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|This article is reprinted from the Winter 1998 issue of FIDELIO Magazine.
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3. The principle of hypothesis
The formalist, such as that pathetic creature, the mere logician, is a reductionist duped into believing that definitions, axioms, and postulates are given implicitly beforehand (as if a priori). The formalist presupposes, that one might discover such definitions, axioms, and postulates by means of deduction, a method of deduction which presumes to recognize these terms as if they had been given a priori. On the basis of such presumptions, such as those presumed by an Aristotle or Immanuel Kant, it is decreed that all acceptable theorems are derived by deduction from those initial presumptions.
The Socratic method of Plato proceeds in a directly opposite direction.
With Plato, one begins with propositions being entertained as prospective theorems, and then follows the approach taken in his dialogues, as a way of searching out discoverable fallacies in those underlying presumptions (definitions, axioms, and postulates) which are the adducible motives for those propositions which our prejudices have imposed upon us. The challenging of such prejudices, provides the user of Platos method with what appears to be, for the moment, a refined array of mutually non-contradictory definitions, axioms, and postulates; this refined array, taken as a whole, is an hypothesis. For example, what was traditionally taught to modern students as Euclidean geometry was such an hypothesis.
The method of Plato starts with the recognition that all propositions, and, therefore, all hypotheses, including what were previously the most refined ones, must include some significant, axiomatic fallacy of some kind. In the method of Plato, we show that a sufficiently rigorous such exploration of previously accepted sets of definitions, axioms, and postulates, leads us to what are empirically contrary, mutually contradictory results. If that discovered contradiction is itself empirically truthful up to that point, then there must exist some previously overlooked, or unknown principlesome new definition, axiom, or postulatewhich, as correction, resolves that contradiction. The result of a validated such correction represents a radically new set of definitions, axioms, and postulates: in other words, a new hypothesis.
Truth, then, does not lie in any one choice of hypothesis. Such deductively consistent hypotheses are merely conditional upon such tests; there is no certainty of settled truth in any method of deduction. Truth lies in the always radically revolutionary process, by means of which valid new principles are generated, new principles which take into account the contradictions inhering in the previously proposed hypothesis. The method by which such new principles are ordered, in overcoming successively ordered contradictions, thus represents a notion of higher hypothesis, the latter a verifiable ordering principle which is demonstrated, repeatedly, to generate successively improved hypotheses. That notion of higher hypothesis coincides with the domain of reason, a domain above and beyond any mere logic, the domain within which truth and true knowledge lie.
Riemanns 1854 habilitation dissertation supplies us the exemplary case.
Given any physical hypothesis, eliminate all a priori notions of space, time, and other dimensionalities. In place of dimensions, employ principles which are each based on a crucial-experimental validation. These n principles, then constitute an n-fold manifold of physical principles: principles of physical space-time.
Next, given the case, in which experimental evidence shows a persistent error of magnitude in what had been earlier assumed to be a valid n-fold manifold.50 Take the case, that there be no experimental error internal to the n-fold manifold as defined previously. In the case that the self-contradictory evidence is crucially valid, there must be some previously overlooked, hidden physical principle, which accounts for the fact that an otherwise empirically validated n-fold manifold is contradicted by some adducibly persistent, crucial margin of error. The task posed is twofold: first, to discover a principle which resolves this contradiction, and, second, to provide a crucial-experimental demonstration of both the validity of the new principle and the factor which must be measured as the margin of difference between the characteristic of the n-fold and its replacement, the (n+1)-fold manifold which supersedes it.
The lesson of Platos Parmenides haunts us once more. In such a physical geometry, neither space by iself, nor time by itself, have an a priori, self-evident existence. Space exists only as an empirically defined physical principle; the same is the case for time. All other notions of dimensionality are subject to the same condition.
Such is Platos dialectical method. Instead of fashioning an hypothesis from sheer prejudice, or other presumptions, use the Socratic method of dialectical negation, to locate errors of presumption, and to adduce principles which not only account for the falsity of earlier presumptions, but which are demonstrably a guide to the needed corrections.
The exemplary case is Cusas discovery of a rigorous, superbly elementary proof, that, by the standard of Eratosthenes sieve, &Mac185; is what mathematician Georg Cantor later defined as a transcendental magnitude, rather than merely a Classical-Greek, irrational magnitude, as Eratosthenes contemporary and correspondent, Archimedes, had imagined it to be.51
To indicate the connection between Platos dialectical method and Riemannian manifolds, compare the earliest known, reasonably valid forms of ancient sidereal-solar astronomical calendars.52 From this, derive a relatively simple type of multiply-connected manifold.
The simplest quality of change defined in respect to solar-sidereal observation, from a position on the surface of the Earth, is the solar day: apparently a circular orbit. The next choice, for example, could be the solar year. The next choice, might be the complexity of the apparent movement of Moon and Sun. A next one, the equinoctial cycle. A next one, is the evolutionary change of the solar orbit, a phenomenon associated with the periodicity of ice ages. And, so on. Keplers adducing of the elliptical orbits from observation of Mars, is an example of this same approach.53
The universe, as far as we know it, is a wonderful, vastly, perhaps endlessly complex process. This complexity begins to be transparent as we attempt to define a relatively universal frame of reference, a reference with which to compare the depicting of some motion observed from a fixed point on Earth to the same motion represented by a more universal standpoint. As we increase the number of interacting orbits considered, and include sundry other kinds of regular, semi-regular, and other pulsations, we recognize that there could be no point in the universe so smally infinitesimal, that any interval of action could be linear. The universe is, thus, Leibnizs domain of a calculus of non-constant curvature.
That considered, we shift our focus from orbits and analogous periodicities and quasi-periodicities, to physical principles. We view the universe as a multiply-connected manifold of such physical principles. This is Bernhard Riemanns domain, in which we are supplied no estimate of foreseeable limits to the number of such colligating principles. We abandon the notions of dimensions in their naive sense, in favor of an orderable accumulation of successive physical principles.
Looking at this matter from Riemanns standpoint, we have a useful way of defining a transfinite architecture for scientific progress. For this purpose, scientific progress, as envisaged by Nicolaus of Cusa,54 is expressed in chiefly two ways.
