The idealist metaphysical and economic implications of von Neumann’s mathematics of quantum theory

Reading | Metaphysics

Matthew Cocks, PhD | 2025-01-24

John von Neumann was one of the most extraordinary figures of the twentieth century. In a 1999 biography, Norman Macrae wrote that von Neumann “was a prodigious child and a prodigious student, and through his brief fifty-three years grew steadily more prodigious. In each century there are a handful of people who … write a few equations on a few blackboards, and the world changes” [1]. In a more recent review of von Neumann’s life entitled The Man from the Future, former editor at Nature, Ananyo Bhattacharya, relates how

At the Institute of Advanced Study in Princeton, where he was based from 1933 to his death in 1957, von Neumann enjoyed annoying distinguished neighbors such as Albert Einstein and Kurt Gödel by playing German marching tunes at top volume on his office gramophone. Einstein revolutionized our understanding of time, space and gravity. Gödel … was equally revolutionary in the field of formal logic. But those who knew all three concluded that von Neumann had by far the sharpest intellect. [2]

Von Neumann’s intellectual contributions were many and varied. He applied his mathematical gifts to a wide range of disciplines and was revolutionary in many of them. He is probably best known for his contributions to mathematics and computer science, as well as central involvement with the Manhattan Project. His work in all these areas helped shape the modern world.

But whilst his legacy is, as Bhattacharya observes, “omnipresent in our lives today” [3], it may be through innovations in areas other than computing and military technology that von Neumann has the potential to have an even greater societal impact over the coming decades. In particular, in the perhaps seemingly unrelated fields of theoretical physics and economics.

At different stages in his career, von Neumann was heavily involved in the development of economic theory and to this day is credited with making substantial contributions to the discipline. Indeed, his daughter Marina von Neumann Whitman became a noted economist and was the first woman to serve on the United States President’s Council of Economic Advisors [4].

Von Neumann’s 1928 paper, ‘On the Theory of Parlour Games,’ is today recognized as the founding work of game theory and, although the paper only briefly considers economic issues, it laid the groundwork for the extensive application of game theory to economic matters. Von Neumann later returned more explicitly to the connection in 1944 with the publication of the highly influential co-authored, Theory of Games and Economic Behavior.

Addressing a separate area of economics, von Neumann’s 1937 paper, ‘A Model of General Economic Equilibrium,’ was revolutionary in shaping present day economic methodology. Bhattichari notes that because of the paper “Mathematicians, inspired by von Neumann’s achievement, poured into economics and began applying fresh methods to the dismal science. By the 1950s the subject was transformed” [5].

Around the time of his 1928 paper on game theory, von Neumann was concurrently turning his mathematical attention towards the problems in physics resulting from the 1925 discovery of quantum mechanics. His 1932 Mathematical Foundations of Quantum Mechanics presented the first rigorous mathematical framework for quantum theory. Bhattacharya notes that, to this day, the formulation “remains definitive … [von Neumann] presented the theory as coherently and lucidly as anyone could” [6]. Physicists Bruce Rosenblum and Fred Kuttner have called quantum theory the most successful in the history of science, writing:

Quantum theory works perfectly … [It] has been subject to challenging tests for eight decades. No prediction by the theory has ever been shown wrong. It is the most battle-tested theory in all of science. It has no competitors … [7]

However, in formulating the theory, von Neumann seriously put to question prevailing assumptions about the nature of reality, arriving at the extraordinary conclusion that the mind plays a direct role in the physical world. In the contemporary context, the relationship between physics and consciousness has been receiving renewed attention, but the specific rationale behind von Neumann’s original perspective on this issue often seems to go overlooked. Either his formulation is not mentioned at all, or his conclusion is simply noted without an explanation, before the discussion then moves on.

But von Neumann’s theoretical thought process is remarkably straightforward for the lay person to grasp. He discusses the issue in the final chapter of the book, which focuses on the now famous ‘measurement process.’ In this chapter, von Neumann describes how the prediction of the flow of events in the physical world cannot proceed without including a ‘measurement,’ or more fundamentally, an ‘observation.’ To use an analogy, without incorporating the observation it would be like trying to mathematically model the flow of water out of a hose pipe without acknowledging the existence of the hose pipe.

