Jews From Germany

"Nothing ought to be said or done which could create the impression that unbiased reconsideration of the most elementary premises of philosophy is a merely academic or historical affair."

"It is of the essence of traditions that they cover or conceal their humble foundations by erecting impressive edifices on them."

"To avert the danger [posed by theory] to life, Nietzsche could choose one of two ways: he could insist on the strictly esoteric character of the theoretical analysis of life—that is, restore the Platonic notion of the noble delusion—or else he could deny the possibility of theory proper and so conceive of thought as essentially subservient to, or dependent on, life or fate... If not Nietzsche himself, at any rate his successors [Heidegger] adopted the second alternative."

"History teaches us that a given view has been abandoned in favor of another by all men, or by all competent men, or perhaps by only the most vocal men; it does not teach us whether the change was sound or whether the rejected view deserved to be rejected. Only an impartial analysis of the view in question—an analysis that is not dazzled by the victory or stunned by the defeat of the adherents of the view concerned—could teach us anything regarding the worth of the view and hence regarding the meaning of the historical change."

"Philosophizing means, then, to ascend from public dogma to essentially private knowledge."

"Even by proving that a certain view is indispensable for living well, one proves merely that the view in question is a salutary myth: one does not prove it to be true."

"Once we realize that the principles of our actions have no other support than our blind choice, we really do not believe in them anymore... In order to live, we have to silence the easily silenced voice of reason, which tells us that our principles are in themselves as good or as bad an any other principles. The more we cultivate reason, the more we cultivate nihilism..."

"Liberal relativism has its roots in the natural right tradition of tolerance or in the notion that everyone has a natural right to the pursuit of happiness as he understands happiness; but in itself it is a seminary of intolerance."

"According to our social science, we can be or become wise in all matters of secondary importance, but we have to be resigned to utter ignorance in the most important respect: we cannot have any knowledge regarding the ultimate principles of our choices, i.e. regarding their soundness or unsoundness... We are then in the position of beings who are sane and sober when engaged in trivial business and who gamble like madmen when confronted with serious issues."

"It is a general observation that people write as they read. As a rule, careful writers are careful readers and vice versa. A careful writer wants to be read carefully. He cannot know what it means to be read carefully but by having done careful reading himself. Reading precedes writing. We read before we write. We learn to write by reading. A man learns to write well by reading well good books, by reading most carefully books which are most carefully written."

"The works of the great writers of the past are very beautiful even from without. And yet their visible beauty is sheer ugliness, compared with the beauty of those hidden treasures which disclose themselves only after very long, never easy, but always pleasant work. This always difficult but always pleasant work is, I believe, what the philosophers had in mind when they recommended education. Education, they felt, is the only answer to the always pressing question, to the political question par excellence, of how to reconcile order which is not oppression with freedom which is not license."

"An exoteric book contains then two teachings: a popular teaching of an edifying character, which is in the foreground; and a philosophic teaching concerning the most important subject, which is indicated only between the lines."

"Writings are naturally accessible to all who can read. Therefore a philosopher who chose the second way could expound only such opinions as were suitable for the nonphilosophic majority: all of his writings would have to be, strictly speaking, exoteric. These opinions would not be in all respects consonant with truth. Being a philosopher, that is, hating "the lie in the soul" more than anything else, he would not deceive himself about the fact that such opinions are merely "likely tales," or "noble lies," or "probable opinions," and would leave it to his philosophic readers to disentangle the truth from its poetic or dialectic presentation. But he would defeat his purpose if he indicated clearly which of his statements expressed a noble lie, and which the still more noble truth."

"Persecution, then, gives rise to a peculiar technique of writing, and therewith to a peculiar type of literature, in which the truth about all crucial things is presented exclusively between the lines. That literature is addressed, not to all readers, but to trustworthy and intelligent readers only."

"Society did not recognize philosophy or the right of philosophizing. There was no harmony between philosophy and society. The philosophers were very far from being exponents of society or of parties. They defended the interests of philosophy and of nothing else. In doing this, they believed indeed that they were defending the highest interests of mankind. The exoteric teaching was needed for protecting philosophy. It was the armor in which philosophy had to appear. It was needed for political reasons. It was the form in which philosophy became visible to the political community. It was the political aspect of philosophy. It was "political" philosophy."

