The Ontological Superiorityof Nicolaus of Cusa's Solution
Over Archimedes' Notion of Quadrature
by Lyndon H. LaRouche, Jr.
Archimedes' theorems for quadrature of the circle are given in The Works of Archimedes, T. L. Heath, ed., Dover, New York, pps. 91-98, 233-252, and also conveniently referenced in Ivor Thomas, trans., Greek Mathematical Works I. "Thales to Euclid," Loeb Classical Library, No. 335 (1939), 1980, pp. 316-333 of Section IX.2., pp. 308-346. The kernel of Archimedes' construction is given in the two diagrams in the latter work., on pp. 318, 319, respectively. For our purposes here, consider the entirety of pp. 308-346 as the relevant portion of the background against which this appended note is written.
The issue addressed here, will almost certainly prove to have been the principal, putatively scientific objection to our portrait of Nicolaus of Cusa's reformulation of Archimedes' quadrature of the circle. We shall focus narrowly upon that ontological point of difference between Cusa's and Archimedes' constructions which defines Cusa and his radiated influence, on the point of this single crucial issue, as the initiator of all progress in mathematical science over the interval A.D. 1440-1897, and beyond. Our proof of this point is very elementary, indeed, but we believe also rigorous.
Reference our description of the construction of the paired transfinite series of inscribed and circumscribed regular polygons, under sub-topic "2. Creativity Defined," above. Compare that with the construction given for Archimedes, e.g., as in Thomas p. 318. Now, consider what has been passed down over the millenia since as Archimedes' triangular solution, e.g. Thomas p. 319. Describe Archimedes' solution as follows.
Represent the circumference of the circle as an unknown multiple of the diameter of that circle: "πd." Thus, the radius of circle being designated by "r," the circumference may be expressed in the alternative by "2πr." Archimedes uses the iterative process of construction of the transfinite series of polygons, as detailed in all essentials by the Thomas text, to reduce the putative limit of that iteration to equivalence to a right triangle, whose short leg is of length "r," whose long leg is of length "2πr," and those area is, therefore, "2πr2⁄2."
The crucial issue posed by that construction is this.
Archimedes has proven [see Thomas pp. 320-333] that the value of π must lie between two values, the perimeter of the inscribed and of the circumscribed regular pologons, respectively. He has also proven, in the same way, that the estimated numerical value of π, "(circumference)/2r," can be refined to enormously great relative precision, by extending the transfinite series of regular polygons to a very large value of n for the expression "2n," as we have noted under topic "2. Creativity Defined." This arithmetic achievement by Archimedes' eudoxian construction is not contested, as Cusa emphasized, and is as matters should be on that account.
The remaining issue is akin to the fallacious, but commonplace assertion by numerous mathematicians, that the volumes of the sphere and relevant pseudosphere are equal, when they are not. In the sense of near-approximation, they are equal, to an enormous degree; but, as in the related case of quadrature, they are neither equal, nor of the same ontological species of existence. This is where Cusa's genius shone above all his leading contemporaries and most of the mathematicians who came after him, to the present day. This is, in terms of the relevant formalities, the point of Cusa's discovery from which the entire progress of modern mathematical science has been derived. In respect to the formalities, this is the point of generation of all modern science's achievements.
Cusa accomplished a fundamental discovery in mathematical physics, at exactly the junctureit must be said fairlyonly a relative few leading mathematical physicists to date, before him or since have not failed. His genius is expressed, at first glance, as a quality for which Karl Weierstrass is famous, his determination to to stick to the fact, that, although this (transfinite) difference, between Archimedes' construction of the estimated value for π and the actuality of the circular perimeter, is very tiny, even virtually zero arithmetically, it has a fundamental significance for mathematical thinking. This difference, however smallhowever clearly virtually null-dimensional, defines an absolute mathematical discontinuity, a singularity, as an ontological quality of difference between two species of constructive-geometrical existence.
Beginning from the mathematical thinking of Classical Greek culture, we subsume the thinking about mathematics by Greeks such as Archimedes by saying that, today, we know four types of number: rational, irrational, transcendental ("non-algebraic"), and transfinite. Of these, only the first two were known formally to Greek mathematics. Archimedes believed that π was an irrational magnitude, to be treated as the best Greek constructive geometry of that time addressed the problem of "incommensurables," as if they were "irrationals." The idea of a "transcendental" magnitude did not exist in his ontological vocabulary for the formal side of constructive geometry. What Cusa did, on this latter account, was to recognize that π is not, ontologically, an irrational, but a number of a higher ontological type than irrationals, of a higher species.