Physicist Nick Herbert has noted that we see in the chapter a “severe test for his professionalism” [8], as von Neumann follows the mathematical logic to arrive at his conclusion. Henry Stapp, who collaborated with some of the founders of quantum mechanics, has stated that he considers von Neumann’s logic in the chapter to be “impeccable” [9]. The final conclusion comes not from a vague extrapolation or speculation (as sometimes characterized) but, as Herbert summarizes, “from one of the world’s most practical mathematicians deducing the logical consequences of a highly successful and purely materialistic model of the world” [10].

Starting on page 419, von Neumann considers the situation of measuring a temperature using a standard thermometer. He then proceeds to effectively pursue a search for the ‘observer.’ He begins with the measuring device itself (the thermometer) and, having incorporated all the physical processes taking place in the thermometer fully into the mathematical model (in principle at least), notes that it remains necessary for the theorist to say that the thermometer “is seen by the observer” [11].

He then follows mathematically the sequence of physical events from the thermometer to the person’s eye, through the eyeball to the image formed on the retina, incorporating all these processes into the model. Having done so, he notes that it continues to be necessary to say “this image is registered by the retina of the observer” [12]. He then persists, following this logic right through to the chemical reactions in the individual’s brain. But, as he notes, “no matter how far we calculate— … to the scale of the thermometer, to the retina, or into the brain, at some time we must say: and this is perceived by the observer” [13]. That is, he continues, “we must always divide the world into two parts, the one being the observed system, and the other the observer” [14].

Having pushed the boundary between the two as far as he can, he finally concludes that “it is inherently entirely correct that the measurement or the related process of the subjective perception is a new entity relative to the physical environment and is not reducible to the latter. Indeed, subjective perception leads us into the intellectual inner life of the individual …” [15].

Despite his statement that “we must always divide the world into two parts,” the analysis implies metaphysical idealism, not dualism. Reflecting upon the application of the theory, von Neumann states that “experience only makes statements of this type: an observer has made a certain (subjective) observation; and never any like this: a physical quantity has a certain value” [16].

Discussing the use of the word ‘observation’ in quantum theory, astronomical physicist Richard Conn Henry has said that “unfortunately the word ‘observation’ carries an implication that they must be observations of something. But the observations are not of anything. They are just observations. Period” [17]. In a short 2005 essay in Nature, Conn Henry bluntly laid out the metaphysical implications, writing that “The only reality is mind and observations … The Universe is entirely mental” [18].

It is well known that many early quantum physicists concurred with von Neumann on the fundamental role of the mind in quantum mechanics. Famously, Max Plank admitted publicly to regarding “consciousness as fundamental” [19]. Sir Author Eddington similarly wrote that the “substratum of everything is of mental character” [20]. And von Neumann’s friend Eugene Wigner reflected that “it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness” [21].

But over the course of the twentieth century these metaphysical implications became ignored and obscured within the physics community, and therefore with the public at large. It is well documented that a culture of what physicist David Mermin called “shut up and calculate” [22] became prevalent amongst physicists, and to this day even the mention of consciousness can be taboo in many physics departments. David Chalmers and Kelvin McQueen have identified that consciousness has also been sidelined by physicists due to the difficulties of being mathematically precise and potentially the association with Eastern religious traditions [23]. A range of other more materialist ‘interpretations’ [24] have therefore been developed over the decades and received greater attention.

But a wider acknowledgement of the implications of von Neumann’s formulation of quantum theory, in combination with other emerging evidence pointing in a similar metaphysical direction [25], would likely lead to a profound cultural shift in worldview [26]. It therefore becomes a pertinent question as to how such a fundamental societal shift could influence another of von Neumann’s areas of interest: economics.

Most commentators agree that the development of modern economics has been largely underpinned by a materialist metaphysic. From the start, economic thought was heavily influenced by the method of the natural sciences and the Newtonian mechanistic worldview. Carol Leutner Anderson has written that “the historical development of both capitalism and socialism shows them to be metaphysically linked to the concept of a reality as revealed through scientific discovery” [27].

The founder of modern economics, Adam Smith, was strongly predicated in this direction, reducing the study of society down to its smallest parts—in his case, that of the self-seeking individual. Smith once wrote:

Human society, when we contemplate it in a certain abstract and philosophical light, appears like a great, an immense machine, whose regular and harmonious movements produce a thousand agreeable effects. [28]

Economist Lewis Hill has observed how David Ricardo’s “secularized rationalism,” Karl Marx’s “dialectical materialism,” and the influence of the positivist philosophical tradition in economics carried forward a materialist approach [29]. Donald Oswald has discussed the “creed of classical science” that influenced John Stewart Mill’s view of reality and that, in Mill’s view, “the basic intelligibility of nature is guaranteed by its conformity to mechanical principles” [30]. Nicholas Georgescu-Roegen has observed how the Marginalist Revolution of the late 19^th century depicted “the economic process as a mechanical analogue” [31] and Barry Smith has written about how Carl Menger and the influential Austrian School of economics subscribed to a “commonsense realism” [32] and scientific realism.

