Mandelbrot: Mathematics

Zitat

„A contribution to mathematics and/or science does not consist of a picture, but rather of a picture combined with a description. Without words and formulas, a picture can, at best, be praised for artistic quality. Without an interest in pictures and other aspects of ‚reality,‘ pictures can play no role whatsoever.“ (p. 26) #Mandelbrot #mathematics #picture

Bourbaki: A Mathematical Theory

Zitat

„A mathematical theory (or simply a theory) contains rules which allow us to assert that certain assemblies of signs are terms or relations of the theory, and other rules which allow us to assert that certain assemblies are theorems of the theory.“ (p. 16) #Bourbaki #theory #relation #theorem

Bourbaki: Mathematics and Truth

Zitat

„Mathematicians have always been convinced that what they prove is ‚true‘. It is clear that such a conviction can be only of a sentimental or metaphysical order, and cannot be justified, or even ascribed a meaning which is not tautological, within the domain of mathematics. The history of the concept of truth in mathematics therefore belongs to the history of philosophy and not of mathematics; but the evolution of this concept has had an undeniable influence on the development of mathematics, and for this reason we cannot pass over it in silence.“ (p. 306f.) #Bourbaki #mathematics #truth

Bourbaki: Greek Mathematics

Zitat

„The originality of the Greeks consists precisely in a conscious effort of arranging mathematical proofs in a sequence so that the passage from one step to the next leaves nothing in doubt and compels universal assent. Of course, the Greek mathematicians, just like their present-day successors, made use of ‚heuristic‘ rather than rigorous arguments in the course of their researches“. (p. 297) #Bourbaki #Greek #mathematics #proof #passage

Neu :: Bühlmann: Mathematics and Information in the Philosophy of Michel Serres

Zitat

„This book introduces the reader to Serres‘ manner of ‚doing philosophy‘ that can be traced throughout his entire oeuvre: namely as a novel manner of bearing witness, for which ‚mathematical thinking‘ plays a crucial role. It traces how Serres takes note of a range of epistemologically unsettling situations, which he witnesses as arising from addressing contemporary physics from within a production rather than a communication paradigm, and in consequence from the short-circuit of a proprietary notion of capital with a praxis of science that commits itself to a form of reasoning which privileges the most direct path (simple method) in order to expend minimal efforts while pursuing maximal efficiency. In Serres‘ universal economy, value is considered as a function of rarity, not as a stock of resources. This book demonstrates how Michel Serres has developed an architectonics that is coefficient with reality. Mathematics and Information in the Philosophy of Michel Serres acquaints the reader with Serres‘ code-relative and information-theoretic manner of addressing the universality and the nature of knowledge. Such knowledge is relative to the anonymous, objective cogito of the third person singular: we should say ‚it thinks‘ as we say ‚it rains‘, Serres maintains. The book will demonstrate and discuss how there is a definite but indetermined subjectivity (agency) of incandescent, inventive thought involved in such knowledge. It proceeds in a twofold manner: on the one hand, the chapters of the book demarcate, problematize and contextualize some of these epistemologically unsettling situations within the techno-scientific domains that have propelled their formation. On the other hand, careful attention is given to the particular manner in which Michel Serres responds to and converses with these situations, testifying for an “exodic” rather than “methodic” praxis of a science that is entirely of this world, and yet not deprived of its dignity.“ #Bühlmann #Serres #Mathematics #Information