One of the collateral problems contributing to relevant misjudgment of this issue among modern mathematicians, is the myth fostered in part by Georg Cantor's pro-hegelian philosophical opponent, Professor Felix Klein, the myth attached to Lindemann's formalist's proof of the transcendental quality of π.
The proof, that π can not be an irrational number, was provided conclusively, for geometry, by Cusa in 1440, 1453, and other locations. The physical proof that Cusa's π must be a "non-algebraic" (transcendental) magnitude, was supplied implicitly by J. Bernoulli, Leibniz, et al., in 1697. Cusa's proof was premised upon the most rigorous ontological grounds; Bernoulli's and Leibniz's on the crucial experimental evidence supporting a universally efficient principle of least action (physics).
Exaggerated emphasis upon the late-19th century formalist arguments cited by Klein, those of Hermite and Lindemann, falsifies science fundamentally, not by denying their constructions, but, rather, by using the apparent success of these formalities as a pretext for overlooking the earlier, already conclusive proofs supplied during the relevant four-and-a-half- centuries-long, then-preceding internal history of modern science on this very issue. Those conclusive proofs obviusly include those most celebrated instances we have pointed out here (1440, 1697). That misplaced emphasis on late-nineteenth-century formalism, puts the mere formalities (however ingenious they might be) above recognition of the ontological issues crucial to any genuine proof. Thus, Klein, otherwise of sometimes awesome achievement, exhibited a want of simple scientific rigor in his omissions. His savage outburst against Cantor's work on the transfinite is obviously relevant to the fallacy of composition implicit in his oversights in treating the transcendence of π.
More broadly, shockingly, most among the modern views examined can be fairly described as lacking literacy in this and related matters. Notably, they do not take properly into account, or they even wilfully ignore the relevant preceding work of Dirichlet, Riemann, Weierstrass, and others on the related ontological implications of formal discontinuities manifest in the very small.
Such comparisons show us more forcefully, that the outstanding feature of Cusa's genius on this, is his recognizing that the proof of the ontological quality of an apparently absolute mathematical discontinuity in the very, very small, lies not merely in the form of that discontinuity, but in its manifestly correlated, demonstrable efficiency of existence. To the same general effect, in the Cusa tradition of Leibniz, we have the relevant concluding sentence from Riemann's Habilitationschrift:
Es fuehrt dies hinueber in das Gebeit einer andern Wissenschaft, in das Gebiet der Physik, welches wohl die Natur der heutigen Veranlassung nicht zu betreten erlaubt. [White trans. (loc. cit.) "This path leads into the domain of another science, into the realm of another science, into the realm of physics, into which the nature of this present occasion [devoted to the formalities of presenting an Habilitationschrift on matters of mathematicsLaR] forbids us to penetrate."
What Cusa proved, contrary to Archimedes' failure to ovecome blind faith in the ontological assumptions of the generally accepted Greek "classroom" mathematics (constructive geometry) of this time, was that to accept Archimedes' solution blindly, in the fifteenth century, would depend implicitly upon aadopting a wildly exaggerated, unprovable claim: that there did not exist an ontologically absolute mathematical discontinuity between the two transfinite series of regular polygons, the inscribed and the circumscribed. Cusa saw that this absolute mathematical discontinuity between the two curvatures, the inside and outside of the circular perimeter, was admittedly of virtually zero-dimensional magnitude, but, that this apparently almost non-existent was nonetheless, efficiently, of some magnitude.
The issue of that efficiency of a true mathematical discontinuity rages, in various guises, down through the present date. That efficiency, located in the virtually-null dimensionality of an absolute mathematical discontinuity within the mathematical formalist's customarily denumerable ordering of mere space-time, is the physics of the cited passage from Riemann's Habilitationschrift, is the foundation for the notion of a physical space-time in which causation dwells, out of the reach of the mathematical formalist.
