【正文】 hemselves being ?nite sequences of signs, which only operate by purely mechanical ‘‘sequencematching’’ and ‘‘sequencereplacement’’—as do lambdacalculus and Turing machines, for instance, two paradigms for any effective formalism, following the equivalence results. To be fair, some recentrevitalization of Hilbert’s program try to extend this notion of ‘‘formal’’, sometimes in reference to writings by Hilbert as well. One may surely propose new notions, yet the de?nition of what a formal system is, is formally given by inpleteness theorem and Turing’s work. AsGo 168。家譜學，包括黎曼，龐加萊在內(nèi)，對以提高經(jīng)常被忽視的基礎分析（數(shù)學認知結(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。這里我們忘了,在數(shù)學方面, 作為數(shù)學家工作的重要組成部分，如果有必要制造證據(jù)，數(shù)學活動的基礎首先是命題或者是對概念和結(jié)構(gòu)的施工。它制造的這些奇妙的邏正式機器圍繞著我們，行動變得沒有意義。什么可以說是無限的概念如果沒有參考的歷史？迭代的姿態(tài)和其隱喻的映射（極限）是信息的想法，但它們卻是不充足的。將繼續(xù)占統(tǒng)治地位。一個人肯定不會進入這個后續(xù)質(zhì)疑的細節(jié)，但它是認識論項目的一部分：在歷史上，如果數(shù)學可以被構(gòu)成，它可以幫助我們避免應用數(shù)學物理處處相同的工具，因為如果他們是絕對的柏拉圖的或完全的形式主義的世界，包括對生命現(xiàn)象的分析，新的工具和觀測（新的不變量）是需要的。見：佩魯齊（ED）巴伊樓隆戈克（2009）生物時間幾何計劃。相反，這個領域的研究（以及認知神經(jīng)科學的）的目標似乎加強，如果想要描述反思的過程，則是由全體居民共同的決定的。什么是生物學的偉大的不變性？如果我們參考分子生物學，我們會發(fā)現(xiàn)一些不變量，但是，盡管他們目前的存在只是生活的現(xiàn)象，它們涉及到化學，而不是生物學。偉大的穩(wěn)定性和可靠性39。 2認識和不變性從數(shù)學的認知分析開始，這里從假設的角度來看，我們強調(diào)這一調(diào)查認識論的內(nèi)容。這就是新的數(shù)學方面，這也是認識論的認知基礎工程項目的目的。值得一提的是,算術(shù)一致性的正式調(diào)查 (正式數(shù)論、是否產(chǎn)生矛盾?)和幾何研究可以被算術(shù)中分析工具所編碼（所有的人，希爾伯特1899 ：他們至少一致？)。第一，我們指的顯化和正式證明原則的分析，主要是指后天的，一般的扣除規(guī)則的證明和綱要的分析。delGirard, various forms of inpletenessindependence in Set Theory and Arithmetics), and produced spinoffs with farreaching practical consequences: the functions for the putation of proofs (Herbrand, Go 168。del says in his ‘‘a(chǎn)dded note’’ of 1963, we have, since Turing, a ‘‘certain, precise, adequate notion of the concept of formal system’’. And, not only Turing Machines, but, we stress, also the inpleteness theorem, by its use of the same notion of formal system makes it perfectly stable:de?nitions, in mathematics, are de?nitely stabilized by the(important) theorems where they apply.Of course, there is circularity in any formal de?nition of a formal system, in the same way there is circularity when the notion of word is de?ned by means of other words: Turing Machines also need to be de?ned as a formal system (yet, a very basic one). Nothing serious, we are accustomed to this, just as when we do not stop speaking, and we continue to talk about sentences using sentences. But there is far more than that: the formalist foundation of Mathematics refers to the absolute certainty of notions such as ‘‘?nite’’ and ‘‘discrete’’. Yet, as for ?niteness, following the Overspill Lemma in Arithmetics and, more notably, since inpleteness, we know that we cannot formally de?ne the notion of ‘‘?nite’’. In fact, an axiom of in?nity is required in order to formally ‘‘isolate’’ the standard ?nite integers. A result which demolishes the core of any ?nitistcertitude, including that which is internal to logical formalism. In short, the notion of ?nitude is very plex,requires in?nity, if one wants to grasp it formally: it is far from being ‘‘obvious’’, in the Cartesian sense. And it is not an absolute: ?niteness makes little absolute sense, for instance, in cosmology—consider the question: Is the Relativistic Universe ?nite or in?nite? The Riemann sphere is ?nite but unlimited against t