However, as mentioned, there were notable exceptions. In parallel with his Newtonian approach, and like Newton [33], Adam Smith held a broader metaphysical worldview. Smith was, after all, primarily a moral philosopher. Jerry Evensky writes about how “Smith sees the world as the Design of the Deity, a perfectly harmonious system reflecting the perfection of its designer” [34]. Lewis Hill suggests that, taken within the larger context of his writings, both Smith’s “obvious and simple system of natural liberty” and famous “invisible hand” analogy can be understood to reflect the metaphysical assumptions more explicit in his other writings. Hill concludes that Smith’s “metaphysical preconceptions gave his economics direction and purpose” [35] and suggests that the discipline later lost sight of these metaphysical roots.

More recently, Bernardo Kastrup has argued that the dominant materialist metaphysics in the West is “highly symbiotic with our economic system,” underpinning society’s love affair with material goods and motivating the drive towards material success. He writes that “The materialist worldview has caused many of us to project numinous value and meaning onto things” [36].

How economics would be conceived differently under idealist assumptions, therefore, is an open question and would depend upon the consensus form of idealism reached. But a few clues may perhaps be found in the philosophical literature. For instance, in the writings of the British Idealists of the late 19^th and early 20^th century. Significantly influenced by German Idealism, they were particularly noted for the way in which their metaphysics directly influenced their writings on social, political, and economic issues.

In some respects, the British Idealists took economics back to its Smithian roots by giving central concern to issues of morality and ethics. The Idealist Edward Caird wrote that “Economic science is of equal extent with moral science” [37]. The Idealists saw moral development as inextricably bound with an individual’s progress towards ‘self-realization,’ broadened to take in, as W. J. Mander writes, “our wider potential for full human personhood” [38]. David Boucher and Andrew Vincent have summarized:

Idealism was often an intensely moralistic philosophy … It emphasized both the responsibilities of individuals to seize the opportunities to make themselves more virtuous, and of the owners of capital to transform their workshops into schools of virtue. [39]

Daily work therefore was seen as a means towards self-realization. Whilst not considered one of the British Idealists, the connection between daily work and character growth was also brought out by the famous Cambridge University economist Alfred Marshall, who was influenced by idealism. Simon Cook observes that “Marshall’s specifically economic ideas were developed against the background of an idealist philosophy” [40]. Whilst Marshall’s metaphysical leanings are not explicit in his writings, they are potentially detectable, as can be seen in the definition given on the first page of his famous 1890 textbook:

Economics is the study of mankind in the ordinary business of life … It is on the one side a study of wealth; and on the other, and more important side, a part of the study of man. For man’s character has been moulded by his every-day work … more than by any other influence unless it be that of his religious ideals … [41]

This immediate focus on the role of economic participation in the development of an individual’s character stands in contrast to the more technical definitions provided in contemporary economics textbooks.

Whilst the British idealists were deeply concerned with the alleviation of poverty and other social ills, they did not eschew private property, and indeed even saw property ownership as a means towards self-realization. For instance, the influential idealist T.H. Green supported private property as “a way of manifesting and developing ourselves as persons” [42].

A cultural shift towards idealism could, therefore, potentially see the overarching purpose of the economy called into question more explicitly than at present, with the relationship between economics, morality, and personal growth given more central attention [43].

Idealism could also lead to a revised relationship with material possessions, which would have significant implications for consumption patterns. In his 2016 book, Quantum Economics, theoretical physicist Amit Goswami takes von Neumann’s conclusions at face value and discusses an ‘Economics of Consciousness.’ He suggests that a post-materialist economy would see a reduction in material consumption as the population focuses more on its “higher needs” [44], and people would also seek greater meaning from their daily work [45]. This, he writes, would lead to a more sustainable economic model and general rise in overall well-being.

Philosopher Robert Koons has also considered how a post-materialist political economy could evolve [46]. He argues that materialism is at the root of both Marxism and modern liberalism and that both the right (libertarianism) and left (egalitarian) wings of liberalism have their origins in the materialism of the early modern period. This, he suggests, has led to a dominance of economic models in political theory.