In the first approximation, the experimental physical science of Cusa obliges us to recognize and prove outright fallacies, such as the fallacy of Archimedes argument on the squaring of the circle, in previously enshrined scientific opinion.55 In the next approximation, we are presented with more interesting challenges. In the leading features of the internal history of modern scientific progress since Cusa, we have to consider something other than pure and simple fallacies. In the best scientific work of discovery, we have to consider the cases, in which a particular colligating set of principles is in error only because it lacks some additional principle. On this account, at some point in the history of scientific progress, physics, for example, exhibits to us some newly discovered, persistent margin of empirical error, which we must suspect to correspond to existence of some previously unrecognized, additional physical principle. Thus, physical science assumes the form of a process of transformation from a valid n-fold manifold of physical principle, to a higher one of (n+1)-fold manifold.
In the latter type of case, we are presented with the case in which some physics, for example, was truthfully constructed, yet is shown, now, to be also untrue. This is a paradox of the type appropriately recognized as a metaphor. The discovery of the relevant new principle, together with the crucial experimental proof of that principle, is the reality which corresponds to that metaphor. So, in physical science, we give the name of the discoverers of the paradoxes and their solutions to the paradox and its solution, just as we give the name of a composer and of the relevant metaphor to a Classical-artistic composition.
In physical science, it is such experimental solutions to well-defined such paradoxes, which define knowledge, as distinct from mere learning. One knows a principle only if one has replicated the relevant paradox and its corresponding, discovered principle of solution. Knowledge is the accumulation of such replications of validated discoveries of principle. That is to emphasize, that knowledge lies in the succession of valid discoveries which have been mastered by the student, for example; what one may have learned in other ways, does not constitute knowledge. Merely passing written and oral examinations, does not measure knowledge, but, usually, measures only the inferior mental condition of mere learning.
This is precisely parallel to the case we identified for Classical artistic composition. The composition does not lie in the details produced, but rather in the process of development which lies outside and above anything so produced. Just so, the paradoxes which force the audience to recognize the need for a higher principle of change, shift the location of the drama (for example) from the literal features of the composition, to the principle of ordering which underlies the succession of changes in state, those transformations of hypothesis, which is the unity of the entire composition.
To restate the crucial issue once again: Reality does not lie in a deductive form of representation of experiences as those phenomena are situated in terms of a fixed hypothesis. Reality lies in that higher authority which exists above any one hypothesis, which exists in the ordering of a valid succession of hypotheses. The reality experienced in that succession, is the substance of the experience of this succession. That is the crucial ontological issue of physical science; there lies the efficient interconnection between the ordering of realized scientific progress and the development of the principles of Classical culture.
At this point, on this account, a deeper problem confronts us.
The more thoroughly we attempt to exhaust the lessons of physical scientific progress as such, such as a Riemannian representation of such progress, the more stubbornly a certain perplexity confronts the scientific thinker. There are two leading issues. First, what is the nature of that creative process, by means of which the mind generates valid solutions of principle for crucial experimental-scientific paradoxes? Second, what is the active ordering-principle associated with such valid discoveries of principle? If we reflect carefully on what these considerations imply, we must recognize that there is no adequate formal-scientific answer for these two questions. This leads us to discover a second manifold, an m-fold manifold of principles of Classical-artistic composition. This m-fold manifold expresses the passion, the driving and directing force which underlies and otherwise governs both scientific and artistic progress.
4. Order in physical science
Since Platos dialogues, the leading intellectual currents of European civilization have focussed upon the implications of a certain central paradox, a central metaphor, as the central issue of scientific principle respecting our universe taken as a whole. From the root supplied by Platos emphasis upon a parallel between the characteristic of living processes and principles of musical composition, Plato, Luca Pacioli, Leonardo da Vinci, and Johannes Kepler, among others, have emphasized two qualitatively distinct kinds of ordering within the physical universe: those orderings cohering with the Golden Section, and those which do not. Living processes, in particular, cohere with the former, but, as Kepler emphasized, also ostensibly non-living systems, such as the Solar System as a whole. For our purposes, we associate non-living systems generally with entropic processes, and living ones as the most exactly paradigmatic expression of not-entropic processes in general.56
Perhaps the most efficient approach to conceptualizing those distinctions, is the case of the not-entropic physical-economic process. There is nothing to be properly viewed as accidental in this view of physical economy. The central practical question of all knowledge, is the question: Is mans knowledge of the physical universe, merely his conceit, or is there some objective proof, by means of which one kind of thinking corresponds, demonstrably, to the lawful ordering of our universe, and a contrary kind of thinking does not? In this matter, there ought to be no objection to the proposition, that the test of human knowledge is posed by the question: Does a certain method of transformation of human knowledge result, unquestionably, in a process of increase of mankinds mastery of the universe?
The general form of the answer to this question, appears at the moment, we shift the issue of mastery, from focus on the practice of the particular, isolated individual, to measuring the increase of the human species power to increase its per-capita power over nature. This increase must be defined with the attached condition, that the potential relative population-density is also increased by this change. To express this connection in a rigorous way, we must introduce the notion of the progressive ordering of higher hypothesis and increase of mankinds potential relative population-density.
We are confronted, then, with two distinct, but interdependent aspects of the human species increase of its potential relative population-density. One, is the relationship of the human species to the given biosphere within which it is presently, or recently located; the other, is the actions of mankind affecting the increase of potential of the biosphere to serve as a foundation for increase of mankinds potential relative population-density. The simplest way to force attention to these combined considerations, is to look at such challenges of the coming century as colonizing another planet, or even terra-forming it.
Ask ourselves: Given, the total set of preconditions, including the biospheres current state of development, upon which we must depend for the per-capita and per-square-kilometer perpetuation of the total current output of our species. What must we produce, to maintain at least a continuous supply of that quality and quantity of consumption?
Situate the notion of potential relative population-density, per capita and per square kilometer, in respect to investment in maintaining and improving the output of our species, per capita and per square kilometer.
