Academics From Germany

"The Geschick of being: a child that plays... Why does it play, the great child of the world-play Heraclitus brought into view in the aiôn? It plays, because it plays. The "because" withers away in the play. The play is without "why." It plays since it plays. It simply remains a play: the most elevated and the most profound. But this "simply" is everything, the one, the only... The question remains whether and how we, hearing the movements of this play, play along and accommodate ourselves to the play."

"Everywhere we remain unfree and chained to technology, whether we passionately affirm or deny it. But we are delivered over to it in the worst possible way when we regard it as something neutral; for this conception of it, to which today we particularly like to do homage, makes us utterly blind to the essence of technology."

"Das Bedenklichste in unserer bedenklichen Zeit ist, dass wir noch nicht denken."

"Agriculture is now a motorized food industry, the same thing in its essence as the production of corpses in the gas chambers and the extermination camps, the same thing as blockades and the reduction of countries to famine, the same thing as the manufacture of hydrogen bombs."

"Those in the crossing must in the end know what is mistaken by all urging for intelligibility: that every thinking of being, all philosophy, can never be confirmed by "facts," ie, by beings. Making itself intelligible is suicide for philosophy. Those who idolize "facts" never notice that their idols only shine in a borrowed light. They are also meant not to notice this; for thereupon they would have to be at a loss and therefore useless. But idolizers and idols are used wherever gods are in flight and so announce their nearness."

"This Europe, which in its ruinous blindness is forever on the point of cutting its own throat, lies today in a great pincers, squeezed between Russia on one side and America on the other. From a metaphysical point of view, Russia and America are the same: the same dreary technological frenzy, the same unrestricted organization of the average man..."

"What is peddled about nowadays as philosophy, especially that of N.S. [National Socialism], but has nothing to do with the inner truth and greatness of that movement [namely the encounter between global technology and modern humanity] is nothing but fishing in that troubled sea of values and totalities."

"Warum ist überhaupt Seiendes und nicht vielmehr Nichts? Das ist die Frage."

"Transcendence constitutes selfhood."

"The grandeur of man is measured according to what he seeks and according to the urgency by which he remains a seeker."

"The desire to philosophize from the standpoint of standpointlessness, as a purportedly genuine and superior objectivity, is either childish, or, as is usually the case, disingenuous."

"Finally, there is Heidegger's stunning silence about the Holocaust. For the hundreds of pages that he published on the dehumanizing powers of modern civilization, for all the ink he spilled decrying the triumph of a spiritless technology, Heidegger never saw fit, as far as I know, to publish a single word on the death camps. Instead, he pleaded ignorance of the fate of the Jews during the war—even though the Jewish population of Baden, where Heidegger lived, dropped dramatically from 20,600 in 1933 to 6400 in 1940, and even though virtually all of the 6400 who remained were deported to France on October 22, 1940, and thence to Izbica, the death camp near Lublin. As Heidegger was lecturing on Nietzsche in the Forties, there were only 820 Jews left in all of Baden. We have his statements about the six million unemployed at the beginning of the Nazi regime, but not a word about the six million who were dead at the end of it."

"In its essential meaning, “ontological difference” is the way in which Heidegger's thesis of Kant's synthetic character of existential judgements [...] and, in general, the fundamental principle of Western thought that the unity of being and existing has an accidental character, is presented. For Heidegger, “being” (unlike the absolute, divine “Being” of the metaphysical tradition) “has no power over entities”; it is a letting-be of entities. But both traditional “Being”, which has power over entities, and allowing entities to be have the same foundation: faith in becoming; and becoming is that with respect to which one can take a position either through the power of metaphysical Being (or the scientific-technological apparatus) or by allowing it to be in its freedom and “naivety”. Even the “impotence” with which “being”, according to Heidegger, lets being be is based on the absolute will to power, that is, on the will that wants the existence of becoming. (chap. XXXIII, p. 318)"

