most folks do not know kurt Godel. yet his work challenged all the nice assumptions inherant in mathematics and by extension physics. This is as close as we can now get to having a personal converstion with the man.
understand that he did not appreciate the sixth operator, and neither did i for decades. my conjecture is that his incompleteness theorem is a direct result of of our accepted five operator system of logic. Understanding the proper role of the sixth operator closes up the algebra of symbolic logic to exclude negative surfaces.
Way more important it clearly defines GOD as built into our universe. none of this was in his mind.
he had to get there by another path and the fact is that the empirical path is a broad highway that has been intellectusly excluded.
We’ll meet again
The intrepid logician Kurt Gödel believed in the afterlife. In four heartfelt letters to his mother he explained why
Kurt Gödel poses for a portrait at the Institute for Advanced Study in Princeton, New Jersey. 1 May 1956. Photo by Arnold Newman Properties/Getty
is a research associate at the Institute for Advanced Study in Princeton, New Jersey. He researches Kant, Hegel, and the German Idealist tradition, as well as ethics, epistemology, and religion.
As the foremost logician of the 20th century, Kurt Gödel is well known for his incompleteness theorems and contributions to set theory, the publications of which changed the course of mathematics, logic and computer science. When he was awarded the Albert Einstein Prize to recognise these achievements in 1951, the mathematician John von Neumann gave a speech in which he described Gödel’s achievements in logic and mathematics as so momentous that they will ‘remain visible far in space and time’. By contrast, his philosophical and religious views remain all but hidden from view. Gödel was private about these, publishing nothing on this subject during his lifetime. And while scholars have grappled with his ontological proof of God’s existence, which he circulated among friends towards the end of his life, other tenets of his belief system have received no significant discussion. One of these is Gödel’s belief that we survive death.
Why did he believe in an afterlife? What argument did he find persuasive? It turns out that a relatively full answer to these questions is buried in four lengthy letters written to his mother, Marianne Gödel, in 1961, to whom he makes the case that they are destined to meet again in the hereafter.
Kurt and Marianne Gödel pictured together in 1964. Courtesy the Vienna City Library
Before exploring Gödel’s views on the afterlife, I want to recognise his mother as the silent heroine of the story. Although most of Gödel’s letters are publicly accessible via the digital archives of the Wienbibliothek im Rathaus (Vienna City Library), none of his mother’s letters are known to have survived. We possess only his side of their conversation, left to infer what she said from his replies. This creates a mystique when reading his letters, as if one were provided a Platonic dialogue with all the lines removed, except for those uttered by Socrates. Although we lack her own words, we owe a debt of gratitude to Marianne Gödel. For, without her curiosity and independence of thought, we would have one less resource in understanding her famous son’s philosophy.
Thanks to Marianne’s direct question about Gödel’s belief in an afterlife, we get his mature views on the matter. She asked him for this in 1961, a time when he was in top intellectual form and thinking extensively about philosophical topics at the Institute for Advanced Study (IAS) in Princeton, New Jersey, where he had been a full professor since 1953 and a permanent member since 1946. The nature of the exchange compelled Gödel to detail his views in a thorough and accessible manner. As a result, we have (with some supplementation) the equivalent of Gödel’s full argument for belief in an afterlife, intentionally aimed at comprehensively satisfying his mother’s questions, which appear in the series of letters to Marianne from July through to October 1961. While Gödel’s unpublished philosophical notebooks present a space in which he actively worked out views and experimented through often gnomic aphorisms and remarks, Gödel wanted these letters to be understandable and to provide a definitive answer to an earnest enquiry. And because the correspondence was private, he did not feel the need to hide his true views, which he might have done in more formal academic settings and among his colleagues at the IAS.
Albert Einstein and Kurt Gödel photographed at the IAS by the economist Oskar Morgenstern, c1948. Morgenstern recounted how Einstein confided that his ‘own work no longer meant much, that he came to the Institute merely … to have the privilege of walking home with Gödel’. Photo courtesy the Shelby White and Leon Levy Archives Center, IAS, Princeton, NJ, USA.