To this purpose, we must place emphasis upon the demographic characteristics of the population. Rate of growth of the population, is a consideration. Consider life-expectancy, examined for the cost of developing a new individual, as against the loss to society from high rates of infant mortality and lowered life-expectancy in general. For example, consider the quality of development of the physical-economic investment by the society in scientific and technological potential of the new individual as a desired improvement in the physical-economic demographic characteristics of the population.
Consider some elements of basic economic infrastructure: transport, water, and energy. To the extent we can slow down the rate at which water, originating as rainfall, is emptied into the seas and oceans: in how many ways can the useful turnover of that water-flow be increased? Can we increase, thus, the effective amount of water available per capita and per square kilometer? How can we better manage forests, fields, and so forth, to increase and effectively maintain water-tables, streams, and create weather-systems which moderate weather and increase the amount of rainfall regenerated from evaporation? How can we better develop water as a means of relatively low-cost transport, while also using the same water for other purposes? Similarly, how can we increase not only the raw energy supplies per capita and per square kilometer, but how might we also increase the effective energy-flux density deployed per capita and per square kilometer, for the benefits expressed in the environment generally, and in per-capita productivity?
As we increase the range of applied scientific principles and derived technologies, we increase the complexity of the division of labor. We also increase the level of education required to produce a population which has assimilated a relatively higher level of scientific and artistic principles. This requires an increase in the number of years, prior to biological maturity, devoted to education and related matters; that expenditure for education and Classical culture, is a part of the necessary cost of increasing and maintaining the potential productivity of the population, per capita.
For the simplest representation of the result, we divide the physical-economic output of society into three categories: Total useful output, cost of maintaining that magnitude and rate of total output, and the ratio of total output to total required inputs, the latter including the necessary maintenance and further development of basic economic infrastructure. To maintain a culture, is therefore expressed in the following general constraints. The technological level must be raised; total output per capita and per square kilometer, must increase; yet, the ratio of total output to total required inputs, must increase; meanwhile, the total required inputs, per capita and per square kilometer, must also increase. This set of constraints typifies a not-entropic process. This physical-economic model must be used to supply a competent, rigorous definition of the very terms not entropic, or anti-entropic.
The physical-economic condition under which that not-entropic requirement is satisfied, expresses the result of applying the creative-mental potential of the species to mans increasing power over nature. The creative process so realized as applied advances in knowledge, expresses the lawful composition of our universe. That is, the condition under which mankinds willful actions, to proceed from a previous to a higher quality of hypothesis, satisfy that not-entropic requirement, expresses the power of our species to command such obedience from the universe in general. In other words, the universe as a whole is lawfully non-entropic. In competent science, no law of universal entropy is tolerated.
Consider two additional implications of this physical-economic expression of anti-entropy: first, the form in which anti-entropy is expressed in terms of a Riemannian n-fold manifold of physical principles; second, a similar expression in Classical art-forms. The simpler case is the straight realization of an n- to (n+1)-fold progress in discovery of scientific principles as realized technological progress in the productive powers of labor. The second case, is that of increasing density of discovered and realized Classical-artistic principles. In both implications, anti-entropic action is of the form and content of F[(n+1)/n], or, F′[(m+1)/m]. It is through this action upon the universe by the creative powers of the individual human mind, that human activity realizes anti-entropic growth, and related progress, in mankinds relationship to the universe at large.
Clearly, in addressing the notion of anti-entropy in a more general way than is required by the subject of culture as such, we could not overlook two other cases. First, obviously, we must take into account those characteristics of life as such, which lie entirely outside entropy, as these are expressed, for example, in the development of the biosphere even before the existence of the human species. Second, we must go further, as Plato, Pacioli, Leonardo, and Kepler did, to recognize that the same principle of anti-entropy underlies the deeper principles of ordering in the universe at large.
Pending that attention to these latter two, other expressions of anti-entropy, the crucial fact on which to focus here, is that human creativity occurs solely within the bounds of the individual mental-creative processes, and does not occur as a product of interaction among those individuals. That is to stress, that all evidence of that creative mentation which generates either a validated new physical principle, or comparable principle of Classical artistic development, occurs only within the individual mind. Such discoveries of principle can be spread in society, but only through replicating the original act of discovery, one mind at a time.
The special fact to be stressed here, is that Classical artistic creativity, as typified by Platos notion of the idea, is the only case in which the creative powers of the individual mind are applied directly to those creative mental processes themselves. It is the study of the progressive development of those social processes associated with progress, in terms of Classical-humanist art-forms which, alone, provides the human mind access to comprehension of the potential of the individuals human creative processes themselves. Therein lies the manifestly superior position of Classical art-forms over all other forms of knowledge. The treatment of education from the standpoint of Schiller and of his friend Wilhelm von Humboldt, represents, thus, the highest expression of statecraft, the development of those young minds which must supply future progress in statecraft.
5. Education and the Tragic Principle
The essential issue of an individuals personal morality, is posed by the question, whether personal self-interest is located as the fascists such as Nazi existentialist philosopher Martin Heidegger did, in the pettiness of day-to-day and similarly small-minded personal and family responsibilities and gratifications, or, rather, in terms of the outcome one seeks for ones life, from birth to death, taken in the totality of that lifes outcome for the past and future existence of the human species in general. This requirement must be read as a life conducted to supply an enhanced role for ones participation in ones culture, ones nation, a life lived as the instrument through which the universal outcomes of ones life are realized.
Restate and amplify that crucial issue of morality as follows. The essence of the individuals life, is the simple fact, that each among us is born and will die. On this account, the fundamental self-interest of each individual is located in the continuing outcome of that mortal life, an outcome which reverberates far beyond the time prior to ones birth, and after ones demise.
The corresponding peculiarity of that individuals self-interest, in absolute distinction from the nature of the beasts, is that our effect upon the importance of the individual for the human species as a whole, is located in the value for all mankind of those Platonic ideas which represent the accumulation of valid, discovered principles of the universe which we have assimilated from our forebears, and will thus, and otherwise transmit to our posterity. These ideas include not only the n-fold manifold of physical science, but also the m-fold manifold of cultural principles.
