IN-DEPTH | Logic takes on the physics paradoxes: Review essay on The Spacetime Model: A Theory of Everything by Jacky Jerôme
/The history of science is the record of the achievements of individuals who…met with indifference or even open hostility on the part of their contemporaries…A new idea is precisely an idea that did not occur to those who designed the organizational frame, that defies their plans, and may thwart their intentions.
—Ludwig von Mises, The Ultimate Foundation of Economic Science[1]
A few days after watching CERN’s Higgs boson press conference, it occurred to me that if the hypothesized Higgs field is supposed to be responsible for mass, and gravity is directly related to mass, it should be fairly obvious that mass, gravity, and the Higgs field might all turn out to be aspects of the same deeper phenomenon, rather than separate, interacting layers.
A search soon revealed some theorizing out there to this effect. Given the list of seemingly impossible paradoxes that have been generated in the name of quantum physics over the past century, and which have spun off an entire quantum mysticism genre, I became curious as to whether there might be alternative models that attempt to bridge the usual list of physics paradoxes in a way that made more sense.
In a free 222-page PDF (Version 6.00, 2 July 2012 [Originally 2005]) replete with illustrations, Jacky Jerôme of France claims to have elaborated a single model capable of suggesting rational accounts of most of the headline physics enigmas. He characterizes it as a substantial build off of the basics of Einstein’s four-dimensional spacetime, that does not resort to any fantastic additional dimensions, yet is still consistent with experimental evidence and the accepted descriptive mathematics of both quantum mechanics and general relativity.
That is a big claim, yet he still tries to avoid overhyping it: “Despite the fact that this theory is logical, coherent, and makes sense, the reader must be careful, bearing in mind that the Spacetime Model has not yet been validated by experimentation.” That said, he offers reasoned degrees of confidence as he applies his underlying concepts to particular issues, and at several points suggests further experiments to test claims.
His work appears to be both compatible with the laws of logic and a provocative contender for the holy grail of physics, a “Theory of Everything,” that is, a physics model that accounts for the behavior of both the very large and the very small using the same principles.[2]
Students of economics in the tradition of Ludwig von Mises might quickly recognize the potentially large gains to be had if formerly separate “micro” and “macro” specialties can really be integrated into a unified model.[3] They will also recognize the possibility that in certain situations, thinkers outside of the current establishment can be offering superior ideas that are built on fundamentally different perspectives than the conventionally accepted ones. The dual themes of logic and physics here might also capture the attention of fans of the epic rationalist-fantasy storyworld of Ayn Rand’s Atlas Shrugged, in which philosophy and physics are portrayed as the dual-pinnacle disciplines of the “rational mind.” Finally, serious students of contemplative traditions curious about the popular claims of quantum mysticism will have a fresh opportunity to consider whether and how the contrasting Spacetime Model may or may not relate to various traditional contemplative claims about the fundamental nature of reality.
Two ways to look at banging a drum
Jerôme’s writing caught my attention early when he made a critical distinction between the mathematical description of physical phenomena and their causal-rational explanation:
We could think that the basic laws of physics are extremely complex since the mathematics of general relativity and quantum mechanics are. Such is not the case…It is thus advisable to distinguish the basic phenomena, generally very simple, from the laws governing them, generally using mathematics, which may be extremely complex.[4]
He gives the example of a child knowing how to produce noise by banging a drum. We can readily understand in causal-rational terms that noise results from impacts on the drum, whereas describing the surface waves in physical-mathematical terms requires complex know-how and calculations including Bessel functions. Thus, causal-rational explanation and mathematical description are revealed as two different modes or aspects of knowledge about the same phenomena.
The claim I have sometimes heard that “one can only understand quantum physics through mathematics” always struck me as a little suspicious. It speaks of a mystery that is inherently unapproachable to the non-math-genius. Yet the above distinction enables an alternative interpretation. What if this claim only signals that while the speaker understands this rarefied mathematics, he also simply lacks a rationally acceptable causal explanation of what it describes? After all, even if the subject is the same, these are two different approaches to knowledge of that subject. Each employs different languages, skills, and methods. If these approaches form a team, isn’t it possible that one of those partners (causality) could go astray even as the other (math) remained on track?
