I find Hofstadter's concept of strange loop and how it explains consciousness to be very compelling.

However I find the writing style in "Goedel Escher and Bach" to be too distracting and "I am a strange loop" to be too gee-whiz pop-sciency. I'm also generally suspicious of authors who bypass academic peer reviewed publications and go straight to general public literature with their ideas.

Has anybody published a formal, more rigorous exposition of the concept of strange loop from the point of view of the philosophy of mind? Is there at least a formal definition of the concept?

  • 1
    I think you mean exposition or explication rather than “exposé.” Commented Apr 10, 2015 at 3:37
  • @ChristopherE - I guess it could be an exposé if the point was exposing how the concept makes little sense after being confronted with empirical data.
    – Rex Kerr
    Commented Apr 10, 2015 at 17:38
  • @ChristopherE, you're right. I fixed it now. Commented Apr 10, 2015 at 21:27
  • Does the Wikipedia article for Strange Loop provide answers to your question? It seemed to have something of a formal definition, but it might not be as formal as you would like it.
    – Cort Ammon
    Commented Apr 10, 2015 at 21:37
  • @RexKerr True enough! Commented Apr 10, 2015 at 21:52

4 Answers 4


There's no need.

The idea of 'strange loop' is Hofstadter's informal term to help explain non-technically the self-reference in the logical ideas surrounding Gödel's theorems, which already have the formal treatment.

Turning your question around,

"Has Gödel's concepts of proof and encoding been given a more informal treatment?" has the answer "Yes, many times, including by Hofstadter"

If this doesn't seem sufficient, because it doesn't invoke philosophy of mind, then just consider that the mathematics of logic and proof is just one very very technical hyper formalization of one part of 'philosophy of mind'.

  • 2
    In the preface to the 20th anniv. edition of GEB, he makes more clear that he was trying to draw an analogy between the strange loops found in Godel's theorem and certain intuitions about strange loops in brain function, saying "GEB approaches these questions by slowly building up an analogy that likens inanimate molecules to meaningless symbols, and further likens selves ... to certain special swirly, twisty, vortex-like, and meaningful patterns that arise only in particular types of systems of meaningless symbols". More on this in Metamagical Themas, esp. the section starting on p. 631
    – Hypnosifl
    Commented Jun 1, 2020 at 0:18

Interesting question.

Antonio Damasio is a neuroscientist who explicitly mentioned strange loops in his TED talk on the search for the origins of consciousness. Having a look on his Wikipedia page it seems like various of his papers touch on strange loop ideas, but indirectly.

I found this paper on the tax implications of corporate cross-ownership, which means indirect self-ownership, with a formal treatment referencing strange loops http://www.dsllp.com/content/pdfs/Strange_Loops.pdf

This article does a great job of highlighting strange loops as being key to the work of Wittgenstein, Nietzsche & Rorty, and is all round just a great read https://absoluteirony.wordpress.com/2014/09/17/nagarjuna-nietzsche-rorty-and-their-strange-looping-trick/comment-page-1/#comment-342 Though I guess it doesn't strictly meet the OPQ

Autopoeisis, or self-replication and maintenance, in biology and especially abiogenesis. As a simpler 'special case' of a strange loop, and by making definite predictions about relational complexity, and entropy, it is a more testable and evidence-able concept. Not sure how much it has been though. There are at least a few papers on strange loops in abiogenesis though, which surely count as formal treatment https://cosmosmagazine.com/biology/new-theory-for-life-on-earth

And an interesting article on the contributions of fractals to biology, which widens the biological loopiness https://www.medicographia.com/2013/01/fractals-and-their-contribution-to-biology-and-medicine/


Most people apparently appreciate that Hofstadter's books synthesize many ideas in a non-academic style. In his concept of the strange loop two main components are noted: self-reference and intransitivity. The best known variations of the first one are the liar's paradoxes and for the other one - the rock-paper-scissors games. Both have received extended treatments which can be easily transposed in the philosophy of mind

The intransitivity (or game) has been explored most notably after Arrow's pardox gained popularity. As a material proof of existence Efron dice are a popular exemple. Actually a non-transitive relation can form a loop without being self contradictory, that is A>B and B>C are compatible with C>A, the sign '>' denoting an ordering. Usually this ordering is valued (eg. as 'better', 'prefers', etc) and at each step an illusory ascent is perceived. In the cyclic triad A>B>C>A>B>C... if the mediating element B is skipped, one gets the structure of a paradox 'the egg is before the hen which is before it'... A popular two terms form of the liar's paradox is 'Plato says: Aristotle speaks true. & Aristotle says: Plato lies'. It is not entirely certain that philosophy of mind does not view these problems mostly as a source for headaches.


Theories of meaning that rely upon central aspects that remain in existence by directly or indirectly referring to themselves are seldom as simple as Hoffstadter's notion of a strange loop. But you can see Lacan's version of signification theory as being the same thing writ large.

The central concepts around which everything is organized are not fixed, but are maintained by continual usage, because the definitions of the less central concepts are all in terms of those central concepts.

Take the notion of 'Father'. It can be seen as the source of a concept of hierarchy. We cannot shake our social notion of male superiority because our notions of hierarchy are so embedded in our related notions of Father, Name, Deserving etc. are tied up through circular references back to their source in our experience of realizing we are in some way 'owned' by something of which we are not and have never really been a part (to our mind as an infant). But, in fact, it is a legal fiction maintained only by usage. One need to be the biological offspring of one's father. You will make others into a father if you are born without one, (If you are deeply gifted you might invent a transcendental father that shapes several cultures for the next two millennia ;) etc. Paternity suits can be based on genetics, but also on established obligation to the mother unrelated to genetics.

It is all part of one big multilayered strange loop: I am a father because I own this child, and the assignment of this ownership and its concomitant duties is a legal feature of my nationality which is defined in terms of bloodline and negotiated obligation, the former is directly related to fatherhood, the latter is an aspect of being partially owned, ownership is modeled on fatherhood, so both, I ultimately understand most basically in terms of my relationship to this child.

Even if you reject all this psychoanalysis, the theory of meaning remains compelling. Ultimate references are empty, and are refined by their dependent notions which are nailed down by their daily uses, which are identified by filling the roles in relation to other notions, which are defined in terms of the ultimate references.

One can continually 'descend' because containment and reference are dual ways of anchoring meaning, each is more basic than the other in different ways. Moves that feel 'down' can really move you 'up', and moves that feel 'lateral' are almost always really moves 'up' or 'down'. And if you try to consistently move 'up' or 'down' you end up at the same heavily-referenced points over and over again.

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