外文翻譯---數(shù)學(xué)直覺和認(rèn)知的根源(文件)
【正文】 功能,邏輯計(jì)算機(jī)(圖靈)；因此我們有了數(shù)位機(jī)器。家譜學(xué)，包括黎曼，龐加萊在內(nèi)，對(duì)以提高經(jīng)常被忽視的基礎(chǔ)分析（數(shù)學(xué)認(rèn)知結(jié)構(gòu)的歷史構(gòu)成）和可證不完備的舉證原則的推論分析是非常必要的。 numerous authors refer to the ‘‘great stability and reliability’’ of Mathematics which would need to be accounted for. Wigner’s article, which everybody quotes—due to its so very effective and memorable title—and which very few read, presents examples that are not astounding).Do linguists (cognitivists, for example) consider the following problem: What a miracle! How languages are unreasonably effective! When we talk, we understand one another! Languages were born for purposes of munication and while municating, to tell each other things possibly nonexisting things (this is why human language was invented), to understand one another. As regards stability and invariance, as said extensively in (Bailly and Longo 2006) in connection to Physics’ theoretical principles, we can even de?ne Mathematics as the fragment of our forms of construction of knowledge which is maximally invariant and stable, from a conceptual viewpoint. Now if Mathematics is maximally stable and invariant by construction, among our forms of knowledge and of munication, that is also where its limitations are to be found. It was born around the invariants and transformations which preserve them, beginning with the rotations and translations in Euclid’s geometry. What are the great invariants in Biology? If we refer to Molecular Biology, we do ?nd some invariants, but, despite their being present only within life phenomena, they pertain to Chemistry, not Biology. Life phenomena are very stable,globally,We need to account for this instability/stability, variance/invariance, order/disorder,integration/separation…, which the Mathematics of Physics describes badly (see Longo 2009).One can surely not go into the details of this subsequent questioning, but it is part of the epistemological project: If Mathematics is constituted, it can help us avoid applying everywhere the same tools of Mathematical Physics, as if they were Platonic absolutes or plete formalisms of the world, including for the analysis of life phenomena, where new tools and observables (new invariants) are needed.3 IntuitionThe notion of intuition plays a large part in mathematics,yet the term ‘‘intuition’’ is highly polysemic, and may refer to different meanings depending on the context in which it is used. In particular, a distinction is monly made between the intuition that takes place in the practice ofmathematics, and the intuition conceived as grounding the constitution of a mathematical concept or the progress of mathematics itself. In both cases the way the notion of mathematical intuition is approached often involves inquiring into its legitimacy, ., the extent to which one should rely on it in the practice or, in a more foundational perspective。 the purely deductive ponent will follow. Now, as the keenestamong the founding fathers would say, let’s put aside this ‘‘heuristic’’ and rather focus our attention on the a posteriori reconstruction of the logical certitude of proof. An absolutely indispensable program, as we were saying, at the beginning of the twentieth century, following thetechnical richness as w
環(huán)評(píng)公示相關(guān)推薦
鄂ICP備17016276號(hào)-1