Cusa solved the ontological paradox posed by Archimedes' exaggeration, by treating the matter according to the platonic solution-principle typical of Plato's Parmenides. For the reasons identified above, in the section "2. Creativity Defined," Cusa recognized that circular action: (a) could not be defined ontologically within the implicitly axiomatic formalities of Greek mathematics, since the circular perimeter, the locus of that action, was an absolute mathematical discontinuity between the two transfinite series, inscribed and circumscribed, of polygonal processes. (b) Moreover, since those polygonal processes themselves were externally bounded by circular constructions, the axiomatic formalities implicitly underlying Archimedes' constructions could not access efficiently the ontological domain of circular action, but circular action could determine, and thus access efficiently the processes of the polygonal constructions' domain. (c) Therefore, we must discard the implied set of axioms of Archimedes'use of the euclidean domain, and replace those with the axiomatic quality (platonic hypothesis) of universal circular action (later, universal least action).
The use of the combined physics of Roemer and Huyghens, to derive a general case for the cycloid-related form of refraction of light radiation bounded by a constant, externally bounding limit of retarded propagationby Huyghens, J. Bernoulli, and Leibniz, established Cusa's discovery as the correlative of an efficient, universal principle of least action. This was presented in 1697 as the hallmark of a "non-algebraic," or transcendental mathematics, superseding the algebraic mathematics then in favored use by the followers of Descartes, Newton, et al. Thus, it was Bernoulli and Leibniz (1697), who had already proven the transcendental quality of πas a refutation of the mathematical standpoints of Descartes and Newton, et al.precisely 200 years prior to Klein's 1897 commentary, in his Famous Problems of Geometry, on the formalist constructions by Hermite and Lindemann.
From Cusa's stubborn genius on this point, came the methodological approach adopted by that famous student of Cusa's writings, Leonardo da Vinci, and the first founding of a comprehensive mathematical physics, by rightly self-avowed student of the work of Cusa and Leonardo, Johannes Kepler. In this virtually null-dimensional existence defended by Cusa, Leibniz found the presence of the monad. Despite a politically corrupted Euler's fraudulent 1761 attack upon Leibniz's monadology on this very point, Cantor proved Euler absurd on every relevant point, and proved afresh, within the domain of the transfinite, the corresponding principles, on the subject of existent absolute mathematical discontinuities of space-time, by Cusa and Leibniz.
Both of these five-hundred-fifty-year-old issues, bearing upon the limitations of generally accepted classroom mathematics, have yet to be recognized adequately in those precincts: the formal issue respecting absolute mathematical discontinuities, and the fact that the metrical characteristics of a continuum can only be addressed in terms of the efficiency of such singularities, and addressed so only outside the limits of space-time, within physical space-time. In the domain of physical economy, the neglect of precisely those issues assaults the ill-prepared mathematical formalist with a deafening, blinding force of shock.
The greatest of all faults in the refusal of so many professionals to make themselves competently informed upon this discovery by Cusa, is that they have thus, wittingly or not, denied the entire foundation in higher hypothesis of that fifteenth-century revolution in mathematical method which is the germ of all valid modern science. If we do not prompt our young students to relive, as in secondary education, the experience of that elementary discovery by Cusa, how shall those deprived youth ever grow up with the mental development indispensable to judge competently much of anything about modern history?
Appendix A Footnotes
1. Felix Klein, Famous Problems of Geometry (1897) in Famous Problems and Other Monographs (New York: Chelsea Publishing Co., 1955), pp. 61-77.
2. Cardinal Nicolaus of Cusa, De Docta Ignorantia (On Learned Ignorance), trans. by Jasper Hopkins as Nicholas of Cusa on Learned Ignorance (Minneapolis: Arthur M. Banning Press, 1985); see also "De Circuli Quadratura" ("On the Quadrature of the Circle"), trans. by William F. Wertz, Jr., Fidelio, Vol. III, No. 1, Spring 1994, pp. 56-63.
3. Johann Bernoulli, "Curvatura radii..." ("The curvature of a ray..."), Acta Eruditorum, May 1697; trans. in D.J. Struik, A Sourcebook in Mathematics, 1200-1800 (Princeton, N.J.: Princeton University Press, 1986), pp. 391-396.
4. Bernhard Riemann, Habilitationsschrift, Über die Hypothesen, welche der Geometrie zu Grunde liegen, in Collected Works of Bernhard Riemann, ed. by Heinrich Weber (New York: Dover Publications, 1953), pp. 285-286; trans. by Henry S. White, "On the Hypotheses Which Lie at the Foundations of Geometry," in David Eugene Smith, A Source Book in Mathematics (New York: Dover Publications, 1959), pp. 411-425.