Bridging these two approaches, Jerôme tackles paradoxes such as the wave-particle duality, the nature of photons, the constancy of the speed of light amid the relative motion of matter, the behavior of black holes, the location of the mysteriously missing antimatter in the universe, how such high energy is produced by nuclear reactions, and how fantastic numbers of electrons and positrons everywhere could have the same volume and charge (just either positive or negative) to unimaginably high degrees of precision.
By the end, he even offers a fascinating alternative to the “Big Bang” theory of the start of the universe. He claims the Spacetime Model makes much more sense of the relevant issues and observations, while accounting for a long list of otherwise “mysterious” phenomena in the process.
Any attempt at an account of the origin of the universe must ultimately be speculative to some degree, but here we must also note that any knowledge claim in the natural sciences can never be validated 100%, as those in the more abstract disciplines such as logic, praxeology, and geometry can be. Natural science hypotheses must compete with rivals on the relative question of which available contender better accounts for the observations. Yet this is not a matter of “empirical” experimentation alone. Logic (internal consistency, etc.) must also play a role in evaluating competing hypotheses. Jerôme notes that:
Wrong reasoning can lead to wrong results. For example, we know three different theories of mass and gravity, which are mathematically verified: the Higgs boson, Superstrings, and the Spacetime Model. At least two of these three theories are wrong, despite the fact that they are all three mathematically verified.
Here is a typical example of the way Jerôme attempts to make sense out of the numerous established mathematical principles that have been left to appear mysterious in causal-rational terms: “E = mc2. This formula is fully verified using mathematics and experimentation, but no one is able to explain it using logic and good sense. However, the solution is quite simple within the Spacetime Model.”
Positivism still roosting at home?
Such an advance of mathematical description over causal-rational explanation in fundamental physics should not be surprising in view of the relevant history of controversies regarding the respective roles of reason and empirical observation. Radical empiricism and logical positivism viewed axiomatic logical principles as unscientific, metaphysical anachronisms, not “really real” because they could not be empirically “observed” (meaning measured). As Ludwig von Mises noted:
…the category of regularity is rejected by the champions of logical positivism. They pretend that modern physics has led to results incompatible with the doctrine of a universally prevailing regularity...In the microscopic sphere, they say…The categories of regularity and causality must be abandoned and replaced by the laws of probability.[5]
It was just this mindset that accompanied the emergence of enigmas allegedly implied in a series of experiments and models in fundamental physics. The slit experiments, Schrödinger's cat, Heisenberg’s uncertainty principle, and so on, were trotted out as evidence that logic and causality had met their match, that the universe is at bottom governed by chance and uncertainty and that some entities (not really being entities as old-school philosophers might have understood them) can exist in one place and another at the same time. Maybe quarks are telepathic!
Proponents of such claims did not seem to notice the possibility that it was their previous rejection of logic that enabled an environment in which stop-gap speculations could gain sober recognition. Instead of these enigmas being viewed as no more than bemusing placeholders awaiting more coherent replacements, they were instead embraced and cited as evidence against old-fashioned reason and its “metaphysical,” a priori conceits.
However, such thinking not only missed its own circularity, it also missed that an experimental result and the quality of a hypothesis forwarded to explain it are entirely different matters. The quality of a hypothesis depends in part on applying the very axiomatic logic that had been abandoned. Paradoxes that appeal to the minds of those who have rejected the strictures of logic show no mystical insight, but only the failure to apply to their thinking the inescapable, ancient rules for forming and validity-checking explanations of anything whatsoever.
In this light, Jerôme’s comment is telling: “As a physicist, it is necessary to leave this philosophical aspect to the philosophers and try to solve this enigma in a scientific way, with a logical and rational explanation.”
This could be from the pages of Atlas Shrugged, since his let’s-get-practical use of the word “philosophers” in this sentence seems to imply that these are by definition anti-rationalist philosophers. Yet rationalist philosophers, part of whose message is precisely to uphold the requirements of logic and consistency for any valid knowledge claim, demand exactly the kind of “logical and rational explanation” that Jerôme sets as his goal.
A breath of relatively reasonable quantum air
Against this backdrop, I found refreshing Jerôme’s unabashed resort to “deduction,” “possibility,” and “logical consistency.” The results are consistently fascinating and provocative. He appears to make fairly short work of one physics paradox after another within a unified framework.
