PD Dr. Kay Herrmann

About myself:

After the "Diplom" ("The Reflexion Algebra of the Space-Time (M4) and Finite Bispinor-Transformations") in physics (University of Jena 1991) doctoral thesis about philosophical aspects of higherdimensional field theories (University of Jena 1994); after that research assistant at the institute of philosophy (University of Jena); "Habilitation" (Technical University of Chemnitz 2011) with a thesis about the apriorities of science.

Scientific interests:

Philosophy of science, philosophical foundations of science, Critical Philosophy (especially Friesian and Neo-Friesian philosophy)

Publications, Books:

K. Herrmann/ J. Schroth (Editors):Leonard Nelson - Kritische Naturphilosophie, Heidelberg 2004. (Leonard Nelson - Critical Natural Philosophy)
K. Herrmann:Mathematische Naturphilosophie in der
. Jakob Friedrich Fries und die Wissenschaften,
Göttingen 2000.
(Mathematical Natural Philosophy in Basic Debates. Jakob Friedrich Fries and the Sciences)
W. Hogrebe/ K. Herrmann
Jakob Friedrich Fries. Philosoph, Naturwissenschaftler und Mathematiker. Verhandlungen des Symposions "Probleme und Perspektiven von Jakob Friedrich Fries' Erkenntnislehre und Naturphilosophie" vom 9. - 11. Oktober 1997 an der Friedrich Schiller Universität Jena. Studia Philosophica et Historica, Bd. 25 (1999).
(Jakob Friedrich Fries. Philosopher, Natural Scientist and Mathematician. Proceedings of the Symposion "Problems and Perspectives of the Friesian Theory of Cognition and Natural Philosophy" from October 9 - 11th at the Friedrich-Schiller-University Jena)
K. Herrmann::Einheit und Höhendimensionalität, Frankfurt a.M./ Berlin/ Bern/ New York/ Paris/ Wien 1994.
(Unitarity and Higher Dimensionality)
K. Herrmann::What is the Competence of Philosophy of Science?
Welche Kompetenz hat Wissenschaftsphiloshopie? Antrittsvortrag zur Erlangung des Titels Privatdozent der Philosophischen Fakultät am 25.10.2011. -- Chemnitz : Universitätsverlag, 2012. - 60 S., ISBN 978-3-941003-59-0

Contact: kay.herrmann@phil.tu-chemnitz.de

Dr. Kay Herrmann

Leonard Nelson - Critical Natural Philosophy

Mathematical Natural Philosophy in Basic Debates -- Jakob Friedrich Fries and the Sciences

Jakob Friedrich Fries (1773-1843):  A Philosophy of the Exact Sciences

Kay Herrmann in Conversation with Rene Saran.

Nelson's Proof of the Impossibility of the Theory of Knowledge, Dr. Kay Herrmann, 2011

Leonard Nelson's Program of a Scientific Philosophy, 2008

Return to Jakob Fries

Faszination Zeitreisen – Eine Vision zwischen Science und Fiction. Chemnitz 2014.
Permalink: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-153695


Time travel is one of mankind's most ancient dreams. It inspires our imagination and provides material for bizarre stories. H. G. Wells' novel, "The Time Machine" (1895), marks the beginning of a long history of science fiction literature devoted to the subject of time travel.

A work on the subject of time travel forces us to re-examine our concept of "time". The complexity and the contradictory nature this subject makes it difficult to be more precise about "time". On its deepest subjective side, time is a means of perception, a biological rhythm, a social phenomenon in terms of our collective understanding of time. But it is also a physical parameter.

Einstein's Theory of Relativity revolutionised our idea of space and time by freeing us from the Newtonian concept of absolute space and absolute time. The "problem of time travel", a subject that Wells wrote about just ten years before as mere fiction, was now a discussion worthy of physics. Einstein's Special Theory of Relativity (1905), by predicting the effects of time dilation, allowed for "travels into the future" and Einstein's Theory of Gravity used closed time-like lines for solutions to calculations about time travel (for example, the Gödel Universe and the Anti-de Sitter Universe). However, a trip to a time warp would immediately involve a whole set of paradoxes (for example, the grandfather paradox and the information paradox) and semantic inconsistencies.

This work discusses approaches for "time machines" which are consistent with modern physics. Some of the discussions that will be presented are the tachyon hypothesis, Tipler's rotating cylinder, the Gödel Universe, the Anti-de Sitter Universe and so-called "wormholes". At the same time, approaches will be presented (for example, Eternalism, the Many-Worlds Interpretation and the Consistent Histories Approach) that will provide attempts to find a solution for paradoxes regarding time travel to the past.

Surprisingly, the fundamental laws of physics (apart from extremely rare and non-emergent macroscopic quantum mechanical effects) are not violated by the concept of time reversal. Yet, in nature, there still seems to be a fundamental prohibition against time travel to the past. Physicist Dieter Zeh, whose position is more closely presented in the final chapter of this work, supports the view that science fiction literature on the subject of "time travel" is overwhelmingly based on simple conceptual errors. The processes used in this literature, which are based on the General Theory of Relativity, at best, are just as "theoretically possible" as a gas which gathers itself into the corner of a container.

Questions about time travel to the past are like the questions asked on Radio Yerevan. The answer is always, "In principle yes, but…" But the fascination about time travel will continue to provide material for "fiction".

The Apriori and the Question of the Validity of Scientific Knowledge,
Das Apriori und die Frage der Geltung wissenschaftlicher Erkenntnis.



The problem of synthetic judgments touches upon the question whether philosophy is in fact capable of making independent truth statements. According to Kant, synthetic judgments formulate the conditions for the possibility of objectively valid knowledge a priori. As far as empirical attempts at reinterpretation of the aprioristic fall short of this ambition, Kant’s a priori goes deeper. This is because modern science strives towards objective knowledge, although its statements are fundamentally fallible. The topic of synthetic a priori thus continues to be relevant.

This paper will show that, in order to be viable at all, a modernized version of transcendental philosophy must ‘depart from’ the concepts of “independence from empirics” and/or the “purity” of the aprioristic. Kant’s reflections on non-pure synthetic a priori knowledge already contain attempts at this. Furthermore, the aprioristic validity of knowledge does not exclude the possibility, that it can be discovered empirically. Fries and, subsequently, Nelson proceeded with this separation (initially ascribed to Reichenbach) between the contexts of validity and discovery of knowledge, pointing out that the a priori can indeed be discovered empirically, yet never be proven.

Currently, there are still a number of valid reasons for arguing that concepts from transcendental philosophy continue to be of fundamental importance for the modern sciences. However, it must not be neglected that, even within a modernized framework of transcendental philosophy various unsolved problems remain and/or are created (such as the unfeasibility of the aprioristic claim to general validity and necessity, the problem of drawing a clear boundary between the noumenal and phenomenal worlds). Moreover, the “beautiful structure” of the Kantian system, which constitutes much of its persuasive strength, is lost.

Titel: Das Apriori und die Frage der Geltung Wissenschaftlicher Erkenntnis

Verfasser: Herrmann, Kay

Dokumenttyp: Konferenzveröffentlichung

Erscheinungsdatum: 2014

Publikation in MIAMI: 05.09.2014

Datum der letzten Änderung: 12.09.2014

Zeitschrift/Periodikum: XXIII. Kongress der Deutschen Gesellschaft für Philosophie 2014 Münster / 27

Schlagworte: Philosophie; Geschichte; Gesellschaft; Geltung; DGPhil

Fachgebiete: Philosophie

Sprache: Deutsch

URN: urn:nbn:de:hbz:6-92319359771

Permalink: http://nbn-resolving.de/urn:nbn:de:hbz:6-92319359771

Onlinezugriff: artikel_herrmann_2014.pdf

K. Herrmann,

What is the Competence of Philosophy of Science?

Welche Kompetenz hat Wissenschaftsphiloshopie? Antrittsvortrag zur Erlangung des Titels Privatdozent der Philosophischen Fakultät am 25.10.2011.

Chemnitz: Universitätsverlag, 2012. -- 60 S., ISBN 978-3-941003-59-0

Many prominent scientists have pointed out that philosophy is of no benefit to science. Stephen Hawking asserts:  Philosophy is dead.

The sciences use conceptions like natural laws, matter, nature, theories, etc. But science is also confronted with questions such as:  "What is a natural law?" "What is nature?" "What is matter?" and "What is a scientific theory?" These (metatheoretical) questions exceed the sphere of competence of science -- they are items of the philosophy of science. The philosophy of science is a metatheory of science. Philosophy of science overlaps epistemology, ontology, and metaphysics by exploring whether scientific results are true, or whether entities like quarks or electrons really exist.

More detailed investigations bring questions under consideration such as:  "How do we define the boundaries between different scientific disciplines?" "Is there a relation between the beauty and the truth of a scientific theory?" and "How do we distinguish between science and pseudoscience?" Additionally the philosophy of science is concerned with ethical problems of modern technology, with methodological questions, with the reconstruction of the structure and the development of scientific theories, and with revealing of any indoctrination of science.

The optimistic conclusion of this paper is:  Philosophy is still alive -- but the philosopher has to seek a critical dialogue with scientists. We just want philosophers talking to scientists.

Publication Webpage

Herrmann, K.:
Apriori im Wandel
Für und wider eine kritische Metaphysik der Natur
Universitätsverlag C. Winter. Heidelberg 2012. ISBN 978-3-8253-6102-0
(The a priories in transition
Pros and cons of a critical metaphysics of nature)


In the 19th century, a transition took place from the classical to the modern ideal of science: Science would no longer be regarded as a categorical-deductive system of absolute truths, but instead as a hypothetical-deductive system of problematically conditional propositions. In this process, the synthetic a priori also took on more and more of the status of something problematically conditional, which could be found out and corrected empirically, and was itself even ultimately contingent upon empiricism. Along the way, it lost its original purpose, namely to formulate the conditions for the possibility of objective knowledge. To the extent that one continues to attribute objectivity to scientific knowledge, however, the question of the synthetic a priori remains current. The present volume aims to trace the historical roots and varied interpretations of the synthetic a priori while also seeking new approaches toward a contemporary reinterpretation of this fundamental concept.

K. Herrmann/ J. Schroth (Editors)

Leonard Nelson - Critical Natural Philosophy

Metaphysics as the foundation of science, philosophy as an exact method to discover this foundation: These are central themes in the Kant-Friesian philosophy which, at the beginning of the 20th century, Leonard Nelson, using the methods of mathematical axiomatics, further developed into interdisciplinary research programmes. Nelson carried out this research programme in his ethics but his untimely death prevented a systematic presentation of his natural philosophy and his doctrine of method. The present volume contains four transcripts of his seminars on natural philosophy which he held over a period of 15 years. The transcripts, which may be taken as a comparatively complete presentation of Nelson's natural philosophy, supplement the writings published during his lifetime and convey a representative picture of his natural philosophy.

Return to Kay Herrmann

Return to Jakob Fries

Kay Herrmann

Mathematical Natural Philosophy in Basic Debates
Jakob Friedrich Fries and the Sciences




251 pages, 7 indexes, 20 pictures, 1 table
DM 78,-/ öS 569,- / Sfr 73,-
ISBN 3-525-30516-8

Jakob Friedrich Fries is one of the most important representatives of the Critical Philosophy, someone who built immediately on the original Kantian philosophy.

Fries was born in 1773 in Barby (on the Elbe). In 1805 he was extraordinary professor for philosophy in Jena and in the same year was ordinary professor for philosophy in Heidelberg. Returning to Jena in 1816, one year later he was compulsorily retired because of his participation at the nationalistic and republican Wartburg Festival. In 1824 he obtained a professorship for physics and mathematics, and in 1838 he was given back a professorship for philosophy. He died in 1843 in Jena.

The book summarizes the research results of the DFG-Project "Jakob Friedrich Fries' Influence on the Sciences of the 19th Century". The research project was carried out by Dr. Kay Herrmann (Institute of Philosophy, Jena University) and Prof. Dr. Wolfram Hogrebe (Institute of Philosophy, Bonn University). Such a study has special importance. There is available a large amount of literature about the "speculative contemporaries" of Fries, like Fichte, Schelling, and Hegel. In contrast to the "speculative philosophy", there has been published only a few studies about the Friesian natural philosophy. Fries was, in his natural-philosophical studies, looking for a link between philosophy and modern sciences, wheras his "speculative philosophical" contemporaries felt obligated to stick primarily to a descriptive, phenomenal view of nature. So far the question "How was mathematical natural philosophy regarded by scientists and mathematicians of the 19th century?" has hardly been investigated. Archival studies showed that this gap in Fries-research can be filled. The Friesian correspondence turned out to be a rich gold mine.

The present publication is more than a research report. The monographic first part is intended to introduce the foundations of the Friesian theory of cognition, the Friesian methodology, and the Friesian natural philosophy. This should facilitate entry into Friesian philosophy.

The Friesian theory is analyzed from two points of view:

Chapters 3 and 4 are scientific-historically oriented. These chapters analyze the Friesian position in scientific and mathematical debates (debates about the a priori foundations of physics, the problem of the identification of physics as an independent discipline, the problem of the boundary between chemistry and physics, the problem of mathematization of the sciences, the theory of the imponderabilia, the systematics and structure of sciences and mathematics, problems of infinity, the differential calculus, the theory of parallel lines) and the relation between Fries and the scientists of the 19th century. The book contains the latest findings gained by evaluation of the Friesian unpublished work (for example the correspondence with W. Weber, C. F. Gauß, E. F. Apelt, O. Schlömilch, Ch. Reichel, B. A. v. Lindenau, L. Gmelin, E. G. Fischer, A. N. Scherer, J. S. C. Schweigger)

One result of the research project is that some important scientists took a favourable view of the Friesian theory, but the influence of the Friesian philosophy on the sciences of the 19th century was very limited. The causes are very complex: An anti-natural-philosophical spirit of age, the limits of the Kantian inspired philosophy and some unfavourable aspects in the biography of Fries.

For the first time the voluminous Fries-Reichel-correspondence was evaluated. The Fries-Reichel-correspondence contains the Friesian approach to prove the 11th Euclidean axiom, and the whole transcript of the Friesian attempt at proof is given.

The author
Dr. Kay Herrmann studied physics at the University of Jena and received there a Doctorate in Philosophy.
The present publication is the result of his research project, "Jakob Friedrich Fries' Influence on the Sciences of the 19th Century".

Interested parties
Philosophers, historians and natural scientists

The present study was published with the aid of the Fries-Foundation.

Return to Jakob Fries.

Kay Herrmann

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. Extracts from Fries' biography

His statue stands in the Fürstengraben, a street in Jena which connects the Pulverturm (one of the corner towers of the former Jena town wall) with the main building of the university, and is flanked by the busts of famous Jenenser scholars. Two schools of philosophy follow his teachings, famous scientists have presented their views on his works, and, nevertheless, his name is relatively little known: Jakob Friedrich Fries. Who was he, and what was it about his philosophy that made it so attractive for mathematicians and scientists?

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 Herrnhutischen Teaching Institution in Niesky in 1778. Jakob Friedrich Fries writes of this period: "Through my mathematical studies I received a firm measure of security and certainty, which gave my spirit its philosophical direction." [1]

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:

"This was a method of applying philosophy in such a way as I had never previously encountered. Mathematics provided a way to find basic, enlightened truths." [2]

During this period he also read Friedrich 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 this 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). As regards Reinhold, Fichte, Schelling and Hegel, he expressed himself in a rather ungentlemanly manner. He criticised Schelling's philosophy because it uses "external natural teachings", with no reference or use of mathematical methodology, instead using uncertain concepts. In a confidential letter he expressed himself on Schelling: "In Schelling, philosophical reasoning has become quite amazing; do not take my opinion on the beggar; here he comes again, more stupid by the day." [3]

The relationship between G. W. F. Hegel and Fries did not develop favourably. Only a few slighting remarks can be found regarding Fries amongst Hegel's notes. He 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"." [4]. In this work, Fries appears to argue with Hegel in an objective manner, and expresses a positive attitude to the work, despite its "unfortunate need to turn to superstition", which, in his opinion, stands in the way of a differentiation between accidental and necessary philosophical truth.

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, unprepared 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, laws of philosophy, 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), and "History of Philosophy" (1837/40) 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." [5]

3. Continuation of Fries' work through the Friesian School

Due to the fact that mathematics holds such an esteemed position amongst philosophers, Fries' ideas found general acceptance amongst scientists and mathematicians. A large part of the following 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 "Abhandlungen der Fries'schen Schule, Neue Folge" 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 attaches a "metaphysical ABC of the natural sciences" to Kant, as well as to the natural-philosophical works by J. Kepler, I Newton, Leibniz and J. L. Lagrange. He 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." [6]

Fries is of the opinion that science can attain completeness only by the subordination of the empirical facts to the general mathematical laws. This science consists of two steps:

  1. Empirical observation
  2. Subordination of the empirical facts to the generally accepted 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:

  1. A study of geometrical movement, which considers solely the direction of the movement
  2. A study of kinematics, which considers velocity in addition
  3. 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, according to which its development is accompanied by theories qualified by maxims. Fries calls these "leading maxims" "heuristic", "because they are principal rules for scientific invention". With the help of the leading maxims, mathematic theories are asserted, which enable the observation findings to be brought into a relationship with one another. Fries' study of the heuristic maxims has been successfully applied by Schleiden in his examination of living organisms.

The way that physicist Wilhelm Weber, who had been in contact with Fries, constructs his electromagnetic interaction law theory study model reminds us of the Fries' mechanism, although Weber indicates no particular leaning towards Fries' teachings. Weber begins with the implementation of his interaction law - as Schleiden also does - using the leading maxims which were determined in an empiric way:

"In order to gain as certain an empirical guide as possible for this investigation, three special events which can be partially based on indirect observation, and are partially self-explanatory, in that all of its measurements can be verified by the basic AMPÈRE laws, must be accepted as a basis."[7]

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."[8]

The publishers of Fries' works suppose that Fries' rejection of the actual infinite could have influenced the Gaussian point of view.

"It is not improbable, that the ancient Aristotelian thesis that: The infinite exists only in the "realms of the mere possibility, and within the scope of exhaustive procedures", which has made a comeback with the mastery of more 'modern' basic problems, actually made its way from Fries to Gauss."[9]

This interpretation is motivated by a remark in a letter from Gauss to Schuhmacher from the 12th of July, 1831. However, this was energetically contradicted in the 1920's by A. Fraenkel.

The new Fries school of thought also argued intensely with the philosophical problems of mathematics. Amongst the mathematicians of the 20th century who appreciates Fries' philosophy of mathematics are P. Bernays and G. Hessenberg. The starting point of this 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. "[10].

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.

5. References

WWFries, J. F.: Sämtliche Schriften. Compiled from the issue of the last authorised editions, with a foreword and a Fries lexicon provided by G. König/L. Geldsetzer. Aalen 1967 ff.
AFSNFAbhandlungen der Fries'schen Schule. Neue Folge. 1906-1937

6. Notes

1. Henke, Jakob Friedrich Fries, p. 388.

2. Ebd., p. 389.

3. Ebd., S. 394.

4. Fries: Geschichte der Philosophie. Bd. 1, p. XV (WW 18, p. XV).

5. Fries: System der Metaphysik, p. 55 (WW 8, p. 55).

6. Fries, Die mathematische Naturphilosophie nach philosophischer Methode bearbeitet, p. 621 f. (WW 13, p. 621 f.)

7. Weber, Werke, Bd. 3, p. 134.

8. Published in: AFSNF, Bd. 1, Heft 3 (1906), S. 437 f.

9. König/Geldsetzer: Publisher's notes for the 13th volume (WW 13, p. 36*f., footnote 54).

10. Cube, Die Auffassungen Jakob Friedrich Fries' und seiner Schule über die philosophischen Grundlagen der Mathematik und ihr Verhältnis zur Grundlagentheorie, p. 27.