5. Poul Rasmussen, "Ole Rømer and the Discovery of the Speed of Light," 21st Century Science & Technology, Vol.
6, No. 1, Spring 1993, pp. 40-46.
6. Christiaan Huygens, A Treatise on Light, (New York: Dover Publications, 1962).
7. Op. cit.
8. See Text Footnote 19.
Adam Smith Smashes The Decalogue
The concluding section of "The Truth of Temporal Eternity" begins with a proposition for which it is claimed: "To promote the practice of 'free trade' is to break every part of the Decalogue into little pieces." For those who require additional proof of that claim, this appended note is supplied. The argument presented as follows rests upon two congruent bodies of evidence, the formal and the historical.
This writer has stressed repeatedly in sundry locations such as The Science of Christian Economy, that the central principle of Adam Smith's doctrine of "free trade" is derived from a dogma set forth in his 1759 Theory of the Moral Sentiments. The kernel of that is:
"Hunger, thirst, and 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."
Pause for a moment, to consider the most obvious of the implications of this Adam Smith dogma for the observance of the Mosaic Ten Commandments, What, then of four most plainly relevant articles of that Law: Thou shalt not kill; thou shalt not steal; thou shalt not bear false witness; thou shalt not covet? Smith's law is: (1) Hunger, (2) Thirst, (3) Sexual Passion, (4) Pleasure, (5) Pain.
Whence comes the ungodly law of British "moral philosopher" Adam Smith? From his immediately preceding sentence in that same 1759 passage:
"Nature has directed us to the greater part of these by original
and immediate instincts."
Then, read both of these cited excerpts within the immediate setting of the crucial features of the entire passage of which they are part. This excerpting is as presented in this present writer's The Science of Christian Economy, op. cit., pp. 291-292:
"The administration of the great system of the universe ... [and]
the care of the universal happiness of all rational and sensible
beings, is the business of God and not of man.
To man is
alloted a much humbler department, but one much more suitable to
the weakness of his powerss and to the narrowness of his
comprehension: the care of his own happiness, of that of his
family, his friends, his country ... But though we are endowed
with a very strong desire of these ends, it has been entrusted
to the slow and uncertain determinations of our reason to find out the proper means of bringing them about. Nature has directed us to the greater part of these by original and directed us to the greater part of these by original and immediate instincts. Hunger, thirst, the passion which unites immediate instincts. Hunger, thirst, the passion which unites the two sexes, the love of pleasure, and the dread of pain, the two sexes, the love of pleasure, and the dread of pain, prompt us to apply these means for their own sake, and without prompt us to apply these means for their own sake, and without any consideration of their tendency to those beneficent ends any consideration of their tendency to those beneficent ends which the great Director of nature intended to produce by them.which the great Director of nature intended to produce by them.
(Emphasis added to originalLaR
No Christian, or other follower of the Mosaic heritage could tolerate such doctrine. This is the core of the argument for "free trade" in Adam Smith's 1776 British India Company tract, The Wealth of Nations.
That 1759 passage is plainly an echo of John Locke's authorship of the colonial constitution for the Carolinas. That latter served as the predecessor of the treasonous Constitution of the racist Confederate States of America, as this issue is illuminated most simply by contrasting the preambles of the Confederate and U.S. Federal constitutions.
Compare the U.S. Federal Constitution's Preamble with the cited passage from Adam Smith. The Constitution prescribes:
"We the people of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States."
This is exactly what David Hume's disciple, Adam Smith, prohibits. On the same premises, in his 1766 Wealth of Nations, Smith defends the opium-trafficking of his employer, for whom that latter book was written as an anti-American tract, the British East India Company. That opposition to the principles of the Constitution is in the tradition of John Locke. Yet, as an explicit statement, the cited passage from the 1759 Adam Smith goes far beyond what British Calvinists, for example, or even David Hume, had understood Locke to have intended. Already, Adam Smith stands out as devotee of what is sometimes termed "British nineteenth-century philosophical radicalism."