In a key early move, he specifies a more consistent definition for volume as “closed volume.” In doing so, he notes conventional inconsistences in volume definitions across scales, highlighting the importance of what is and is not “counted” as closed volume. In his model, it is closed volume alone, and not any of the other varieties of volume he details, that creates the central phenomenon of spacetime displacement. Particles and nuclei form closed volumes, but the distributed charges of the outer electrons of atoms are so diffuse that they do not. And whereas waves do not form closed volumes and therefore have no mass; particles do and therefore have. One might also take the converse perspective and define closed volume as “that which displaces spacetime.”
“Particles,” in this model, result from “pieces of wave” that form closed volumes in spacetime. As these move and reopen, they can subsequently turn back into waves. Only closed volumes cause displacement in the elastic four-dimensional spacetime fabric that Einstein described, which produces what we have come to see from two different sets of observations as “gravity” and “mass” (“mass effect”).
Even the hypothesized Higgs field entails an additional dimension. The Spacetime Model claims to be able to dispense with this while still accounting for the observations associated with the entire Standard Model of particle physics, Higgs boson included. As Jerôme puts it:
The 4D expression of the mass effect means that the universe can be described with only 4D expressions, as Einstein thought his whole life. We don’t need extra dimensions such as 5D, 6D, 7D...nD (string theory), or extra fields such as the Higgs field. In reality, the proposed theory is close to the Higgs boson theory. The major difference is that the famous Higgs field is nothing but spacetime....mass and gravitation are nothing but the consequence of the pressure of spacetime on closed volumes.
His conclusion that “Everything is made out of spacetime” can certainly still leave us with a sense of the mysterious, but somehow manages to clean up the mystery compared to the more typical litany of enigmas. As Mises often emphasized, any given state of theory in a field must run up against some “ultimate given,” that is, it can never be expected to explain every possible thing:
Scientific research sooner or later, but inevitably, encounters something ultimately given that it cannot trace back to something else of which it would appear as the regular or necessary derivative. Scientific progress consists in pushing further back this ultimately given. But there will always remain something that—for the human mind thirsting after full knowledge—is, at the given stage of the history of science, the provisional stopping point. It was only the rejection of all philosophical and epistemological thinking by some brilliant but one-sided physicists of the last decades that interpreted as a refutation of determinism the fact that they were at a loss to trace back certain phenomena—that for them were an ultimately given—to some other phenomena (UFES, p. 48).
Jerôme’s ultimate given is quite ultimate indeed: an elastic 4D spacetime with a substructure of Spacetime Cells (sCells). Everything else is built from that.
It may be easiest to start by conceiving of an sCell as a “neutral electron.” However, Jerôme’s real point is the converse: that an “electron” is a “negatively charged sCell.” Its positively charged partner in existence is called a “positron,” which explains the positive charges of protons in this model.
Positrons and electrons always do have the same mass (closed volume) of 510.998918 KeV (electron masses confirmed with “precision of <0.0000086%”) and protons and electrons the same charge (with the opposite pole) of 1.602176565(35) x 10−19 Coulombs. Jerôme writes, “The relative difference between the absolute values is less than 10-21! So, the question is, ‘How can we explain the incredible equality of these electric charges?’”
He hypothesizes a joint origin of both characteristics in the splitting and reproduction of identical sCells that constitutes the ongoing creation of spacetime (more on this below), which would account for this uncanny precision of commonalities. Starting with a fabric of sCells, when the neutral charge of one transfers to another, the result is one below-neutral cell and another nearby and equally above-neutral cell. These two always appear as a precisely opposite pair because the above-average charge of one and the below-average charge of the other are nothing more than two symmetrical results of a single transfer. They always have the same mass because their shared sCell substructure already predefines this in the same way in both cases.
In this view, electrons and positrons are visible to us because of their charges, whereas sCells in their background average neutral state are undetectable (cannot be “observed” directly), precisely because of their neutrality, and are therefore hidden in plain sight. Positrons and electrons are just two types of lit-up sCell.
Electromagnetic waves, massless because they do not form closed volumes, propagate through this sCell fabric at a consistent speed in vacuum, but never any faster (light travelling through transparent matter has been measured at slower speeds and quite slow speeds have been measured under extraordinary experimental conditions within matter cooled to near absolute zero). Jerôme attributes this to a maximum cell-to-cell transfer rate that is a natural limiting characteristic of the medium of sCells themselves. That we have come to call this maximum transfer speed of 299,792,458m/s “the speed of light” reflects the way in which we observed it and can measure it.