In a letter dated 23 July 1961, Gödel writes: ‘In your previous letter you pose the challenging question of whether I believe in a Wiedersehen.’ Wiedersehen means ‘to see again’. Rather than the more philosophically formal terms of ‘immortality’ or ‘afterlife’, this term lends the exchange an intimate quality. After emigrating from Austria to the United States in 1940, Gödel never returned to Europe, forcing his mother and brother to take the initiative to visit him, which they first did in 1958. As a result, one can intuit here what must have been a deep longing for lasting reunification on his mother’s behalf, wondering if she would ever have a meaningful amount of time with her son again. Gödel’s answer to her question is unwaveringly affirmative. His rationale for belief in an afterlife is this:
If the world is rationally organised and has meaning, then it must be the case. For what sort of a meaning would it have to bring about a being (the human being) with such a wide field of possibilities for personal development and relationships to others, only then to let him achieve not even 1/1,000th of it?
He deepens the rhetorical question at the end with the metaphor of someone who lays the foundation for a house only to walk away from the project and let it waste away. Gödel thinks such waste is impossible since the world, he insists, gives us good reason to consider it to be shot through with order and meaning. Hence, a human being who can achieve only partial fulfilment in a lifetime must seek rational validation for this deficiency in a future world, one in which our potential manifests.
His opinions are informed and critical, albeit imbued with optimism
Before moving on, it is good to pause and capture Gödel’s argument in a nutshell. Assuming that the world is rationally organised, human life – as embedded in the world – ought to possess the same rational structure. We have grounds for assuming that the world is rationally organised. Yet human life is irrationally structured. It is constituted by a great potential but it never fully expresses this potential in a lifetime. Hence, each of us must realise our full potential in a future world. Reason demands it.
Let’s linger first with a key premise of the argument, namely, the claim that the world and human life, as part of it, display a rational order. While not an uncommon position to hold in the history of philosophy, it can often seem difficult to square with what we observe. Even if we are a rational species, human history often belies this fact. The first half of 1961 – permeating the background of Gödel’s awareness – was filled with rising Cold War tensions, violence aimed at nonviolent protestors during the civil rights movement, and random suffering such as the loss of the entire US figure-skating team in a plane crash. Folly and unreason in human events seem the historical rule rather than the exception. As Shakespeare’s King Lear tells Gloucester when expounding on ‘how this world goes’, the conclusion seems to be: ‘When we are born, we cry that we are come to this great stage of fools.’
It would be a mistake, however, to think that Gödel was naive in his insistence that the world is rational. At the end of a letter dated 16 January 1956, he asserts that ‘This is a strange world.’ And his discussions in his correspondence with his mother show that he was up to speed on political topics and world events. Throughout his letters, his opinions are informed and critical, albeit imbued with optimism.
What is tantalising, and perhaps unique, about his argument for an afterlife is the fact that it actually depends on the inevitable irrationality of human life in an otherwise reason-imbued world. It is precisely the ubiquity of human suffering and our inevitable failures that gave Gödel his certainty that this world cannot be the end of us. As he neatly summarises in the fourth letter to his mother:
What I name a theological Weltanschauung is the view that the world and everything in it has meaning and reason, and indeed a good and indubitable meaning. From this it follows immediately that our earthly existence – since it as such has at most a very doubtful meaning – can be a means to an end for another existence.
Precisely in virtue of the fact that our lives consist in unfulfilled or spoiled potential makes him confident that this lifetime is but a staging ground for things to come. But, again, that is only if the world is rationally structured.
If humanity and its history do not display rational order, why believe the world is rational? The reasons that he gives to his mother in the letters display his rationalist proclivities and belief that natural science presupposes that intelligibility is fundamental to reality. As he writes in his letter dated 23 July 1961:
Does one have a reason to assume that the world is rationally organised? I think so. For it is absolutely not chaotic and arbitrary, rather – as natural science demonstrates – there reigns in everything the greatest regularity and order. Order is, indeed, a form of rationality.
Gödel thinks that rationality is evident in the world through the deep structure of reality. Science as a method demonstrates this through its validated assumption that intelligible order is discoverable in the world, facts are verifiable through repeatable experiments, and theories obtain in their respective domains regardless of where and when one tests them.
