Academics From Germany

"Die tiefsten Probleme des modernen Lebens quellen aus dem Anspruch des Individuums, die Selbständigkeit und Eigenart seines Daseins gegen die Übermächte der Gesellschaft, des geschichtlich Ererbten, der äußerlichen Kultur und Technik des Lebens zu bewahren - die letzterreichte Umgestaltung des Kampfes mit der Natur, den der primitive Mensch um seine leibliche Existenz zu führen hat."

"Objectivity may also be defined as freedom: the objective individual is bound by no commitments which could prejudice his perception, understanding, and evaluation of the given."

"When one says, for example, that superiority and inferiority is a formation to be found in every human association, though the proposition certainly involves very profound insight into the essence of human nature and human relationship, yet the assertion is so general that it affords little knowledge of particular societary formations. In order to reach such particular knowledge we must study separate types of superiority and inferiority, and we must master the special features of their formation, which in proportion to their definiteness of course lose generality of application."

"Cities are, first of all, seats of the highest economic division of labor. They produce thereby such extreme phenomena as in Paris the remunerative occupation of the quatorzième. They are persons who identify themselves by signs on their residences and who are ready at the dinner hour in correct attire, so that they can be quickly called upon if a dinner party should consist of thirteen persons. In the measure of its expansion, the city offers more and more the decisive conditions of the division of labor. It offers a circle which through its size can absorb a highly diverse variety of services."

"Every social occurrence as such, consists of an interaction between individuals. In other words, each individual is at the same time an active and a passive agent in a transaction. In case of superiority and inferiority, however, the relation assumes the appearance of a one-sided operation ; the one party appears to exert, while the other seems merely to receive an influence."

"The brutality of a man purely motivated by monetary considerations … often does not appear to him at all as a moral delinquency, since he is aware only of a rigorously logical behavior, which draws the objective consequences of the situation."

"The individual who is subordinate to an objective law feels himself determined by it, while he, in turn, in no way determines the law, and has no possibility of reacting to it in a manner which could influence it—quite in contrast to even the most miserable slave, who, in some fashion at last, can still in this sense react to his master."

"The social game has a deeper double meaning—that it is played not only in a society as its outward bearer but that with its help people actually "play" "society.""

"Der Fremde ist uns nah, insofern wir Gleichheiten nationaler oder sozialer, berufsmäßiger oder allgemein menschlicher Art zwischen ihm und uns fühlen; er ist uns fern, insofern diese Gleichheiten über ihn und uns hinausreichen und uns beide nur verbinden, weil sie überhaupt sehr Viele verbinden."

"I understand the task of sociology to be description and determination of the historical-psychological origin of those forms in which interactions take place between human beings. The totality of these interactions, springing from the most diverse impulses, directed toward the most diverse objects, and aiming at the most diverse ends, constitutes "society.""

"Man's position in the world is defined by the fact that in every dimension of his being and behavior he finds himself at every moment between two boundaries. This condition appears as the formal structure of our existence, filled always with different contents in life's diverse provinces, activities, and destinies. We feel that the content and value of every hour stands between a higher and a lower; every thought between a wiser and a more foolish; every possession between a more extended and a more limited; every deed between a greater and a lesser measure of meaning, adequacy, and morality."

"Man is something that is to be overcome. Logically considered, this, too, presents a contradiction: he who overcomes himself is admittedly the victor, but he is also the defeated. The ego succumbs to itself, when it wins; it achieves victory, when it suffers defeat. Yet the contradiction only arises when the two aspects of this unity are hardened into opposed, mutually exclusive conceptions. It is precisely the fully unified process of the moral life which overcomes and surpasses every lower state by achieving a higher one, and again transcends this latter state through one still higher. That man overcomes himself means that he reaches out beyond the bounds that the moment sets for him. There must be something at hand to be overcome, but it is only there in order to be overcome. Thus even as an ethical agent, man is the limited being that has no limit."

"One of the first theorists to acknowledge the deep and important impact of urbanization on social life was the German scholar, Georg Simmel. Simmel developed a sociology that focused on the special ways that forms, such as the number of people in groups, influenced social life. His effort to understand the nature of urbanization and, in particular, the metropolis of the late nineteenth and early twentieth centuries, displayed his characteristic method of analysis."

"This Reger is a sarcastic, churlish fellow, bitter and pedantic and rude. He is a sort of musical Cyclops, a strong, ugly creature bulging with knotty and unshapely muscles, an ogre of composition. In listening to these works...one is perforce reminded of the photograph of Reger which his publishers place on the cover of their catalogue of his works, the photograph that shows something that is like a swollen, myopic beetle with thick lips and sullen expression, crouching on an organ bench."

"Ein Philosoph, der keine Beziehung zur Geometrie hat, ist nur ein halber Philosoph, und ein Mathematiker, der keine philosophische Ader hat, ist nur ein halber Mathematiker."

"A judgment, for me is not the mere grasping of a thought, but the admission of its truth."

"Equality gives rise to challenging questions which are not altogether easy to answer... a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names 'a' and 'b' designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing."

"Logic is an old subject, and since 1879 it has been a great one."

"Bertrand Russell found Frege's famous error: Frege had overlooked what is now known as the Russell paradox. Namely, Frege's rules allowed one to define the class of x such that P(x) is true for any "concept" P. Frege's idea was that such a class was an object itself, the class of objects "falling under the concept P." Russell used this principle to define the class R of concepts that do not fall under themselves. This concept leads to a contradiction... argument: (1) if R falls under itself then it does not fall under itself; (2) this contradiction shows that it does not fall under itself; (3) therefore by definition it does fall under itself after all."

"From the medieval development of Aristotle's logic through Leibniz's Characteristica Universalis through Frege and Russell and up to the present development of symbolic logic, it could be argued that exactly the reverse [of Jacques Derrida's argument] is the case; that by emphasizing logic and rationality, philosophers have tended to emphasize written language as the more perspicuous vehicle of logical relations. Indeed, as far as the present era in philosophy is concerned, it wasn't until the 1950s that serious claims were made on behalf of the ordinary spoken vernacular languages, against the written ideal symbolic languages of mathematical logic. When Derrida makes sweeping claims about "the history of the world during an entire epoch," the effect is not so much apocalyptic as simply misinformed."

"Our representative absolutist is Gottlob Frege, whose writings did as much as anything to revive the 'mathematizing' approaches of the Platonist tradition around 1900, and did so—quite explicitly—as a means of protecting philosophy from subordination to the facts of history and psychology. ...The Platonist strand in Descartes' philosophy was revived... by... Frege, who promulgated the original programme of 'conceptual analysis' in his Foundations of Arithmetic. ...Frege ...was rebelling ...against the tendency to telescope formal and prescriptive 'laws of thought', which were the proper concern of logic, with the empirical and descriptive 'laws of thinking', which were the business of cognitive psychologists... [W]e should ignore all merely empirical discoveries, whether about the development of understanding in the individual mind or about the historical evolution of our communal understanding. ...Philosophers must concern themselves with 'concepts' only as timeless, intellectual ideals, towards which the human mind struggles, at best, painfully and little by little. ...[A]ctual conceptions current in any existing community are philosophically significant only as an approximation to the eternal system of ideal 'concepts'. ...[A]ny actual, historical set of conceptions has a legitimate intellectual claim on us, only to the extent that it approximates that ideal."

"Gottlob Frege created modern logic including "for all," "there exists," and rules of proof. Leibniz and Boole had dealt only with what we now call "propositional logic" (that is, no "for all" or "there exists"). They also did not concern themselves with rules of proof, since their aim was to reach truth by pure calculation with symbols for the propositions. Frege took the opposite track: instead of trying to reduce logic to calculation, he tried to reduce mathematics to logic, including the concept of number."

"Is it always permissible to speak of the extension of a concept, of a class? And if not, how do we recognize the exceptional cases? Can we always infer from the extension of one concept's coinciding with that of a second, that every object which falls under the first concept also falls under the second?"

"The historical approach, with its aim of detecting how things began and arriving from these origins at a knowledge of their nature, is certainly perfectly legitimate; but it also has its limitations. If everything were in continual flux, and nothing maintained itself fixed for all time, there would no longer be any possibility of getting to know about the world, and everything would be plunged into confusion."

"We suppose, it would seem, that concepts grow in the individual mind like leaves on a tree, and we think to discover their nature by studying their growth; we seek to define them psychologically, in terms of the human mind. But this account makes everything subjective, and if we follow it through to the end, does away with truth. What is known as the history of concepts is really a history either of our knowledge of concepts or of the meanings of words."

"A scientist can hardly meet with anything more undesirable than to have the foundations give way just as the work is finished. I was put in this position by a letter from Mr. Bertrand Russell when the work was nearly through the press."

"Often it is only after immense intellectual effort, which may have continued over centuries, that humanity at last succeeds in achieving knowledge of a concept in its pure form, by stripping off the irrelevant accretions which veil it from the eye of the mind."

"If the task of philosophy is to break the domination of words over the human mind [...], then my concept notation, being developed for these purposes, can be a useful instrument for philosophers [...] I believe the cause of logic has been advanced already by the invention of this concept notation."

"This ideography is a "formula language", that is, a lingua characterica, a language written with special symbols, "for pure thought", that is, free from rhetorical embellishments, "modeled upon that of arithmetic", that is, constructed from specific symbols that are manipulated according to definite rules."

"I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction."

"Nur im Zusammenhange eines Satzes bedeuten die Wörter etwas. Es wird also darauf ankommen, den Sinn eines Satzes zu erklären, in dem ein Zahlwort vorkommt."

"Without some affinity in human ideas art would certainly be impossible; but it can never be exactly determined how far the intentions of the poet are realized."

"Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic."