Jerôme identifies neutral, positive, and negative states of sCells as the basic building blocks of all other particles. He proceeds to suggest how these components alone can account for the formation, disappearance, properties, masses, and charges of up and down quarks, protons, neutrons, hydrogen atoms, and onward. Neutral sCells can contribute to mass effects themselves, but only when they become enclosed within a subatomic particle or nucleus and thereby come to “count” as part of a closed volume.
This pair model simultaneously accounts for the location of antimatter in the universe. Rather than being hidden many light years away, it is hidden right under our noses, concealed quite near its partner in existence within other particles. Jerôme also claims to dispose of the hypothesized Strong force as a separate force; those effects result from the enveloping rubber-band-like effect of “distributed charge fields.” In fact, according to this model, there are only two fundamental forces from which the other apparently separate forces derive: Hooke’s Force (constraint and pressure), which applies to all particles, and Coulomb’s Force (attraction and repulsion), which applies only to charged particles (Figure 5-1).
He argues that the concept of a photon as a particle makes no sense. He explains why a photon must be a “quantified wave” and never a particle, and how a quantified wave travelling through an sCell substructure is both consistent with experimental evidence and in principle logically comprehensible. As for black holes, he writes: “Inside a closed volume, as inside a black hole, nothing happens. The light doesn’t exist and therefore can’t escape…”
He also claims to have solved the wave-particle duality. His method of doing so is largely logical and deductive, working from a simple set of widely accepted observations. And in another illustration of differentiating mathematical description and causal-rational explanation, whereas “Schrödinger’s probability concept must be replaced by a more realistic concept called the Distributed Charge Model,” the Schrödinger equation can still be used just as before!
For the finale, he offers a simple, elegant, and unified account of the beginning and ongoing growth (“expansion”) of the universe through sCell expansion and division reminiscent of the way that living cells divide and reproduce in vast quantities with nearly unimaginable precision and a few extremely rare minor variations. This approach simultaneously supplies accounts of a long list of observations for which the Big Bang offers only question marks.
A single internally consistent model is thus able to suggest accounts of the major observations at both the micro and macro levels of physics, including most of the usual list of enigmas. The real nature of spin and some other points remain relatively elusive, he admits, but ventures some tentative parameters and possibilities in each case.
Simplifications are used to get the basics across to general readers, while the math-heavy sections and recalculations of fundamentals using closed volume definitions are set off as supplemental information, which can be skimmed or skipped by the non-specialist. Most of the book should be within reach of those with a reasonable general science education (though more would make things easier) and might be read in a motivated afternoon or two. The prose is brief and clear and the illustrations helpful in bringing home the arguments. The English is “off” just enough to reveal that it is not the author’s first language, but the meaning remains clear and easy to follow. Although the book is clear, a quick copyediting by a native speaker would still lift the quality level.
Any bones left for quantum mysticism?
If this model does pass the tests of internal logical consistency, it is still left to face tests of experimentation. In contrast, some of the competing paradox-ridden and n-dimensional theories it targets do not appear to pass the tests of logic, Ockham’s Razor included. Some may be rejected on logical grounds alone. Others might be rejected if there exists a competing theory that both explains the observations and better passes the tests of logic.
Ideological opponents of “metaphysical” a priori logic would have been loath to reject a hypothesis based on logic alone. Yet not doing so has probably contributed to allowing dead-end speculations to run, permeating scientific culture, and poisoning tendencies in pop philosophy for a century.
The Spacetime Model could put a damper on many of the popular claims of the “new physics supports mysticism” genre, particularly claims that logic, predictability, and consistent causality are mere illusions, or that subject-object differentiation is not to be relied upon. That said, there are still some extraordinary and mind-bending claims to be found in the Spacetime Model itself that might easily be viewable as resonant with certain claims found in some traditional contemplative traditions.
In the Spacetime Model, it is not only that “all is spacetime”, but more specifically that particles (matter), waves (energy), and space (medium) all consist of the same stuff, which is, in this view, “elastic four-dimensional spacetime substructure.” From there, consider some traditional formulations such as the Tibetan “non-duality of form and formlessness” and the typically pithy Zen “not one; not two.” Matter, energy, and space are presented as being both different from each other (not one) and also consisting only of the same spacetime stuff as one another (not two).[6]
However strange images from our attempts to understand the deep structures of physics may appear, and even though atoms are quite clearly “99.999% vacuum with 0.001% waves or matter-energy,” as Jerôme puts it, none of this has any bearing on the reality in which we as persons do and must live and act. Matter, however strange its ultimate substructure, still behaves according to the laws of causality, and so does its substructure.
