{"resolved":true,"match_type":"uuid","source_type":"original_book","book_id":"ea3b7167-0435-4a94-84b9-80a5359326a4","title":"递归与偶然","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787576004694","requested_by":"printed_page","book":{"source_type":"original_book","book_id":"ea3b7167-0435-4a94-84b9-80a5359326a4","id":"ea3b7167-0435-4a94-84b9-80a5359326a4","uuid":"ea3b7167-0435-4a94-84b9-80a5359326a4","title":"递归与偶然","normalized_title":"递归与偶然","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787576004694","isbns":["9787576004694"],"parsed":true,"ai_readable":true,"document_type":"book","page_count":401,"navigation_url":"https://workshop.closeclaw.top/ai/book/ea3b7167-0435-4a94-84b9-80a5359326a4","title_url":"https://workshop.closeclaw.top/ai/title/%E9%80%92%E5%BD%92%E4%B8%8E%E5%81%B6%E7%84%B6","fixed_page_url_template":"https://workshop.closeclaw.top/ai/book/ea3b7167-0435-4a94-84b9-80a5359326a4/page/{printed_page}","path_api_url_template":"https://workshop.closeclaw.top/api/ai/book/ea3b7167-0435-4a94-84b9-80a5359326a4/page/{printed_page}","read_url":"https://workshop.closeclaw.top/api/ai/read/ea3b7167-0435-4a94-84b9-80a5359326a4","page_url":"https://workshop.closeclaw.top/api/ai/books/ea3b7167-0435-4a94-84b9-80a5359326a4/page","search_url":"https://workshop.closeclaw.top/api/ai/books/ea3b7167-0435-4a94-84b9-80a5359326a4/search"},"page":{"printed_page":146,"pdf_page":158,"physical_index":158,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"4238f39223da26e43ca8f6f2b3ede6783762c5e0a2a01b38f972e3c3508b8331"},"chapter":"第二章逻辑与偶然","content":"至于无限和有限的关系，这是莱布尼茨类比符号操作和思维的基础，它意味着无限刻写在有限之中。对笛卡尔主义者而言，推理要想是完美的，应当包含有限的步骤，这样心灵才能依序前进；莱布尼茨的贡献则是将无限刻写在有限中，这样心灵就能通过有限的符号理解无限。比如，莱布尼茨可以把著名的无理数π呈现为一个由有限的符号组成的公式：$1 - 1 / 3 + 1 / 5 - 1 / 7 + 1 / 9 - \\cdots = \\pi / 4$\n\n146\n\n递归与偶然\n\n① 克莱尔·施瓦茨(Claire Schwarz)，《莱布尼茨——存在的合理性》，巴黎：Belin，2017年，第140页。\n\n② 莱布尼茨，《莱布尼茨短文及未出版的片段集》(Opuscules et fragments inédits de Leibniz)，路易·库蒂拉(Louis Couturat)编，巴黎： Alcan, 1903 年，第 28 页：“surtout pour exterminer les controverses dans les matières qui dépendent du raisonnement, car alors raisonner et calculer sera la même chose.","previous_page":145,"next_page":147}