter’s recognition of the importance and power of analogical thought is in itself a remarkable and distinctive contribution to a philosophical scene in which analogy is largely dismissed or ignored.

The book’s twenty-four chapters (each one divided into idiosyncratically titled sections) can, grosso modo, be divided into two main parts: in chapters 1-14, Hofstadter gradually builds up his theory of the Self (or “soul” or “I” or “consciousness” – all synonymous terms for him); in chapters 15-24, he draws some consequences from his central insight, responds to objections, and takes a stab at some traditional and contemporary philosophical problems.

The core ideas of the book all come together in Chapter 20, featuring a dialogue (a form familiar to GEB readers), between two characters, Strange Loops #641 and #642, who represent, respectively, Hofstadter and an imaginary skeptic. Now, the challenge for Hofstadter is to make comprehensible (without necessarily proving) how the notion, nay even the feeling of identity – that there is “something it is like” to be me – emerges from a merely physical substrate, such as – but not necessarily limited to –  the human brain, which is composed of neurons, which are in turn composed of molecules, and so on all the way down to quantum particles – which, for Hofstadter, is where the “true causality” of the physical universe ultimately resides (SL, 297) – and this, without having recourse to any form of metaphysical or supernatural dualism. To the skeptic, then, who balks at the very prospect of providing an account of consciousness in such a framework, he offers the following hypothesis:

I sympathize with your sense of the barrenness of a universe made of physical phenomena only, but some kinds of physical systems can mirror what’s on their outside and can launch actions that depend upon their perceptions. That’s the thin end of the wedge. […] When perception takes place in a system with a truly rich, fluidly extensible set of symbols [e.g. a non-embryonic, non-infantile human brain], then an ‘I’ will arise just as inevitably as strange loops arise in the barren fortress of Principia Mathematica (SL, 282).

Now, the “symbols” invoked here do not designate arbitrary tokens, nor the images encountered in myth or dream, but rather the physical correlates (in the case of a human brain, the specific neural structures) ‘triggerable’ by certain abstract concepts; “perception” is just the ‘triggering’ or activation of such structures, whether through sensation, memory, or imagination. For example, the specific brain structure activated when you see or think of the Eiffel Tower is your “Eiffel Tower symbol”, and this activation is just what it is to perceive the Eiffel Tower (SL, 76). Crucially, the human brain’s system of symbols is so complex that it possesses a virtually unlimited or “universal” representational capacity (in Turing’s sense of “universal computability,” described in Chapter 17).

This is where the central analogy with Gödel’s ‘Incompleteness Theorem’ comes in: according to Hofstadter, Gödel’s great discovery consisted in showing, by means of a sophisticated mapping technique, that the formal system contained in Russell and Whitehead’s Principia Mathematica inevitably produces, because of its universal representational capacity, certain self-referential statements, or “strange loops”. An analogous phenomenon is just as inevitably produced in the brain, and this, combined with humans’ “innate blindness” to the inner workings of our own brains, i.e. “our inability to see, feel or sense in any way the constant, frenetic churning and roiling of micro-stuff, all the unfelt bubbling and boiling that underlies our thinking” (SL, 204) effectively makes us hallucinate an “I”, a Self which – or rather, who – seems to run the show, i.e. whose apparent causal agency according to beliefs and desires feels like the “realest” thing in the world (SL, 202). In a word, the “I” is not the starting-point, but rather the gradual outcome of a complex process of perception that twists back on itself, thereby giving rise, over time, to an ineradicable, yet indispensable, illusion: “I” (SL, 204). Again, Hofstadter is not necessarily trying to prove this claim as a definitive theory of consciousness, but rather sees himself as offering a new perspective on the mind, a sort of ‘Copernican Revolution’{{5}}[[5]]Hofstadter seems to have arrived at this analogy independently of Kant, who is never mentioned. See the Preface to the second edition of the Critique of Pure Reason (B xvii) for the latter’s famous “Copernican Revolution” in metaphysics, also presented as a justification for a change of theoretical perspective.[[5]]: “My claim that an ‘I’ is a hallucination perceived by a hallucination is somewhat like the heliocentric viewpoint – it can yield new insights but it’s very counterintuitive, and it’s hardly conducive to easy communication with other human beings, who all believe in their ‘I’s with indomitable fervor” (SL, 293). More fundamentally, Hofstadter offers a distinctive vision of the human condition (or at least a new variation on an ancient and recurring theme): insofar as we cannot help believing in the “story” we tell ourselves – namely, that each one of has, or rather is, an “I” – it then follows that “the human condition is, by its very nature, one of believing in a myth” (SL, 295).

