The Principle of Higher Hypothesis

The Physical Implications of This Distinction

Take as an illustration of this distinction the case of the development of the principle of universal least action by Leibniz and Johann Bernoulli.²⁶ Bernoulli's work on refraction of light in a medium of constantly increasing density, showed that curvature's manifest correspondence to the primary isochronic curvature, the cycloid. This is an example of a Riemannian unique measurement of the curvature of physical space-time, a measurement effected in terms of the shadows which the actual universe casts upon the domain of the visual imagination.

This demonstration satisfied the issues of both “shortest time” (brachystochrone) and “constant time” (isochrone). This showed, in terms of the preceding work of Christiaan Huyghens and Ole Rømer,²⁷ that the treatment of motion by the algebraic methods of Galileo, Descartes, and Newton must be superseded by the higher geometry of the transcendental domain.

That is sufficient identification of the brachystochrone case for our purposes here. The relevant point situated at the center of that case, is the relationship between Leibniz's notion of least constraint²⁸ and Kepler's use of reason where the empiricists put cause.

Formally, as the term may be attributed to Plato, Nicolaus of Cusa, Leonardo da Vinci, Kepler, or Leibniz, for example, reason signifies the rigorous employment of those faculties of valid discovery of principle coinciding with what has been termed “hypothesis” here, and in other of this present writer's locations.

This discovered principle has the approximate force of an estimation of God's Law [natural law], which the impulse for action in this universe must obey. The natural law's principle acts upon the impulse for action as a constraint; the bending of the impulse to that constraint may be viewed as analogous to a “bending” of the action according to what appears to our visual imagination as a curvature of physical space-time. The imagination of a bending of the shadows of reality serves thus as the representation, in a mathematical way, of our knowledge of the reality so reflected.

Thus, among the most relevant predecessors of Riemann's 1854 dissertation on hypothesis is the work of Johann Bernoulli and Leibniz, in using the characteristics of the general principle of refraction of light to demonstrate Leibniz's principle of universal least constraint.²⁹ The fact that the shortest distance in time corresponds to an isochronic pathway, the primitive cycloid, suffices to prove that vision itself is not located within the algebraic space of the Galileo-Newton notions of causality.

Leibniz, Bernoulli, et al., employed this crucial experiment to discredit the reliance upon algebraic methods by the Cartesians and Newtonians, and to insist upon the non-algebraic (transcendental) domain instead. However justified and important that correction was (and remains), this must not be read to the effect of locating causality within the transcendental, rather than the algebraic domain. One must not forget the agency, creative reason, by means of which the ascension from the algebraic to transcendental domain was accomplished: one must focus upon the act of discovery which effected this axiomatic-revolutionary change to a mathematical domain of higher cardinality. From the standpoint of the claims to final authority by the high priests of today's generally accepted classroom mathematics, the implication of these two combined considerations—the matters of curvature and the act of its discovery—is devastating.

This brings us to the final step in the core argument of our point: the ontological relevance of the economics proof of the principle of hypothesizing the higher hypothesis. First, consider the outline of the proof:

1. The ontological actuality of the existence of any discovery, whether of a new theorem, or a new principle of nature (an hypothesis of the Platonic quality), is the method employed to generate that discovery. In the instance of a consistent new theorem of a theorem-lattice, the method is the hypothesis which is the method of that theorem-lattice. In the instance of a succession of theorem-lattices of respectively higher cardinality (power), we have a lattice of hypotheses, each ordered with respect to the others in terms of cardinality, and all subsumed by a constant method of generating such a succession of hypotheses, an higher hypothesis.

    

2. In both examples, every new discovery poses the issue of truthfulness of prior knowledge. (a) In the inferior case, the valid new theorem of a theorem-lattice, the prior knowledge, if measured in theorems, is tainted by a demonstrated fallacy of composition; however, the principle (the hypothesis) commonly underlying the generation of all the valid theorems of that lattice, both old and new, is affirmed to be relatively truthful, transfinitely truthful. (b) In the superior case, the discovery of a new hypothesis supersedes the claims of the previously existing hypotheses; each prior hypothesis suffers the taint of fallacy of composition, relative to the new. However, the succession of such discoveries, if they are of a (transfinite) type of discovery, is affirmed to be relatively truthful.

