“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
“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
“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
“The Object of Geometry, its not being sufficiently understood, cause of Difficulty and useless Labour in that Science.
By this time, I suppose, ’tis clear that neither Abstract, nor Visible Extension makes the Object of Geometry. The not discerning of which might, perhaps, have created some Difficulty, and useless Labour in Mathematics. Sure I am, that somewhat relating thereto has occur’d to my Thoughts, which, tho’ after the most anxious and repeated Examination I am forced to think it true, doth, nevertheless, seem so far out of the common road of Geometry, that I know not, whether it may not be thought Presumption, if I shou’d make it publick in an Age, wherein that Science hath receiv’d such mighty Improvements by new Methods; great Part whereof, as well as of the Ancient Discoveries, may perhaps lose their Reputation, and much of that Ardor, with which Men study the Abstruse and Fine Geometry be abated, if what to me, and those few to whom I have imparted it, seems evidently True, shou’d really prove to be so.” (no. CXL) #Berkeley #geometry #mathematics
“We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic.” (p. 115) #Russell #mathematics #inference #logic