The skeptic’s recurring objection to this picture is the following: “Where, in this picture, am I? Where is the something-it-is-like to be me? Where are my qualia{{6}}[[6]]The felt quality of certain states of consciousness, often, but not limited to, sensation; e.g.: the ‘blueness’ of the light coming through a stained-glass window, the ‘tastes-like-cheap-coffeeness’ of a cheap cup of coffee, the ‘pastoralness’ of the note F-major, etc.[[6]]?” In a paradoxical vein, Hofstadter (i.e. Strange Loop #641) replies that this ‘special feeling’ combined with the skeptic’s very resistance to the idea that the “I” could merely be the product of blind and invisible particles, just are the illusion he has described; furthermore, the I arises only out of a special kind of physical system: one characterized by an abstract, recursive pattern called a “strange loop,” analogous to a Gödelian self-referential statement.

It is at this exact point, I believe, that this crucial analogy between the strange loop in the brain and Gödel’s strange loop is at its weakest. Specifically, one could object that the ways in which the self-referential patterns emerge in the two cases do not seem to be analogous at all. On the one hand, Hofstadter is committed to saying that the Self emerges from the brain “automatically,” or “inevitably,” as only in this way can the emergence of consciousness be envisaged as taking place under the strictly physical, deterministic laws that constitute the “true causality” of the universe; otherwise, some sui generis mental substance (which he mockingly dubs “feelium” or “élan mental”) would ostensibly be required to explain the insertion of the “I” into the otherwise barren physical universe, devoid of properly ‘mental’ phenomena. Now, Hofstadter repeatedly justifies this claim by analogy with the way in which Gödel’s “strange loop” arises, as at the end of the longer passage quoted above (SL, 282), and again quite clearly here:

Consciousness […] is an inevitable emergent consequence of the fact that the system has a sufficiently sophisticated repertoire of categories. Like Gödel’s strange loop, which arises automatically in any sufficiently powerful formal system of number theory, the strange loop of selfhood will automatically arise in any sufficiently sophisticated repertoire of categories, and once you’ve got self, you’ve got consciousness. Élan mental is not needed (SL, 325, my emphasis in bold).

But does this analogy really hold? More precisely, does it make sense to say that a self-referential Gödelian statement “arises automatically” qua “natural and inevitable outcome of the deep representational power” of Principia Mathematica’s formal system (SL, 161)?

