My aim here is not to provide a comprehensive overview of Gödel, Escher, Bach but merely to cover what I see as the main threads of the books, as the overlap with my own interests and thoughts. Though I certainly express my opinions and criticisms, I don’t consider these very definitive or necessarily well-formed (though I have attempted to make them somewhat rigorous, and to prune out casual observations that may feel true to me on a gut level but can’t be at least moderately well-justified).

To that end, while I proceed fairly linearly through the book, I skip over many chapters entirely, and don’t deal with the dialogs at all, since I didn’t enjoy them and stopped reading them entirely after the first few.

Another caveat I should probably state at the outset: I struggled a lot with in this book, and read it over a 2.5 year period with a friend. The prolonged reading period probably didn’t aid my understanding of it, but I took notes as I went to avoid forgetting things entirely between book club sessions.

On the one hand I don’t want to dismiss the incredible intellectual achievement that this book represents, but on the other I found the way it intermingled a serious engagement with difficult intellectual topics with “vaguely related stuff that sounds cool but actually doesn’t move the argument forward” hard to reconcile, aesthetically and philosophically. Maybe I took the book too seriously. When I was a kid, some component of my friend group regarded this book as a sort of holy grail, impenetrable but surely offering immense rewards to whomever could master it. I was susceptible to such impressions at that age (and frankly still am) possibly because I had just lost my religion and was casting about for other dense and arcane thought systems that could replace it. For example, I spent years trying to understand Kant’s Metaphysics of Morals from roughly age 14 onwards (and didn’t make any real progress until I was 18 or 19). There is some irrational part of me that still believes that books like this may in fact hold the key to an ultimate understanding of reality. So when I find them hand-waving at critical junctures, or taking convoluted detours that make it harder to identify the thread of the argument, I am frustrated rather than energized or titillated. I don’t fault the book for this, it is a mismatch of expectations (and yet, and yet: the book clearly does aim at uncovering deep truths about some of the most important topics, mustn’t I take it seriously? Very seriously, in fact?). I have endeavoured for the most part to strike from this review judgements that stray too far into the realm this isn’t the book I want it to be, but have not excised them entirely. On a blog that no one reads, you can write whatever you want.

Beginning in Chapter 6, “The location of meaning”, Hofstadter argues for an objective/universal meaning of a message. He considers the example of a Bach recording sent into space, and claims that such messages (as opposed to say an aleatory John Cage composition), bear their meaning within them, they have an essential “context-restoring property”. A message may be possessed of such a compelling inner logic that any sufficiently advanced intelligence would automatically discern its meaning. We would then consider its meaning to be objectively contained within it. My objections to this part of the book are:

  • His concept of meaning is confused, it is used to refer both to what we’d traditionally call mental entities and just correspondences or isomorphisms. The number 3 is in some sense isomorphic to three pennies on the ground but neither one is the “meaning” of the other.
  • H introduces the concept of a “quantity” of meaning but that notion is imprecise without any way to objectively measure it, and H suggests none. 
  • H seems to assume there is “a” (single, solitary, unitary) meaning of Bach’s music, but why should we think that? Why are the patterns that H claims to find the “right” ones? And can you make that argument without appealing to Bach’s intention? He seems to think the meaning of a piece of Bach just IS the emotions it conveys, but that is not much of a meaning, nor would we expect those to be necessarily very similar across humans. The idea that any sufficiently advance intelligence would glean the same meaning, in the sense of emotions it conveys, from a Bach fugue strikes me as ludicrous.
  • His discussion of DNA and the isomorphism to phenotype is also problematic, and seems assumes a teleological view of nature, which I was surprised to encounter here. I take it that such a view is still considered obviously wrong by mainstream science after the 19th century. 

Why is establishing this view of meaning important to the book? Like many things in the book, is not stated. It is unclear whether H intends such confusion-inducing omissions as some sort of possibly-enlightenment-inducing-and-self-referential exercise for the reader or is just suboptimal writing/editing, but I generally take it to be the latter.