3. In both cases, it is the transfinite relative One which is relatively truth, and the terms of the subsumed Many terms, each taken by itself, is shown to be tainted by fallacy of composition. In all cases, the truth lies only in the transfinite Becoming, the type of principle of axiomatic-revolutionary discovery employed, not in the experimental facts associated with the particular case. That type of principle of discovery (e.g., higher hypothesis), rather than any particular hypothesis, is always the ontological location of relative truthfulness.

4. This poses the formal question, whether the relative truthfulness of higher hypothesis is merely the truthfulness of the observer (truth of commentary), or whether this knowledge represents efficient truthfulness, in the ontological sense? If the principle of higher hypothesis employed is shown to correspond to something which bounds externally the phenomena of change in natural processes, such as the apparent laws of motion, then that correspondence shows the relative truthfulness of the knowledge of principle to be ontologically efficient, rather than merely contemplative.

The fact, that technological progress in the productive powers of labor causes an increase in the potential population-density of the human species, in terms of consumption and productivity per capita, per household, and per square kilometer, reflects the process of scientific progress, premised upon Plato's Academy at Athens, and unleashed by the mid-Fifteenth Century Golden Renaissance. The fact that the increase in humanity's (re)productive power correlates with the measurable increase of power (cardinality) of the geometrical-mathematical representation of the succession of discoveries employed, shows that the anti-Aristotelian, Platonic principle of creative discovery underlying the Renaissance and its heritage is the relevant standard of ontologically valid truthfulness, and the relative falsehood of the arguments raised by the Enlightenment and other opponents of that Renaissance.

It would be an error to imply that this progress has been solely, or even almost entirely the result of progress in natural science so-called. What we are able to demonstrate formally in mathematical terms reflects the same principle nunderlying creative composition in the Classical (e.g., anti-Romantic, anti-modernist) forms of poetry, drama, music, and painting. It is the whole development of the mind, as poetry, drama, music, and painting typify such breadth, which is the generator of progress, as the creative compositions in Classical art-forms are the principal means by which the individual's capabilities for creative scientific work are developed.

The function of mathematical physics is properly defined in formal terms as Riemann's hypothesis dissertation defines it. We act upon, and are acted upon by a universe unseen by our sense-impressions, a universe whose imaginable reflections are the shadows which the real universe casts upon the screens of our combined visual and auditory imagination. By aid of the scientific tricks of a higher sort of “geodesy,” the task of mathematical physics is to decode the actions which are represented to us by means of those sensory shadows, to adduce the reality of that real universe which exists only outside the ken of our mere sense impressions.

If we can prove in such ways that there are changes in the shadowy actions which cannot be accounted for by the action of shadows, as shadows, upon shadows, but that these actions belong to a universe which has a different curvature than that of our visual imagination, we have shown that Plato was right on this point, and all of his critics in fundamental and pervasive error.

In that case, the notion of the ontologically primary expression of existence is shifted away from Aristotle and his quibbling, “Trotskyist-like” imitators. What is ontologically primary is the change upon which datum the geodetic measurement of physical space-time is premised.³⁰

In that case, then we cannot project “laws of motion” from assumptions respecting percussive or radiant interactions among seen or assumed³¹ shadows. Rather, we must demonstrate that the laws of motion, or analogous action of change are of the form of laws which act “externally,” as outside constraints, upon the motion of the shadows. These laws are represented by our highest appreciation of the principles, of the form of higher hypothesis, which have been generated by creative discovery as our present state of knowledge. Thus, we must substitute the universality of “least constraint”—constrained by the law reflected to us as higher hypothesis—in place of the mechanistic Galileo-Newton hypotheses respecting motion.

We must see Kepler's development of the first comprehensive mathematical physics from the starting-point of the uniqueness of Plato's five regular solids as a prime example of the application of this principle of least constraint prior to Leibniz. Hence, Kepler employs “reason,” where his plagiarists, the inferior Galileo and Newton, put the mechanistic term “cause.”

Once we have adduced the relevant application of such a principle of least constraint, the relations among the actions reflected to us as shadows are to be judged according to the common constraint which those interacting actions must satisfy. Thus, the notion of a definite, non-zero curvature of the physical space-time reflected as shadows upon the visual imagination, is the most important working conception in all mathematical physics.

The other principal topics bearing upon this matter have been more or less adequately treated afresh in previously published recent locations (in addition to those treatments of the same matters in print or public lectures one or several decades earlier). Nonetheless, the following feature of the matter of metaphor requires a bit of special emphasis here.

