{"id":10962,"date":"2025-12-15T10:27:15","date_gmt":"2025-12-15T02:27:15","guid":{"rendered":"https:\/\/www.invbus.com\/blog\/?p=10962"},"modified":"2025-12-15T10:27:15","modified_gmt":"2025-12-15T02:27:15","slug":"%e7%a7%91%e5%ad%a6%e7%9a%84%e5%9f%ba%e7%9f%b3%ef%bc%8c%e8%bf%98%e6%98%af%e6%b2%99%e4%b8%8a%e7%9a%84%e5%9f%8e%e5%a0%a1%ef%bc%9f-%e7%94%a8%e8%b4%9d%e5%8f%b6%e6%96%af%e6%a6%82%e7%8e%87","status":"publish","type":"post","link":"https:\/\/www.invbus.com\/blog\/?p=10962","title":{"rendered":"\u79d1\u5b66\u7684\u57fa\u77f3\uff0c\u8fd8\u662f\u6c99\u4e0a\u7684\u57ce\u5821\uff1f\u2014\u2014 \u7528\u8d1d\u53f6\u65af\u6982\u7387\u56de\u5e94\u4f11\u8c1f\u7684\u4e16\u7eaa\u6311\u6218"},"content":{"rendered":"\n<p>\u672c\u6587\u4e3aGemini 2.5 Pro&nbsp;<strong>AI\u751f\u6210\u7684\u5185\u5bb9<\/strong>\uff0c\u6700\u540e\u66f4\u65b0\u4e8e2025\u5e746\u670826\u65e5\u3002<\/p>\n\n\n\n<p>\u572818\u4e16\u7eaa\uff0c\u82cf\u683c\u5170\u54f2\u5b66\u5bb6\u5927\u536b\u00b7\u4f11\u8c1f\uff08David Hume\uff09\u5411\u4eba\u7c7b\u7406\u6027\u6295\u63b7\u4e86\u4e24\u679a\u201c\u601d\u60f3\u70b8\u5f39\u201d\u3002\u5b83\u4eec\u662f\u5982\u6b64\u5f3a\u5927\uff0c\u4ee5\u81f3\u4e8e\u4e24\u767e\u591a\u5e74\u540e\u7684\u4eca\u5929\uff0c\u5176\u51b2\u51fb\u6ce2\u4ecd\u5728\u6574\u4e2a\u79d1\u5b66\u548c\u54f2\u5b66\u9886\u57df\u56de\u8361\u3002\u8fd9\u5bf9\u95ee\u9898\u88ab\u7edf\u79f0\u4e3a\u201c\u4f11\u8c1f\u95ee\u9898\u201d\uff0c\u5b83\u65e0\u60c5\u5730\u62f7\u95ee\u7740\u6211\u4eec\u77e5\u8bc6\u4f53\u7cfb\u4e2d\u6700\u6838\u5fc3\u7684\u4e24\u4e2a\u4fe1\u5ff5\uff1a\u6211\u4eec\u51ed\u4ec0\u4e48\u76f8\u4fe1\u672a\u6765\u4f1a\u548c\u8fc7\u53bb\u4e00\u6837\uff08\u5f52\u7eb3\u95ee\u9898\uff09\uff1f\u6211\u4eec\u53c8\u51ed\u4ec0\u4e48\u76f8\u4fe1\u4e8b\u4ef6\u4e4b\u95f4\u5b58\u5728\u5fc5\u7136\u7684\u56e0\u679c\u8054\u7cfb\uff1f<\/p>\n\n\n\n<p>\u4f11\u8c1f\u7684\u7ed3\u8bba\u662f\u98a0\u8986\u6027\u7684\uff1a\u6211\u4eec\u6ca1\u6709\u4efb\u4f55\u7edd\u5bf9\u7684\u7406\u6027\u57fa\u7840\u53bb\u76f8\u4fe1\u8fd9\u4e24\u8005\u3002\u6211\u4eec\u5bf9\u79d1\u5b66\u5b9a\u5f8b\u548c\u56e0\u679c\u5173\u7cfb\u7684\u4fe1\u5ff5\uff0c\u53ea\u4e0d\u8fc7\u662f\u4e00\u79cd\u6e90\u4e8e\u91cd\u590d\u89c2\u5bdf\u7684<strong>\u5fc3\u7406\u4e60\u60ef<\/strong>\uff0c\u800c\u975e\u575a\u5982\u78d0\u77f3\u7684\u903b\u8f91\u771f\u7406\u3002\u8fd9\u65e0\u5f02\u4e8e\u5ba3\u79f0\uff0c\u6574\u5ea7\u5b8f\u4f1f\u7684\u79d1\u5b66\u5927\u53a6\uff0c\u53ef\u80fd\u53ea\u662f\u5efa\u7acb\u5728\u4e00\u7247\u6d41\u6c99\u4e4b\u4e0a\u3002<\/p>\n\n\n\n<p>\u7136\u800c\uff0c\u572820\u4e16\u7eaa\uff0c\u4e00\u4e2a\u6e90\u4e8e18\u4e16\u7eaa\u7684\u6570\u5b66\u5de5\u5177\u2014\u2014<strong>\u8d1d\u53f6\u65af\u6982\u7387\u8bba<\/strong>\u2014\u2014\u88ab\u91cd\u65b0\u53d1\u6398\u548c\u53d1\u5c55\uff0c\u5b83\u4e3a\u56de\u5e94\u4f11\u8c1f\u7684\u6311\u6218\u63d0\u4f9b\u4e86\u4e00\u4e2a\u524d\u6240\u672a\u6709\u7684\u5f3a\u5927\u6846\u67b6\u3002\u5b83\u867d\u7136\u6ca1\u6709\u5728\u6b63\u9762\u6218\u573a\u4e0a\u201c\u6d88\u706d\u201d\u4f11\u8c1f\u7684\u903b\u8f91\u5e7d\u7075\uff0c\u4f46\u5374\u5de7\u5999\u5730\u4e3a\u79d1\u5b66\u7684\u5408\u7406\u6027\u5efa\u7acb\u4e86\u4e00\u4e2a\u5168\u65b0\u7684\u3001\u575a\u5b9e\u7684\u907f\u96be\u6240\u3002<\/p>\n\n\n\n<p><strong>\u7b2c\u4e00\u90e8\u5206\uff1a\u4f11\u8c1f\u7684\u201c\u65ad\u5934\u53f0\u201d\u2014\u2014\u4e3a\u4f55\u6211\u4eec\u65e0\u6cd5\u201c\u8bc1\u660e\u201d\u592a\u9633\u660e\u5929\u4f1a\u5347\u8d77<\/strong><\/p>\n\n\n\n<p>\u4f11\u8c1f\u7684\u8bba\u8bc1\u5982\u624b\u672f\u5200\u822c\u7cbe\u51c6\u3002\u4ed6\u6307\u51fa\uff0c\u6211\u4eec\u6240\u6709\u5173\u4e8e\u4e16\u754c\u7684\u77e5\u8bc6\u90fd\u4f9d\u8d56\u4e8e<strong>\u5f52\u7eb3\u6cd5<\/strong>\u2014\u2014\u4ece\u6709\u9650\u7684\u8fc7\u53bb\u7ecf\u9a8c\uff0c\u63a8\u65ad\u51fa\u666e\u9002\u7684\u672a\u6765\u89c4\u5f8b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5f52\u7eb3\u95ee\u9898 (The Problem of