That view of ideas, is the basis upon which the thoughtful persons asks, What is the outcome of my having lived? Is it, perhaps, the deeds I do, or the pain or pleasure which I experienced? Or, is it something less mortal, less perishable than mere deeds, mere acquisitions, mere pleasures? What endured when Classical Greece died?
What was enduring was the efficiency of those ideas corresponding to validatable discovery of principle. When we relive the valid discoveries of those who have gone before us, we perpetuate the good they have bequeathed to us, and we relive in ourselves that which is enduring, which they have given to us in this way. Thus, we, the bearers of the gifts of knowledge of ideas from past generations, may not only perpetuate the precious ideas passed down to us from earlier generations, even after the death of those ancients, but we may add something valid and new to that stock of principles to be transmitted to the benefit of the future. In such ways, we may impart living immortality to the gifts of the past, and become also a necessary part of that which follows the end of our mortal existence.
Persons who meet that standard, become world-historical beings. They never die, because that which is essential in their having lived, lives on as the benefit which ideas from the past have bequeathed to the future.
Consider the pupil from the elementary and secondary grades of education. Consider the pupils education from the standpoint just summarized.
Is it important that the student learn in school? Or, is it relatively unimportant? Know, that learning is almost nothing; know that knowing is almost everything. The essence of morality in all education of the young, is the replication of the act of discovery of valid ideas. When the student has generated, or replicated the act of a validatable discovery of principle, he or she knows that principle, and is able to transmit it to others, not as mere learning, but, rather, as knowledge for practice. A moral educational institution, is one in which the pupils relive the experience of knowing valid principles, both those principles relived, as discovery, from the past, or added to the stock of such principles. That connection to ideas, rather than mere learning, locates all of us who follow the path of such ideas, both as students and adults, as a continuation of the history of ideas, as a person embodying the past in acting to create the future.
The order in which notions of principle are generated, is the procession of history. Only persons who locate their personal self-interest and identity in that kind of relationship to ideas, are world-historical individuals.
Consider again the difference between the definition of morality in the mouth of a bestialized existentialist, such as a follower of Nazi philosopher Martin Heidegger, or his depraved clone, Jean-Paul Sartre. The existentialist has merely learned; he, or she lacks that notion of morality natural to a world-historical individal. That existentialist, that follower of Thomas Hobbes, John Locke, or Immanuel Kant, has no true morality. It is the continuing outcome of my having once lived, which is the essence of the known self-interest of the world-historical individual. My pleasures, my pains, my losses, my gains, are as nothing compared to what I gain, or lose, in securing, or failing to serve the immortal meaning of my world-historical existence.
Situate Platonic ideas as existing, ontologically, within the domain of higher hypothesis. Reality is, thus, that process by means of which mans mind is transformed from relatively lower, to higher states, as from the state of a relatively valid n-fold manifold of physical science, to a higher one, (n+1)-fold. Or, in respect of moral principles, from m-fold, to (m+1)-fold. The process of change, in Heraclitus and Platos sense of change, is the location of the continuing substance of change, from relatively lower to higher states.
In this view, every person who meets the moral requirement of being, effectively, a world-historical individual, dwells in the eternity of change. In other words, in the brief time we live and act as world-historical individuals, we exist forever, in the simultaneity of eternity. So, each of us must be judged. So, each of us must judge himself or herself. So, our conscience is to be ruled in all matters of moment-to-moment behavior; so, our conscience must situate our notion of our primary self-interest, our interest as efficiently located within the simultaneity of eternity.
That view, which locates the fundamental self-interest of both the individual person, culture, and nation, as its world-historical self-interest, is the standpoint from which Classical tragedy is to be composed, performed, and assimilated; this is the standpoint of Aeschylos Prometheus Bound, and the tragedies of Shakespeare and Schiller. What is the world-historical interest of a Prometheus, enduring immortal torment, that he might keep the secret, and thus ensure the self-induced doom of those common enemies of the Creator and mankind, the ruling oligarchy of satanic Zeus Olympus? What is the world-historical duty which Hamlet, as Prince of endangered Denmark, must adopt, overriding all merely personal issues to the end of serving that duty? What were the world-historical duties variously shirked by Posa, Don Carlos, and King Philip? It is that world-historical view which must excite our passions to do good, to act as, and to be a world-historical person rooted in the simultaneity of eternity.
Consider a more general expression of the world-historical issues so defined.
Until the revolutionary changes introduced by the Fifteenth-Century Council of Florence, and by the ensuing reconstruction of France under King Louis XI, approximately ninety-five percent of mankind, in all cultures, lived in a condition of degradation to the status of virtual human cattle. The society within which these human cattle were herded, was a society ruled by an oligarchy. This oligarchy was composed of a blending of several types: a landed aristocracy, such as that of feudal Europe; a financier aristocracy, such as that of Venice or todays London; or an administrative oligarchy of the bureaucratic type. The definition of law under such oligarchies, was, predominantly, a privilege of the ruling oligarchy, an oligarchy which possessed the society and its people, as a feudal landlord of Dr. François Quesnays evil type owned land, cattle, and serfs.
All forms of oligarchical society, including the principle of western feudal Europe, as of Byzantium, were, and are essentially evil. The essential evil in all forms of oligarchical society, is the denial of the individuals right to participate in the rule of society by the process of development of valid ideas. In other words, the essence of evil, is the crime of the very mere existence of satanic Zeus Olympian oligarchy, or, Olympus surrogate, the cult of Apollo (Apollo-Gaea-Python-Dionysus). The essence of evil is the denial of the right to be developed, and to become a world-historical individual, a participant in the simultaneity of eternity.
At this juncture, a crucial point must be interpolated. U.S. President Polk was an evil man, and his war against Mexico was a crime against the vital interests of the United States. On these matters, U.S. Representative (and later President) Abraham Lincoln was consistently right; but, on the larger issues of culture, Henry David Thoreau was a wicked man. There was no more evil doctrine ever concocted, than the myth of the noble savage, or the related notion of the nobility of the simple life.
Indeed, the role of the British agents, and agents of influence, Philippe Egalité, and the Jacobins Danton, Marat, Robespierre, Saint-Just, et al.,57 exemplifies the evil which shocked such German apostles of liberty as Friedrich Schiller. The instrument which these sundry British agents and assets mustered to destroy France from within, was the rabble called into Paris for such enterprises as the storming of the Bastille, for Philippe Egalités raid on Versailles, and the Jacobin Reign of Terror.