"The purpose of Plato, or of Aristotle, as Fārābī conceived of it, is sufficiently revealed in this seemingly conventional praise of philosophy."

"Political Zionism is problematic for obvious reasons. But I can never forget what it achieved as a moral force in an era of complete dissolution. It helped to stem the tide of ‘progressive’ leveling of venerable, ancestral differences; it fulfilled a conservative function."

"The Jewish people and their fate are the living witness for the absence of redemption. This, one could say, is the meaning of the chosen people; the Jews are chosen to prove the absence of redemption."

"We are confronted with the incompatible claims of Jerusalem and Athens to our allegiance. We are open to both and willing to listen to each. We ourselves are not wise but we wish to become wise. We are seekers for wisdom, philo-sophoi."

"The emancipation of the scholars and scientists from philosophy is according to [Nietzsche] only a part of the democratic movement, i.e. of the emancipation of the low from subordination to the high. … The plebeian character of the contemporary scholar or scientist is due to the fact that he has no reverence for himself."

"No bloody or unbloody change of society can eradicate the evil in man: as long as there will be men, there will be malice, envy and hatred, and hence there cannot be a society which does not have to employ coercive restraint."

"Science, as the positivist understands it, is susceptible of infinite progress. That you learn in every elementary school today, I believe. Every result of science is provisional and subject to future revision, and this will never change. In other words, fifty thousand years from now there will still be results entirely different from those now, but still subject to revision. Science is susceptible of infinite progress. But how can science be susceptible of infinite progress if its object does not have an inner infinity? The belief admitted by all believers in science today — that science is by its nature essentially progressive, and eternally progressive — implies, without saying it, that being is mysterious. And here is the point where the two lines I have tried to trace do not meet exactly, but where they come within hailing distance. And, I believe, to expect more in a general way, of people in general, would be unreasonable."

"The kingdom is Yours, and You will reign in glory for all eternity. As it is written in Your Torah: "The Lord shall reign for ever and ever." And it is said: " And the Lord shall be King over all the earth: on that day the Lord shall be One, and His name One." No nobler dream was ever dreamt. It is surely nobler to be a victim of the most noble dream than to profit from a sordid reality and to wallow in it. Dream is akin to aspiration. And aspiration is a kind of divination of an enigmatic vision. And an enigmatic vision in the emphatic sense is the perception of the ultimate mystery, of the truth of the ultimate mystery. The truth of the ultimate mystery — the truth that there is an ultimate mystery, that being is radically mysterious — cannot be denied even by the unbelieving Jew of our age. That unbelieving Jew of our age, if he has any education, is ordinarily a positivist, a believer in Science, if not a positivist without any education."

"All political action aims at either preservation or change. When desiring to preserve, we wish to prevent a change for the worse; when desiring to change, we wish to bring about something better. All political action is then guided by some thought of better or worse."

"It is remarkable that this generalization of plane geometry to surface geometry is identical with that generalization of geometry which originated from the analysis of the axiom of parallels. ...the construction of non-Euclidean geometries could have been equally well based upon the elimination of other axioms. It was perhaps due to an intuitive feeling for theoretical fruitfulness that the criticism always centered around the axiom of parallels. For in this way the axiomatic basis was created for that extension of geometry in which the metric appears as an independent variable. Once the significance of the metric as the characteristic feature of the plane has been recognized from the viewpoint of Gauss' plane theory, it is easy to point out, conversely, its connection with the axiom of parallels. The property of the straight line as being the shortest connection between two points can be transferred to curved surfaces, and leads to the concept of straightest line; on the surface of the sphere the great circles play the role of the shortest line of connection... analogous to that of the straight line on the plane. Yet while the great circles as "straight lines" share the most important property with those of the plane, they are distinct from the latter with respect to the axiom of the parallels: all great circles of the sphere intersect and therefore there are no parallels among these "straight lines". ...If this idea is carried through, and all axioms are formulated on the understanding that by "straight lines" are meant the great circles of the sphere and by "plane" is meant the surface of the sphere, it turns out that this system of elements satisfies the system of axioms within two dimensions which is nearly identical in all of it statements with the axiomatic system of Euclidean geometry; the only exception is the formulation of the axiom of the parallels. The geometry of the spherical surface can be viewed as the realization of a two-dimensional non-Euclidean geometry: the denial of the axiom of the parallels singles out that generalization of geometry which occurs in the transition from the plane to the curve surface."