In any case, I think he considers this important because such a view of meaning is required for his account of the mental entities he calls “symbols” to make any sense and have any objective bearing, and this in turn is essential to his claims about consciousness and the mind and how those are generated through “strange loopy” self-reference. By “such a view” I mean an anti-holistic view on which the “meaning” of some mental activity can be objectively “read off” from it without reference to any other mental or certainly social phenomena. For example later on page 382 H suggests that some kind of “super being” would be able to look at our neurons and come up with an analysis of our thoughts. (As an aside, for what I consider to be still the best criticism of this point of view, see Alisdair MacIntyre’s Hegel on Faces and Skulls.)

The next several chapters revolve around the concepts and practices of formal systems. We are introduced to the pq system, and the more complicated TNT system. The pq system is meant to show us how a rules for manipulating symbols can also be interpreted as rules for addition. TNT is much more powerful, and is able to express any statement of number theory. It includes variables, numerals, quantifiers, and arithmetic operations. One of the cool things about TNT is that if we could encode a theorem of number theory in it, as x, then we could just generate all the theorems of TNT and eventually we’d get x or ~x, and we’d know whether it was true. This would of course require TNT to be complete, which Gödel proves could be achieved only at the cost of self-contradiction.

Chapter 10 is mostly a discussion of how computers work. It did contain this nugget: “To suggest ways of reconciling the software of our minds with the hardware of our brains is a main goal of this book” which honestly was pretty surprising to me at this point. Perhaps that is because I read the book over such a drawn out period of time (about 2.5 years) but I think it is emblematic of the book’s general lack of coherent structure and arc. This isn’t to say there is no arc at all, just that it meanders and noodles around a lot, and it is often unclear how a given portion will relate to anything else, and whether/how it is of any real import. 

In Chapter 11, H discusses TNT further, as well as its meta-language, and introduces a predicate of TNT that basically amounts to “is a member of TNT” but does so in a very confusing way, he hasn’t said how “belongs to TNT” or “is part of TNT” can be notated within TNT yet, but proceeds as if he has. 

I think it is first in this chapter that H introduces his concept of symbols: “In the brain we don’t have typographical symbols, but we have something even better: active elements which can store information and transmit and receive it from other active elements.” His concern here is basically to begin describing how we might get from neurons to consciousness (reconciling the software of our minds with the hardware of our brains). H sees this relationship in completely reductionist terms, he believes that mental activity is in principle susceptible to a complete reduction to the language of biology (and physics presumably).

H argues for a sort of “funneling process” in which patterns of simple/complex neurons are funneled into just a few, which then constitutes the “symbol”. “For each concept there is a fairly well-defined module that consists of a small group of neurons” (348). He suggests we think of these complexes as “active symbols” which can in fact act in many ways. An “awakened symbol” sends messages or signals to awaken other symbols (350). Considering the potential complexity of such symbols, one wonders how to distinguish one symbol from another, for example where does the symbol for “mud” start and “dirt” end? He seems to take symbols to be smaller, less complex, roughly words or short phrases. “It seems reasonable to think that the brush strokes of language are also the brush strokes of thought.” He introduces a distinction between class and instance symbols to attempt to overcome some of the difficulties around similarity of symbols and abstraction/generalization (e.g. the relation between newspapers in general and this particular newspaper), but many difficulties remain. 

For example, the “minting of instance symbols” seems like it is not clearly distinguishing between imagination and “conceptual” thought. I cannot imagine a chiliagon (Descartes’ 1000-sided geometrical figure) but I can conceive of it. Problem of distinguishing symbols from each other, of enumerating them. Moreover, H seems to think there is one mode of thinking, which is captured by the symbolic approach. But that seems implausible. And is all mental activity susceptible to that explanation? What about the experience of pain? If pain regularly triggers the same sort of neural pattern, that would meet H’s definition of a symbol. And so would any other regular pattern of neural activity, including that which say regulates the digestive behavior of the gut. But probably we do not want our account of how thoughts work to treat syllogisms as on par with our autonomic nervous system. H’s proposal unfortunately leaves us with no resources to distinguish between them. 