Probability is ultimately a measurement of our own degree of ignorance about the precise operations of physical causality.[7] Moreover, what is visible at one level of magnification (atomic level: mostly empty) does not necessarily also apply to the view at another level of magnification (the scale at which we live and act, where stuff does bounce off walls).
As Hans-Hermann Hoppe has pointed out,[8] Paul Lorenzen, in Normative Logic and Ethics,[9] argues that all of our knowledge of natural sciences, even physics itself, presupposes certain a priori true assumptions and norms that are not derivable from “empirical” experimentation, a set of knowledge types he labels protophysics, which are “definitions and the ideal norms that make measurements possible” (p. 60). Nothing we discover by measurement can validly contradict the presuppositions of measuring or we will have taken the rug from under the basis of our own claims, rendering them nothing more than sounds, chirps or barks!
And the winner is…?
So where is the grand reaction to Jerôme’s rather comprehensive challenge to conventional physics models and hypotheses? I have not been able to find much of one online, either by specialists or anyone else.
Is it because our Mr. Jerôme is just dead wrong and hopelessly naïve in his imaginings? Is it because there are so many competing “theories of everything” out there, a dime a dozen? Or might there be something special about this one?
What if this Spacetime Model really is a simpler, more elegant explanation of all the observations than the mixed and matched crop of better-known theories it challenges, and is compatible with experimental results and QM/GR mathematics, as claimed? What if it does explain much of what is in need of explaining in a better way – not perfect, just better – than the competition?
A conventional mindset would have to quickly reject such possibilities: Let’s get real. He has no official position in the physics community. His speculations and diagrams are self-published on his own website! Certainly it must just be an amateur effort compared to the real experts in the establishment with their mysterious, peer-reviewed ways!
Maybe. But in light of our earlier discussions of the philosophical background radiation and our distinction between mathematical description and causal-rational explanation, such a conclusion may now look less reasonable than it might have. There certainly are mathematical geniuses at work and checking on each other in a language very few people can speak well enough to even listen in. That is all to the good as far as it goes (gains from specialization), but is it also a good excuse for not making sense in causal-rational terms? Maybe these are two separate matters that deserve more robust differentiation.
So I retain doubts about just writing this all off based on institutional factors such as academic pedigree and position. Yet speaking of institutional factors, we do know that establishments in many fields tend to want to remain…established. We also know that one of the ways guilds and priesthoods have always tried to preserve advantages and privileges is through the construction and preservation of a public image that highlights the great mystery and impenetrability of their subject, which is obviously accessible only to the anointed!
The very first line of the copyright notice page of Jerôme’s book reminds us that: “Scientific peer journals do not accept papers from independent researchers whatever their content.”
Whatever their content?
Including author bio as one factor among others in accepting papers would surely make sense, but it is hard to imagine something less “scientific” and more pre-modern and guild-like than excluding intellectual work based on the author’s institutional status alone.
Fortunately, in this day and age, Mr. Jerôme’s carefully developed, clearly presented set of arguments are just a click away at no cost but time and mental effort for anyone to review, consider, and attempt to refute or improve upon (or maybe print out and tape to the doors of CERN?).
However this comes out, though, we ought to keep up the hard work of applying the laws of logic even when it is not easy, and not start mumbling in resigned despair: “It doesn’t really matter. Who is Jacky Jerôme anyway?”
Postscript: What about Beckmann?
After initially writing a draft of this review of Jerôme's book, an early reader led me to Questioning Einstein: Is Relativity Necessary by Tom Bethel, which is largely a presentation and update for general readers of the ideas of Petr Beckmann, as presented in the more technical Einstein Plus Two. This is certainly also worthy of a careful reading and also touches many issues of the relationship between empirical knowledge, the role of logic, and problems with “official” knowledge institutions that I address in the review of Jerôme’s book. However, the Beckmann/Bethel line of thinking operates only at the "macro" relativity level. In quick summary, it argues that contrary to conventional wisdom, Einstein’s special theory of relativity is on weaker, not stronger, empirical grounds, than general relativity, whereas general relativity is stronger empirically, but was made unnecessarily complex in order not to contradict the earlier special relativity claims. The observed evidence for general relativity, claim these authors, can be explained using classical physics, whereas special relativity is essentially “unfalsifiable” (its assumptions inevitably "don’t apply" to any case of evidence that actually threatens to contradict it).