Rejection of that "philosophical radicalism," the British Liberal Establishment's late-eighteenth-century break with respect for customary morality, is the basis which German empiricist Immanuel Kant cites, in his Prolegomena to a Future Metaphysic, as the motive for his open break with his former mentor, David Hume. Kant identifies Hume's turn away from toleration for customary morality as the issue of this break.
Smith's 1759 Theory of the Moral Sentiments and his 1776 Wealth of Nations typify the more radical reading of John Locke which was imported into the circles of Britain's powerful Second Earl of Shelbourne from the work Shelbourne's venetian contemporary, Giammaria Ortes. This is Adam Smith's foreshadowing Jeremy Bentham's outline of what became known later as the nineteenth-century British utilitarian's hedonistic calculus. One must see the fuller exposition of Smith's radicalism in Bentham's The Principles of Morals and Legislation, "In Defence of Usury," and "In Defence of Pederasty." This radicalism of Giammaria Ortes' type, expressed openly by Smith as early as his 1759 book, is the characteristic belief and practice of the leading intellectual and political circles ruling Britain throughout the several concluding decades of the eighteenth century, as also during Benthamite Lord Palmerston's nineteenth and Benthamite Bertrand Russell's twentieth centuries.
This representation of the sundry texts of Locke, Hume, Adam Smith, Bentham, et al. is validated by considering the historical issues of the U.S. war of 1776-1783. The irrepressible conflict between the Americans and London was forced into a state of open warfare against the British monarchy by the implications of the British East India Company's direct takeover, by outright purchase, of the British parliament and monarchy. The war was fought explicitly against the already practiced dogma of "free trade" presented publicly, only in 1776, as The Wealth of Nations. Our obligation to review this history is imposed upon us here by the widespread popularization of the plain lie, that the United States of America was founded upon the notions of "democracy" and "free trade," as associated respectively with John Locke and Adam Smith.
The United States' Declaration of Independence avows the principles of "pursuit of happiness" associated with Gottfried Leibniz, principles in direct opposition to John Locke's neo-Hobbesian dogma of "life, liberty, and property." In addition to the plain anti-Locke and anti-Adam Smith language of the Preamble to the U.S. Federal Constitution, Article I of that Constitution prescribes principles of governmental role in protectionism, the national currency, and regulation of foreign and interstate commerce which are explicitly irreconcilable with British "free trade" dogma.
These key issues of the U.S. War of Independence go back explicitly to the Massachusetts Bay Colony of 1688-1689, in the resistance to Royal Governor Andros and such key issues as the Royal suppression, by Locke's circles in London, of the Commonwealth's power to issue public credit in the form of currency. Cotton Mather's 1691 Some considerations of bills of credit, and Benjamin Franklin's famous 1729 A Modest Inquiry Into The Nature and Necessity of Paper Currency are forerunners of both Article I of the U.S. Federal Constitution and of U.S.Treasury Secretary Alexander Hamilton's famous Reports to the U.S. Congress on the design of the anti-British "American System of political-economy" (under the rubrics of "Public Credit," "A National Bank," and "Manufactures").
The principal source of confusion over these matters, is that academic liberalism, including its Fabian offshoots, has long defended the ideas of Locke and Adam Smith as upholding a Protestant principle against the allegedly medieval, statist propensities of Roman Catholicism. The specious argument which the liberal academic tradition derives from this sly sophistry of theirs, isLo and Behold!the Mathers, Franklin, and the overwhelming majority among the English- and German-speaking populations of eighteenth-century North America were stoutly Protestant, in such cases as the Mathers the Winthrops some notably radical denominations of dissenters. That line of argument is all bad history and worse theology.
The disgusting history of such phenomena as existentialist heterodoxies within the churches, ought to remind us that the essential basis for Christian belief, in particular, is not indoctrination, but the fact that each person is born in the image of God.
Admittedly, indoctrination as such can impose a relatively superficial obedience to a confession, to a doctrine, even a kind of hysterical posture of adherence. However, from the standpoint of that truth of temporal eternity which governs matters in the longer term, Christianity's only link to the person is the appeal to that creative power within which is the substance of imago Dei. Even Anatole France submitted to the evidence that one should not baptize penguins blindly.