All rational human knowledge is derived from the beginning-point of a rigorous definition of the absolute distinction between a mental act of valid creative-mental discovery and a mere deductive opinion, the latter premised upon citing some authority. Without a grounding in that prerequisite, all said in the name of philosophy in general or science in particular is unproven assertion. The Platonic notion of higher hypothesis, as I have repeatedly emphasized the provable (regeneratable) reading of that notion, is the precondition for all competent statements on matters of fundamental principle in philosophy in general, or science in particular. It is here, in respect to an explicit notion of such higher hypothesis, that all truthful human knowledge is rooted, in that all notions of ontological reality are rooted.

The principal difficulty throughout European civilization (in particular) today, may be fairly described as merely a difficulty of false opinion. That false opinion is derived from Venice's Sixteenth Century and later reassertion of the authority of Aristotle's method. The central feature of that Venetian damnation of the human soul is typified by the cases of Pomponazzi, Henry VIII's Zorzi, by the influential Bellarmino and his contemporary Paolo Sarpi. The common ruse for that Venetian damnation of the soul is the Venetian's war against Cardinal Nicolaus of Cusa's method of docta ignorantia, the Venetian's argument that the basis for knowledge is the interpretation of sense-impressions, excluding consideration of those kinds of ideas by means of which axiomatic-revolutionary discoveries in knowledge were achieved.

Thus, on these grounds, for example, no adherent of Aristotle's method can be a Christian, or a Jewish follower of Moses. For, that which separates man from the beasts, which places man above the beasts, is the power of creative reason, the quality of creative reason which defines man as in the image of the Creator. Creative reason is the substance of that human soul which the Aristotelian Pomponazzi insisted he did not possess (except, perhaps, in the Orphic way, of being awarded one on his entry into Hades). Creative reason is imago dei, is capax Dei; without it, there is no imago Dei, no capax Dei.

Here, in the matter whether the poor have creative reason (and, therefore souls), lies the key objection to Christianity by the Venetian oligarchy. That is the international Venetian oligarchy headed by the ruling “Primate among Parasites” of our time, the “Doge of Edinburgh's” British Royal Family.³² For these oligarchs, like the evil tyrants of Canaan's thalassiarch Tyre before its imitators, Venice and the London Levant Company, the lower classes must not be educated “above their station,” or fed too well, lest those lower classes become more numerous than the better classes find tolerable, or, might even become misled to believe, that members of the lower classes are at least as much in the image of the Creator as those decadent, one might say even “degenerate,” royal and other oligarchical families of today.

In short, if the understanding were to spread, that each of us is equally in the image of the Creator at our birth, by virtue of possessing creative powers absent in the beasts, the time allowed for the continuation of usury, Malthusianism, and other expressions of oligarchical degeneracy upon this planet might be greatly foreshortened. That, the oligarchy of this planet will not tolerate. Hence, the perpetuation of the Venetian Party, whose current headquarters is generally considered to be London's financial center, the monarchy, and the lackeys who attend to those reputed potencies.

Putting this point most inelegantly (but without error), the rise of the human species' potential population-density above that of the higher apes is due entirely to what are fairly, if loosely described as improvements in culture, improvements which are entirely the product of new ideas generated through mankind's capacity for the kinds of changes in ideas which formal logic must regard as “axiomatic revolutionary.” Man, unlike all other species, is a species which reproduces itself through the production of ideas, ideas whose existence depends upon the special faculty, however mutilated, which exists even within those oligarchs who may deny its presence within themselves. Thus, the history of mankind is the history of ideas, a history which cannot be judged competently except by reference to that agency which all Aristotelian and analogous method implicitly denies to exist: creative reason, that which sets the existence of mankind above the beasts.

The consciousness of this distinction is the essential quality of the individual's ability to achieve a valid sense of personal identity. Whenever one either effects an axiomatic-revolutionary discovery, as in scientific hypothesis, or a comparable achievement in art, or, failing that, nonetheless re-experiences the act of such discovery by earlier scientific discoverers or creative Classical artists, one is participating in an idea, a principle which is itself of “world-historical” importance and benefit for all of humanity. In this way, and only in this fashion, can the individual participate in fulfilling the work of generations before, and contributing to the advancement of all humanity, present and future.

The person who has achieved a conscious sense of his or her participation in history through individual powers of creative reason, ceases to be an individual within the immediate, local here and now of a human herd, and becomes consciously a participant in humanity as a whole. That person is no slave, no serf. That person is qualified to vote intelligently, to speak in the councils of self-government, and to be elected to responsible office in those processes of self-government, or some other executive function in society. In a prudent society, no lesser qualification is demanded as prerequisite for the individual's performance of any among those functions. Without such qualifications, the individual is a tragic wretch, either perhaps a Don Quixote, living shrewdly in a world of fantasy, or, a Sancho Panza, who could never govern an island, because his head cannot govern the passions below his own waistline.

For such reasons, since Paolo Sarpi and his faction elected it were better to take over and corrupt the new institutions of science, rather than seek to suppress them by brute force, the principal concern of Sarpi and his followers has been to work toward the general “dumbing down” of the human species through the exclusion of all consideration of the creative principle of discovery from the mathematical and related representations of science. Sarpi played a direct hand in arranging this practice, through such assets as Galileo, Robert Fludd, and Francis Bacon. Descartes and Newton typify the long list of intellectually corrosive, Venice-controlled figures in the history of actually and putatively scientific institutions. In the Eighteenth Century, the Berlin Academy's Voltaire, Maupertuis, Algarotti, Euler, Lagrange, Lambert, and the French Encyclopaedists typify those corrupted figures of influence operating within scientific institutions directly under the control of Venice intelligence agents, such as Conti and Algarotti, to the purpose of eliminating the heritage of Cusa, Leonardo da Vinci, Kepler, and Leibniz from science. Immanuel Kant, the Marquis de LaPlace, Augustin Cauchy, and the circles of Germans and others under the control of Britain's Lord Kelvin, typify the continuation of this Venice tradition during the Nineteenth Century.

Thus, because of the influence of Paolo Sarpi's cult of empiricism, and kindred influences, one of the more popular hallmarks of pseudo-scientific practice is that tactic employed by the ever-juvenile idiot savant, John Von Neumann, in his own and Oskar Morgenstern's The Theory of Games and Economic Behavior, in which the authors premise Von Neumann's entire dogma upon the axiomatics of a “Robinson Crusoe model.”³³ Similarly, the naive, or miseducated student of science, deludes himself that his observation of the “repeatability” of a phenomenon is in the nature of scientific proof, or, similarly, that science is statistics. The failure to see one's individual self as imago Dei and capax Dei in terms of consciousness of generation of hypothesis by means of creative mental acts, is the key to toleration of a quality of academic serfdom, is key to the unfortunate condition of a man who might have become a scientist if he had met the first prerequisite, of knowing himself to be in the living image of the Creator by virtue of conscious deployment of his own creative powers of hypothesis.

The “Robinson Crusoe” model was directly a reflection of the influence of the Sarpi school's version of Aristotelian empiricism, the dogmas of Francis Bacon, Galileo Galilei, Thomas Hobbes, René Descartes, John Locke, Isaac Newton, David Hume, Adam Smith, Jeremy Bentham, et al. This model begins with man as an individual beast, the solitary individual, governed by an inner repository of what Adam Smith describes with the words: “Nature has directed us to the greater part of these by original and immediate instincts. Hunger, thirst, the passion which unites the two sexes, the love of pleasure, and the dread of pain, prompt us to apply those means for their own sake, and without any consideration of their tendency to those beneficent ends which the great Director of nature intended to produce by them.”³⁴

This same argument, copied directly from such Venetian agents as Maupertuis and Giammaria Ortes, posed so in Smith's 1759 Theory of the Moral Sentiments, served as the basis for his notorious dogma of the “Invisible Hand” in his famous anti-American tract, the 1776 Wealth of Nations.³⁵

In historical reality, human existence is the result of the generation (and regeneration) of valid new higher hypotheses, hypotheses, and theorems, an accomplishment achieved in no other way than through development and exercise of those creative powers of individual minds which the Aristotelians such as Pomponazzi and the empiricists deny to exist, and which the agnostic Aristotelian Immanuel Kant of the Critiques, like Orphic Gasparo Contarini, professes to be unknowable this side of Hades. Thus, the vital interest of the human species is the social role of the creative mental powers of the individual in producing and reproducing the ideas upon which the continued existence of society as a whole depends absolutely. Thus, the only moral individual is one whose adopted primary self-interest is not what Smith terms “original and immediate instincts,” but, rather, precisely a preoccupation with those kinds of ideas which are formulated and employed in “consideration of their tendency to those beneficent ends” which are plainly identified in the Judeo-Christian Book of Moses, Genesis 1:26-28.

The entire empiricist/Enlightenment method of the Seventeenth and Eighteenth Centuries is premised upon the same irrationalist Aristotelian principle which Smith presents in the cited, radically gnostic³⁶ version. Empiricist method always returns to two presumptions. First, the Hobbesian, Lockean presumption described by Smith, of man as the primal-instinct-governed individual actor and observer as the “cell-form” of all knowable reality. Hence, Robinson Crusoe as the aboriginal founder of political-economy and “chaos theory.” Second, the dogmas of Aristotle's method of deductive irrationalism: the denial, by evasion or other means, of the existence of a “divine spark of reason” in the individual person, the denial of a quality of creative reason which is typified by the axiomatic-revolutionary overthrow of each and every claim made by Aristotle respecting either existence or the interpretation of phenomena and dogma.

For more than two thousand years, Aristotle has been the most influential adversary of reason and science, and the most potent force in the weakening of Christianity through resort to that corrupting method. Were it not for the corrosive influences of empiricist Paolo Sarpi and his like, the corruption of science by Sarpi's Venetian methods, as Galileo and Newton typify this, would have been obvious, had it ever come to exist within the leading institutions of science.

Typical of the institutionalized problem of our decadent civilization of today: “Political science” is a pseudo-science, invented by the “Madame Blavatsky” of the French and German Enlightenment, the notorious Madame de Stael.³⁷ Rip that lying abomination out of our universities, to reside with astrology, witchcraft, Malthusianism, and phrenology among the pathetic superstitions which set poor ignorant wretches apart from sane men and women. In the vacant place in academia so provided, place the study of dirty Venetian and kindred politics within the history of science. Had there not been such dirty politics in the highest places of political authority within the institutions of science (and the charitable oligarchs who fund, and thus control science's peer-review and educational programs), the mechanistic notion of causality would never have supplanted the principle of reason upon which such figures as Plato, Cusa, Leonardo, Kepler, and Leibniz founded it.

Notes:

1. The Collected Works of Berhnard Riemann (Bernhard Riemann's Gesammelte Mathematische Werke), ed. by Heinrich Weber (New York: Dover Publications, 1953; Liechtenstein: Sändig Reprint Verlag Hans R. Wohlend), p. 525. (“The distinction which Newton makes between laws of motion or axioms on the one hand, and hypotheses on the other, does not appear to me tenable. The law of inertia is the hypothesis: If there did exist such a thing in the universe as an isolated material point, and if it moved in space at a determinate velocity, then this velocity would be maintained indefinitely.”)

2. Lyndon H. LaRouche, Jr., The Science of Christian Economy, in The Science of Christian Economy and Other Prison Writings (Washington, D.C.: Schiller Institute, 1991), Appendix V, “How Newton Parodied Kepler's Discovery,” pp. 374-377.

3. The inclusion of the Aristotle of his Organon among the materialists here, is no mistake. Philosophical materialism is any dogma which is consistent with the axiomatic assumption that ontological knowledge of the actual world is based upon acceptance of formal consistency among nominal definitions of sense-perception, excluding ideas. Thus, all anti-Platonists are intrinsically materialists: Eleatics, sophists, Aristotelians, empiricists, positivists, etc.

4. This is also the Christian Platonist's method of docta ignorantia, associated with Nicolaus of Cusa's De Docta Ignorantia and later writings.

5. Bernhard Riemann, “Über die Hypothesen, welche der Geometrie zu Grunde liegen,” in Collected Works, op. cit., pp. 272-287.

6. Lyndon H. LaRouche, Jr., “The Truth About Temporal Eternity,” Fidelio, Vol. III, No. 2, Summer 1994, pp. 19-23.

7. Lyndon H. LaRouche, Jr.. “An Economist's View of Gauss's 'Pentagramma Mirificum,' ” 21st Century Science & Technology, Vol. 7, No. 2, Summer 1994, pp. 44-55.

8. Once the Academy at Athens had carried the work of the Pythagoreans to the point of demonstrating conclusively the existence of “incommensurables,” it was sheer professional incompetence to attempt to derive a mathematics from the standpoint of the so-called “natural numbers” alone. All formal mathematics must be defined as a product of a set of underlying geometrical axioms; any professional's defiance of the obligation to present proofs in geometrical terms is therefore a fraud against science, a willful fallacy of composition.