Although the philosophical basis for the overcoming of oligarchical society was supplied by Plato et al., the actual transformation was the cumulative result of Christianity, the ministries of Jesus Christ and the Apostles John and Paul most notably. The obvious root of the modern notion of freedom and equality, is the principle first established by Christianity, that all persons are equally made in the image of the Creator, with no preference to one or another national, cultural, or ethnic discrimination allowed. Notable, is the fact that this work of Christianity was undertaken within the scope of a Hellenistic Mediterranean culture which was derived from the Classical Greek of Plato and his influential Academy. The Apostles John and Paul made that cultural heritage of Plato the medium in which the Christian mission was continued. It was these Christian Platonic conceptions, typified by the role of the Augustinian tradition, which became the leading edge of the centuries-long struggle out of which the Fifteenth-Century Golden Renaissance emerged.
That struggle, typified by the work of Abelard of Paris, of Frederick II, of Dante Alighieri, of Petrarch, of teaching orders such as the Brothers of the Common Life, and so on, was a struggle to establish a form of society based upon the nation-state, rather than some oligarchical classes which placed themselves above accountability to the idea of a nation as belonging to its people, rather than some intrinsically oligarchical institution placed above the people. This idea of the nation-state republic had nothing to do with the perverted notions of democracy associated with John Locke, but rather, the accountability of the ruling institutions of society to the principle of universal truth and justice, the principle that all persons must have the right to develop and live as world-historical personalities.
There are two great evils predominating in the known existence of our species. One, is the evil of oligarchism, as typified by the administrative oligarchies of ancient Mesopotamia and Rome, the feudal aristocracy of Europe, and the financier oligarchy of such institutions as the Delphi cult of Apollo, Venice, and London today. The other great evil, is the moral degeneracy deeply imbued in those subject populations whose moral condition and impulses have been degraded, by oligarchical rule, into the relative bestiality of human cattle. The practical ordinary person may have the nobler impulses of the human individual, but, under oligarchical traditions, the circumstances of practical life cause that person to be self-dominated by relatively brutish, practical considerations. Therein lies that evil among the ordinary people, by means of which, usually, oligarchy preserves its control over the popular will.
The great issue of culture, is the task of freeing the majority of the population from that moral and intellectual self-degradation which tradition imbues within prevailing popular opinion.
The issue of individual human freedom, is not the issue of democracy, not democracy as the moral degenerates of todays National Endowment for Democracy misuse the term, not like degenerates such as John Dewey, nor as Nazi-like existentialists such as Schopenhauer, Nietzsche, Heidegger, and Jean-Paul Sartre generally define democracy. The issue is the right of every newborn child to be developed in a way which represents access to, and imposition of the rule of truth and justice, to ensure that quality of progress in the human condition which meets the need of the individual to be a world-historical personality, to be a resident of the simultaneity of eternity. This means the obligation of society to direct the shaping of the policies of practice of the society to bring about progress in such upward directions of individual world-historical participation in ideas.
The essential feature of persons who lack freedom, is their emulation of the condition of human cattle. They are conditioned to respond to what human cattle would consider the matters of personal self-interest, the motives of the Seven Deadly Sins, the motive of my narrowly defined personal and family self-interests, and of society as a whole, either a poor second, or, like the typical existentialist, virtually not at all. It is their attachment to those baser motivations which constitutes the shackles upon the self-enslaved individual degraded to a moral condition like that of virtual human cattle. These are the motivations of the Ku Klux Klanner and similar Jacobin rabble. For such human cattle, the definition of freedom to choose is nothing other than those depravities by which they are self-enshackled into the moral condition of virtual human cattle. It is by such libertarians moral self-debasement, pursued in my personal interest, or, my freedom to choose, that the popular masses usually choose the pathway to their own self-debasement and oligarchical enslavement.
It is these world-historical concerns which define morality and true Classical culture. It is those principles of culture, of social and political life, which correspond to advancement of the condition of the individual and society to higher states, to relatively more not-entropic states, which represent the m-fold manifold of culture. The relationship between the m-fold and n-fold manifolds, is that the social requirements of progress in the former respect must direct the practical requirements of the latter respect.
The essence of freedom, is the right to define oneself as a world-historical individual, rather than some self-debased libertarian fool.
The essential difference between the raw, half-educated human being, and what Schiller identifies as the beautiful soul, is located in the kind of change in the adolescent personality (for example) accomplished by aid of the kind of Classical-humanist education upon which stress is placed here. The point at which the individual passes over from a raw, morally semi-literate brute, into a beautiful soul, is the point at which the student (for example) makes a qualitative transition, from selfishness to the moral impulses of an efficiently conscious world-historical personality. It is at the point, that the moral imperative of judgment, of personal commitment, is located entirely in a sense of devotion to ones world-historical soul. That transformation in the individuals sense of personal, world-historical identity, is the proper object of education; that transformation represents the threshold at which the immature adolescent (of all ages) is superseded by spiritual metagenesis into emerging as a true, world-historical citizen of a republic.
6. Classical composition
The general moral requirement which sets Classical forms of artistic culture apart from, and above all alternatives, is the urgency of freeing human beings from the degraded state describable as symbol-mindedness.
In plastic art, for example, Leonardo da Vinci exemplifies the duality of all Classical art. This duality is expressed, on the one side, as the obligation to subordinate the composition of plastic art to scientific truthfulness. On the other side, truth demands that we recognize the ironies, the metaphors, to which we must be led by any truthful scrutiny of principles of composition. Leonardos revolutionary view of the vanishing-point, is an example of this ironical principle.58 The role of two sources of light in Leonardos Virgin of the Rocks, is a model of such metaphor.59 The fact that Raphael Sanzios The School of Athens60 and Transfiguration must be conceptualized as the integration of the ambiguity of two (lower versus higher) viewpoints, is another.61
These ambiguities oblige the mind to abandon the literalness of sense-certainty, to subsume contradictory impressions by a resolving metaphor resident within the domain of ideas. In other words, to abandon deceitful sense-certainty, and also the intellectual and moral degradation expressed by the symbolic, or, related, mannerist views of art, in favor of truth.
Take the exemplary case of the Acropolis. Studies show that the Acropolis is the result of the unfolding of a single, coherent plan, always subsumed by the Classical Greek notion of Golden-Section-pivotted beauty in plastic art.62 In effect, the resulting construction has the quality of a single, if polyphonic act of composition.63
Now, shift the focus: to, first, the principle of Classical tragedy, next, science in its aspect as a moral principle of art, and, finally, the substance which subsumes the process of development of Classical motivic thorough-composition, from J.S. Bachs development of polyphony, through the elaboration which Haydn, Mozart, Beethoven, Schubert, Brahms, et al. developed on the basis of the always-polyphonic foundation supplied by the later composers study of Bachs work.
In their entirety, the dialogues of Plato, are exemplary works of Classical art. When the Homeric epics and the related Classical Greek tragedies are taken as the standpoint of reference for the entire body of Platos collection of dialogues, we are able to trace the modern tragedies of Shakespeare and Schiller from this route, and also situate, similarly, the role of Platos and other Classical-Greek models in the late-Eighteenth- and early-Nineteenth-Century efforts to revive the Classical tradition in poetry and drama. The most fruitful standpoint from which to view this entire Classical tradition, from ancient Greece into the Nineteenth Century, is the standpoint of historian-poet-tragedian Schillers intended audience, the audience transformed into better people leaving the theater than had entered it a few hours earlier.
The essential feature of the Classical tragedy, and poem, is to induce the members of the audience to situate themselves as world-historical figures, as persons provoked into viewing the Classical performance as the prompting of the viewing of the subject-matter from a world-historical standpoint. In other words, the member of the audience must adopt a sense of world-historical responsibility for the real-life issues addressed by the drama or poem: Could such characters not see the nature and consequences of their folly, for their society in their time? Must we, in our time, not learn the lesson of this, that we, in our time, must address the issues specific to our historical setting as those should have done in the historic specificity of the time shown on stage?
To this end, it is essential that a Classical tragedy never be dressed up in modern costume, or otherwise presented as a timeless fable equally appropriate to past or present times.
The essence of history is the history of ideas. History is a record of variously forward, backward, and sideways movements in the course of mankinds obligation to progress to the level of higher manifolds of both physical-scientific and moral practice. The sundry diverging and interwining branches of the sundry, forward, sideways, and degenerative developments, are the skein of history, the skein of reality. The essential problem of historiography, as Classical tragedy exemplifies this, is to develop and maintain a sense of historic specificity in respect to the evolving mental, moral, and physical condition of mankind.
This sense of historic specificity, is best conveyed by Schillers work in his functioning as both historian and tragedian. Significant ideas, if they are true, are never mere fiction; they are matters of historically specific kinds of ideas as they are situated, as a matter of principle, with respect to specific historical problems. It is a keen sense of the actual history in which these ideas are situated, which enables an audience to adduce a truthful sense of the solution to the paradox presented by the Classical tragedy.
The same rule of historic specificity applies to the history, and prehistory of modern music. Without the influence of the Fifteenth-Century Florentine bel canto voice-training, the development of Classical well-tempered polyphony, by J.S. Bach, would not have been possible. Without the indirect influence of J.S. Bach, as through C.P.E. Bach, Haydns pre-1782 contributions to musical development would not been possible. All of this is intermingled with the influences of the Italian schools, such as Alessandro Scarlatti, et al., on the musical development of pre-Nineteenth-Century northern-Germany and southern-Germany music. Without the direct influence of J.S. Bach upon Mozart, Beethoven, et al., from the early 1780s onward, the post-1781 works of Mozart, Haydn, Beethoven, et al. had not been possible.64 The entirety of the development of well-tempered, polyphonic forms of motivic thorough-composition, from Bach through Brahms, is a sequentially ordered process of successive developments of musical ideas.
This process of development, in music, in Classical tragedy, in Classical plastic arts, has a metrical quality. There are sequences, if not always simple, linear ones, and there is also a sense of density. Both notions, of sequence and density, are to be compared with the notion of Riemannian and quasi-Riemannian notions of interacting m-fold and n-fold manifolds.
The case of music
In our focussing upon the case of music, here, we emphasize the importance of situating the particular development and performance of Classical musical composition in some medium whose primary content is nothing but sequence and density. This signifies that we must define a specific quality of impassioned idea which parallels and underlies the development of the composition and performance of Classical polyphony. This medium of passion is not hearing as such, but rather an idea of composition, addressed to the medium of hearing, but an idea superimposed upon hearing.
In music, certain things come naturally. Primarily, the human speaking-singing voice is naturally predisposed to what are termed register shifts. Although there are additional means which may be developed for the purposes of Classical-poetical coloration and dynamical expression of the human singing voice, natural registration is the dominant feature underlying both polyphony in general and the well-tempered polyphony clearly defined, in exemplary fashion, by Bachs polyphonic works for both singing and instrumental voices combined.65
The Florentine bel canto demonstrates the register-shifts most effectively. The effect of bel canto development, respecting the ratio of effort to what is heard, demonstrates the unique agreement of the bel canto voice-training with the natural potentialities of the voice. Similarly, voices which perform at a bel canto-determined C=256 survive longer, and better, than those burned out prematurely by overwork at artificially elevated pitches at, or above A=440, for example.
Then, once the ranges of the register shifts of the respective species of singing voices are determined, the mere task of employing a relevant counterpoint for such polyphony defines a primary approximation of a bel canto-determined well-tempered scale. At that point, a further refinement is required. The mind hears the inversion of any interval (e.g., C-E-G heard as G-E-C), to such effect that a simple Lydian scale is derived as an inversion of a C-minor, F# pivotted scale. The effort to bring the intervals represented by the scale indicated by the inversion, with the scale which has been inverted, introduces a further degree of refinement of the well-tempering. Add, then, inversions heard across the polyphonic parts to the inversions generated within each part, and a further refinement is introduced. Never is a precise, algebraic frequency determined; the infinitesimal approximation is always a non-linear one.
In other words, if we continue polyphonic and related developmental considerations, there is no simply algebraic determination of a well-tempered scale, but rather a counterpoint-determined interval of non-constant curvature, just as Johannes Keplers approach, and Platos earlier, point in that direction.
Once we pass from the level of considerations posed by J.S. Bachs A Musical Offering and The Art of the Fugue, into the generalized use of Lydian intervals by Mozart in the manner epitomized by his K. 475 (and, later, Beethovens Opus 111), the span of Classical musical development, from Mozart of 1782-1783 through Brahmss Vier Ernste Gesänge, is opened up for us as a process of motivic thorough-compositional development, a process of increasing density, in the sense of Riemannian series of the n-fold type. When we combine the apparent, formal considerations with the implications of a new mode of song composition, by Mozart, Beethoven, Schubert, Schumann, Brahms, with all of the resulting interpretive considerations bearing upon the training and use of the singing voice, all Classical musical composition opens up for us through this Rosetta Stone-like medium of Classical song.66
On this account, the musician must hear with two sets of ears. One is the ear of simple hearing; the other, the minds ear, which locates the driving passion of a composition in its developmental processes of change, the latter the ear which, like Wilhelm Furtwänglers, sings between the notes. In music, for Pablo Casals, as for Heraclitus and Plato, nothing is constant but change. It is that principle of change which is the ontological foundation of all Classical art. In music, that foundation is located in the developmental process of constant change, which is the minds ear.
Thus, when we sing with Bach, Haydn, Mozart, Beethoven, Schubert, Schumann, Brahms, and so on, we are expressing the essence of that playful domain in which the ontological essence of all art, and all morality, are supplied the ontological medium best suited to their expression. On this account, all great Classical music is, in its own way, sacred music, the souls yearning toward its rightful, beautiful place in the simultaneity of eternity, as Bachs great student, Ludwig van Beethoven, best understood this.
Truth in statecraft
At this moment, the worldincluding the United States itselfis securely embarked on a journey to Hell, and, although the helmsman, including the current President of the United States, might deplore the ruin reaching to engulf us all, that President, thus far, has shown no inclination to reject the course of action, in economic policy, which ensures the impending destruction of both the United States and civilization as a whole. Although the President deplores the injustice and other sufferings into which the current direction of policy is carrying us all, so far he is unwilling to reject any of those of his own current policies which contribute to ensuring the worst result.
Take the case of the modern-day Henry Morgan, British privateer George Soros. Soros is outstanding among those whose predatory role has ruined such nations as Russia, and all among the nations of Southeast Asia, and much of East and South Asia otherwise. Yet, as in the case of looted Croatia, or Russia, the U.S. government repeatedly defends the role of Soros and his kind in destroying these nationssuch as Malaysia, Thailand, Indonesia, the Philippines, etc., and in fostering those lunatic policies of the IMF and others which ensure the homicidal ruin of most of those economiesincluding our ownwhich the U.S. government professes itself dedicated to defend.
How is such folly possible? How is it possible that a President manifestly inclined to deeds of good will, could act so stubbornly contrary to the vital interests of his own administration, his nation, and civilization as a whole?
Two interacting factors are among those prominently to be considered. One is the political pragmatism of a heavily besieged President. The second, leading, interacting factor, is the Presidents own laundry-list of chosen agenda items: globalization, democracy, information economy, achievements of the Golden Generation, etc. On this account, the prevailing, implicitly suicidal policy-shaping trend is, that the choice of certain policies as our policies, becomes not merely a substitute for truth, but, in practice, its direct opposite.
For example, for the better part of thirty years, the U.S. physical economy has been contracting consistently at rates averaging in excess of two percent per year. Over most of that period, a formerly (1946-1966) prosperous agro-industrial economy, has been looted by financial parasites, transforming a prosperous economy into what is now threatening to explode, momentarily, as the greatest financial bubble-collapse in world history. During the recent quarter-century, the physical-economic income and output of the U.S. population, per capita, has been contracting. The number of jobs taken, per household, in a futile effort to maintain a falling income-rate, does not keep up with the rate at which average household income is contracting. Yet, the current administration speaks of the successes of this economy, praising the futility of increasing the number of jobs by methods which reduce the per-capita family income for all but the super-rich parasites of Wall Street and like precincts! What happened to the truth?
To make short of a long list of kindred clinical evidence, we have come into a time when democracy has become a synonym for a fanatical sort of lying. Whatever is perceived to be popular opinion, whether it is actually popular opinion, or not, becomes the adopted policy which governs practice, that in defiance of all truthful evidence, and contrary to all sane reason.
Down among the hoi polloi, this folly is expressed as: I dont care what you say, I have a right to my personal opinion, even when the evidence is entirely contrary to that misguided opinion. Truth is no longer a standard for policy-shaping practice. Such is the condition of a society which has lost the moral fitness to survive, the condition of a democracy which no longer either deserves to survive, or will survive. Such democracy is the sure road to a hellish tyranny under a regime whose subjects will, for better or worse, do precisely as they are told.
The root of this loss of moral fitness to survive, is readily and accurately traced back to such plainly immoral creatures as Paolo Sarpis Francis Bacon and Thomas Hobbes, to John Locke, Bernard Mandeville, David Hume, Adam Smith, Jeremy Bentham, Immanuel Kant, Karl Savigny, and John Stuart Mill. On the one side, public and private morality is divorced from science; on the other side, science is divorced from morality. In the meantime, popular morality itself is degraded to the level of Mandevilles followers among the Eighteenth-Century British Hell Fire Clubs, the level depicted by Hogarth, the level of Hell as depicted in the most famous triptych of Hieronymous Bosch. The essence of our self-destruction during the recent thirty-five years of our downhill slide, has been the growth of what passes today for popular opinion and popular culture.
Where are the men and women fit to lead us out of this peril? Where are those who will lead in the pathway toward safety, the pathway toward rule by the principles of truth and justice, not popular opinion?
50. Treat Wilhelm Webers correction and proof of Ampères notion of a longitudinal , or angular force as an example of this. See Laurence Hecht, The Significance of the 1845 Gauss-Weber Correspondence, 21st Century Science & Technology, Fall 1996.
51. See Lyndon H. LaRouche, Jr., On The Subject of Metaphor, Fidelio Fall 1992. See also Nicolaus of Cusa on Learned Ignorance, trans. by Jasper Hopkins, pp. 52-53, and On the Quadrature of the Circle, trans. by William F. Wertz, Jr. Toward a New Council of Florence (Washington, D.C.: Schiller Institute, 1995), pp. 595-610. Compare Archimedes, Measurement of a Circle, and Quadrature of the Parabola, in The Works of Archimedes, T.L. Heath, ed. (New York: Dover Publications), pp. 91-98 and 233-252. See also Lyndon H. LaRouche, Jr., The Ontological Superiority of Nicolaus of Cusas Solution Over Archimedes Notion of Quadrature, Fidelio, Spring 1994, pp. 31-34.
Contrast the popularized, academic delusion, which, like Professor Felix Klein, insists that the proof of the transcendental quality of &Mac185; was first established by the successive work of Hermite and Lindemann. Note, that Klein himself traces the hereditary origins of Hermites and Lindemanns argument to what was in fact an outright, petitio principii hoax by Berlin-based avowed enemy of Gottfried Leibniz, Venetian asset Leonhard Euler. Eulers argument against Leibnizs monadology rests upon Eulers arbitrary adoption of an axiom which presumes perfect continuity of linear extension, down to the smallest infinitesimal. Eulers proof, and the derived arguments of Hermite, Lindemann, and Klein, is thus a product of Eulers assertion, as an axiom of his argument, of the very conclusion, against Leibniz, which he professes to have proven.
52. As a result of the ideological fanaticism of the British Israelite movement, the growth of political influence of Venices clone, the Anglo-Dutch financier-maritime oligarchy, wild-eyed hoaxsters such as the London-based Victorian archeologists degraded archeology in general virtually to a search for the exact street address of Abraham in ancient Ur. As a result of this British cults influence, the most generally accepted doctrines respecting history, physical science, and culture generally were pivotted upon the notorious Bishop Ushers dating of Creation to an event located in Mesopotamia circa 4004 B.C.E. One consequence of this British Israelite hoax, is the popular delusion which dates astronomy from the lunar obsessions of early Mesopotamia. Similarly, although it is readily demonstrated that the earlier civilization in Mespotamia was the Dravidian colony known as Sumer, the British Israelites insist that Sumer was founded by Semites. The latter dogma continues to be asserted by both fanatics and their dupes, a teaching deployed in the interest of dating Creation from the place where Gods foot stood in 4004 B.C.E. In fact, known solar-sidereal calendars are dated to no later than Vedic calendars from between 6000 and 4000 B.C.E.; evidence of still more ancient solar-sidereal calendars is known. The related fact is, as the Greek Herotodus reported, that the ancient cultures of Sumer, Sheba (modern Yemen), Ethiopia, and Canaan, were colonies of an ancient Dravidian culture which dominated the maritime regions of South and Southeast Asia, probably long before the close of the last Ice Age. The modern cultural heritage of India and Southeast Asia, as in the case of Thailand, for example, is predominantly a result of interactions among Dravidian, Vedic, and Chinese cultural interactions over millennia.
53. For Keplers proof of the elliptical character of the Mars orbit, see Johannes Kepler, New Astronomy, trans. by W.H. Donahue (Cambridge, U.K.: Cambridge University Press, 1992). The proof is discussed in Jonathan Tennenbaum and Bruce Director, How Gauss Determined the Orbit of Ceres, Fidelio, Summer 1998 (in press).
54. Cusa, loc. cit.
55. The proof of the transcendental character of &Mac185; is a perfect model of this kind of proof of existence of a necessary, new physical principle.
56. E.g., consider Vernadskys notion of the noösphere.
57. Danton and Marat were both directly agents trained and deployed, from London, by the head of the British foreign service, Jeremy Bentham. Philippe Egalité was an agent of the pro-London faction, and was the organizer of that farce, known as the storming of the Bastille, which Philippe organized, armed, and led as an election-campaign stunt on behalf of the Swiss banker (and father of the the evil Madame de Staël), Jacques Necker, who had just earlier bankrupted France on behalf of Londons strategic interest.
58. See D. Stephen Pepper, Leonardo da Vinci, Founder of Modern Technology, New Solidarity, May 2, 1983, and Karel Vereycken, The Invention of Perspective, Fidelio, Winter 1996.
59. Leonardo da Vinci, The Virgin of the Rocks, the Louvre Museum, Paris.
60. Raphael Sanzio, The School of Athens, Vatican Museum.
61. Raphael Sanzio, The Transfiguration, Vatican Museum.
62. On the Golden Section, see Timaeus, in Plato: Vol. IX, Loeb Classical Library (Cambridge, Mass.: Harvard University Press, 1975). The Loeb Classical Library translations have the advantage of including the Greek text on the facing page. See also, the translation commissioned by Lyndon LaRouche, Platos Timaeus: The Basis of Modern Science, The Campaigner, February 1980.
63. Pierre Beaudry, The Acropolis of Athens: The Classical Idea of Beauty, New Federalist, June 24, 1988.
64. Baron Gottfried van Swietens music seminars in Vienna, in which Mozart participated, met every Sunday afternoon to play and study the manuscripts of Bach and Handel. See Bernhard Paumgartner, Mozart (Zürich: Atlantis Verlag, 1945), pp. 300-308; Hermann Abert, W.A. Mozart (Wiesbaden: Breitkopf & Härtel, 1983), pp. 75-79 and 117-165; and David Shavin, The Battle Mozart Won in Americas War with Britain, Executive Intelligence Review, Sept. 6, 1991.
65. See A Manual on the Rudiments of Tuning and Registration, op. cit., Chapter 2.
66. The exemplary case is the conflict between Goethe and Reichardt, on the one side, and Mozart, Beethoven, Schiller, and Schubert, on the opposing side. See A Manual on the Rudiments of Tuning and Registration, op. cit., pp. 202-203.Back to Part I
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