The trouble is that such an interpretation of the analogy does not appear to be consistent with Hofstadter’s own characterization of Gödel’s proof. In Chapters 8-12, Hofstadter mounts an impressive attempt to explicate Gödel’s procedure and to convey his own sense of its significance. According to this picture, however, Gödel’s “strange loop” seems to be the very opposite of “natural and inevitable”: indeed, the sophisticated and recondite procedure by which the young Austrian mathematician painstakingly crafted his proof appears entirely artificial and arbitrary. And crucially, it is this very procedure that constitutes the “why” of Gödel’s strange loop: the latter did not “automatically” emerge from within Principia Mathematica’s formal system, but was, rather, intentionally produced from the outside. As Hofstadter himself writes: “Gödel carefully concocted a statement about numbers and revealed that, because of how he had designed it, it had a very strange alternate meaning” (SL, 171, my emphasis in bold). In other words, the representational power of the formal system described in Principia Mathematica is merely the condition of the possibility of the emergence of a strange loop, not its cause (in logical terms: a merely necessary, not a sufficient condition). Therefore, one cannot say that the strange loop is a “natural and inevitable” product of the formal system itself; rather, it is clearly the artificial and arbitrary product of Gödel’s artificial and arbitrary design which, it could be argued, clearly presupposes a deliberate act of consciousness to begin with. In other words, while the formal system may indeed talk about itself, as Hofstadter insists, it does not do so by itself, but only because Gödel makes it speak. So, returning to the analogy with the brain/consciousness, we must now ask: if Gödel’s strange loop does not in fact arise “automatically” from a substrate of meaningless formal symbols, then why should we think that consciousness emerges “automatically” from a substrate consisting of inanimate matter? Indeed, we could even invert the analogy, in true Hofstadteresque fashion, substituting ‘God’ for ‘Gödel’: just as Gödel’s strange loop only emerges as the product of his consciousness, so are the strange loops constitutive of our respective ‘I’s produced in the consciousness of God! From Hofstadter’s physicalism we end up with full-blown idealism à la Berkeley. We need not go so far, of course; the point is just to stress that Gödel’s intentional mathematical procedure does not seem to be an adequate analogue for the blind physical process through which consciousness ostensibly arises.

Now, Hofstadter would surely respond to the above objection as follows: while the ultimate source of the Self does indeed reside at the level of physical particles governed by universal causal laws, the strange loop as such only arises at a much higher level of abstraction, namely, the level of perception, categories, and symbols:

The sole root of all these strange phenomena is perception, bringing symbols and meanings into physical systems. To perceive is to make a fantastic jump from William James’ “booming, buzzing confusion” to an abstract, symbolic level. And then, when perception twists back and focuses on itself, as it inevitably will, you get rich, magical-seeming consequences. Magical-seeming, mind you, but not truly magical. You get a level-crossing feedback loop whose apparent solidity dominates the reality of everything else in the world (SL, 300, my emphasis in bold).

The most obvious objection here, from an idealist-phenomenological perspective, is of course that this symbolic, meaningful perception presupposes consciousness: meaning is not ‘read off’ the raw data of sensation, but rather ‘read into’ the latter. The same presupposition holds, a fortiori, for Gödel’s proof of the Incompleteness Theorem, qua deliberate cognitive act: Gödel’s strange loop only arises as a meaningful statement to the extent that it has been consciously constructed, i.e., produced by an intentional “act” or “arbitrary synthesis,” to use Kant’s terms{{7}}[[7]]See the chapter of the Critique of Pure Reason on mathematical method, “On the Discipline of Pure Reason in Its Dogmatic Use” (A 712-738 / B 740-766), as well as the paradigmatic example of ‘Thales’ proof’(B xi-xiii)[[7]]. Obviously, explaining consciousness with consciousness can’t be what Hofstadter intends, as it amounts to begging the question, and even worse, begging it in the wrong way, as all true, ‘non-magical’ explanation, for him, must ultimately be in physical terms. But this makes the following question all the more pressing: in what sense are we to understand his claim that perception, qua abstract-physical process, will “inevitably” twist back on itself? Exactly what kind of necessity is being invoked here? Are we talking about the blind necessity proper to the physical substratum of the universe or we are talking at the abstract, symbolic, meaningful level? In the first case, we retain “inevitability” qua “true causality” of the universe, but on the other hand we lose abstract perception at this unfathomably lower level of neurons and seething particles. In the second case, we keep all of the ingredients for self-referential ‘strangeness’, i.e., perception, abstract categories, symbols, etc.; however, at this higher level of abstraction, we lose any meaningful (i.e. physical) sense of “inevitability”. However, these two levels are – indeed must be – incommensurable: recall that perception, and with it, the very possibility of ‘strangeness’, according to Hofstadter, depend on our “blindness” to the physical substrate of our thinking (SL, 204, quoted above). Whence the following dilemma: self-referential “strange loops”, as such, can only arise inevitably to the extent that they are not strange and, conversely, can only be strange to the extent that they are not inevitable. In other words, consciousness and physical necessity, as characterized by Hofstadter, do not seem to be conceptually or ontologically compatible. The fundamental question that Strange Loop was meant to answer must be posed anew: Whence the “fantastic jump” from the physical substrate to consciousness?