Koons argues that materialist assumptions have led to a conception of political theory as fundamentally a theory of conflict. If human beings are conceptualized as fundamentally material systems, then there is no reason to assume a natural harmony between them. This, he says, is distinct from the Aristotelian view, which sees a human essence; the meaning or significance of being human, which leads to a natural formation of friendships and cooperation in society.  Once the confidence in natural harmony is given up, then society is forced to the opposite extreme of seeing conflict as natural. The constant possibility of conflict then leads to a range of actions to prepare for this possibility—such as the accumulation of power, reputation, and resources.

Koons discusses how the early non-materialist philosophy of the feudal world revolved around ideas of harmony, multiple centers of authority, and local custom. Consequently, under an alternative to materialism (Koons favors an Aristotelian model, but is open to idealism as a possibility), he expects that this could lead to more localism or variation from place to place, more traditional customary ideas, a more complex web of political and social institutions, production that’s both less market driven and less bureaucratic—more local and familial in nature—and an emphasis on small-scale sustainable technologies.

And so, however a post-materialist economy would ultimately pan out, it seems clear that it could look quite different to the one we see today. Whilst undoubtably revolutionary, John von Neumann’s contributions to economics were primarily aligned with the materialist tradition of the discipline, extending and advancing the mathematical and mechanistic approach. But it is perhaps through his work in theoretical physics that he could indirectly have his most significant and long-lasting impact. The cultural transformation that would likely result from a wider acknowledgement of the metaphysical implications of his 1932 Foundations could fundamentally transform how the economy is conceived, structured, and lived.

 

References

[1] Norman Macrae (1999) John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More, American Mathematical Society, pp. 3-4.

[2] Ananyo Bhattachrya (2021) The Man from the Future: The Visionary Ideas of John von Neumann, Allen Lane, p. xi.

[3] Bhattachrya (2021), p. xiv.

[4] The 2012 book launch talk at the Columbia School of International Public Affairs for her memoir The Martian’s Daughter: A Memoir can be viewed at: https://www.youtube.com/watch?v=Dfg_vsnTRBA

[5] Bhattachrya (2021), p. 151

[6] Bhattachrya (2021), p. 60-61

[7] Bruce Rosenblum and Fred Kuttner (2011) Quantum Enigma: Physics Encounters Consciousness, Oxford University Press, p. 269 and p. 54

[8] Nick Herbert (1987) Quantum Reality: Beyond the New Physics, an Excursion into Metaphysics, Knopf Doubleday Publishing Group, p. 156

[9] Conversation with Henry Stapp, Beyond Science and Religion podcast.  Available at: https://webtalkradio.net/internet-talk-radio/2012/10/07/conversations-beyond-science-and-religion-henry-stapp-and-the-mindlike-reality/

[10] Nick Herbert (1993), p. 157

[11] John von Neumann (1955) The Mathematical Foundations of Quantum Mechanics, Princeton University Press. [Originally published in German in 1932], p. 419

[12] John von Neumann (1955), p. 419

[13] John von Neumann (1955), p. 419

[14] John von Neumann (1955), p. 420

[15] John von Neumann (1955), p. 418

[16] John von Neumann (1955), p. 420

[17] Conversation with Richard Conn Henry, 25 August 2014, Beyond Science and Religion podcast. Available at: https://www.spreaker.com/episode/conversations-beyond-science-and-religion-the-mental-universe–14298531

[18] Richard Conn Henry (2005) ‘The mental Universe’, Nature, Vol. 436, Issue 29, p. 29. Perhaps remarkably, in a 2014 interview, nine years after its publication (see [16]), Conn Henry noted that he was not aware of having received any public criticism for the article.

[19] Plank, M., interview in The Observer, 25 January 1931, 17 (column 3)

[20] Eddington, A. (1928) The Nature of the Physical World, Macmillan, p. 281

[21] Wigner, E. (1961) ‘Remarks on the mind-body question’, reprinted in Wheeler, J.A. and Zurek, W.H. (eds) (1983) Quantum Theory and Measurement, Princeton University Press, p. 172

[22] David N. Mermin (2004) ‘Could Feynman have said this?, Physics Today, Vol. 57, Issue 5, pp. 10-12.