"...the principle of the limiting character of the velocity of light. This statement... is not an arbitrary assumption but a physical law based on experience. In making this statement, physics does not commit the fallacy of regarding absence of knowledge as evidence for knowledge to the contrary. It is not absence of knowledge of faster signals, but positive experience which has taught us that the velocity of light cannot be exceeded. For all physical processes the velocity of light has the property of an infinite velocity. In order to accelerate a body to the velocity of light, an infinite amount of energy would be required, and it is therefore physically impossible for any object to obtain this speed. This result was confirmed by measurements performed on electrons. The kinetic energy of a mass point grows more rapidly than the square of its velocity, and would become infinite for the speed of light."

"If the definition of simultaneity is given from a moving system, the spherical surface will result when Einstein's definition with є = 1/2 is used, since it is this definition which makes the velocity of light equal in all directions."

"Why is Einstein's theory better than Lorentz's theory? It would be a mistake to argue that Einstein's theory gives an explanation of Michelson's experiment, since it does not do so. Michelson's experiment is simply taken over as an axiom."

"Clocks are inherently four-dimensional instruments, since the endpoints of their unit distances are events. Measuring rods, on the other hand, are three-dimensional measuring instruments; their end points are space points and they can be changed into four-dimensional measuring instruments only if events are produced at their end points according to a special rule."

"Light signals alone provide the metrical structure of the four-dimensional space-time continuum. The construction may be called light axioms."

"Once a definition of congruence is given, the choice of geometry is no longer in our hands; rather, the geometry is now an empirical fact."

"This fact... proves that space measurements are reducible to time measurements. Time is therefore logically prior to space."

"For the Lorentz transformation spatial measurements are also changed, because they are obtained relative to a moving system. In our example only time was transformed, while the distances between points at rest remained the same; the spatial coordinates, therefore, retain their identity."

"...the famous assertion by Einstein that the length of a rod depends on its velocity and on the chosen definition of simultaneity. ...is based on the fact that we do not measure the length of the rod, but its projection on a system at rest. How the length of the projection depends on the choice of simultaneity can be illustrated by reference to a photograph taken through a focal-plane shutter. Such a shutter... consists of a wide band with a horizontal slit, which slides down vertically. Different bands are photographed successively on the film. Moving objects are therefore strangely distorted; the wheels of a rapidly moving car for instance, appear to be slanted. The shape of the objects in the picture will evidently depend on the speed of the shutter. Similarly, the length of the moving segment depends on the definition of simultaneity. One definition of simultaneity differs from another because events that are simultaneous for one definition occur successively for another. What may be a simultaneity projection of a moving segment for one definition is a "focal-plane shutter photograph" for another."

"...absolute time would exist in a causal structure for which the concept indeterminate as to time order lends to a unique simultaneity, i.e., for which there is no finite interval of time between the departure and return of a first-signal..."

"We define: any two events which are indeterminate as to their time order may be called simultaneous. ...Simultaneity means the exclusion of causal connection. ...Yet we must not commit the mistake of attempting to derive from it the conclusion that this definition coordinates to any given event at a given different place. This would be the case only for a special form of causal structure, a form that does not conform to physical reality."

"...introduce the auxiliary concept of first-signal...defined as the fastest message carrier between any two points in space. We now send a first-signal from P, calling the event of departure E1... The event of its arrival at P' is called E'. Simultaneously with the arrival of this signal, another first signal is sent from P'. The arrival of this signal at P is the event E2. ...the time interval between E1 and E2 is coordinated to the event E', [E1 is earlier than E' and E2 is later than E'] and every event of this time interval except for the endpoints is inderterminate as to the time order relative to E'."

"If along the path of truth, success (which was often near-failure unnoticed) is subjected to the same scrutiny and desire for improvement as failure, we may find ourselves in closer proximity to trees."

"Occasionally one speaks... of signals or signal chains. It should be noted that the word signal means the transmission of signs and hence concerns the very principle of causal order..."