To become adopted as knowledge, rather than superficially induced assertion of belief, taught doctrine is a promissory note which must be redeemed at the bank of imago Dei. That redemption may occur by methods which cohere with the Christian forms of Classical humanist education, as exhibited from the Brothers of the Common Life through the Humboldt reforms in nineteenth-century Germany. The authority of a Christian confession, as a matter of knowledge, springs from this quality of imago Dei. The authority of that body of religious confession, as an institutionalized body of knowledge, is dependent upon its role as a teacher according to the same principled method of education which the accompanying paper here attributes to Classical Christian humanist education generally.
The issue of confession is an issue of truthfulness. Leave any part of that confession's belief relegated to arbitrary dogma, and sooner or later that vulnerability will be discovered efficiently by someone, in some way, to one kind of effect, or another. Thus, the fifteenth century Christian Renaissance which brought Christianity out of the wreckage it had become during the preceding "New Dark Ages," emphasized that principle of intelligibility which shines so brightly in the work of Nicolaus of Cusa.
Once again, historically:
It is in those terms,that the role of religious confession within the historical process of the American revolution must be examined.
No historical figure since Nicolaus of Cusa embodies that principle more efficiently in modern times than Gottfried Leibniz. Leibniz's powerful influence was among those international networks of the late seventeenth and eighteenth centuries which organized the emergence of the United States under its 1789 Federal Constitution. At every turn in the period of the United States' three principal wars against the British empire, 1776-1865, it was the followers of John Locke and Adam Smith, such as the members of the Perkins and Russell opium-trading syndicates, who supplied the tories and traitors, and the influence of Leibniz which shaped the impulses and policies of the patriots. Let it be said, "God works in mysterious ways"; in this writer's experience, God works through the creative powers of reason of the person, through imago Dei. So, it was with every nobler movement of the history and pre-history of these United States.
The essential principle at center of knowledge derived by the power of creative reason, is what Plato termed the Good, as this is treated in the accompanying paper. The certainty of the existence of that Good as Intelligent Being above the constraints of transfinite time and transfinite space is accessed as knowledge as Raphael's referenced mural reminds its viewer: through hypothesizing temporal eternity in terms of social relations defined not by linear relations of time and space, but by creative reason. It is the loving nurture of that creative development within the person, through childhood's nurture to this purpose within the family, and through educational institutions so governed, which enables the person to nurture the quality of imago Dei within, to turn his or her inner eyes upward, to recognize God's efficient existence.
Without that, a person knows virtually nothing of importance, and is therefore well-suited to embrace the pseudo-deistic, paganist atheism of Locke, Adam Smith, Bentham, the satanic General Albert Pike of Morals and Dogma, and the Victorian Liberals generally. It is dedication to the general welfare of others, to justice for all humanity as imago Dei, which marks the essential difference between any among those North American patriots and a libertarian oligarch's lackey, such as professional turncoat variety of lackey John Locke, or Shelburne's lackey Adam Smith. The lesson to be learned from the patriots of the American revolution, such as President Abraham Lincoln, is the lesson of St. Paul's I Corinthians 13: Without love of mankind as imago Dei, there can be no true knowledge, of God or nature.
Locke's society is symbolically a galactic billiard table, whose balls, representing individual persons, have those built-in emotional spins to which British empiricism attaches the label of "human nature." The cited passage from Adam Smith's The Theory of the Moral Sentiments accords perfectly with that representation of the schema of Locke's entropic ordering of convenant-generation, Locke's "democracy." It accords similarly with the derived "free trade" dogma of "The Wealth of Nations."
If we extend that entropic model of political and economic processes to the Decalogue, we have the following principal results:
(1) God does not exist in any form but the psychopathetic fantasms of Professor William James' Varieties of Religious Experience.
(2) Jeremy Rifkin's entropy is the pagan god of such liberal conceits.
(3) The name of "God" is used only as a manipulative sophistry.
(4) "What 'Sabbath"?"
(5) "My parents should die with dignity before they spend all of my inheritance on such frivolities as food and medical care."
(6) "If God didn't wish them to die, he would not permit my instincts to guide me to kill them."
(7) "My sex life is my own business; if it feels good, it is right for me."
(8) "Don't steal unless you think you can get by with it."
(9) "Truth is strictly a matter of one man's opinion."
(10) "If I feel the need, I do my thingor yours."
The lying hypocrisy of a "Christian advocacy of 'free trade," should be accorded the treatment appropriate for all concoctions which are truly disgusting.
Appendix Part A Footnotes
To Part 1
To Part 2
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