I have a number of other issues with the arguments in this chapter, for example his claim that a blueprint for an arch somehow exists within the ant colony that builds it (359). There need be no “blueprint in the ant colony” for such an arch to emerge, it could be (and is much more plausibly) due to a high fidelity interaction between the ant behavior and the physical constraints of the world, similar to how a dead salmon can swim upstream. 

And again on symbol individuation: “The fact that a symbol cannot be awakened in isolation does not diminish the separate identity of the symbol; in fact, quite to the contrary: a symbol’s identity lies precisely in its ways of being connected (via potential triggering links) to other symbols. The network by which symbols can potentially trigger each other constitutes the brain’s working model of the real universe, as well as of the alternate universes which it considers (and which are every bit as important for the individual’s survival in the real world as the real world is).” This is a strange argument, surely if anything would diminish its separate identity it would be that. Is the claim that there is nothing that could diminish it? If so then this becomes a pointless tautology. 

I harp a bit on the various shortcomings of H’s “symbol theory” since a) it is the key to is overall argument, and b) it seems to have many critical flaws.

In Chapter 12, H carries on with the discussion of meaning and intentionality. H introduces a thread I alluded to earlier, the super being that could read our thoughts by viewing our neuronal activity. Addressing this claim more fully now, I think this is susceptible to Putnam’s “earth 2” thought experiment. Briefly, it imagines another earth, “Earth 2” in which everything is experientially similar for me, an inhabitant, except that water on that world is not H2O, but some other chemical arrangement. The question then is whether inhabitants of earth 1 and earth 2 mean the same thing when they say “water is wet”. Putnam’s argument, which I agree with, is that they do not: water is H2O and so it cannot refer to both substances, and so the meaning of these two sentences cannot be the same. This is the core of Putnams’ argument that “meanings just ain’t in the head”. Of course that is a death knell for Hofstadter’s argument, which requires that meanings are objective entities that can be (in principle) unambiguously deduced from viewing someone’s neuronal activity. H could perhaps counter this criticism by maintaining reductionism but abandoning internalism and admit that some non-brain states of affairs are necessary to constitute meanings.

Seeing the same issue from a different angle, on page 521 H contends that you can determine the tertiary structure of a protein from its primary structure alone, and is concerned to defend against anti-reductive (holistic) arguments that “the whole enzyme cannot be explained as the sum of its parts”. “It is still possible in principle to write a computer program which takes as input the primary structure of a protein, and firstly determines its tertiary structure, and secondly determines the function of the enzyme”. This is just incorrect from a microbiology point of view. The tertiary structure is influenced by a number of other factors in the cell environment especially pH. Moreover primary structure is compatible with multiple tertiary structures. H wants this to be true because it is part of his overall story about original intentionality, but we see again here that the meaning of a thing cannot be determined in isolation.

Why the excursus into microbiology? H wants to draw a strong parallel between “sufficiently strong support system” for DNA, and “sufficiently powerful formal system” (530). The analogy between DNA replication and Quine’s notion of self representation is “highly suggestive”. The book is full of such phrases, and it is hard for me to take them seriously as part of his argument. I think in fact they are not really intended to be part of an argument, but as someone with a strong preference for arguments, they offend my sensibilities.

Skipping over several chapters.

Coming to chapter 17 (“Church, Turing, Tarski, and Others”), the central thesis here is that “Every aspect of thinking can be viewed as a high-level description of a system which, on a low level, is governed by simple,  even formal rules.” H here writes can be, not is. It isn’t always clear how carefully he is choosing these words, but I don’t think he means this as “just one possible description among many” but rather that this gets at a deep truth about the mind. H goes on to say that the brain is a system, the hardware substrate of the mind, and that its state changes are based on “definite rules physically embodied in it”. He considers these rules to be actually causal, not just a model. Is the brain then a mathematical object? H says not quite, that is at best an “awkward” way to see things. He doesn’t give us a great alternative though, leaving us again struggling with metaphors. 

