Leonard Nelson was born the 11th of July in Berlin. The maiden name of his mother, Elizabeth, was Lejeune-Dirichlet. His mother was the great-granddaughter of the well known mathematician Gustav Peter Lejeune-Dirichlet, the successor of the famous mathematician Carl Friedrich Gauss. She was also related to the families of Felix-Mendelsohn-Bartholdy, of Du Bois-Reymond and to the philosopher Paul Hensel.
Elisabeth Nelson was an artist and Nelson's father Heinrich had artistic interests too. He wrote novels and novellas and translated, e.g. sonnets of Michelangelo, into the German. The parents' home was a center of attraction for people of different professions, such as the astronomer Wilhelm Foerster, the sons of the physiologist Du Bois-Reymond and the mathematician Carl Runge. They awakened Nelson's interests in the sciences and mathematics.
Leonard Nelson attended the French Grammar School in Berlin. Because science and mathematics had a low profile at this school, he received private tuition from the mathematician Gerhard Hessenberg. The lessons soon became a philosophical discussion. They discussed, for example, the axiomatic system of geometry. Later the axiomatic method became important in Nelson's philosophy. Hessenberg was the first scientist who influenced Nelson's philosophical interests. At that time Nelson started to read the works of I. Kant and J.F.Fries.
He started his university studies Heidelberg. Between 1901 and 1903 he studied in Berlin. Finally (1903/04) he changed to Göttingen.
In 1903 Nelson founded the Neo-Friesian School. Members were: Gerhard Hessenberg, Otto Meyerhof, Ernst Blumenberg, Carl Brinkmann, Heinrich Goesch, Aexander Rüstow, Rudolph Otto, Karl Kaiser, and Walter Baade. Later on Kurt Grelling and Richard Courant joint the School. Shortly after the foundation of the School The Proceedings of the Friesian School (New Series) were published. The editors included Gerhard Hessenberg and Karl Kaiser. Authors included O. Meyerhof, M. Djuvara, A. Kastil, and P. Bernays.
In 1904 Nelson published a paper entitled "Critical Method and the relationship of Psychology to Philosophy". It is a program for the Neo-Friesian School. In his paper Nelson gives a definition of the notion of "regessive method." Nelson shows a parallelism between Hilbert's axiomatic program and Fries' notion of "deduction." The regressive method leads to metaphysics. Metaphysics is a system of principles which are a priori synthetic judgments.
Nelson's philosophy of nature is influenced by close contacts with scientists and mathematicians. The Nelsonian philosophy of nature is an interdisciplinary research project. A complex network of relations can be demonstrated between the "Fries-Nelsonian Project" and well known scientists, mathematicians and philosophers. Figure 1 shows some of those relations.
Figure 1: The Network of Friesian Philosophy of Science and Nature
But there is also a big difference between those concepts. Nelson follows the approach of Fries: Deduction has to justify judgments by reducing them to their underlying immediate knowledge. But neither Nelson nor his followers succeeded in deducing mathematical axioms.
Besides, Hilbert had another intention. The basic idea of his Axiomatic Programme was the following: To describe the interrelations of the axioms by making them an object of meta-mathematics. With help of meta-mathematics the completeness, the independence and the consistency of the axioms can be proved. Therefore the task of Hilbert's Axiomatic Program is to find a complete, independent and consistent set of axioms for arithmetic. Nelson didn't reflect the details of the Axiomatic Program. He showed parallels only.
2 can't be defined without (aesthetic) ideas.
According to Nelson neither (aesthetic) ideas nor (philosophical) immediate knowledge can err. Error is always caused by reflection. Judgements are results of reflection. Therefore only judgments can be true or false.
Nelson gives a surprising solution to this antinomy. Every law has the general form:
If P, then S, or P -> S
But P must be realized to conclude S. P is the so called initial condition. To elucidate the events of nature we have to premise both: the laws of nature and initial conditions. But the choice of the initial conditions is a matter of the free volition. Our choice depends on special dictums and principles. Insofar as we deliberately select initial conditions our volition is free. There is no contradiction between ethics and physics. Quite the contrary, the existence of the laws of nature is an important precondition for the freedom of human volition. We couldn't act freely if we couldn't anticipate the results of our act.
He defines:
The scientific view of nature is targeted on a unity in the diversity of appearances of nature. It starts at individual appearances of nature, but asks for an underlying (deeper) connection.
Theory: A systematic composition of conclusions. The conclusions subordinate the objects of our perception to laws of nature.
Nature: A connection that is arranged by general laws. We can't imagine but conceptualize that connection.
Laws of nature: They are not laws of thinking. The laws of nature have objective validity.
Explanation of an appearance: reduction of the appearance of nature to a law of nature
Aesthetic view of nature: The single object is considered regardless of its being embedded in the connection of laws of nature. Object of the aesthetic view of nature is the single phenomenon. The single object is regarded in its individuality. The central notion is that of beauty. The notion of beauty can't be reduced to other notions, e.g. to the notion of usefulness.
Aesthetic judgments are general and necessary. They are apodictical. According to Nelson there is a close relation between the aesthetic view of nature and ideas. Nelson distinguishes between logical and aesthetic ideas. Logical ideas are notions without perception. They give us intimations of things-in-themselves. Such an idea is the idea of the complete unity of the world. We can think this idea, we can't perceive it.
Aesthetic ideas are perceptions that can't be determined conceptually. They give us an intimation of beauty.
Nelson shows a parallelism between the judgments of science and aesthetic judgments. Both are general and necessary. What is the reason? The reason for the universality and the necessity of the theoretical knowledge of science is the underlying laws of nature. But what is the reason of the universality and the necessity of aesthetic judgments? Nelson asserts that the reason can be found in logical ideas. Logical ideas form the basis of aesthetic judgments in like manner as the laws of nature form the basis of theoretical knowledge of science.
Figure 2: Logical and Aesthetic Ideas
Nelson doesn't investigate if there are relations between aesthetic judgments and the laws of nature. According to our interpretation there is a close relation between the notion unity of the world (object of aesthetic judgments) and the notion of the connection of the laws of nature (object of the judgments of theoretical science). According to our interpretation Nelson provides a model for the heuristic importance of aesthetic judgments.
A lot of important physical theories weren't established by hard facts, but by mathematical-aesthetic criteria. Examples are the General Theory of Relativity, the Program of the Unified Field Theory, and the Superstring Theories. Mathematical-aesthetic criteria are also important for the development and the acceptance of physical theories. Special aesthetic qualities make physical theories credible. Examples of such qualities are simplicity of the structure, smart mathematical composition and the achieved unification. Mathematical symmetries are also mathematical-aesthetic qualities of physical theories. There is a relation between special symmetries of physical equations and laws of nature (e.g. boost corresponds to the conservation of momentum). Special mathematical-aesthetic qualities of physical theories could indicate new physical laws. Nelson's theory of aesthetic judgments gives reasons: aesthetic judgments may contain hints on the world of things-in-themselves.