"The being to which Heidegger [...] reasonably thinks, is [...] that which differs from all determinations, differs from entities and is precisely [...] this difference [...] – it is the central figure of Heidegger's discourse – which Heidegger calls ontological difference [...] inasmuch as being is the appearance of entities, inasmuch as it differs from entities, it is non-entity, and Heidegger explicitly says it is nothingness; being is nichts, but when he introduces this nothingness, he intends to introduce precisely that which is in no way an entity, but not that which – and here Heidegger is quite explicit – is constituted as nihil negativum, that is, nihil absolutum. I have expressed my opinion on the relationship between Heidegger and nihil absolutum several times, saying that it is strange how Heidegger treats the concept of nihil absolutum with arrogance and rarely asks himself [...] what the historical derivation of this concept is. He is particularly keen to emphasise that being [...], das Sein, Being is not entity and in this sense is nothing, but not nihil absolutum. Now, when Heidegger speaks of entity, he explicitly characterises it as not nihil absolutum: the tree, the wall, the house are not absolute nothingness. [...] once with Gadamer [...] precisely on the subject [...] of the ontological difference, I tried to show him the necessity that above the ontological difference between being and entity, there was a more original plane of the entity that includes what Heidegger calls entity and what Heidegger calls Being. And the observation I made to him was this: but if it is being, nichts, if being is nothing, being that is nothing in the sense indicated is not a nihil absolutum and if, in turn, entity is not a nihil absolutum, then the two that constitute the ontological difference, however radically different, agree in their not being a nihil absolutum, so that then the trait of not being a nihil absolutm unites [...] the radically different; if this step is taken, then we see that [...] the traditional concept of being as a common feature of the totality of differences, properly thought out, is capable of encompassing within itself that ontological difference which, for Heidegger, should radically and definitively lead [...] outside the classical concept of being as koinón [...], as the commonality of differences; therefore, koinón lies [...] in not being an absolute nothing on the part of Sein [Being] and on the part of Seiendes [Entity].."

"The philosophical tradition that goes from Descartes to Husserl, and indeed a large part of the philosophical tradition that goes back to Plato, involves a search for foundations: metaphysically certain foundations of knowledge, foundations of language and meaning, foundations of mathematics, foundations of morality, etc. […] Now, in the twentieth century, mostly under the influence of Wittgenstein and Heidegger, we have come to believe that this general search for these sorts of foundations is misguided."

"After several decades of courageous scholarship by Hugo Ott, Victor Farias and Emmanuel Faye in Europe, and related work by American scholars Thomas Sheehan, Richard Wolin, Tom Rockmore and others, no sensible observer today doubts that Heidegger, the most celebrated figure in twentieth-century German philosophy, lied his inauthentic head off about his relationship to the Nazis. Far from being a reluctant sympathizer for a brief period in the early 1930s, as he sought to convince his denazification committee, Heidegger had been an enthusiastic believer in National Socialism’s “inner truth and greatness.” He hoped to become the Fuhrer of the university system, to play philosopher-king to Hilter’s Fuhrerstaat..."

"Heidegger's Nazism and the failure to confront it are philosophically significant for Heidegger's philosophy, for its reception, and for philosophy itself. At a time when some are still concerned to deny the existence of the Holocaust, in effect to deny that Nazism was Nazism, and many still deny that Nazism had a more than tangential appeal to one of the most significant theories of this century, merely to assert the philosophical significance of an abject philosophical failure to seize the historical moment for the German Volk and Being is not likely to win the day. Yet there is something absurd, even grotesque about the conjunction of the statement that Heidegger is an important, even a great philosopher, perhaps one of the few seminal thinkers in the history of the tradition, with the realization that he, like many of his followers, entirely failed, in fact failed in the most dismal manner, to grasp or even to confront Nazism. If philosophy is its time captured in thought, and if Heidegger and his epigones have basically failed to grasp their epoch, can we avoid the conclusion that they have also failed this test, failed as philosophers?"

"I appeal to the philosophers of all countries to unite and never again mention Heidegger or talk to another philosopher who defends Heidegger. This man was a devil. I mean, he behaved like a devil to his beloved teacher [i.e., Husserl ], and he has a devilish influence on Germany. … One has to read Heidegger in the original to see what a swindler he was."