Induction)<\/strong>\uff1a\u6211\u4eec\u89c2\u5bdf\u4e86\u4e00\u4e07\u6b21\u592a\u9633\u4ece\u4e1c\u65b9\u5347\u8d77\uff0c\u5e76\u5f97\u51fa\u7ed3\u8bba\uff1a\u201c\u592a\u9633\u660e\u5929\u4e5f\u5fc5\u7136\u4f1a\u4ece\u4e1c\u65b9\u5347\u8d77\u201d\u3002\u4f11\u8c1f\u8d28\u95ee\uff1a\u8fd9\u4e2a\u201c\u5fc5\u7136\u201d\u7684\u98de\u8dc3\uff0c\u5176\u903b\u8f91\u4f9d\u636e\u4f55\u5728\uff1f\u6211\u4eec\u552f\u4e00\u7684\u8fa9\u62a4\u7406\u7531\u662f\u201c\u56e0\u4e3a\u8fc7\u53bb\u4e00\u76f4\u5982\u6b64\u201d\u3002\u4f46\u8fd9\u5c31\u7b49\u4e8e\u5728\u7528\u201c\u5f52\u7eb3\u6cd5\u201d\u6765\u4e3a\u201c\u5f52\u7eb3\u6cd5\u201d\u672c\u8eab\u8fa9\u62a4\uff0c\u8fd9\u662f\u4e00\u4e2a\u65e0\u6548\u7684\u5faa\u73af\u8bba\u8bc1\u3002\u6211\u4eec\u65e0\u6cd5\u5728\u903b\u8f91\u4e0a\u6392\u9664\u201c\u7b2c\u4e00\u4e07\u96f6\u4e00\u6b21\u592a\u9633\u4f1a\u4ece\u897f\u65b9\u5347\u8d77\u201d\u7684\u53ef\u80fd\u6027\u3002<\/li>\n\n\n\n<li><strong>\u56e0\u679c\u95ee\u9898 (The Problem of Causation)<\/strong>\uff1a\u5f53\u6211\u4eec\u770b\u5230\u767d\u7403\u649e\u51fb\u9ed1\u7403\uff0c\u9ed1\u7403\u6eda\u52a8\u65f6\uff0c\u6211\u4eec\u58f0\u79f0\u524d\u8005\u201c\u5bfc\u81f4\u201d\u4e86\u540e\u8005\u3002\u4f11\u8c1f\u6307\u51fa\uff0c\u6211\u4eec\u771f\u6b63\u89c2\u5bdf\u5230\u7684\uff0c\u4ec5\u4ec5\u662f\u4e24\u4e2a\u4e8b\u4ef6\u5728\u65f6\u7a7a\u4e0a<strong>\u6052\u5e38\u76f8\u7ee7<\/strong>\uff08Constant Conjunction\uff09\u3002\u6211\u4eec\u4ece\u672a\u3001\u4e5f\u6c38\u8fdc\u65e0\u6cd5\u76f4\u63a5\u89c2\u5bdf\u5230\u90a3\u4e2a\u6240\u8c13\u7684\u3001\u795e\u79d8\u7684\u201c\u56e0\u679c\u4e4b\u529b\u201d\u6216\u201c\u5fc5\u7136\u8054\u7cfb\u201d\u3002\u6211\u4eec\u5bf9\u56e0\u679c\u7684\u4fe1\u5ff5\uff0c\u662f\u6211\u4eec\u7684\u5927\u8111\u56e0\u4e60\u60ef\u800c\u4ea7\u751f\u7684\u4e00\u79cd<strong>\u5fc3\u7406\u671f\u671b<\/strong>\uff0c\u5e76\u5c06\u5176\u9519\u8bef\u5730\u6295\u5c04\u5230\u4e86\u5916\u90e8\u4e16\u754c\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u4f11\u8c1f\u7684\u6311\u6218\u5728\u4e8e\uff0c\u4ed6\u8981\u6c42\u6211\u4eec\u4e3a\u77e5\u8bc6\u63d0\u4f9b\u4e00\u79cd<strong>\u7edd\u5bf9\u7684\u3001\u6f14\u7ece\u903b\u8f91\u5f0f\u7684\u786e\u5b9a\u6027<\/strong>\u3002\u800c\u5728\u8fd9\u4e2a\u4e25\u82db\u7684\u6807\u51c6\u4e0b\uff0c\u6574\u4e2a\u7ecf\u9a8c\u79d1\u5b66\u90fd\u5c06\u5d29\u584c\u3002<\/p>\n\n\n\n<p><strong>\u7b2c\u4e8c\u90e8\u5