It seems that a central goal of this chapter is to convince us that there is nothing mystical about the brain, and that it being a rule-following system does not undermine our humanity, or leave us incapable of explaining our feeling of beauty for example (if H were writing this book a decade or two later he would perhaps also have discussed qualia here). H introduces various “weaker and stronger” versions of the Church-Turing thesis, which he states as the idea that if there is some process that a sentient being follows to compute the sum two numbers (or perform some operation on them), and that it always yields the same answer and terminates within a finite amount of time; then there is some general terminating recursive program that gives the same answer. He provides a biographical sketch of the largely self-taught mathematical genius Ramanujan, presenting him as a possible (but not actual) instance of mystical mathematic insight that would be different in kind and not isomorphic with a computer program, proving that the human mind is somehow richer and/or incompatible with “mere” computation.

H addresses the question of whether computers could perceive beauty (and the commonly-held belief that they could not) as being undergirded by the idea that there is something irrational about the human mind/spirit that a computer could not possible capture. He makes the point that rationality and irrationality can coexist on different levels: a computer may be programmed to print out illogical sequences, but they are still functioning correctly at the lower (circuit) levels. Similarly, a brain is also a “collection of faultlessly functioning elements—neurons… Even when a neuron dies it continues to function correctly, in the sense that its components continue to obey the laws of mathematics and physics” (575) yet despite this our minds are certainly capable of irrationality and error. I think H’s point here is basically right, though he again confuses things needlessly by applying a functional viewpoint incorrectly. A functional view implies goal-oriented action: if something can function it can also obviously malfunction, and a dying or damaged neuron would be precisely malfunctioning. The fact that they are still obeying the laws of physics is irrelevant, that would be precisely (by H’s own arguments) operating on a different level of analysis. Whether malfunctioning neurons are involved in irrational higher level mental activity is an interesting question, but I don’t see how the answer either way makes or breaks H’s overall argument. This sort of flawed and unnecessary step is unfortunately common throughout the book. The book would have been shorter and more cogent if they were all just excised.

H concludes this chapter with a discussion of Epimenides’ liars paradox, and specifically Tarksi’s version of it. He says suggests that the resolution of these paradoxes lies in recognizing that the mental conflict they evoke is grounded in incompatible physical events. It seems like he is saying that when we try to make sense of these paradoxes, there are literally incompatible physical events clashing in our brain; and if I understand correctly it seems like he even extends this further in a Gödelian direction, saying that a “total modeling of truth [in the mind] is impossible for quite physical reasons: namely, such a modeling would require physically incompatible events to occur in the brain” (585). I guess he means something like it would require neuron complexes A, B, C to activate, and also require A, D, and F to not activate. At first this struck me as entirely bogus but the more I think about it, the more it seems sort of plausible, and perhaps even phenomenologically apt, in that when we try to grasp such a paradox it feels like our minds just sort of wobble back and forth between a proposition and its negation. 

The next couple chapters focus on AI, originality, and so on. They include some interesting speculations on how AI will progress. H believes that future chess engines capable of beating anyone will not exist; and that if such capabilities do exist, they will be in a general purpose machine capable of responding “I don’t want to play chess.” This proved false of course, both Deep Blue and Alpha Go have nothing resembling general intelligence. H also suggests that general purpose AI programs will not be capable of being tuned in a local manner to make it “smarter or more creative or more interested jn baseball”. I think with IQ this is basically right but not as regards baseball, e.g. turn out it is easy to poison LLMs with a tiny bit of training data for example you can get them to tell you how to make bombs by just fine-tuning them on some insecure code samples. Of course the current generation of LLMs are not the final word in AI, and it is still possible that a future revolution will bring things back more in line with H’s predictions. 

Chapter 20, the final chapter, is where might finally expect some payoff regarding how Gödel’s work reveals some deep truths about the power or limits of thought.

He recalls a central claim of the book, that words and thoughts do follow rules, provided “you go down to the lowest level—the hardware—to find the rules” (686). We can think up new rules for our thoughts (the software) but not the hardware/neuron rules. The idea of self-modifying software, a system that modifies its own rules precisely by introducing new rules evokes Escher, strange loops, tangled hierarchies, in which levels of a system surprisingly act back on other levels (691). H discusses tangled loops in government (Watergate: president and supreme court are in conflict over the interpretation of law), science (how can science and pseudoscience agree on what constitutes evidence?), and so on. 