It is this result that shook the mathematical community to its core
In the letter from 6 October 1961, Gödel expounds his position: ‘The idea that everything in the world has meaning is, by the way, the exact analogue of the principle that everything has a cause on which the whole of science is based.’ Gödel – just like Gottfried Wilhelm Leibniz, whom he idolised – believed that everything in the world has a reason for its being so and not otherwise (in philosophical jargon: it accords with the principle of sufficient reason). As Leibniz puts it poetically in his Principles of Nature and Grace, Based on Reason (1714): ‘[T]he present is pregnant with the future; the future can be read in the past; the distant is expressed in the proximate.’ When seeking meaning, we find that the world is legible to us. And when paying attention, we find patterns of regularity that allow us to predict the future. For Gödel, reason was evident in the world because this order is discoverable.
Although unmentioned, his belief in an afterlife is also imbricated with the results from his incompleteness theorems and related thoughts on the foundation of mathematics. Gödel believed the world’s deep, rational structure and the soul’s postmortem existence depend on the falsity of materialism, the philosophical view that all truth is necessarily determined by physical facts. In an unpublished paper from around 1961, Gödel asserts that ‘materialism is inclined to regard the world as an unordered and therefore meaningless heap of atoms.’ It follows too from materialism that anything without grounding in physical facts must be without meaning and reality. Hence, an immaterial soul could not count as possessing any real meaning. Gödel continues: ‘In addition, death appears to [materialism] to be final and complete annihilation.’ So materialism contradicts both that reality is constituted by an overarching system of meaning, as well as the existence of a soul irreducible to physical matter. Despite living in a materialist age, Gödel was convinced that materialism was false, and thought further that his incompleteness theorems showed it to be highly unlikely.
The incompleteness theorems proved (in broad strokes) that, for any consistent formal system (for example, mathematical and logical), there will be truths that cannot be demonstrated within the system by its own axioms and rules of inference. Hence any consistent system will inevitably be incomplete. There will always be certain truths in the system that require, as Gödel put it, ‘some methods of proof that transcend the system.’ Through his proof, he established by mathematically unquestionable standards that mathematics itself is infinite and new discoveries will always be possible. It is this result that shook the mathematical community to its core.
In one fell swoop, it terminated a central goal of many 20th-century mathematicians inspired by David Hilbert, who sought to establish the consistency of every mathematical truth through a finite system of proof. Gödel showed that no formal mathematical system could ever do so or prove definitively by its own standards that it was free of contradiction. And insights discovered about these systems – for instance, that certain problems are truly non-demonstrable within them – are evident to us through reasoning. From this, Gödel concluded that the human mind transcends any finite formal system of axioms and rules of inference.
Regarding the incompleteness theorems’s philosophical implications, Gödel thought the results presented an either/or dilemma (articulated in the Gibbs Lecture of 1951). Either one accepts that the ‘human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine’, from which it follows that the human mind is irreducible to the brain, which ‘to all appearances is a finite machine with a finite number of parts, namely, the neurons and their connections.’ Or one assumes that there are certain mathematical problems of the sort employed in his theorems, which are ‘absolutely unsolvable’. If this were the case, it would arguably ‘disprove the view that mathematics is only our own creation.’ Consequently, mathematical objects would possess an objective reality all its own, independent of the world of physical facts ‘which we cannot create or change, but only perceive and describe.’ This is referred to as Platonism about the reality of mathematical truths. Much to the materialist’s chagrin, therefore, both implications of the dilemma are ‘very decidedly opposed to materialistic philosophy’. Worse yet for the materialist, Gödel notes that the disjuncts are not exclusive. It could be that both implications are true simultaneously.
How does this connect with Gödel’s view that the world is rational and the soul survives death? The incompleteness theorems and their philosophical implications do not in any way prove or show that the soul survives death directly. However, Gödel thought the theorem’s results dealt a heavy blow to the materialistic worldview. If the mind is irreducible to the physical parts of the brain, and mathematics reveals a rationally accessible structure beyond physical phenomena, then an alternative worldview should be sought that is more rationalistic and open to truths that cannot be tested by the senses. Such a perspective could endorse a rationally organised world and be open to the possibility of life after death.