"If E1 is the cause of E2, then a small variation (a mark) in E1 is associated with a small variation in E2, whereas small variations in E2 are not associated with variations in E1. If we wish to express even more clearly that this concept does not contain the concept of temporal order, we can express it in the following form, where events that show a slight variation are designated E*: E1E2, E1*E2*, E1E2* and never the combination E1*E2."

"Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery. One might think that time can now be conceived as a kind of space and try in vain to add visually a fourth dimension to the three dimensions of space. It is essential to guard against such a misunderstanding of mathematical concepts. If we add time to space as a fourth dimension it does not lose any of its peculiar character as time. ...Musical tones can be ordered according to volume and pitch and are thus brought into a two dimensional manifold. Similarly colors can be determined by the three basic colors red, green and blue... Such an ordering does not change either tones or colors; it is merely a mathematical expression of something that we have known and visualized for a long time. Our schematization of time as a fourth dimension therefore does not imply any changes in the conception of time. ...the space of visualization is only one of many possible forms that add content to the conceptual frame. We would therefore not call the representation of the tone manifold by a plane the visual representation of the two dimensional tone manifold."

"Some philosophers have believed that a philosophical clarification of space also provided a solution of the problem of time. Kant presented space and time as analogous forms of visualization and treated them in a common chapter in his major epistemological work. Time therefore seems to be much less problematic since it has none of the difficulties resulting from multidimensionality. Time does not have the problem of mirror-image congruence, i.e., the problem of equal and similarly shaped figures that cannot be superimposed, a problem that has played some role in Kant's philosophy. Furthermore, time has no problem analogous to non-Euclidean geometry. In a one-dimensional schema it is impossible to distinguish between straightness and curvature. ...A line may have external curvature but never an internal one, since this possibility exists only for a two-dimensional or higher continuum. Thus time lacks, because of its one-dimensionality, all those problems which have led to philosophical analysis of the problems of space."

"We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics."

"If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. ...Hence the question of whether axioms are a priori becomes pointless since they are arbitrary."

"We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds."

"Carnap calls such concepts as point, straight line, etc., which are given by implicit definitions, improper concepts. Their peculiarity rests on the fact that they do not characterize a thing by its properties, but by its relation to other things. Consider for example the concept of the last car of a train. Whether or not a particular car falls under this description does not depend on its properties but on its position relative to other cars. We could therefore speak of relative concepts, but would have to extend the meaning of this term to apply not only to relations but also to the elements of the relations."

"The main objection to the theory of pure visualization is our thesis that the non-Euclidean axioms can be visualized just as rigorously if we adjust the concept of congruence. This thesis is based on the discovery that the normative function of visualization is not of visual but of logical origin and that the intuitive acceptance of certain axioms is based on conditions from which they follow logically, and which have previously been smuggled into the images. The axiom that the straight line is the shortest distance is highly intuitive only because we have adapted the concept of straightness to the system of Eucidean concepts. It is therefore necessary merely to change these conditions to gain a correspondingly intuitive and clear insight into different sets of axioms; this recognition strikes at the root of the intuitive priority of Euclidean geometry. Our solution of the problem is a denial of pure visualization, inasmuch as it denies to visualization a special extralogical compulsion and points out the purely logical and nonintuitive origin of the normative function. Since it asserts, however, the possibility of a visual representation of all geometries, it could be understood as an extension of pure visualization to all geometries. In that case the predicate "pure" is but an empty addition, since it denotes only the difference between experienced and imagined pictures, and we shall therefore discard the term "pure visualization." Instead we shall speak of the normative function of the thinking process, which can guide the pictorial elements of thinking into any logically permissible structure."

"There is no pure visualization in the sense of a priori philosophies; every visualization is determined by previous sense perceptions, and any separation into perceptual space and space of visualization is not permissible, since the specifically visual elements of the imagination are derived from perceptual space. What led to the mistaken conception of pure visualization was rather an improper interpretation of the normative function... an essential element of all visual representations. Indeed, all arguments which have been introduced for the distinction of perceptual space and space of visualization are base on this normative component of the imagination."

"Common to the two geometries is only the general property of one-to-one correspondence, and the rule that this correspondence determines straight lines as shortest lines as well as their relations of intersection."

"The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry."