Throughout this book, Gooch tells and retells the stories of Socrates and Jesus as he examines perennial human issues: why would anyone willingly die? To what do these two martyrlike deaths bear witness? What are the limits of words in explanation and defense? Why was Jesus silent during his trial? Why did Socrates' most powerful apologia fail? What words, if any, work in prayer? Do words work against the fear of death? Out of this philosophical and religious questioning, Reflections on (...) Jesus and Socrates throws new light on these two compelling figures and on the continuing meanings of their stories for us today. (shrink)

More than 30 years ago in Annals of Science, Dr. Eric Forbes of the University of Edinburgh published the correspondence between Carl Gauss and Great Britain's Astronomer Royal, Nevil Maskelyne. Five of the letters he listed as missing have now been discovered, along with two entirely new letters he was unaware of. Their nearly complete correspondence can now be read for the first time in 200 years.

This paper publishes the correspondence between S. Germain and C.F. Gauss. The mathematical notes enclosed in her letters are published for the first time. These notes, in which she submitted some of her results, proofs and conjectures to Gauss for his evaluation, were inspired by her study of the Disquisitiones Arithmeticae. The interpretation of these mathematical notes not only shows how deeply she went into Gauss’s treatise and mastered it long before any other mathematician, but also, more (...) importantly, shows that she obtained interesting results in the theory of power residues that have never previously been attributed to her. (shrink)

Jakob Friedrich Fries (1773-1843): A Philosophy of the Exact Sciences -/- Shortened version of the article of the same name in: Tabula Rasa. Jenenser magazine for critical thinking. 6th of November 1994 edition -/- 1. Biography -/- Jakob Friedrich Fries was born on the 23rd of August, 1773 in Barby on the Elbe. Because Fries' father had little time, on account of his journeying, he gave up both his sons, of whom Jakob Friedrich was the elder, to (...) the Herrnhut Teaching Institution in Niesky in 1778. Fries attended the theological seminar in Niesky in autumn 1792, which lasted for three years. There he (secretly) began to study Kant. The reading of Kant's works led Fries, for the first time, to a deep philosophical satisfaction. His enthusiasm for Kant is to be understood against the background that a considerable measure of Kant's philosophy is based on a firm foundation of what happens in an analogous and similar manner in mathematics. -/- During this period he also read Heinrich Jacobi's novels, as well as works of the awakening classic German literature; in particular Friedrich Schiller's works. In 1795, Fries arrived at Leipzig University to study law. During his time in Leipzig he became acquainted with Fichte's philosophy. In autumn of the same year he moved to Jena to hear Fichte at first hand, but was soon disappointed. -/- During his first sojourn in Jenaer (1796), Fries got to know the chemist A. N. Scherer who was very influenced by the work of the chemist A. L. Lavoisier. Fries discovered, at Scherer's suggestion, the law of stoichiometric composition. Because he felt that his work still need some time before completion, he withdrew as a private tutor to Zofingen (in Switzerland). There Fries worked on his main critical work, and studied Newton's "Philosophiae naturalis principia mathematica". He remained a lifelong admirer of Newton, whom he praised as a perfectionist of astronomy. Fries saw the final aim of his mathematical natural philosophy in the union of Newton's Principia with Kant's philosophy. -/- With the aim of qualifying as a lecturer, he returned to Jena in 1800. Now Fries was known from his independent writings, such as "Reinhold, Fichte and Schelling" (1st edition in 1803), and "Systems of Philosophy as an Evident Science" (1804). The relationship between G. W. F. Hegel and Fries did not develop favourably. Hegel speaks of "the leader of the superficial army", and at other places he expresses: "he is an extremely narrow-minded bragger". On the other hand, Fries also has an unfavourable take on Hegel. He writes of the "Redundancy of the Hegelistic dialectic" (1828). In his History of Philosophy (1837/40) he writes of Hegel, amongst other things: "Your way of philosophising seems just to give expression to nonsense in the shortest possible way". In this work, Fries appears to argue with Hegel in an objective manner, and expresses a positive attitude to his work. -/- In 1805, Fries was appointed professor for philosophy in Heidelberg. In his time spent in Heidelberg, he married Caroline Erdmann. He also sealed his friendships with W. M. L. de Wette and F. H. Jacobi. Jacobi was amongst the contemporaries who most impressed Fries during this period. In Heidelberg, Fries wrote, amongst other things, his three-volume main work New Critique of Reason (1807). -/- In 1816 Fries returned to Jena. When in 1817 the Wartburg festival took place, Fries was among the guests, and made a small speech. 1819 was the so-called "Great Year" for Fries: His wife Caroline died, and Karl Sand, a member of a student fraternity, and one of Fries' former students stabbed the author August von Kotzebue to death. Fries was punished with a philosophy teaching ban but still received a professorship for physics and mathematics. Only after a period of years, and under restrictions, he was again allowed to read philosophy. From now on, Fries was excluded from political influence. The rest of his life he devoted himself once again to philosophical and natural studies. During this period, he wrote "Mathematical Natural Philosophy" (1822) and the "History of Philosophy" (1837/40). -/- Fries suffered from a stroke on New Year's Day 1843, and a second stroke, on the 10th of August 1843 ended his life. -/- 2. Fries' Work Fries left an extensive body of work. A look at the subject areas he worked on makes us aware of the universality of his thinking. Amongst these subjects are: Psychic anthropology, psychology, pure philosophy, logic, metaphysics, ethics, politics, religious philosophy, aesthetics, natural philosophy, mathematics, physics and medical subjects, to which, e.g., the text "Regarding the optical centre in the eye together with general remarks about the theory of seeing" (1839) bear witness. With popular philosophical writings like the novel "Julius and Evagoras" (1822), or the arabesque "Longing, and a Trip to the Middle of Nowhere" (1820), he tried to make his philosophy accessible to a broader public. Anthropological considerations are shown in the methodical basis of his philosophy, and to this end, he provides the following didactic instruction for the study of his work: "If somebody wishes to study philosophy on the basis of this guide, I would recommend that after studying natural philosophy, a strict study of logic should follow in order to peruse metaphysics and its applied teachings more rapidly, followed by a strict study of criticism, followed once again by a return to an even closer study of metaphysics and its applied teachings." -/- 3. Continuation of Fries' work through the Friesian School -/- Fries' ideas found general acceptance amongst scientists and mathematicians. A large part of the followers of the "Fries School of Thought" had a scientific or mathematical background. Amongst them were biologist Matthias Jakob Schleiden, mathematics and science specialist philosopher Ernst Friedrich Apelt, the zoologist Oscar Schmidt, and the mathematician Oscar Xavier Schlömilch. Between the years 1847 and 1849, the treatises of the "Fries School of Thought", with which the publishers aimed to pursue philosophy according to the model of the natural sciences appeared. In the Kant-Fries philosophy, they saw the realisation of this ideal. The history of the "New Fries School of Thought" began in 1903. It was in this year that the philosopher Leonard Nelson gathered together a small discussion circle in Goettingen. Amongst the founding members of this circle were: A. Rüstow, C. Brinkmann and H. Goesch. In 1904 L. Nelson, A. Rüstow, H. Goesch and the student W. Mecklenburg travelled to Thuringia to find the missing Fries writings. In the same year, G. Hessenberg, K. Kaiser and Nelson published the first pamphlet from their first volume of the "Treatises of the Fries School of Thought, New Edition". -/- The school set out with the aim of searching for the missing Fries' texts, and re-publishing them with a view to re-opening discussion of Fries' brand of philosophy. The members of the circle met regularly for discussions. Additionally, larger conferences took place, mostly during the holidays. Featuring as speakers were: Otto Apelt, Otto Berg, Paul Bernays, G. Fraenkel, K. Grelling, G. Hessenberg, A. Kronfeld, O. Meyerhof, L. Nelson and R. Otto. On the 1st of March 1913, the Jakob-Friedrich-Fries society was founded. Whilst the Fries' school of thought dealt in continuum with the advancement of the Kant-Fries philosophy, the members of the Jakob-Friedrich-Fries society's main task was the dissemination of the Fries' school publications. In May/June, 1914, the organisations took part in their last common conference before the gulf created by the outbreak of the First World War. Several members died during the war. Others returned disabled. The next conference took place in 1919. A second conference followed in 1921. Nevertheless, such intensive work as had been undertaken between 1903 and 1914 was no longer possible. -/- Leonard Nelson died in October 1927. In the 1930's, the 6th and final volume of "Treatises of the Fries School of Thought, New Edition" was published. Franz Oppenheimer, Otto Meyerhof, Minna Specht and Grete Hermann were involved in their publication. -/- 4. About Mathematical Natural Philosophy -/- In 1822, Fries' "Mathematical Natural Philosophy" appeared. Fries rejects the speculative natural philosophy of his time - above all Schelling's natural philosophy. A natural study, founded on speculative philosophy, ceases with its collection, arrangement and order of well-known facts. Only a mathematical natural philosophy can deliver the necessary explanatory reasoning. The basic dictum of his mathematical natural philosophy is: "All natural theories must be definable using purely mathematically determinable reasons of explanation." Fries is of the opinion that science can attain completeness only by the subordination of the empirical facts to the metaphysical categories and mathematical laws. -/- The crux of Fries' natural philosophy is the thought that mathematics must be made fertile for use by the natural sciences. However, pure mathematics displays solely empty abstraction. To be able to apply them to the sensory world, an intermediatory connection is required. Mathematics must be connected to metaphysics. The pure mechanics, consisting of three parts are these: a) A study of geometrical movement, which considers solely the direction of the movement, b) A study of kinematics, which considers velocity in Addition, c) A study of dynamic movement, which also incorporates mass and power, as well as direction and velocity. -/- Of great interest is Fries' natural philosophy in view of its methodology, particularly with regard to the doctrine "leading maxims". Fries calls these "leading maxims" "heuristic", "because they are principal rules for scientific invention". -/- Fries' philosophy found great recognition with Carl Friedrich Gauss, amongst others. Fries asked for Gauss's opinion on his work "An Attempt at a Criticism based on the Principles of the Probability Calculus" (1842). Gauss also provided his opinions on "Mathematical Natural Philosophy" (1822) and on Fries' "History of Philosophy". Gauss acknowledged Fries' philosophy and wrote in a letter to Fries: "I have always had a great predilection for philosophical speculation, and now I am all the more happy to have a reliable teacher in you in the study of the destinies of science, from the most ancient up to the latest times, as I have not always found the desired satisfaction in my own reading of the writings of some of the philosophers. In particular, the writings of several famous (maybe better, so-called famous) philosophers who have appeared since Kant have reminded me of the sieve of a goat-milker, or to use a modern image instead of an old-fashioned one, of Münchhausen's plait, with which he pulled himself from out of the water. These amateurs would not dare make such a confession before their Masters; it would not happen were they were to consider the case upon its merits. I have often regretted not living in your locality, so as to be able to glean much pleasurable entertainment from philosophical verbal discourse." -/- The starting point of the new adoption of Fries was Nelson's article "The critical method and the relation of psychology to philosophy" (1904). Nelson dedicates special attention to Fries' re-interpretation of Kant's deduction concept. Fries awards Kant's criticism the rationale of anthropological idiom, in that he is guided by the idea that one can examine in a psychological way which knowledge we have "a priori", and how this is created, so that we can therefore recognise our own knowledge "a priori" in an empirical way. Fries understands deduction to mean an "awareness residing darkly in us is, and only open to basic metaphysical principles through conscious reflection.". -/- Nelson has pointed to an analogy between Fries' deduction and modern metamathematics. In the same manner, as with the anthropological deduction of the content of the critical investigation into the metaphysical object show, the content of mathematics become, in David Hilbert's view, the object of metamathematics. -/-. (shrink)

This essay explores Hegel’s treatment of Carl Friedrich Gauss’s mathematical discoveries as examples of “Analytic Cognition.” Unfortunately, Hegel’s main point has been virtually lost due to an editorial blunder tracing back almost a century, an error that has been perpetuated in many subsequent editions and translations.The paper accordingly has three sections. In the first, I expose the mistake and trace its pervasive influence in multiple languages and editions of the Wissenschaft der Logik. In the second section, I (...) undertake to explain the mathematical significance of Gauss’s discoveries. In the third section, I take a look at the deeper implications of Hegel’s treatment of Gauss’s work as a window onto the nature and limitations of analytic cognition. In conclusion, I seek to explain how the linear method embodied in deductive reason leads by its own inner principle, according to Hegel, to its dialectical Aufhebung (sublation). The result is a kind of deliberately circular reasoning that he describes as “the Absolute Idea.”. (shrink)

The article analyses the components of the presumption of innocence and tries to clarify some of the conceptual and logical difficulties surrounding the notion of ‘innocence’ and the structure of legal presumptions. It is argued that all conceivable literal interpretations of the maxim make little or no sense, and that the presumptions form is, as such, devoid of original content: presumptions do not explain nor justify anything but are auxiliary norms which refer to the legal consequences spelled out in other (...) norms. Therefore, the presumption of innocence can be used to express any kind of requirement and standard for the criminal process and the treatment of suspect citizens only in a tautological, albeit rhetorically forceful, way. This instrumental use of the presumption of innocence is theoretically without merit but can be practically beneficial as long as there is no developed system of fundamental rights and protections of individual freedoms in a given legal order. Finally, a functional understanding of the presumption of innocence is proposed which gives it an original, though limited field of application as a guarantee of the procedure itself, in particular of the openness of the outcome. (shrink)

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Unter dem Titel "Lebenswelt und Wissenschaft" hat der XXI.

Ausgehend von einer Analyse des "Begründungsstreits", der in den letzten Jahren im Anschluß an H. Alberts Kritik des methodischen Prinzips der Begründung v.a. in der deutschen Philosophie geführt worden ist, werden zunächst die Positionen von K. O. Apel und J. Habermas einer immanenten methodischen Kritik unterzogen. Beide Programme erweisen sich als undurchführbar. Ausgehend von einer Präzisierung des Begriffes "Begründung" wird durch systematische Einführung begründungstheoretischer Termini ein begriffsiches Instrumentarium vorgeschlagen, das eine Rekonstruktion von Begründungssituationen erlauben soll. Mit seiner Hilfe werden die (...) im "Münchhausen-Trilemma" unterstellten Begründungssituationen genauer analysiert. Das "Münchhausen-Trilemma" wird als Argumentation für eine konstruktivistische und gegen eine reduktivistische Begründungskonzeption gewertet. (shrink)

Das Buch bietet einen systematischen Gesamtentwurf der Allgemeinen Ethik und damit für den interessierten Leser einen Zugang zu den wichtigsten Fragestellungen der Disziplin Ethik. Dazu werden im Anschluß an eine systematische und historische Einleitung propädeutische Fragen behandelt und die bekannten drei Paradigmen ethischer Reflexion (Tugendethik, Nutzenethik und Verpflichtungsethik) in Orientierung an den klassischen Texten dargestellt. Darauf aufbauend wird die mögliche Komplementarität dieser Paradigmen im Sinne eines Filtermodells sukzessiver ethischer Urteilsbildung entwickelt. Das Buch zeigt, ausgehend von den sprachphilosophischen und wissenschaftsphilosophischen Arbeiten (...) der Erlanger Schule, darüber hinaus, daß moralische Verpflichtungen und Berechtigungen mit ihren unterschiedlichen Graden von Verbindlichkeit ohne starke "realistische" und wertphilosophische Unterstellungen rekonstruiert werden können. (shrink)