Suppose we – cynics and all – accept that the world, in this deep sense, is rational. Why presume that human beings deserve anything beyond what they receive in this lifetime? We can guess that something similar troubled his mother. Gödel says in his next letter’s theological portion: ‘When you write that you pray to creation, you probably mean that the world is beautiful all over where human beings cannot reach, etc.’ Here, Marianne might have agreed that much in creation appears ordered, but challenged the assumption that all of reality is so ordered, in particular when it comes to human beings. Must the whole world be rational? Or might it be that human beings are irrational aberrations of an otherwise rational order?
Gödel’s response reveals extra degrees of nuance to his position. In the first letter, Gödel had only loosely referenced a ‘wide field of possibilities’ that go underdeveloped but which demand completion. In his subsequent letters, he details what it is about humanity that requires existence to continue – that is, what is essential to humanity.
It is first important to explain what Gödel meant by an ‘essential’ property. We have, of course, many properties. I have the property, for example, of standing in a relationship of self-identity (I am not you), of being a US citizen, and of enjoying the horror genre. Although there is no unanimity on exactly how to understand Gödel’s use of ‘essential’, his ontological proof for the existence of God includes a definition of what he means by an essential property. According to that definition, a property is essential of something if it stands in necessary connection with the rest of its properties such that, if one possesses said property, then one necessarily possesses all its other properties. It follows that every individual has an individuated essence, or as Gödel notes in the handwritten draft of the proof: ‘any two essences of x are nec. [sic] equivalent.’ Gödel, like Leibniz, believed that each individual possessed a uniquely determinable essence.
It’s the human ability to learn from our mistakes in a way that gives life more meaning
At the same time, even if essence is defined as individual-specific in the proof, there is evidence that Gödel thought that essences could also be kind-specific. He thought all human beings are destined for an afterlife because they all share a property in virtue of their being human. There are sets of necessary properties that hang together and that are interrelated across individuals such that the possession of this set would entail something being the kind of thing it is. In his ontological proof, for example, he defines a ‘God-like’ being as one that must possess every positive property. As for human beings, I am a human being in virtue of possessing a kind-specific set of properties that all human beings possess necessarily and that at least some of which are completely unique to us (just as only a God-like being can have the property of possessing every positive property).
In Gödel’s letter of 12 August 1961, he points out the crucial question, which is too often overlooked: ‘We not only don’t even know whence and why we are here, but also don’t know what we are (namely, in essence and seen from within).’ Gödel then notes that if we were capable of discerning with ‘scientific methods of self-observation’, we would discover that every one of us has ‘completely determined properties’. Gödel playfully in the same letter remarks that most individuals believe the opposite: ‘According to the common conception, the question “what am I” would be answered such that I am something that has absolutely no properties in its own right, something along the lines of a coat rack on which one can hang anything one pleases.’ That is, most people assume that there is nothing essential about the human being and that one can ascribe to humanity any trait arbitrarily. For Gödel, however, such a conception presents a distorted picture of reality – for if we have no kind-specific essential properties, on what grounds can categorisation and determination of something as something begin?
So what essentially human property points towards a destiny beyond this world? Gödel’s answer: the human ability to learn, and specifically the ability to learn from our mistakes in a way that gives life more meaning. For Gödel, this property hangs necessarily together with the property of being rational. While he admits that animals and plants can learn through trial and error to discover better means for achieving an end, there is a qualitative difference between animals and human beings for whom learning can elevate one into a higher plane of meaning. This is the heart of Gödel’s rationale for ascribing immortality to human beings. In the 14 August 1961 letter, Gödel writes:
Only the human being can come into a better existence through learning, that is, give his life more meaning. One, and often the only, method to learn arises from doing something false the first time. And that occurs of course in this world truly in abundant quantity.
