{"resolved":true,"match_type":"uuid","source_type":"original_book","book_id":"de9b4263-c277-4979-9f00-91fe8d8660f7","title":"差异与重复","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787567591363","requested_by":"printed_page","book":{"source_type":"original_book","book_id":"de9b4263-c277-4979-9f00-91fe8d8660f7","id":"de9b4263-c277-4979-9f00-91fe8d8660f7","uuid":"de9b4263-c277-4979-9f00-91fe8d8660f7","title":"差异与重复","normalized_title":"差异与重复","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787567591363","isbns":["9787567591363"],"parsed":true,"ai_readable":true,"document_type":"book","page_count":538,"navigation_url":"https://workshop.closeclaw.top/ai/book/de9b4263-c277-4979-9f00-91fe8d8660f7","title_url":"https://workshop.closeclaw.top/ai/title/%E5%B7%AE%E5%BC%82%E4%B8%8E%E9%87%8D%E5%A4%8D","fixed_page_url_template":"https://workshop.closeclaw.top/ai/book/de9b4263-c277-4979-9f00-91fe8d8660f7/page/{printed_page}","path_api_url_template":"https://workshop.closeclaw.top/api/ai/book/de9b4263-c277-4979-9f00-91fe8d8660f7/page/{printed_page}","read_url":"https://workshop.closeclaw.top/api/ai/read/de9b4263-c277-4979-9f00-91fe8d8660f7","page_url":"https://workshop.closeclaw.top/api/ai/books/de9b4263-c277-4979-9f00-91fe8d8660f7/page","search_url":"https://workshop.closeclaw.top/api/ai/books/de9b4263-c277-4979-9f00-91fe8d8660f7/search"},"page":{"printed_page":302,"pdf_page":321,"physical_index":321,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"bc1d8ff8006ee74b5f9ccfc0bab8878886cede8ae0dea7dbc166d8a48c9d799f"},"chapter":"第四章 差异的理念综合","content":"无限小在微分学中的无用性\n\n微分学的阐释问题无疑是以如下形式呈现出来的：无限小是真实的还是虚构的？但从一开始，真正要紧的却是另一件事情：微分学的命运是否要与无限小联系在一起？[229]或者说，从有限表象的观点看来，微分学难道不应当获得一种严格的身份规定吗？对现代数学起界定作用的真正前沿并非微分学，而是诸如集合论(théorie des ensembles)之类的其他发现。即使集合论本身需要一条无限的公理，它还是对微分学做出了精确的有限论阐释。实际上，人们知道极限概念已经失去了它的运动学(phoronomique)特征，并且它所包含的只是一些静态的考查；可变性不再表现一种贯通了一个区间内的所有值的渐进的过渡，它现在只意谓着这一区间中的某个值的选言的假定；导数与积分不再是量的概念，而是变为了秩序的概念;微分最终只是意指着一个停留在未规定状态的量，以便人们在必要时使它变得比指定的数更小。结构主义正由此诞生，但同时，微分学也丧失了发生论或动力论的雄心。当人们谈论微分学的“形而上学”时，这恰恰涉及无限表象与有限表象的这种非此即彼的取舍。形而上学与这种非此即彼的取舍仍然严格地内在于微分学自身的方法。所以，形而上学问题一开始就以如下方式得到陈述：从方法的层面上说，微分为何可以忽略不计？它们为什么就应当消失在结果之中？显然，在此诉诸于无限小与误差的无限小特征(假如有“误差”的话)不仅毫无意义，而且还预先判定了无限表象。卡诺在其著名的《沉思录》(Réflexions)中对上述问题做出了严格回答，而这一回答恰恰是以有限论阐释的观点为依据：微分方程是简单的“辅助方程”，其表现了与所寻求的方程相对应的问题的种种条件;但是，在它们之间产生出了一种严格的误差补偿，这种误差补偿不允许微分继续存在于结果之中，因为结果只能被建立在固定量或有限量之间。\n\n302\n\n差异与重复","previous_page":301,"next_page":303}