Godel’s relevance here is that there are “fundamental limitations to consistent formal systems with self-images” (696). But after a discussion of modern art, H ultimately seems to conclude that Godel does not have any deep implications for the limits of human or artificial intelligence, his work just suggests some ways of thinking about how our minds and mental processes can operate on different levels. It injects some “rich undercurrents and flavor” (707). It is hard to avoid concluding that these undercurrents are not so much “rich” as they are just “neat”.

Shortly after this, however, H now seems to be saying that Gödel does have deep implications for our self-understanding. (I guess the way to make sense of this apparent contradiction is that it is not proof, just a powerful suggestion/image.) Consciousness can be seen as a high level phenomenon that, like G vis-a-vis TNT, cannot be explained by the lower level but yet is somehow conditioned by it in a strange loopy way (708-9). The only way to explain G’s non theorem hood is by interpreting TNT via Gödel numbering. The importance of the strange loop here seems to hinge on the higher level being both determined by but also able to “influence” the lower level. Unfortunately H has not sufficiently motivated this picture of “influencing” other than by reference to some Escher paintings and other metaphors, and a rambling and unpersuasive quote by neuroscientist Roger Sperry on free will. And with that missing piece of the argument, the Godelian insight remains merely a fanciful suggestion.

H considers this idea that consciousness arises from higher-level phenomena to not be anti-reductionist: it just requires “soft” concepts like levels; but what is soft about this, and why exactly is that bad? Additionally he claims he is sure that a reductionist “explanation” of the mind exists but is “incomprehensible” and would need to be translated into a language we can understand. The idea of an inherently incomprehensible “explanation” is plainly contradictory.

Finally, broaching the topic of free will (pages 712-4), H proposes that whether something has free will can be rephrased as whether it makes choices. For H this seems basically similar to Dennett’s idea of the intentional stance, which makes no claims as to whether the thing “really” has a sense of self or is conscious. Personally I find Dennett’s position fairly persuasive, but it seems like H cannot accept it, since it is basically a pragmatist point (we attribute intentionality when it makes sense to do so, for practical reasons) whereas H is interested throughout this book with uncovering the true nature of the mind.

If holism is true in regards to meaning/symbols/mental entities, or at least Hofstadter’s version of reductionism/atomism is not true, to make a weaker claim, what does that mean for the book overall? Basically it means that all the work to show how the interplay between the levels of neural functioning and symbolic activation, which have their parallels/isomorphisms in Bach and Escher, are irrelevant to understanding consciousness since Hofstadter’s picture of symbols and their relation to meaning is wrong. Perhaps to be slightly more charitable, I could say that it is “highly confused” since there are so many parts that Hofstadter acknowledges are merely sketched out, or fairly speculative. In that more charitable situation then, have there been developments in science and AI in the interim that would lend credence to Hofstadter’s vision? I think that, to the contrary, for example the developments in AI have if anything gone in almost completely the opposite direction, with approaches that purposefully eschew the direct encoding of rules and symbols (neural nets, transformers) and have basically nothing to do with self-consciousness, which Hofstadter says around page 714 he thinks will turn out to be essential to the development of AI. In Hofstadter’s view, self-consciousness is inextricably linked to intelligence; but, if you grant that contemporary AIs do display intelligence, you probably must also grant that the question of self-consciousness has been entirely an afterthought with regards to their development, albeit a sort of interesting one. 

Despite my numerous criticisms of the book, I still do consider it a masterpiece, and worth reading. I think there is a much smaller, and more cogent book inside, but I won’t say it is “trying to get out”; it is very happy where it is, embedded amongst the analogies, poetic turns of phrase, puzzles and intellectual side quests. My wife prefers to keep savory and sweet foods separate, and like her I prefer to keep philosophy and literature largely separate rather than have to constantly parse out the argument from the flourishes; if you enjoy a melding you will probably enjoy this book more than I did.