"Being true is different from being taken as true, whether by one or by many or everybody, and in no case is it to be reduced to it. There is no contradiction in something's being true which everybody takes to be false. I understand by 'laws of logic' not psychological laws of takings-to-be-true, but laws of truth. ...If being true is thus independent of being acknowledged by somebody or other, then the laws of truth are not psychological laws: they are boundary stones set in an eternal foundation, which our thought can overflow, but never displace. It is because of this that they have authority for our thought if it would attain truth. They do not bear the relation to thought that the laws of grammar bear to language; they do not make explicit the nature of our human thinking and change as it changes."

"The ideal of strictly scientific method in mathematics which I have tried to realise here, and which perhaps might be named after Euclid I should like to describe in the following way... The novelty of this book does not lie in the content of the theorems but in the development of the proofs and the foundations on which they are based... With this book I accomplish an object which I had in view in my Begriffsschrift of 1879 and which I announced in my Grundlagen der Arithmetik. I am here trying to prove the opinion on the concept of number that I expressed in the book last mentioned."

"It really is worth the trouble to invent a new symbol if we can thus remove not a few logical difficulties and ensure the rigour of the proofs. But many mathematicians seem to have so little feeling for logical purity and accuracy that they will use a word to mean three or four different things, sooner than make the frightful decision to invent a new word."

"'Facts, facts, facts,' cries the scientist if he wants to emphasize the necessity of a firm foundation for science. What is a fact? A fact is a thought that is true. But the scientist will surely not recognize something which depends on men's varying states of mind to be the firm foundation of science."

"If I compare arithmetic with a tree that unfolds upward into a multitude of techniques and theorems while its root drives into the depths, then it seems to me that the impetus of the root."

"Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician."

"It was Rudolf Carnap’s dream for the last three decades of his life to show that science proceeds by a formal syntactic method; today no one to my knowledge holds out any hope for that project."

"Yes, he is one of my heroes. I took a seminar from him under the GI bill after I got out of the Navy. It was not when I was an undergraduate. That was the only graduate course I ever took. It was on the philosophy of science, and it had a big influence on me. Later, when Carnap was giving the course in California, I persuaded him to have his wife tape record it. She typed it up and sent me the typed version. I edited it into a book called Introduction to the Philosophy of Science. That was the only popular book that Carnap ever did. All I did was edit it into language an average person could understand without knowing any math."

"Put in a nut-shell, my thesis amounts to this. The repeated attempts made by Rudolf Carnap to show that the demarcation between science and metaphysics coincides with that between sense and nonsense have failed. The reason is that the positivistic concept of 'meaning' or 'sense' (or of verifiability, or of inductive confirmability, etc.) is inappropriate for achieving this demarcation — simply because metaphysics need not be meaningless even though it is not science. In all its variations demarcation by meaninglessness has tended to be at the same time too narrow and too wide: as against all intentions and all claims, it has tended to exclude scientific theories as meaningless, while failing to exclude even that part of metaphysics which is known as 'rational theology'."

"To be sure, we have to face at this point an important question; but it is a practical, not a theoretical question; it is the question of whether or not to accept the new linguistic forms. The acceptance cannot be judged as being either true or false because it is not an assertion. It can only be judged as being more or less expedient, fruitful, conducive to the aim for which the language is intended. Judgments of this kind supply the motivation for the decision of accepting or rejecting the kind of entities."

"For those who want to develop or use semantical methods, the decisive question is not the alleged ontological question of the existence of abstract entities but rather the question whether the rise of abstract linguistic forms or, in technical terms, the use of variables beyond those for things (or phenomenal data), is expedient and fruitful for the purposes for which semantical analyses are made, viz. the analysis, interpretation, clarification, or construction of languages of communication, especially languages of science."

"For me personally, Wittgenstein was perhaps the philosopher who, besides Russell and Frege, had the greatest influence on my thinking. The most important insight I gained from his work was the conception that the truth of logical statements is based only on their logical structure and on the meaning of the terms. Logical statements are true under all conceivable circumstances; thus their truth is independent of the contingent facts of the world. On the other hand, it follows that these statements do not say anything about the world and thus have no factual content."

"After the new forms are introduced into the language, it is possible to formulate with their help internal questions and possible answers to them. A question of this kind may be either empirical or logical; accordingly a true answer is either factually true or analytic."

"After defining semantical concepts like logical truth and related ones, I proposed to interpret the modalities as those properties of propositions which correspond to certain semantical properties of the sentences expressing the propositions. For example, a proposition is logically necessary if and only if a sentence expressing it is logically true."

"If someone wishes to speak in his language about a new kind of entities, he has to introduce a system of new ways of speaking, subject to new rules; we shall call this procedure the construction of a linguistic framework for the new entities in question."

"Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements."

"The main purpose of this book is the development of a new method for the semantical analysis of meaning, that is, a new method for analyzing and describing the meanings of linguistic expressions. This method, called the method of extension and intension, is developed by modifying and extending certain customary concepts, especially those of class and property. The method will be contrasted with various other semantical methods used in traditional philosophy or by contemporary authors."