"The thing I object to the most about Heidegger was that he was a guru. He practiced philosophy not as a Socratic practice of exchange, where you and I are equal, and it's just a matter of who has the better argument. But no, he was an authority figure, and he fed people's desire to submit themselves to authority. So I think actually his way of teaching was anti-philosophical."

"It is true that M. Fourier had the opinion that the principal end of mathematics was the public utility and the explanation of natural phenomena; but such a philosopher as he is should have known that the unique end of science is the honor of the human mind, and that from this point of view a question of number is as important as a question of the system of the world."

"The best approach to Jacobi is perhaps through his beautiful lectures on dynamics ("Vorlesungen über Dynamik"), published in 1866 after lecture notes from 1842-43."

"Sylvester has given the name "Jacobian" to the functional determinant in order to pay respect to Jacobi's work on algebra and elimination theory. The best known of Jacobi's papers on this subject is his "De formatione et proprietatibus determinantium" (1841), which made the theory of determinants the common good of the mathematicians."

"In 1829, the year that Abel died, Carl Gustav Jacob Jacobi published his "Fundamenta nova theoriae functionum ellipticarum." Jacobi based his theory of elliptic functions on four functions defined by infinite series and called theta functions. ...The addition theorems of elliptic functions can also be considered as special applications of Abel's theorem on the sum of integrals of algebraic equations. The question now arose whether hyper-elliptic integrals could be inverted in the way elliptic integrals had been inverted to yield elliptic functions. The solution was found by Jacobi in 1832 when he published his result that the inversion could be performed with functions of more than one variable. Thus the theory of Abelian functions of p variables was born, which became an important branch of Nineteenth century mathematics."

"Aside from Cauchy, the greatest contributory to the theory [of determinants] was Carl Gustav Jacob Jacobi. With him the word "determinant" received its final acceptance. He early used the functional determinant which Sylvester has called the Jacobian, and in his famous memoirs in Crelle's Journal for 1841 he considered these forms as well as that class of alternating functions which Sylvester has called alternants."

"C. J. Jacobi was especially distressed because on several occasions when he came to Gauss to relate some new discoveries the latter pulled out from his desk drawer some papers that contained the very same discoveries. Jacobi resolved to get even. ...Gauss opened his desk drawer and pulled out some papers ...Jacobi then remarked, "It is a pity that you did not publish this work since you have published so may poorer papers.""

"Among standard works on mechanics are Jacobi's Vorlesungen über Dynamik, edited by Clebsch, 1866."

"Advances in theoretical mechanics, bearing on the integration and the alteration in form of dynamical equations, were made since Lagrange by Poisson, William Rowan Hamilton, Jacobi, Madame Kowalevski, and others. Lagrange had established the "Lagrangian form" of the equations of motion. He had given a theory of the variation of the arbitrary constants which, however, turned out to be less fruitful in results than a theory advanced by Poisson. ...Hamilton's method of integration was freed by Jacobi of an unnecessary complication, and was then applied by him to the determination of a geodetic line on the general ellipsoid. With aid of elliptic coordinates Jacobi integrated the partial differential equation and expressed the equation of the geodetic in form of a relation between two Abelian integrals. Jacobi applied to differential equations of dynamics the theory of the ultimate multiplier. The differential equations of dynamics are only one of the classes of differential equations considered by Jacobi. Dynamic investigations along the lines of Lagrange, Hamilton, and Jacobi were made by Liouville, A. Desboves, Serret, J. C. F. Sturm, Ostrogradsky, J. Bertrand, Donkin, Brioschi, leading up to the development of the theory of a system of canonical integrals."

"The problem of three bodies has been treated in various ways since the time of Lagrange, but no decided advance towards a more complete algebraic solution has been made, and the problem stands substantially where it was left by him. He had made a reduction in the differential equations to the seventh order. This was elegantly accomplished in a different way by Jacobi in 1843."

"Gauss' researches on the theory of numbers were the starting-point for a school of writers, among the earliest of whom was Jacobi. The latter contributed to Crelle's Journal an article on cubic residues, giving theorems without proofs. After the publication of Gauss' paper on biquadratic residues, giving the law of biquadratic reciprocity, and his treatment of complex numbers, Jacobi found a similar law for cubic residues. By the theory of elliptical functions, he was led to beautiful theorems on the representation of numbers by 2, 4, 6, and 8 squares."

"Cauchy made some researches on the calculus of variations. This subject is now in its essential principles the same as when it came from the hands of Lagrange. Recent studies pertain to the variation of a double integral when the limits are also variable, and to variations of multiple integrals in general. ...In 1837 Jacobi published a memoir, showing that the difficult integrations demanded by the discussion of the second variation, by which the existence of a maximum or minimum can be ascertained, are included in the integrations of the first variation, and thus are superfluous. This important theorem, presented with great brevity by Jacobi, was elucidated and extended by V. A. Lebesgue, C. E. Delaunay, Eisenlohr, S. Spitzer, Hesse, and Clebsch. ...In 1852 G. Mainardi attempted to exhibit a new method of discriminating maxima and minima, and extended Jacobi's theorem to double integrals. Mainardi and F. Brioschi showed the value of determinants in exhibiting the terms of the second variation."

"The theory of determinants was studied by Hoëné Wronski in Italy and J. Binet in France; but they were forestalled by the great master of this subject, Cauchy. In a paper (Jour. de l'ecole Polyt., IX., 16) Cauchy developed several general theorems. He introduced the name determinant a term previously used by Gauss in the functions considered by him. In 1826 Jacobi began using this calculus, and he gave brilliant proof of its power. In 1841 he wrote extended memoirs on determinants in Crelle's Journal, which rendered the theory easily accessible."

"The most important of Legendre's works is his Functions elliptiques, issued in two volumes in 1825 and 1826. He took up the subject where Euler, Landen, and Lagrange had left it, and for forty years was the only one to cultivate this new branch of analysis, until at last Jacobi and Abel stepped in with admirable new discoveries."

"I ought also to mention his papers on Abelian transcendants; his investigations on the theory of numbers... his important memoirs on the theory of differential equations, both ordinary and partial; his development of the calculus of variations; and his contributions to the problem of three bodies, and other particular dynamical problems. Most of the results of the researches last named are included in his Vorlesungen über Dynamik."

"Jacobi's most celebrated investigations are those on elliptic functions, the modern notation in which is substantially due to him, and the theory of which he established simultaneously with Abel, but independently of him. Jacobi's results are given in his treatise on elliptic functions, published in 1829, and in some later papers in Crelle's Journal; they are earlier than Weierstrass's researches... The correspondence between Legendre and Jacobi on elliptic functions has been reprinted in the first volume of Jacobi's collected works. Jacobi, like Abel, recognised that elliptic functions were not merely a group of theorems on integration, but that they were types of a new kind of function, namely, one of double periodicity; hence he paid particular attention to the theory of the theta function."

"His [Lagrange's] lectures on differential calculus form the basis of his Theorie des fonctions analytiques which was published in 1797. ...its object is to substitute for the differential calculus a group of theorems based upon the development of algebraic functions in series. A somewhat similar method had been previously used by John Landen in his Residual Analysis... Lagrange believed that he could... get rid of those difficulties, connected with the use of infinitely large and infinitely small quantities, to which philosophers objected in the usual treatment of the differential calculus. ...Another treatise in the same lines was his Leçons sur le calcul des fonctions, issued in 1804. These works may be considered as the starting-point for the researches of Cauchy, Jacobi, and Weierstrass."

"History knew a midnight, which we may estimate at about the year 1000 A.D., when the human race lost the arts and sciences even to the memory. The last twilight of paganism was gone, and the new day had not yet begun. Whatever was left of culture in the world was found only in the Saracens, and a Pope eager to learn studied in disguise in their universities, and so became the wonder of the West. At last Christendom, tired of praying to the dead bones of the martyrs, flocked to the tomb of the Saviour Himself, only to find for a second time that the grave was empty and that Christ was risen from the dead. Then mankind too rose from the dead. It returned to the activities and the business of life; there was a feverish revival in the arts and in the crafts. The cities flourished, a new citizenry was founded. Cimabue rediscovered the extinct art of painting; Dante, that of poetry. Then it was, also, that great courageous spirits like Abelard and Saint Thomas Aquinas dared to introduce into Catholicism the concepts of Aristotelian logic, and thus founded scholastic philosophy. But when the Church took the sciences under her wing, she demanded that the forms in which they moved be subjected to the same unconditioned faith in authority as were her own laws. And so it happened that scholasticism, far from freeing the human spirit, enchained it for many centuries to come, until the very possibility of free scientific research came to be doubted. At last, however, here too daylight broke, and mankind, reassured, determined to take advantage of its gifts and to create a knowledge of nature based on independent thought. The dawn of the day in history is know as the Renaissance or the Revival of Learning."

"Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case."

"Any progress in the theory of partial differential equations must also bring about a progress in Mechanics."

"I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighbouring park I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?"

"The physicist may be satisfied when he has the mathematical scheme and knows how to use for the interpretation of the experiments. But he has to speak about his results also to non-physicists who will not be satisfied unless some explanation is given in plain language. Even for the physicist the description in plain language will be the criterion of the degree of understanding that has been reached."

"Whenever we proceed from the known into the unknown we may hope to understand, but we may have to learn at the same time a new meaning of the word "understanding.""

"The existing scientific concepts cover always only a very limited part of reality, and the other part that has not yet been understood is infinite."

"[E]ven in the most precise part of science, in mathematics, we cannot avoid using concepts that involve contradictions. ...[I]t is well known that the concept of infinity leads to contradictions... but it would be practically impossible to construct... mathematics without this concept."

"The way in which the convergent mathematical schemes did not fulfill the requirements of relativity and quantum theory was... interesting. ...[O]ne scheme ...interpreted in terms of actual events in space and time, led to a...time reversal... The physicists are convinced... that the processes... do not occur in nature... if... separated by measurable distance in space and time. ...If we assume that the laws of nature do contain a third universal constant... of the order of 10-13 cm, then... our usual concepts... apply only to regions in space and time that are large compared to the universal constant. We should... be prepared for phenomena of a qualitatively new character when we... approach regions... smaller than the nuclear radii. The phenomenon of time reversal... might therefore belong to these smallest regions."

"[S]ets of concepts... defined in physics. ...[F]our systems... have ...attained ...final form. The first ...Newtonian mechanics ...for the description of all mechanical systems, ...motion of fluids and ...elastic ..; it comprises , , aerodynamics. The second closed system of concepts... the theory of heat. Though... connected with mechanics through... statistical mechanics, it... [is] not... a part of mechanics. ...[T]he phenomenological theory of heat uses ...[some] concepts that have no [physics] counterpart ...like: , specific heat, entropy, free energy, etc. ...[F]rom ...phenomenological ...to a statistical interpretation ...considering heat as energy, distributed statistically among ...many degrees of freedom due to ...atomic structure... heat is no more connected with mechanics than with electrodynamics or other ...physics. The central concept ...is ...probability, closely connected with ...entropy ...Besides this ...the statistical theory of heat requires the concept of energy. But any coherent set ...in physics will ...contain ...concepts of energy, and and the law that these ...be conserved. This follows if the ...set is ...to describe ...features ...correct at all times and everywhere; ...[i.e.,] features that do not depend on space and time ...[i.e.,] are invariant under arbitrary translations in space and time, rotations in space and the Galileo— or Lorentz—transformation. Therefore, the theory of heat can be combined with any of the other closed systems of concepts. The third... electricity and magnetism... reached... final form... through... Lorentz, Einstein and Minkowski. It comprises electrodynamics, special relativity, optics, magnetism, and one may include the de Broglie theory of s of all different sorts of elementary particles, but not the wave theory of Schrodinger. [F]ourth... the quantum theory... Its central concept is the probability function, or... "statistical matrix"... It comprises quantum and wave mechanics, the theory of atomic spectra, chemistry, and the theory of other properties... like electric conductivity, , etc. ...The first set is contained in the third as the limiting case where the velocity of light can be considered as infinitely big, and is contained in the fourth as the limiting case where of action can be considered as infinitely small. The first and partly the third set belong to the fourth as a priori for the description of the experiments. The second set can be connected with any of the other three sets without difficulty and is especially important in its connection with the fourth. The independent existence of the third and fourth sets suggests the existence of a fifth set, of which one, three, and four are limiting cases. This fifth set will probably be found someday in connection with the theory of the elementary particles."

"Any concepts or words which have been formed in the past through the interplay between the world and ourselves are not really sharply defined with respect to their meaning: that is to say, we do not know exactly how far they will help us in finding our way in the world. We often know that they can be applied to a wide range of inner or outer experience, but we practically never know precisely the limits of their applicability. This is true even of the simplest and most general concepts like "existence" and "space and time". Therefore, it will never be possible by pure reason to arrive at some absolute truth. The concepts may, however, be sharply defined with regard to their connections. This is actually the fact when the concepts become part of a system of axioms and definitions which can be expressed consistently by a mathematical scheme. Such a group of connected concepts may be applicable to a wide field of experience and will help us to find our way in this field. But the limits of the applicability will in general not be known, at least not completely."

"The law of causality is no longer applied in quantum theory and the law of conservation of matter is no longer true for the elementary particles. Obviously Kant could not have foreseen the new discoveries, but since he was convinced that his concepts would be "the basis of any future metaphysics that can be called science" it is interesting to see where his arguments have been wrong."

"The words "position" and "velocity" of an electron... seemed perfectly well defined... and in fact they were clearly defined concepts within the mathematical framework of Newtonian mechanics. But actually they were not well defined, as seen from the relations of uncertainty. One may say that regarding their position in Newtonian mechanics they were well defined, but in their relation to nature, they were not. This shows that we can never know beforehand which limitations will be put on the applicability of certain concepts by the extension of our knowledge into the remote parts of nature, into which we can only penetrate with the most elaborate tools. Therefore, in the process of penetration we are bound sometimes to use our concepts in a way which is not justified and which carries no meaning. Insistence on the postulate of complete logical clarification would make science impossible. We are reminded... of the old wisdom that one who insists on never uttering an error must remain silent."

"Modern positivism...expresses criticism against the naïve use of certain terms... by the general postulate that the question whether a given sentence has any meaning... should always be thoroughly and critically examined. This... is derived from mathematical logic. The procedure of natural science is pictured as an attachment of symbols to the phenomena. The symbols can, as in mathematics, be combined according to certain rules... However, a combination of symbols that does not comply with the rules is not wrong but conveys no meaning. The obvious difficulty in this argument is the lack of any general criterion as to when a sentence should be considered meaningless. A definite decision is possible only when the sentence belongs to a closed system of concepts and axioms, which in the development of natural science will be rather the exception than the rule. In some case the conjecture that a certain sentence is meaningless has historically led to important progress... new connections which would have been impossible if the sentence had a meaning. An example... sentence: "In which orbit does the electron move around the nucleus?" But generally the positivistic scheme taken from mathematical logic is too narrow in a description of nature which necessarily uses words and concepts that are only vaguely defined."

"J. Robert Oppenheimer: You're talking about turning theory into a practical weapons system faster than the Nazis. Leslie Groves: Who have a twelve month head start. J. Robert Oppenheimer: Eighteen. Leslie Groves: How could you possibly know that? J. Robert Oppenheimer: Our fast neutron research took six months. The man they've undoubtedly put in charge will have made that leap instantly. Leslie Groves: Who do you think they put in charge? J. Robert Oppenheimer: Werner Heisenberg. He has the most intuitive understanding of atomic structure I've ever seen. Leslie Groves: You know his work? J. Robert Oppenheimer: I know him. Just like I know Walter Bothe, von Weizsäcker, Diebner... In a straight race, the Germans win. We've got one hope. Leslie Groves: Which is? J. Robert Oppenheimer: Antisemitism. Leslie Groves: What? J. Robert Oppenheimer: Hitler called quantum physics "Jewish science", said it right to Einstein's face. Our one hope is that Hitler is so, so blinded by hate that he's denied Heisenberg proper resources, because it'll take vast resources."