The folly of human beings mentioned above is perfectly consistent with the belief in the world’s rationality. In fact, the world’s ostensible senselessness provides an ideal set-up to learn and develop our reason through the contemplation of our shortcomings, our moments of suffering, and our all-too-human proclivities to succumb to baser inclinations. To learn in Gödel’s sense is not about our ability to improve the technical means for achieving certain ends. Rather, this distinctive notion of learning is humanity’s capacity to become wiser. I might, for example, learn to be a better friend after losing one because of selfish behaviour, and I might learn techniques for thinking creatively about a theoretical approach after multiple experimental setbacks. An essential property of being human is, in other words, being prone to develop our reason through learning of the relevant sort. We are not just learning new ways of doing things, but rather acquiring more meaning in our lives at the same time through reflection on deeper lessons discovered through making mistakes.
All this might lead one to infer that Gödel believed in reincarnation. But that would be overhasty, at least according to certain standard conceptions of it. An intriguing feature of Gödel’s theological worldview is his belief that our growth into fully rational beings occurs not as new incarnations in this world, but rather in a distinct future world:
In particular, one must imagine that the ‘learning’ occurs in great part first in the next world, namely, in that we remember our experiences from this world and come to understand them really for the first time, so that our this-worldly experiences are – so to speak – only the raw material for learning.
And he elaborates further:
Moreover one must of course assume that our understanding there will be substantially better than here, so that we can recognise everything of importance with the same infallible certainty as 2 x 2 = 4, where deception is objectively impossible.
The next world, therefore, must be one that liberates us from our current, earthly limitations. Rather than recycling back into another earthly body, we must become beings with the capacity to learn from memories that are latently brought along into our future, higher state of being.
The belief that it is our essence to become something more than we are here explains why Gödel was drawn to a particular passage in St Paul’s first letter to the Corinthians, which I discovered when perusing his personal library at the archives of the IAS. In a Latin, pocket-sized edition of the New Testament, Gödel jotted at the top of the title page in faint pencil: ‘p. 374’. Following this reference, one is led to Chapter 15 of St Paul’s letter where Gödel marked verses 33 through 49 with square brackets and drew an arrow to one verse in particular. In the bracketed verses, St Paul describes our bodily resurrection. Employing the metaphor of crops, St Paul notes that sown seeds must be destroyed in order to grow into plants that it is their nature to become. So too, he notes, will it be with us. Our lives and bodies in this lifetime are only seeds, awaiting their destruction, after which we will grow into our ultimate state of being. Gödel drew an arrow pointing at verse 44 to highlight it: ‘It is sown in weakness, it is raised in power. It is sown a physical body, it is raised a spiritual body.’ For Gödel, St Paul had apparently arrived at the correct conclusion, albeit by prophetic vision as opposed to rational argument.
We are left largely to wonder about Marianne’s reaction to her son’s views on the hereafter, though it is certain that she was puzzled. In the letter dated 12 September 1961, Gödel assures his mother that her confusion about his position has nothing to do with her age and much more to do with his compact explanations. And in the last letter, from 6 October 1961, Gödel objects against the claim that his views resemble ‘occultism’. He insists, on the contrary, that his views have nothing in common with those who would merely cite St Paul or discern messages directly from angels. He admits of course that his views might appear ‘unlikely’ at first glance, but insists that they are quite ‘possible and rational’. Indeed, he arrived at his position through reasoning alone, and thinks that his convictions will eventually be shown to be ‘thoroughly compatible with all known facts’. It is in this context that he further presents a defence of religion, recognising a rational core to it, which he claims is often maligned by philosophers and undermined by bad religious institutions:
N.B. the current philosophy curriculum doesn’t help much in understanding such questions since 90 per cent of contemporary philosophers see their primary objective as knocking religion out of people’s heads, and thereby work the same as bad churches.
Whether this convinced Marianne or not, we can only guess.
For us who remain with both feet still in this world, Gödel’s argument presents us with a fascinating take on why we might continue to exist after shuffling off this mortal coil. Indeed, his argument glows with an optimism that our future lives, if reason is to be satisfied, must be ones in which we maximise certain essential human traits that remain in a paltry state here. Our future selves will be more rational, and somehow capable of making sense of the raw material of suffering experienced in this life. Can we assume that Kurt and Marianne are now reunited? Let us hope so.
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