206\uff1a\u8d1d\u53f6\u65af\u7684\u201c\u624b\u672f\u5200\u201d\u2014\u2014\u4ece\u8ffd\u6c42\u201c\u786e\u5b9a\u6027\u201d\u5230\u91cf\u5316\u201c\u53ef\u4fe1\u5ea6\u201d<\/strong><\/p>\n\n\n\n<p>\u8d1d\u53f6\u65af\u6982\u7387\u8bba\u7684\u6838\u5fc3\u601d\u60f3\uff0c\u4e0e\u4f11\u8c1f\u7684\u54f2\u5b66\u622a\u7136\u4e0d\u540c\u3002\u5b83\u8ba4\u4e3a\uff0c\u77e5\u8bc6\u5e76\u975e\u4e00\u4e2a\u201c\u975e\u9ed1\u5373\u767d\u201d\u7684\u786e\u5b9a\u6027\u95ee\u9898\uff0c\u800c\u662f\u4e00\u4e2a\u5173\u4e8e\u201c\u4fe1\u5ff5\u53ef\u4fe1\u5ea6\u201d\uff08Degree of Belief\uff09\u7684\u52a8\u6001\u66f4\u65b0\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p>\u5176\u6838\u5fc3\u5de5\u5177\u662f<strong>\u8d1d\u53f6\u65af\u5b9a\u7406<\/strong>\u3002\u8fd9\u4e2a\u5b9a\u7406\u7528\u4e00\u4e2a\u4f18\u7f8e\u7684\u6570\u5b66\u516c\u5f0f\uff0c\u63cf\u8ff0\u4e86\u4e00\u4e2a\u7406\u6027\u7684\u884c\u52a8\u8005\u5e94\u8be5\u5982\u4f55\u6839\u636e\u65b0\u51fa\u73b0\u7684<strong>\u8bc1\u636e\uff08E\uff09<\/strong>\uff0c\u6765\u66f4\u65b0\u81ea\u5df1\u5bf9\u67d0\u4e2a<strong>\u5047\u8bf4\uff08H\uff09\u7684\u4fe1\u5fc3\u6307\u6570<\/strong>\uff1a<\/p>\n\n\n\n<p><strong>\u66f4\u65b0\u540e\u7684\u4fe1\u5ff5 P(H|E) = [\uff08\u8bc1\u636e\u4e0e\u5047\u8bf4\u7684\u5339\u914d\u5ea6 P(E|H)\uff09 * \uff08\u521d\u59cb\u4fe1\u5ff5 P(H)\uff09] \/ \uff08\u8bc1\u636e\u7684\u666e\u904d\u6027 P(E)\uff09<\/strong><\/p>\n\n\n\n<p>\u8fd9\u4e2a\u516c\u5f0f\u7684\u54f2\u5b66\u542b\u4e49\u662f\u9769\u547d\u6027\u7684\uff1a<strong>\u5b83\u4e3a\u201c\u4ece\u7ecf\u9a8c\u4e2d\u5b66\u4e60\u201d\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7406\u6027\u7684\u3001\u6570\u5b66\u5316\u7684\u6846\u67b6\u3002<\/strong><\/p>\n\n\n\n<p><strong>\u7b2c\u4e09\u90e8\u5206\uff1a\u8d1d\u53f6\u65af\u5982\u4f55\u201c\u62ef\u6551\u201d\u79d1\u5b66<\/strong><\/p>\n\n\n\n<p>\u73b0\u5728\uff0c\u6211\u4eec\u7528\u8d1d\u53f6\u65af\u7684\u201c\u624b\u672f\u5200\u201d\u6765\u91cd\u65b0\u89e3\u5256\u4f11\u8c1f\u7684\u4e24\u5927\u96be\u9898\u3002<\/p>\n\n\n\n<p><strong>1. 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