In the second part of the book, Hofstadter goes on to confront this perspective with the conceptions of other philosophers of mind (such as ‘Descartes’{{8}}[[8]]That is, the so-called doctrines of “Cartesian dualism” and the “Cartesian ego” which are widely bandied about, seldom with adequate reference to their original context.[[8]], John Searle, Derek Parfit, David Chalmers, and Daniel Dennett) and tackle some traditional and contemporary problems in the philosophy of mind (e.g. mind-body dualism, the so-called Inverted Spectrum Hypothesis, the free-will problem, etc.). In so doing, he makes heavy use of outlandish “thought experiments”, making this section of the book quite stimulating. He also engages with the conceptual creations of other philosophers, cleverly showing how ambiguous and misleading some of these rival scenarios can be (the ones concocted by Searle, in particular). But the sword is double-edged: after a few such skillful deconstructions, one can’t help but view his own conceptual scenarios with the same measure of suspicion. {{9}}[[9]]That being said, Hofstadter’s ingenious playfulness, unfortunately rare among philosophers, is only to be encouraged; indeed, this aspect of his writing is more reminiscent of the intelligent and creative playfulness exhibited by certain artists and musicians (Glenn Gould comes to mind).[[9]]

Moreover, Hofstadter’s treatment of certain philosophical problems (especially the ones he dubs the ‘Sacred Cows’) can come off as facile. For example, he seems to attack the – inappropriately named – ‘Inverted Spectrum Hypothesis’ as if it were just that, i.e., an empirical hypothesis about more or less rare cases involving human perception, and proceeds to put its empirical plausibility into doubt. It could be noted, first of all, that the slightly milder hypothesis that human beings perceive colours differently as a result of slight variations in their sense organs is not at all implausible from an empirical point of view; it is an established fact. More fundamentally, however, the Inverted Spectrum Hypothesis, from a properly philosophical point of view, has nothing to do with its empirical plausibility (a license that Hofstadter frequently claims for his own thought-experiments). The purpose of the thought-experiment (as employed by Wittgenstein, for example) is rather to paint a logical picture, as it were, from which one ‘reads off’ the conceptual links between ostensible mental states or ‘qualia’, on the one hand, and language, on the other. E.g., how and what am I ‘referring to’ when I utter the sentence: “The stop sign is red.”? Is it philosophically justifiable to invoke qualia here (i.e. the felt ‘redness’ of the sign to me, ‘in my head’, so to speak) or will some form of social convention offer a more plausible account (say, that the ‘redness’ of the sign consists in its use in a particular language-game: in this case, to indicate that one must stop one’s vehicle at the sign)? In the latter case, moreover, the ostensible qualia drop out as irrelevant anyway, empirical (im)plausibility notwithstanding.

Hofstadter is far more insightful, convincing, and at times even poignant – both intellectually and emotionally –when he wrestles with the mysteries of everyday life, his own in particular. Thus, the idea that other people to some extent live on inside us (that we are able, to a certain extent, to reproduce foreign “strange loops” in our brains) can come off as merely bizarre in the imaginary “Twinwirld”, but suddenly becomes, not just more plausible, but deeply insightful, even poetic, in Hofstadter’s passionate and earnest wrestling with the sudden loss of his wife Carol, his own “soul-mate”. Indeed, the earnestness and beauty of these reflections bear witness to the fact that Hofstadter’s work is more than merely idiosyncratic (even if brilliantly so); in reality, he has, in his distinctively playful way, something serious – because deeply personal, and hence genuinely human – to say. And for this reason, perhaps more than any other, his Strange Loop is well worth incorporating into your own.

—Adam Westra

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Adam Westra’s web page is here.

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