9. Draw a straight line connecting the first and last of three successive vertices of a regular pentagon. Consider the acute angle formed between either of the sides of the pentagon and this added straight line: Π/5 (e.g., 36°). Half of the length of the constructed straight line is represented by cos 36°.

10. Nicolaus of Cusa, De Docta Ignorantia, and De Circuli Quadratura.

11. Riemann, Collected Works, op. cit.

12. On the derivation, and proof of the well-tempered system of J.S. Bach et al., see A Manual On the Rudiments of Tuning and Registration, Vol. I, ed. by John Sigerson and Kathy Wolfe (Washington, D.C.: Schiller Institute, 1992). Just as Bach's chorales prove Helmholtz's apologist, Alexander J. Ellis, to have been a fraud on the empirics of tuning [see Herman Helmholtz, The Sensations of Tone, ed. by A.J. Ellis (New York: Dover Publications, 1954)], so the study of the natural genotypes of adult singing-voice species, their naturally determined registrations, and the problems of combining these voice-species in vocal polyphony define the well-tempered tuning as the only “natural” tuning. Confirming B. Riemann [“Mechanik des Ohres,” in Collected Works, op. cit., pp. 338-350], in contrast to the fraud on this same matter by Helmholtz, the construction of the human ear also conforms to this well-tempered tuning centered upon C = 256 and A = 430-432.

13. The Thirteen Books of Euclid's Elements, trans. by Thomas L. Heath (1925) (New York: Dover Publications,

1956); Riemann, Collected Works, op. cit., pp. 272-273.

14. Riemann, Collected Works, op. cit., pp. 273, 276, 507-520.

15. Lyndon H. LaRouche, Jr., “On LaRouche's Discovery,” Fidelio, Vol. III, No@s 1, Spring 1994.

16. When considered in respect to the Earth's polar diameter.

17. Credible, considering the instruments available.

18. The solar hypothesis was well established among the Hellenic astronomers of that period, centuries before the hoaxster Claudius Ptolemy.

19. The members of Frederick the Great's Berlin Academy Voltaire, Maupertuis, and Algarotti were each and all assets of the Venice intelligence service's Abbot Antonio Conti, the latter the inventor of the Newton myth and the coordinator of Europe-wide operations of defamation and other harassment against Gottfried Leibniz and Leibniz's scientific authority. Voltaire, like Maupertuis and Algarotti, was a confederate of Pisa's Abbot Guido Grandi, and also of Giammaria Ortes, in Conti's project to secure the rehabilitation of Galileo Galilei, and to promote the highly exaggerated reputation of Newton as the “British Galileo.” Leonhard Euler was for twenty-five years also a member of that Academy, where he functioned as a “mathematician/hod-carrier” for the anti-Leibniz campaigns of Frederick's “favorites,” Voltaire, Maupertuis, and Algarotti.

20. Cf. Lyndon H. LaRouche, Jr., Christian Economy, op. cit., Appendix XI, “Euler's Fallacies On The Subject of Infinite Divisibility and Leibniz's Monads,” pp. 407-425.

21. For example, the development of so-called “non-Euclidean geometries,” as by Gauss, Bolyai, Lobachevski, and Riemann, superseding “Euclidean” formalism.

22. Just as simple hypothesis, expressed as an interdependent set of axioms and postulates, defines the principle of deductive consistency, so a principle of generation of a type of hypotheses, higher hypothesis, defines a higher, governing “consistency” among all members of array (lattice) of that type. Thus, the combination of Euclidean and all non-Euclidean formal geometries is a Many subsumed by a subsuming principle of purely constructive geometry, a principle which subsumes all possible formal geometries developed in the same axiomatic-revolutionary way.

23. See Lyndon H. LaRouche, Jr., “The Truth About Temporal Eternity,” Fidelio, Vol. III, No. 2, Summer 1994, secs. IV-V, pp. 15-23.

24. The use of capitalized One and Many here is employed to stress the implicit paradoxes and solution-principle of Plato's Parmenides.