[23] David Chalmers and Kelvin McQueen (2021) ‘Consciousness and the collapse of the wave function’, in S. Gao (ed), Consciousness and Quantum Mechanics, Oxford University Press, p. 4.

[24] For a discussion see: Christopher A. Fuchs and Asher Peres (2000) ‘Quantum theory needs no “interpretation”’, Physics Today, Vol. 53, Issue 3, pp. 5-6.

[25] For example, see: Edward Kelly, Adam Crabtree and Paul Marshall (eds) (2015) Beyond Physicalism: Towards Reconciliation of Science and Spirituality, Rowman and Littlefield; Etzel Cardena (2018) ‘The experimental evidence for parapsychological phenomena: A review’, American Psychologist, Vol. 73, No. 5, 663-677; Bernardo Kastrup (2019) The Idea of the World: A Multidisciplinary Argument for the Mental Nature of Reality, John Hunt Publishing; Marco Masi (2023) ‘An evidence-based critical review of the mind-brain identity theory’, Frontiers in Psychology, Vol. 14; Carlos Eire (2023) They Flew: A History of the Impossible, Yale University Press

[26] For a classic discussion on the relationship between science and culture see: Margaret Jacob (1988) The Cultural Meaning of the Scientific Revolution, McGraw-Hill

[27] Carol Leutner Anderson (1982) ‘Economics and metaphysics: Framework for the future’, Review of Social Economy, Vol. 40, Issue 2, p. 216

[28] Cited in Kim, K. (1997) ‘Adam Smith: Natural theology and its implications for his method of social inquiry’, Review of Social Economy, Vol. 55, No. 3, p. 329

[29] Hill, L. (1979) ‘The metaphysical preconceptions of the economic science’, Review of Social Economy, Vol. 37, No. 2, p. 191

[30] Donald J. Oswald (1987) ‘Metaphysical beliefs and the foundations of modern economics’, Review of Social Economy, Vol. 45, No. 3, p. 285

[31] Georgescu-Roegen, N. (1971) The Entropy Law and The Economic Process, Harvard University Press, cited in Martin, D. (1990) ‘Economics as ideology: On making “the invisible hand” invisible’, Review of Social Economy, Vol. 48, No. 3, p. 282.

[32] Smith, B. (1990) ‘Aristotle, Menger, and Mises: an essay in the metaphysics of economics’, History of Political Economy, Annual supplement to vol. 22, p. 268

[33] For a discussion see Part 1 of: Meyer, C. (2020) Return of the God Hypothesis: Three Scientific Discoveries that Reveal the Mind Behind the Universe, HarperCollins

[34] Evensky, J. (1987) ‘The two voices of Adam Smith: moral philosopher and social critic’, History of Political Economy, 19, pp. 447-448

[35] Hill, L. (1979), p. 191

[36] Bernardo Kastrup (2014) Why Materialism is Baloney: How True Skeptics Know There is No Death and Fathom Answers to Life, The Universe, and Everything, Iff Books, p. 8

[37] Colin Tyler (2017) Common Good Politics: British Idealism and Social justice in the Contemporary World, p. 39

[38] W.J. Mander (2016) Idealist Ethics, Oxford University Press, p. 155

[39] David Boucher and Andrew Vincent (2000) British Idealism and Political Theory, Edinburgh University Press, p. 22

[40] Cook, S. (2009) The intellectual foundations of Alfred Marshall’s economic science : a rounded globe of knowledge, New York : Cambridge University Press, p. 3

[41] Alfred Marshall (1997) Principles of Economics, Prometheus Books, p. 1

[42] W.J. Mander (2011) British Idealism: A History, Oxford University Press, p. 237

[43] For discussions on economics and morality see: Amartya Sen (1991) On Ethics and Economics, Wiley and Samuel Bowles (2016) The Moral Economy: Why Good Incentives are No Substitute for Good Citizens, Yale University Press

[44] Goswami, A (2015) Quantum Economics: Unleashing the Power of an Economics of Consciousness, Virginia: Rainbow Ridge Books, p. 171

[45] For a recent overview of the literature on meaningful work see: Blustein, D, Lysova, E. and Duffy, R. (2023) ‘Understanding decent work and meaningful work’, Annual Review of Organizational Psychology and Organizational Behavior, 10, pp. 289–314

[46] Robert C. Koons talk at Texas Tech University, 22 January 2014, ‘The Waning of Materialism and the Future of Western Civilization’. Available at: https://www.youtube.com/watch?v=GZLHKlwue20