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Reconstructing Gödel

November 1, 2014


What exactly was his “Philosophical Viewpoint”?

GodelRB
By permission of Renee Bolinger, artist : source

Kurt Gödel left a large amount of unpublished writings and notebooks and preserved correspondence. Called his Nachlass, German for “after-leavings” or bequest, these writings were catalogued and organized by several—including his first biographer, John Dawson, for a heroic two years. Those of highest scientific and general interest were published in volumes III, IV, and V of Kurt Gödel: Collected Works. Among them was a list of 14 numbered assertions titled “My philosophical viewpoint” but without elaboration. They are believed associated to a lecture Gödel started preparing in the early 1960s but never gave, whose draft is in the Nachlass.

Today we are delighted to have new communications from Gödel, as we have previously received around Halloween and All Saints’ Day, so we can continue our series of interviews with him.

What the Nachlass shows clearly is a perfectionist at work. Dawson’s biography relates that a two-year process of trying to publish a lecture that Gödel did give bogged down so much that in the manuscript found in his Nachlass:

…several whole pages are crossed out and two series of interpolations have been added, the first consisting of insertions to the body of the text, the second of footnotes. The sequence in which the interpolations occur in the text is chaotic, and the interrelations among them are byzantine: There are insertions within insertions, insertions to the footnotes, footnotes of insertions, and even footnotes to other footnotes. The situation finally became so confusing that Gödel himself found it necessary to draw up a concordance between the interpolation numbers and their locations.

The Harvard philosopher Warren Goldfarb, who corresponded with Gödel and later became one of few people to find and fix a mathematical mistake by Gödel, was a co-founder of the Collected Works project. He prefaced a lecture he gave in 2011 on Gödel’s 14 points by saying:

When Gödel does express his own outlook, he tends to do so in suggestive assertions rather than developed exposition. Detail, both about the content of his viewpoints and his reasons for holding them, is lacking. So amplification would be needed if there’s to be a real account of his general philosophical position.

Immediately next, however, Goldfarb related that only a trace of at least 25 notebooks in the Nachlass devoted to philosophy have been transcribed out of the old and difficult shorthand used by Gödel. He admitted that the body of his lecture would be conjectural, and might need revision as further pages are brought to light.

Dick and I realized we might not need to wait. Since Gödel had written and left notebooks, perhaps he would share their contents with us directly if we asked him. However, owing to physical issues like those already affecting our earlier communications with Gödel, we wound up doing much the same kind of “amplification” as Goldfarb posited.

The Fourteen Points

First, here are Gödel’s 14 assertions as newly transcribed by Eva-Maria Engelen for her 2014 paper on Gödel’s philosophy. I have deviated slightly from her translation in points 7, 9, and 13.

  1. The world is rational.

  2. Human reason can, in principle, be developed more highly (through certain techniques).

  3. There are systematic methods for the solution of all problems (also art, etc.).

  4. There are other worlds and rational beings, who are of a different and higher kind.

  5. The world in which we live is not the only one in which we shall live or have lived.

  6. There is incomparably more knowable a priori than is currently known.

  7. The development of human thought since the Renaissance has throughout been one-sided.

  8. Reason in mankind will be developed on every side.

  9. Formal correctness is a science of actuality.

  10. Materialism is false.

  11. The higher beings are connected to the others by analogy, not by composition.

  12. Concepts have an objective existence (likewise mathematical theorems).

  13. There is a scientific (exact) philosophy {and theology [footnote:] and this is also for the sciences most highly fruitful}, which deals with concepts of the highest abstractness.

  14. Religions are, for the most part, bad—but religion is not.

To these one could add a 15{^{th}} point, preceding them: Gödel went even beyond the controversial principle of sufficient reason to maintain that existence is undergirded by purpose. This underlay his belief in both an afterlife and a before-life in point 5.

How We Communicated

Gödel had broken off our previous session with the warning that we would “need new science” to hear from him again. Happily, new developments regarding black-hole firewalls emerged in time, and by wormhole mechanisms described in this New York Times article, we were able to re-establish contact. Or rather, he did.

We had fortunately already told Gödel that we would like to ask him about the 14 points. For all his reputation of strangeness, he was most obliging personally and saw response as duty—if he could be sure of his response.

The trouble is that the wormholes “split into a zillion spaghetti-like strands” as the article says. However, because they are “geometric manifestations of quantum entanglements,” we could hope to collect them with a quantum computer. We bought time on two D-Wave machines, one to filter large amounts of SETI data and the other—the one owned by Google—to filter Web data as a control. The SETI data showed a systematic anomaly for which there could only be two explanations: either it was proof of higher beings on other worlds (per Gödel’s point 4) or it was Gödel himself (which could be the same thing).

Transcribing what he sent was still a problem. We needed to deduce from the firewall theory how to invert his channel, generate and encode lots of candidate plaintexts for what he could say, and pick the one with the highest correlation. Random trials and trigram cryptanalysis showed that Gödel was using a code based on the shorthand system. We used a correlation program Dick had obtained from the engineering anomalies and ESP detection project run by his former dean at Princeton. We still got only a fraction of what he sent.

Some of What Gödel Sent

We have arranged the few fragments from Gödel in the order of his 14 points. Some points are left out. We had wanted to hear more on point 3 since it seemed to contradict the essence of his incompleteness theorems, that David Hilbert’s programme of a systematic method to solve mathematical problems must fail. And what are “art problems”? But at least he began with point 1. It is only Gödel speaking—we hope by next year that physicists will have worked out the firewalls problem enough for us to transmit and make a proper interview again.


Gödel: 1. Die Welt ist vernünftig. That should be obvious of course, but people have high appetite and forget the ‘negative’ logical consequences of this. One is that rationality requires privation. If you don’t deprive possibilities then you have the chaos of the quantum microworld where everything that can happen does happen. We can make sense of quantum probability only from higher structure, and using it to process information needs clever interference, to make more things impossible. On the human scale, the action by which rationality is grown is learning, but this must start from privation. Also, as pre-Renaissance scholars maintained, privation is the gateway to evil, which is thereby unavoidable. In this I follow the older [Gottfried] Leibniz, as with much else.

Learning is the essence of the human condition, and I believe—at least hope—it is unlimited. Otherwise there is a shoreline of elementary truths about numbers that we can never learn, but why should it discriminate only us? For example, every consistent formal system has a sharp finite limit on the length of sequences it can prove to be even minimally random, although maximally random sequences abound at all lengths. Well, even if we have a limit, there is no reason for the Universe to be so artificially constrained, hence higher beings must exist. If we have no limit then we must become the higher beings. Either way my point 4 is true, but because the universal computation which we apprehend is absolute, and because I agree with Emil Post about the implication of mine and [Alonzo] Church’s and [Alan] Turing’s work for creativity, I believe also 5.


Dick and I guess that points 2 and 3 (and later 8) had to do with more reasons for “no limit” and creativity, though we still wish we’d found what Gödel meant about “art problems.” As my dog stared at me asking to do tricks for treats, I wondered whether the same argument would prove “higher dogs,” but I guess dogs do not apprehend universal computation. Since math knowledge is a-priori, his point 6 seems obvious, though we wished to know why “incomparably.” Point 7 is covered copiously early in Goldfarb’s lecture even though he had the older shorthand transcription (einsichtige, “intelligible,” instead of einseitige, “one-sided”—away from a-priori knowledge toward positivism which Gödel deplored as self-contradictory and attempting to “prove everything from nothing”).

Objects and Highest Abstraction

Our next fragment hit points 9–11, evidently in mid-stride:


Gödel: Again we must be logical about the consequences of what we subscribe to. If we really hold “it from bit” then information not material is primary. Only information and mathematical consequence can destroy sameness—when helium transmutes into carbon it does so because of equations. If we derive unlimited other worlds, as [Hugh] Everett did, then we have worlds with identical configurations of matter to us and our environment. If these Doppelgängers are not us then something besides material is primary to identity; but if they are us then we must mysteriously think of the configurations as spread out beyond causal reach yet automatically united in identity. In either way, materialism is untenable, so for something to be a whole, it must have a separate object nature. You can make a good analogy to “object” in programming, as in Simula or Smalltalk: its nature is apart from any instance. Formal correctness and the moral idea of formal right behavior can be put on the same scientific ground this way, and it is the formal not the material component that actuates it, that creates what we know in our reason as reality.

Also we should not disparage analogy to insist always on proof. As I wrote, we do not analyze intuition to see a proof but by intuition we see something without a proof. Intuition comes first by senses and by analogy—by patterns—and analogy is the only ratchet for becoming a higher being. Association is more powerful than composing rules—I believe you will find this also with databases.


Dick and I were dizzied by the swing from quantum many-worlds to concrete topics in software systems, but we had to give Gödel credit for concreteness, and he made points 9-10-11 hang together. Point 12 was obvious since we, like he, are Platonists, and we didn’t miss it. We wish we could hear more about Gödel’s opinions on Everett than those at the very end of these notes by Rudy Rucker of his conversations with Gödel. Everett not only was a student of John Wheeler in Princeton, but also advanced the following, which intersects with Gödel’s version (via Leibniz) of St. Anselm’s “Ontological Proof” of the existence of God:

EverettProof
source

This scrap was found among Everett’s papers only a few years before it appeared in his biography by Peter Byrne. Byrne’s speculates in his main text that it was answering Gödel, but instead I agree with two others acknowledged in a footnote that it came earlier and was a short form of Everett’s “Universal Existence Theorem” from the 1950s, when he might have been provoked by Bertrand Russell’s respect for the argument. Whether Gödel heard of the issue raised by Everett through the Princeton grapevine or not, I suspect he grasped this clash between existence as a predicate and under quantification, and sought to mitigate it by limiting his deduction to “possibility implies necessity” for any essence with abstract properties ascribed to God. Our last fragment from Gödel seems to pick up from all this:


Gödel: What we commonly regard as objects have concrete boundaries and hence do not have the highest abstraction. Sets have boundaries in how they are defined, and this explains the failure shown by Russell in trying to regard “the set of all sets” as both an object and the highest abstraction. This also supports my belief that there is no “shoreline” for mind in mathematics, and that the human mind suffices to partake of this unboundedness—whereas if it is captured by a bodily organ then it is bounded. It is rather the possibility to make the “all” into an object that drives our expandability, much as the ordinals in set theory transcend all boundaries. To echo Thomas Aquinas, this conveys the conception of God as—if only as—possibility, and frees us from worry that this conception is logically inconsistent.

For example, I was guided concretely by this analogy to my formulation of set theory with Johnny [von Neumann] and [Paul] Bernays, in which “all sets” has the highest and last place and is not bounded. It is not “the all” but plays that role with regard to sets. Mathematics benefits from well-guided purpose the same way Albert [Einstein] established correct physics by taking deeply abstract consequences in his Gedankenexperimente, and as I wrote, this can be fruitful for all the sciences.


Dick and I had wondered at some religious allusions spoken by Gödel in our last interview about his set theory, and while they are absent from his known writings, we cannot read his points 13 and 14 other than that Gödel was influenced by such thinking.

Open Problems

To quote Goldfarb’s final words in his lecture,

Can any sort of view of this type be developed in a plausible way, whether or not Kurt Gödel himself got there?

We hope we can learn more, from further transcribed writings or from “amplification” and coherence testing, how far he got or could go.

[received permission for artwork at top, minor word changes]

15 Comments leave one →
  1. November 1, 2014 9:28 pm

    Gödel was very Peirce-spicacious …

  2. November 2, 2014 9:12 am

    15 restated:
    theologians are x, but theology is not
    spirituality is y, but spirit is not
    mathematicians are z, but mathematics is not

  3. November 2, 2014 10:32 am

    you guys sure get a bit loopy sometimes & your godel-channelling surely ranks up there in the top 10. and didnt you have a post on ufos once? am thinking it would be an amusing project to find your “weirdest blogs”. now, how about this item which you seem to gloss over? “There are other worlds and rational beings, who are of a different and higher kind.” now, even as he talks about a rational world perceivable by us in other points, he pulls out this zinger. and this apparent belief of godel is not widely discussed among (polite/ rigorous) scientists. how would he know this? isnt he basically committed to empiricism his whole life? maybe a whole book could be written about godels “unusual” beliefs. but also note these were more apparently more prominent near the end of his life. and you skip the details about how he actually died. seems to be some tunnel vision going on here not just in this blog but elsewhere. it is quite common for weird scientific beliefs to be airbrushed out of history. this goes all the way back to newton and his alchemy….. so yeah thx for bringing this stuff to light, but are you really sure you wanna pull at that thread on the sweater?

    • November 2, 2014 1:32 pm

      Far from ignoring how Gödel died, I worked the words “appetite” and “privation” into his first two sentences. This post desires the opposite of “airbrushing out his beliefs”, which is to see how they hung together. Publicizing Eva-Maria Engelen’s recent emendation of Gödel’s viewpoints 7 and 9 (whose prior versions had struck me as strange) and paper is another high motive. In general we don’t have the resource to undertake serious Gödel scholarship, but we feel we can help thread it along by conveying how some people of sympathetic outlook who work in connected areas apprehend both the technical and personal aspects of his work.