25. As noted in the already referenced “The Truth About Temporal Eternity,” the generalized notion of hypothesizing the higher hypothesis is equivalent to Plato's idea of the Becoming. This notion exists in two forms. In the first, inferior instance, it exists as a transfinite conception, the Becoming; in the second, as an absolute notion, corresponding to Plato's Good. This equation of Cantor's “transfinite” and “absolute” to the “Becoming” and “Good,” respectively, of Plato is qualified in the location referenced. The difference between the transfinite and absolute notions, is between “physical space-time” and the same universality of all possible “physical space-time” free of the distinctions derived from introducing the notions of space and time. In physical space-time, development is defined by its position in physical space-time; in the absolute, development is the One which subsumes every time and everywhere. That latter One is a principle of Pure, Efficient, Creative Intelligence.

26. See Johann Bernoulli on the “brachystochrone” problem, in A Source Book in Mathematics, ed. by David Eugene Smith (New York: Dover Publications, 1959), pp. 644-655. Cf. A Source Book in Mathematics, 1200-1800, ed. by Dirk J. Struik, (Princeton, N.J.: Princeton University Press, 1986), pp. 391-399.

27. Christiaan Huyghens, A Treatise on Light (New York: Dover Publications, 1962).

28. Leibniz's notion is not to be confused with later empiricist efforts to concoct a contrasting, mechanistic principle of “universal least action.” The first instance of the latter, fraudulent concoction was Maupertuis' claim that he had been the first to discover a principle of least action. This Maupertuis brag was such a brazen fraud that even Maupertuis' former patron, the notorious Voltaire, was provoked to break openly with him. There were also protests against the folly of Maupertuis' scientifically illiterate brag from other immediate associates of the Berlin Academy, in addition to the protesting correspondence from the famous Aristotelian fanatic, and opponent of Leibniz, Christian Wolff. It is useful to note, in the context of the recent decades' antics by the famous “Primate among Parasites,” that the same Maupertuis invented the dogma copied by Giammaria Ortes [Riflessioni sulla popolazione delle nazioni per rapporto all'economia nazionale (Reflections on the Population of Nations in respect to National Economy) (1790)], which was later plagiarized by Thomas Malthus [An Essay On Population (1798)], which was the stipulated basis for the methods introduced to biology and social policy by Charles Darwin, and which the Huxley tribes succeeded in embedding in the axiomatic basis of modern empiricist biology and sociology.

29. See footnote 26.

30. This is the change of Heraclitus, and also the change which appears as the given hint for the solution of the ontological paradox posed by Plato's Parmenides.

31. “Assumed” = inference of the existence of unseen discrete objects, in the sense of sense-impression's objects, as, for example, in the very small.

32. Or, perhaps, in deference to Prince Philip's long leadership of the anti-Christian, anti-human, World Wildlife Fund, shall we say, more strictly, the “Brutish royal family”?

33. John Von Neumann and Oskar Morgenstern, The Theory of Games and Economic Behavior, 3rd ed. (Princeton, N.J.: Princeton University Press, 1953), chap. 1, “Formulation of the Economic Problem,” pp. 1-43.

34. Adam Smith, The Theory of the Moral Sentiments (1759) (emphasis added).

35. This 1776 work was the product of an assignment given to Smith by his employer, the British East India Company's Lord Shelburne, beginning 1763. That assignment was to prepare work which would assist Shelburne's British Venetians both in prosecuting London's wars to realize the objective finally realized in 1815, to subjugate France, and in crushing the upstart American colonist's insistence upon economic independence and self-government. Smith was assigned to work with the network of Abbot Antonio Conti's Voltaire and Physiocrats in France and Burgundian Switzerland, to devise a dogma of political-economy which was an adaptation of French Physiocrat dogma to the mercantile and financial inclusions of late-Eighteenth-Century British philosophical radicalism. From the standpoint of economics, the principal targets of Smith's enterprise were the continental cameralists in general, and Colbert and Leibniz in particular. Modern “chaos theory” is no more than a ideological buncombe, dredged out of the gutters of mathematical formalism, packaged to restate the moral indifferentism of the cited passage from Smith's Theory of the Moral Sentiments.

36. Clearly, Adam Smith's “Invisible Hand,” Senator Phil Gramm's remarkable achievement in vulgarizing even the vulgar Professor Milton Friedman, and the modern “chaos theorists,” are each and all preaching a secular form of a “mystery religion,” in the full-blown, Delphic heritage of the Apollo-Dionysus-Orpheus cult.

37. Cf. Michael J. Minnicino, Fidelio (to be published).

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