I do not discuss the Beckmann/Bethel line here in detail so as to focus on Jerôme’s theories, but my general impression is that the Jerôme and Beckmann/Bethel perspectives do not appear necessarily contradictory. Meanwhile, Jerôme’s model appears to make even stronger claims, which go beyond the behavior of gravity and mass to explaining what both gravity and mass are in causal-rational terms that are built up right from the micro level. One Beckmann/Bethel addition to that might presumably be to modify Jerôme’s language for describing the macro level to further remove specifically Einsteinian terminology, even “four-dimensional spacetime,” which Jerôme is still fond of maintaining in his book (and which I will also keep in my review below for simplicity). I found no evidence that either of these parties is aware of the work of the other, and yet I do not see any obvious reason why both alternative theories could not be bounced off of one another and probably cross-improved for the trouble. The Beckmann/Bethel line of thinking is also summarized elsewhere.
[1] Indianapolis: Liberty Fund (2006) 117.
[2] While context does or should limit the meaning of “everything” here, the “Theory of Everything” formulation still ought to be qualified to head off reductionist interpretations. As the American philosopher Ken Wilber has often pointed out, any physics “theory of everything” cannot cover “everything,” as it excludes phenomena of consciousness viewed from the interior, that is, as Mises might phrase it, from the subjective perspective of an acting person. We cannot deny that such a perspective exists without self-contradiction and it is not reducible to material description. Subjective phenomena of consciousness are emergent from, but not reducible to, physical phenomena. Thus, “everything” should at least be used with this reservation to avoid what Wilber calls “flatland,” as described, for example, in Integral Psychology. Boston: Shambala (2000), pp. 70–71.
[3] Ludwig von Mises, Human Action: A Treatise on Economics. The Scholar’s Edition. Auburn, Alabama: Mises Institute (1998 [1949]). Murray N. Rothbard, Man, Economy, and State, with Power and Market. The Scholar’s Edition. Auburn, Alabama: Mises Institute (2004 [1962, 1970]).
[4] While the original text is quite clear and easy to read, the author is not a native speaker of English, and in citing quotations, I have made occasional typographical alterations to language and punctuation only to head off unnecessary distraction for readers of the present article.
[5] The Ultimate Foundation of Economic Science (pp. 19–20).
[6] The Spacetime Model also suggests an uncanny depth to the basic elements of Ken Wilber’s integral four-quadrant model of all phenomena, one element of another “theory of everything,” but one not limited to the field of physics. Various accounts may be found in: The Marriage of Sense and Soul. New York: Random House (1998), esp. Chap. 5; Integral Psychology. esp. Chap. 14; and Integral Spirituality Boston: Integral Books (2006), esp. Introduction and Chaps. 1, 7, and 8. The second stage of the start of spacetime within the Spacetime Model is an expansion of a single sCell until it splits into two identical sCells (and then four, eight, 16, etc.). Here, 14.1 billion years ago, we already have the singular/plural distinction that forms the vertical axis of Wilber’s model. Then, at the very first sign of matter from the rare appearance of density variation in a few sCells, we find a positron and electron pair and with each of those, we already have closed volumes defining an interior and an exterior. That polarity forms the horizontal axis of Wilber’s model. The Spacetime Model thus offers possible root foundations for the construction of the integral four-quadrant model from among the very first things to ever happen in the history of spacetime.
[7] As Mark R. Crovelli recently summarized this view: “If every event and phenomenon which occurs in the world has an antecedent cause of some sort, then we are forced to say that probability is a measure of human ignorance or uncertainty about the causal factors at work in the world…Man’s uncertainty in such a world could only stem from his inability to comprehend or account for all of the relevant causal factors at work in any given situation” (p. 166). in “All Probabilistic Methods Assume A Subjective Definition For Probability,” Libertarian Papers. 4 (1): 163–174.
[8] “On praxeology and the praxeological foundation of epistemology,” The Economics and Ethics of Private Property, 2nd Edition. Auburn: Mises Institute (2006), pp. 265–294.
[9] Mannheim: Bibliographisches Institut (1969).