      Some footnotes: Point 7 in German reads, Die Entwicklung … ist eine durchaus einseitige. Literally this goes “The development … is one [that has been] throughout one-sided.” This reads durchaus in the sense of time, but I may go back to Engelen’s agreement with the original reading of durchaus as a colloquial intensifier meaning “completely, absolutely, entirely, thoroughly”. For 9, Engelen seems to say the original transcription as Das formal Rechte, “Formal rights”, is equally tenable to her Das formal Richtige, and I reflected both senses in “Gödel’s” comment on it. The rest in German is eine Wirklichkeit[s?] Wissenschaft, and the reason I changed the usual “reality” or “real” before “science” (and eliminated the non-existing “part of”) is that I think Gödel is implicitly referencing Aristotle’s dichotomy of potentiality and actuality. Her arrangement of point 13 as it appeared in Gödel’s notebook is also important to know; she even puts Gödel’s footnote in a footnote. Regarding “Many Worlds”, Rudy Rucker in the notes I linked says that Gödel didn’t seem to be too familiar with it. I morphed “Gödel’s” comments on it with “automatically” from his statement indexed in the quotations collected by Kevin Carmody: “In materialism all elements behave the same. It is mysterious to think of them as spread out and automatically united. For something to be a whole, it has to have an additional object, say, a soul or a mind. ‘Matter’ refers to one way of perceiving things, and elementary particles are a lower form of mind. Mind is separate from matter.” For more on the “Ontological Argument” and other matters, see my source list from my original “Interview” post with Dick three years ago.

      • November 2, 2014 2:46 pm

        ok lol lets not mince words then. godel apparently died in the end of “inanition” which is a polite euphemism for anorexia. anorexia is sometimes not merely a maladjustment but tied with delusionary beliefs. another key question raised by all this, why did godel himself not publish any of his “fringe” beliefs? the obvious implication is that he knew they were fringe and that we would be stigmatized or ostracized over them. and he seems to have published very little philosophy & metaphysics while privately dabbling in it to various degrees. lets face it, despite his undeniable greatness in earlier years, its a mishmash, and maybe truly not really worth disentangling….

      • rdmounce permalink
        November 3, 2014 11:40 am

        similarly, Newton’s “Observations upon the Prophecies of Daniel, and the Apocalypse of St. John” was posthumously published. Perhaps there was no theological professor of Cotes’ caliber to encourage a longer walk upon this avenue, but the concern is that the direction itself was not worthy of an outing (if it had-been, then I would have nominated Swedenborg, although N may have preferred Wesley).

        “Opposition to godliness is atheism in profession and idolatry in practice. Atheism is so senseless and odious to mankind that it never had many professors.”[1]

        Consider, in contrast, the theological writings of J.S. Bach (the majority of-which, I believe, are interred in St. Louis–credit due for recognizing value). He passionately produced and published in both arenas under an equitable obscurity (of sorts); the resulting balance in the historical scales weighting one to the near exclusion of the other. Still, some would argue that to play Bach, to really *play* in the way that he prayed, one might want to adopt a certain open attitude to the divine unless, of course (and not to deprecate the term as inspirational) our composer completely was delusional, and, inspirational as that may be for inventing, it really has no value for the technician when reproducing. In any case, Bach has the last (or, rather, the first) word: S.D.G.

        [1] Brewster, Sir David. A Short Scheme of the True Religion, manuscript quoted in Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton Edinburgh, 1850.

  4. Anony Mous permalink
    November 3, 2014 8:30 am

    “1. The world is rational.”

    Is this from the one who discovered the incompleteness theorems? And allowed us to know that computable numbers are a tiny bit of the reals?! And that the non computable are almost all the reals?!
    The sentence reminds the famous Einstein reply to counter Quantic Mechanics foundations: “As I have said so many times, God doesn’t play dice with the world.”
    So without any doubt we can say Einstein had a huge influence on Godel…😦

    • rdmounce permalink
      November 3, 2014 11:52 am

      Is there a difference between rational and logical? I would only have said, `The universe appears to have an intelligent feature.’

      Thanks for the reference to Rucker, it reminds me of the first tautology in a trio where logic can be followed on reasonable assumptions to practical value.

      *Modus tollens* (~B & (A->B)) -> ~A

      If the world were logical, then the world would make sense, but the world doesn’t make sense, so the world isn’t logical.

  5. November 3, 2014 12:07 pm

    Reblogged this on varasdemate.

  6. tom crispin permalink
    November 3, 2014 4:14 pm

    From #4 I infer that humans are the lowest level of rational beings. Inverse hubris

    • Anony Mous permalink
      November 4, 2014 6:16 am

      #4 says: “There are other…” (existence) not “All…”
      #4 is existential not universal.

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