{"id":27697,"date":"2023-06-22T09:35:43","date_gmt":"2023-06-22T01:35:43","guid":{"rendered":"https:\/\/www.danran1967.com\/?p=27697"},"modified":"2023-06-22T09:35:43","modified_gmt":"2023-06-22T01:35:43","slug":"%e7%bd%97%e7%b4%a0%e7%9a%84-%e5%a4%a7%e7%bd%aa-%e3%80%8a%e6%95%b0%e5%ad%a6%e5%8e%9f%e7%90%86%e3%80%8b","status":"publish","type":"post","link":"https:\/\/www.danran1967.com\/?p=27697","title":{"rendered":"\u7f57\u7d20\u7684 \u201c\u5927\u7f6a\u201d\u2014\u2014\u300a\u6570\u5b66\u539f\u7406\u300b"},"content":{"rendered":"<p><strong>\u64b0\u6587\uff1a\u5362\u660c\u6d77<\/strong><\/p>\n<p>\u64c5\u5199\u77ed\u8bd7\u7684\u53e4\u5e0c\u814a\u8bd7\u4eba\u5361\u5229\u9a6c\u79d1\u65af (Callimachus) \u66fe\u7ecf\u8a00\u9053\uff1a \u201c\u4e00\u90e8\u5927\u4e66\u4fbf\u662f\u4e00\u9879\u5927\u7f6a\u201d[\u6ce8\u4e00]\u3002 1959 \u5e74\uff0c \u82f1\u56fd\u54f2\u5b66\u5bb6\u7f57\u7d20 (Bertrand Russell) \u5728\u300a\u897f\u65b9\u7684\u667a\u6167\u300b(Wisdom of the West) \u4e00\u4e66\u4e2d\u5f15\u7528\u4e86\u8fd9\u53e5\u8bdd\uff0c \u5e76 \u201c\u8c26\u865a\u201d \u5730\u8868\u793a\uff0c \u201c\u4ee5\u7f6a\u800c\u8bba\uff0c \u8fd9\u662f\u4e00\u90e8\u5c0f\u4e66\u201d (as evils go, this book is a minor one)\uff1b 1982 \u5e74\uff0c \u5370\u5ea6\u88d4\u7f8e\u56fd\u79d1\u5b66\u53f2\u5b66\u5bb6\u6885\u62c9 (Jagdish Mehra) \u5728 \u300a\u91cf\u5b50\u7406\u8bba\u7684\u5386\u53f2\u53d1\u5c55\u300b (The Historical Development of Quantum Theory) \u4e00\u4e66\u4e2d\u4e5f\u5f15\u8ff0\u4e86\u8fd9\u53e5\u8bdd\uff0c \u4e14\u8ddf\u7f57\u7d20\u4e00\u6837 \u201c\u8c26\u865a\u201d\uff0c \u8868\u793a\u4ee5\u7f6a\u800c\u8bba\uff0c \u4ed6\u90a3\u90e8\u4e5f\u662f\u5c0f\u4e66\u3002<\/p>\n<p>\u5176\u5b9e\uff0c \u6885\u62c9\u90a3\u90e8\u4e66\u662f\u5f88\u5927\u7684\uff0c 6 \u5377 9 \u518c 5,000 \u591a\u9875\uff0c \u6050\u6015\u662f\u6709\u53f2\u4ee5\u6765\u6700\u5927\u7684\u79d1\u5b66\u53f2\u4e13\u8457\uff0c \u7167\u5361\u5229\u9a6c\u79d1\u65af\u7684\u8bf4\u6cd5\uff0c \u7f6a\u662f\u5c0f\u4e0d\u4e86\u7684\u3002 \u5012\u662f\u7f57\u7d20\u7684 \u201c\u8c26\u865a\u201d \u8fd8\u7a0d\u6709\u4e9b\u9053\u7406\uff0c \u56e0\u4e3a\u300a\u897f\u65b9\u7684\u667a\u6167\u300b\u5e76\u4e0d\u662f\u4ed6\u6700\u5927\u7684\u4e66\uff0c \u4ed6\u6709\u4e00\u90e8\u5927\u5f97\u591a\u7684\u4e66\u53eb\u505a\u300a\u6570\u5b66\u539f\u7406\u300b(Principia Mathematica)\uff0c 3 \u5377\u8fd1 2,000 \u9875\uff0c \u90a3\u624d\u662f \u201c\u5927\u7f6a\u201d\u3002 \u4e0d\u8fc7\u90a3\u6050\u6015\u4e0d\u662f\u4e66\u4e4b\u7f6a\uff0c \u800c\u662f\u4e66\u5e26\u7ed9\u4f5c\u8005\u7684\u7f6a\u2014\u2014\u90a3\u90e8\u5927\u4e66\u7740\u5b9e\u8ba9\u4f5c\u4e3a\u4e3b\u8981\u4f5c\u8005\u7684\u7f57\u7d20\u53d7\u4e86 \u201c\u5927\u7f6a\u201d\u3002<\/p>\n<p>\u90a3 \u201c\u5927\u7f6a\u201d \u4ece\u5199\u4f5c\u4e4b\u521d\u5c31\u5f00\u59cb\u4e86\u3002<\/p>\n<p><img src=\"https:\/\/i02piccdn.sogoucdn.com\/cd5dc5daec2dd16d\" \/><\/p>\n<p>\u25b3 \u4f2f\u7279\u5170\u00b7\u7f57\u7d20 (1872-1970)<\/p>\n<p>\u7f57\u7d20\u5e74\u8f7b\u65f6\u96c4\u5fc3\u52c3\u52c3\uff0c \u4e8c\u5341\u51fa\u5934\u5c31\u7acb\u4e0b\u5b8f\u613f\uff0c \u8981\u5199\u4e24\u4e2a\u7cfb\u5217\u7684 \u201c\u5927\u4e66\u201d\uff1a \u4e00\u4e2a\u6db5\u76d6\u6240\u6709\u7684\u79d1\u5b66\u9886\u57df\uff1b \u53e6\u4e00\u4e2a\u6db5\u76d6\u6240\u6709\u7684\u793e\u4f1a\u5b66\u9886\u57df\u3002 \u4ed6\u5e76\u4e14\u7545\u60f3\uff1a \u4e00\u4e2a\u7cfb\u5217\u5c06\u4ece\u62bd\u8c61\u51fa\u53d1\uff0c \u9010\u6e10\u5411\u5e94\u7528\u9760\u62e2\uff0c \u53e6\u4e00\u4e2a\u7cfb\u5217\u5219\u4ece\u5e94\u7528\u51fa\u53d1\uff0c \u9010\u6e10\u5411\u62bd\u8c61\u9760\u62e2\uff0c \u6700\u7ec8\u4ea4\u878d\u6210\u4e00\u4e2a\u5de8\u65e0\u9738\u7cfb\u5217\u3002 \u7f57\u7d20\u540e\u6765\u786e\u5b9e\u7b97\u5f97\u4e0a\u8457\u4f5c\u7b49\u8eab\uff0c \u4f46\u5e74\u8f7b\u65f6\u7684\u8fd9\u4e2a\u5b8f\u613f\u5b9e\u5728\u662f\u8fdc\u8fdc\u8d85\u51fa\u4e86\u4efb\u4f55\u4e2a\u4eba\u7684\u80fd\u529b\uff0c \u7ec8\u5176\u4e00\u751f\u4e5f\u672a\u80fd\u5b9e\u73b0\uff0c \u800c\u53ea\u5728\u67d0\u4e9b\u5c40\u90e8\u9886\u57df\u4e2d\u53d6\u5f97\u8fc7\u5c40\u90e8\u6210\u679c\u3002 \u5982\u679c\u8981\u5728\u5176\u4e2d\u627e\u51fa\u4e00\u4e2a\u52aa\u529b\u5f97\u6700\u7cfb\u7edf\u7684\uff0c \u90a3\u6050\u6015\u662f\u6570\u5b66\u3002<\/p>\n<p>1897 \u5e74\uff0c 25 \u5c81\u7684\u7f57\u7d20\u64b0\u5199\u4e86\u4e00\u672c\u5173\u4e8e\u51e0\u4f55\u7684\u4e66\uff1a \u300a\u8bba\u51e0\u4f55\u7684\u57fa\u7840\u300b(An Essay on the Foundations of Geometry)\uff0c \u968f\u540e\u53c8\u5f00\u59cb\u6784\u601d\u4e00\u672c\u6709\u5173\u6570\u5b66\u57fa\u7840\u7684\u4e66\uff1a \u300a\u6570\u5b66\u7684\u539f\u7406\u300b(The Principles of Mathematics)\u3002 \u8fd9\u672c\u4e2d\u8bd1\u540d\u4ec5\u4e00\u5b57\u4e4b\u5dee\uff0c \u82f1\u6587\u540d\u4e5f\u6709\u4e9b\u76f8\u8fd1\u7684\u4e66\u662f\u300a\u6570\u5b66\u539f\u7406\u300b\u7684\u524d\u8eab\u3002 \u4eff\u4f5b\u5728\u9884\u793a\u300a\u6570\u5b66\u539f\u7406\u300b\u5c06\u8981\u8ba9\u7f57\u7d20\u53d7 \u201c\u7f6a\u201d\uff0c \u300a\u6570\u5b66\u7684\u539f\u7406\u300b\u4e00\u8d77\u5934\u5c31\u4e0d\u987a\u5229\uff0c \u51e0\u6b21\u52aa\u529b\u90fd\u6b62\u4e8e\u7247\u65ad\u3002 \u8fd9\u4e00\u5c40\u9762\u76f4\u5230 1900 \u5e74 8 \u6708\u7f57\u7d20\u5728\u5df4\u9ece\u56fd\u9645\u54f2\u5b66\u5927\u4f1a (International Congress of Philosophy) \u4e0a\u9047\u89c1\u610f\u5927\u5229\u6570\u5b66\u5bb6\u76ae\u4e9a\u8bfa (Giuseppe Peano) \u624d\u6709\u4e86\u88ab\u4ed6\u79f0\u4e3a \u201c\u667a\u529b\u751f\u6d3b\u8f6c\u6298\u70b9\u201d (a turning point in my intellectual life) \u7684\u6539\u53d8[\u6ce8\u4e8c]\u3002<\/p>\n<p>\u76ae\u4e9a\u8bfa\u662f\u7814\u7a76\u6570\u5b66\u57fa\u7840\u7684\u5148\u9a71\u4eba\u7269\u4e4b\u4e00\uff0c \u5728\u601d\u7ef4\u65b9\u5f0f\u4e43\u81f3\u6240\u91c7\u7528\u7684\u6570\u5b66\u7b26\u53f7\u7b49\u65b9\u9762\u90fd\u5bf9\u7f57\u7d20\u6709\u7740\u5de8\u5927\u5f71\u54cd\u3002 \u5728\u8fd9\u79cd\u5f71\u54cd\u4e0b\uff0c\u300a\u6570\u5b66\u7684\u539f\u7406\u300b\u7684\u5199\u4f5c\u5927\u4e3a \u201c\u63d0\u901f\u201d\u3002 \u90a3\u5e74\u7684\u6700\u540e\u4e09\u4e2a\u6708\uff0c \u7f57\u7d20\u51e0\u4e4e\u4ee5\u6bcf\u5929 10 \u9875\u7684\u901f\u5ea6\u63a8\u8fdb\u7740\uff0c \u5e74\u5185\u5c31\u5b8c\u6210\u4e86\u6570\u5341\u4e07\u5b57\u7684\u6587\u7a3f[\u6ce8\u4e09]\u3002 \u5728\u90a3\u6bb5\u88ab\u4ed6\u79f0\u4e3a \u201c\u667a\u529b\u871c\u6708\u201d (intellectual honeymoon) \u7684\u65f6\u671f\u91cc\uff0c \u4ed6\u4e0d\u4ec5\u5199\u4f5c\u795e\u901f\uff0c \u800c\u4e14\u6bcf\u5929\u90fd\u611f\u89c9\u5230\u6bd4\u524d\u4e00\u5929\u591a\u9886\u609f\u4e86\u4e00\u4e9b\u4e1c\u897f\u3002<\/p>\n<p>\u4f46\u597d\u666f\u4e0d\u957f\uff0c \u201c\u667a\u529b\u871c\u6708\u201d \u968f\u7740\u65b0\u4e16\u7eaa\u7684\u5230\u6765\u5f88\u5feb\u5c31\u7ec8\u7ed3\u4e86\uff1a 1901 \u5e74\u6625\u5929\uff0c \u7f57\u7d20\u53d1\u73b0\u4e86\u8457\u540d\u7684\u7f57\u7d20\u6096\u8bba (Russell&#8217;s paradox)[\u6ce8\u56db]\u3002 \u8fd9\u4e2a\u4ee5\u4ed6\u540d\u5b57\u547d\u540d\u7684\u6096\u8bba\u5982\u4eca\u5df2\u662f\u7f57\u7d20\u5934\u4e0a\u7684\u4e00\u9053\u5149\u73af\uff0c \u5f53\u65f6\u5374\u7740\u5b9e\u8ba9\u4eba\u6d88\u53d7\u4e0d\u8d77\uff0c \u5bf9\u64b0\u5199\u4e2d\u7684\u300a\u6570\u5b66\u7684\u539f\u7406\u300b\uff0c \u4e43\u81f3\u5bf9\u6574\u4e2a\u6570\u5b66\u57fa\u7840\u7814\u7a76\u90fd\u9020\u6210\u4e86\u51b2\u51fb\u3002 \u7f57\u7d20\u5728\u5251\u6865\u5927\u5b66\u4e09\u4e00\u5b66\u9662 (Trinity College) \u65f6\u7684\u8001\u5e08\u3001 \u8457\u540d\u54f2\u5b66\u5bb6\u6000\u7279\u6d77 (Alfred North Whitehead) \u5728\u5f97\u77e5\u8fd9\u4e00\u6096\u8bba\u540e\uff0c \u5f15\u4e86\u52c3\u6717\u5b81 (Robert Browning) \u8bd7\u6b4c\u300a\u8ff7\u9014\u7684\u9886\u8896\u300b(The Lost Leader) \u4e2d\u7684\u4e00\u53e5 \u201c\u6109\u5feb\u81ea\u4fe1\u7684\u6e05\u6668\u6c38\u4e0d\u518d\u6765\u201d (Never glad confident morning again) \u4f5c\u4e3a \u201c\u8d60\u8a00\u201d \u5bc4\u7ed9\u4e86\u7f57\u7d20\u3002<\/p>\n<p>\u7f57\u7d20\u6096\u8bba\u4f7f\u672c\u5df2\u63a5\u8fd1\u5b8c\u6210\u7684\u300a\u6570\u5b66\u7684\u539f\u7406\u300b\u7684\u51fa\u7248\u63a8\u8fdf\u4e86\u4e24\u5e74\u5de6\u53f3\uff0c \u4f46\u5373\u4fbf\u5982\u6b64\u4e5f\u672a\u80fd\u89e3\u51b3\u7f57\u7d20\u6096\u8bba\u3002 \u8fd9\u4e00\u70b9\u8ba9\u7f57\u7d20\u6df1\u611f\u6cae\u4e27\uff0c \u5728\u7ed9\u4e00\u4f4d\u670b\u53cb\u7684\u4fe1\u4e2d\u79f0\u300a\u6570\u5b66\u7684\u539f\u7406\u300b\u4e3a \u201c\u4e00\u672c\u611a\u8822\u7684\u4e66\u201d (a foolish book)\uff0c \u751a\u81f3\u8868\u793a\u4e00\u60f3\u5230\u4e3a\u8fd9\u6837\u4e00\u672c\u4e66\u82b1\u8d39\u4e86\u90a3\u4e48\u591a\u65f6\u95f4\u5c31\u611f\u5230\u7f9e\u6127\u3002 \u4e0d\u8fc7\u90a3\u65f6\u5019\uff0c \u771f\u6b63\u7684 \u201c\u5927\u4e66\u201d \u300a\u6570\u5b66\u539f\u7406\u300b\u7684\u64b0\u5199\u65e9\u5df2\u5c55\u5f00 (1900 \u5e74\u5e95\u5de6\u53f3\u5c31\u542f\u52a8\u4e86)\uff0c \u5f7b\u5e95\u89e3\u51b3\u7f57\u7d20\u6096\u8bba\u7684\u4efb\u52a1\u88ab\u987a\u7406\u6210\u7ae0\u5730\u8f6c\u79fb\u5230\u4e86\u300a\u6570\u5b66\u539f\u7406\u300b\u4e0a\u3002<\/p>\n<p>\u300a\u6570\u5b66\u539f\u7406\u300b\u7684\u4f5c\u8005\u9635\u5bb9\u6bd4\u300a\u6570\u5b66\u7684\u539f\u7406\u300b\u6269\u5927\u4e86\u4e00\u500d\uff1a \u5728\u7f57\u7d20\u7684\u52a8\u5458\u4e0b\uff0c \u6000\u7279\u6d77\u6210\u4e3a\u4e86\u5408\u4f5c\u8005\u3002 \u6000\u7279\u6d77\u5bf9\u6570\u5b66\u57fa\u7840\u4e5f\u6709\u6d53\u539a\u7684\u5174\u8da3\uff0c \u66fe\u4e8e 1898 \u5e74\u64b0\u5199\u8fc7\u4e00\u672c\u6807\u9898\u4e3a\u300a\u6cdb\u4ee3\u6570\u300b(A Treatise on Universal Algebra) \u7684\u8457\u4f5c\uff0c \u4e14\u6709\u7eed\u5199\u7684\u60f3\u6cd5\u3002 \u7f57\u7d20\u81ea\u5df1\u7684\u6700\u521d\u6253\u7b97\u5219\u662f\u5c06\u300a\u6570\u5b66\u539f\u7406\u300b\u5199\u6210\u300a\u6570\u5b66\u7684\u539f\u7406\u300b\u7684\u7b2c\u4e8c\u5377\u3002 \u4e0d\u8fc7\uff0c \u8fd9\u4e24\u4f4d\u60f3\u5199 \u201c\u7eed\u96c6\u201d \u7684\u4f5c\u8005 \u201c\u5f3a\u5f3a\u8054\u5408\u201d \u7684\u7ed3\u679c\uff0c \u662f\u5404\u81ea\u629b\u5f03\u4e86 \u201c\u524d\u96c6\u201d\uff0c \u5199\u51fa\u4e86\u4e00\u5957\u7bc7\u5e45\u548c\u6df1\u5ea6\u90fd\u8fdc\u8d85 \u201c\u524d\u96c6\u201d \u7684\u72ec\u7acb\u8457\u4f5c\u3002<\/p>\n<p>\u5408\u4f5c\u4e4b\u521d\uff0c \u7f57\u7d20\u548c\u6000\u7279\u6d77\u5bf9\u5de5\u4f5c\u8fdb\u5c55\u6709\u4e00\u4e2a\u5f88\u4e50\u89c2\u7684\u4f30\u8ba1\uff0c \u8ba4\u4e3a\u4e00\u5e74\u5de6\u53f3\u5373\u53ef\u5b8c\u6210\uff0c \u4f46\u7f57\u7d20\u6096\u8bba\u7684\u51fa\u73b0\u5c06\u8fd9\u4e00\u4f30\u8ba1\u626b\u8fdb\u4e86\u5783\u573e\u7bb1\uff0c \u300a\u6570\u5b66\u539f\u7406\u300b\u7684\u5b9e\u9645\u8017\u65f6\u7ea6\u4e3a\u5341\u5e74\uff0c \u6bd4\u5f53\u521d\u7684\u9884\u8ba1\u9ad8\u4e86\u4e00\u4e2a\u6570\u91cf\u7ea7\u3002 \u800c\u6bd4\u8017\u65f6\u589e\u52a0\u66f4\u53d7\u7f6a\u7684\uff0c \u5219\u662f\u7f57\u7d20\u6096\u8bba\u4f3c\u4e4e\u5728\u5632\u5f04\u7740\u7f57\u7d20\u7684\u76f4\u89c9\u548c\u667a\u529b\u3002 \u5728\u5f88\u957f\u4e00\u6bb5\u65f6\u95f4\u91cc\uff0c \u7f57\u7d20\u59cb\u7ec8\u89c9\u5f97\u7f57\u7d20\u6096\u8bba\u662f\u4e00\u4e2a \u201c\u5e73\u5eb8\u201d (trivial) \u7684\u95ee\u9898\uff0c \u5374\u504f\u504f\u7ed5\u4e0d\u8fc7\uff0c \u4e5f\u7a81\u7834\u4e0d\u4e86\u3002 \u8fd9\u79cd\u4e0d\u5f97\u4e0d\u628a\u7cbe\u529b\u82b1\u5728\u81ea\u5df1\u8ba4\u4e3a\u4e0d\u503c\u5f97\u7684\u5730\u65b9\uff0c \u4e14\u8fd8\u50cf\u6389\u8fdb\u4e86\u65e0\u5e95\u6d1e\u4e00\u6837\u770b\u4e0d\u5230\u5c3d\u5934\uff0c \u65e0\u7591\u662f\u5f88\u53d7\u7f6a\u7684\u611f\u89c9\u3002<\/p>\n<p>\u9664\u4e86\u906d\u9047\u50cf\u7f57\u7d20\u6096\u8bba\u90a3\u6837\u6280\u672f\u6027\u7684 \u201c\u62e6\u8def\u864e\u201d \u5916\uff0c \u64b0\u5199\u300a\u6570\u5b66\u539f\u7406\u300b\u7684\u5341\u5e74\u95f4\u7f57\u7d20\u5728\u751f\u6d3b\u4e0a\u4e5f\u9887\u53d7\u4e86\u51e0\u6869 \u201c\u7f6a\u201d\u3002<\/p>\n<p>\u7b2c\u4e00\u6869\u8ddf\u4e2a\u4eba\u5174\u8da3\u6709\u5173\uff0c \u8d77\u56e0\u4e8e\u6000\u7279\u6d77\u592b\u4eba\u4f0a\u592b\u6797\u00b7\u6000\u7279\u6d77 (Evelyn Whitehead)\uff0c \u800c\u4e14\u53d1\u751f\u5f97\u5f88\u7a81\u7136\u3002 \u6000\u7279\u6d77\u592b\u4eba\u5e74\u8f7b\u65f6\u7ecf\u5e38\u88ab\u7c7b\u4f3c\u5fc3\u7ede\u75db\u7684\u75c5\u75db\u6240\u6298\u78e8\uff0c 1901 \u5e74\u4e0a\u534a\u5e74\u7684\u67d0\u4e00\u5929\uff0c \u7f57\u7d20\u4eb2\u773c\u76ee\u7779\u4e86\u6000\u7279\u6d77\u592b\u4eba\u906d\u53d7\u5267\u70c8\u75c5\u75db\u6298\u78e8\u7684\u60c5\u5f62\u3002 \u90a3\u60c5\u5f62\u5bf9\u7f57\u7d20\u4ea7\u751f\u4e86\u6781\u6df1\u7684\u5f71\u54cd\uff0c \u4ed6\u4ece\u6000\u7279\u6d77\u592b\u4eba\u5b64\u7acb\u65e0\u52a9\u7684\u75db\u82e6\u4e2d\uff0c \u6df1\u5207\u610f\u8bc6\u5230\u4e86\u6bcf\u4e2a\u4eba\u7684\u7075\u9b42\u90fd\u5904\u5728\u96be\u4ee5\u5fcd\u53d7\u7684\u5b64\u72ec\u4e4b\u4e2d\u3002 \u8fd9\u4e00\u610f\u8bc6\u2014\u2014\u7528\u4ed6\u81ea\u5df1\u7684\u8bdd\u8bf4\u2014\u2014\u8ba9\u4ed6\u611f\u89c9\u5230 \u201c\u811a\u4e0b\u7684\u5927\u5730\u5ffd\u7136\u62bd\u8d70\u4e86\u201d\uff0c \u4f7f\u4ed6\u5728\u77ed\u77ed\u4e94\u5206\u949f\u7684\u65f6\u95f4\u91cc \u201c\u53d8\u6210\u4e86\u4e00\u4e2a\u5b8c\u5168\u4e0d\u540c\u7684\u4eba\u201d\uff0c \u7531\u64b0\u5199\u300a\u6570\u5b66\u539f\u7406\u300b\u6240\u9700\u8981\u7684\u4e00\u5473\u8ffd\u6c42\u7cbe\u786e\u548c\u5206\u6790 \u201c\u6da3\u6563\u201d \u4e3a\u4e86\u5bf9\u4eba\u751f\u548c\u793e\u4f1a\u54f2\u5b66\u4e5f\u6709\u4e86\u6d53\u539a\u5174\u8da3[\u6ce8\u4e94]\u3002<\/p>\n<p>\u7b2c\u4e8c\u6869\u8ddf\u5bb6\u5ead\u6709\u5173\uff0c \u4e14\u540c\u6837\u53d1\u751f\u5f97\u5f88\u7a81\u7136\u3002 \u636e\u7f57\u7d20\u81ea\u5df1\u56de\u5fc6\uff0c 1902 \u5e74\u6625\u5929\u7684\u4e00\u4e2a\u4e0b\u5348\uff0c \u4ed6\u5728\u4e00\u6761\u4e61\u95f4\u5c0f\u8def\u4e0a\u9a91\u8f66\uff0c \u5ffd\u7136 \u201c\u987f\u609f\u201d \u5230\u81ea\u5df1\u5df2\u4e0d\u7231\u7ed3\u5a5a\u516b\u5e74\u7684\u59bb\u5b50\u4e86\u3002 \u90a3\u662f\u4e00\u4e2a\u6700\u7b26\u5408\u5b57\u9762\u610f\u4e49\u7684 \u201c\u987f\u609f\u201d\uff0c \u56e0\u4e3a\u5728\u90a3\u4e4b\u524d\u4ed6\u751a\u81f3\u6ca1\u6709\u89c9\u5bdf\u5230\u5bf9\u59bb\u5b50\u7684\u7231\u6709\u4efb\u4f55\u51cf\u5f31\u3002 \u8fde\u51cf\u5f31\u90fd\u6ca1\u6709\uff0c \u7a81\u7136\u5c31\u6d88\u5931\u4e86\uff0c \u5929\u624d\u4eba\u7269\u7684 \u201c\u987f\u609f\u201d \u51fa\u73b0\u5728\u4e0d\u8be5\u51fa\u73b0\u7684\u5730\u65b9\u65f6\uff0c \u770b\u6765\u662f\u5f88\u6709\u4e9b\u53ef\u6015\u7684\u3002 \u7f57\u7d20\u7684\u59bb\u5b50\u7231\u4e3d\u4e1d\u00b7\u76ae\u5c14\u7d22\u5c14\u00b7\u53f2\u5bc6\u65af (Alys Pearsall Smith) \u6bd4\u7f57\u7d20\u5927 5 \u5c81\uff0c \u7f57\u7d20 17 \u5c81\u65f6\u7ed3\u8bc6\u4e86\u5979\uff0c 22 \u5c81\u65f6\u5c06 \u201c\u59d0\u5f1f\u604b\u201d \u4fee\u6210\u6b63\u679c\uff0c \u201c\u4e03\u5e74\u4e4b\u75d2\u201d \u65f6\u56e0 \u201c\u987f\u609f\u201d \u800c\u9677\u5165\u56f0\u5883\uff0c \u4f46\u5728\u7231\u4e3d\u4e1d\u4e00\u5ea6\u4ee5\u81ea\u6740\u4e3a\u5a01\u80c1\u7684\u6297\u4e89\u4e0b\uff0c \u62d6\u4e86\u7ea6 20 \u5e74\u624d\u6700\u7ec8\u79bb\u5a5a\u3002<\/p>\n<p>\u7b2c\u4e09\u6869\u5219\u8ddf\u5408\u4f5c\u8005\u6000\u7279\u6d77\u6709\u5173\u3002 \u636e\u7f57\u7d20\u5728\u81ea\u4f20\u4e2d\u62ab\u9732 (\u90a3\u65f6\u6000\u7279\u6d77\u592b\u5987\u7686\u5df2\u53bb\u4e16\uff0c \u4ece\u800c\u53ea\u80fd\u7b97\u4e00\u9762\u4e4b\u8bcd\u4e86)\uff0c \u5916\u4eba\u773c\u91cc\u51b7\u9759\u660e\u667a\u7684\u6000\u7279\u6d77\u5176\u5b9e\u5e38\u5e38\u9677\u5165\u975e\u7406\u6027\u7684\u51b2\u52a8\uff0c \u6bd4\u5982\u4e00\u65b9\u9762\u5bf9\u7f3a\u94b1\u6df1\u6000\u6050\u60e7\uff0c \u4e00\u65b9\u9762\u53c8\u82b1\u94b1\u65e0\u5ea6\uff1b \u6709\u65f6\u5019\u8fde\u7eed\u591a\u65e5\u4e0d\u542d\u4e00\u58f0\uff0c \u6709\u65f6\u5019\u53c8\u561f\u561f\u54dd\u54dd\u5bf9\u81ea\u5df1\u6a2a\u52a0\u8d2c\u4f4e\uff0c \u4f7f\u6000\u7279\u6d77\u592b\u4eba\u9971\u53d7\u60ca\u5413\uff0c \u751a\u81f3\u62c5\u5fc3\u4ed6\u4f1a\u5d29\u6e83\u6216\u53d1\u75af\u3002 \u4e3a\u4e86\u5e2e\u52a9\u6000\u7279\u6d77\u4e00\u5bb6\u53ca\u7ef4\u6301\u5728\u300a\u6570\u5b66\u539f\u7406\u300b\u4e0a\u7684\u5408\u4f5c\uff0c \u81ea\u5df1\u6709\u65f6\u4e5f\u8fd8\u8981\u501f\u94b1\u5ea6\u65e5\u7684\u7f57\u7d20\u5c0f\u5fc3\u7ffc\u7ffc\u5730\u8865\u8d34\u7740\u6000\u7279\u6d77\u7684\u5bb6\u7528\uff0c \u4e14\u8fd8\u5fc5\u987b\u7792\u7740\u6000\u7279\u6d77\uff0c \u4ee5\u514d\u4f24\u4ed6\u81ea\u5c0a\u5fc3\u3002<\/p>\n<p>\u4e2a\u4eba\u3001 \u5bb6\u5ead\u3001 \u5408\u4f5c\u8005\uff0c \u8fd9\u51e0\u4e4e\u6db5\u76d6\u7f57\u7d20\u6574\u4e2a\u4e16\u754c\u7684\u4e09\u5927\u56e0\u7d20\u7684\u5171\u540c\u714e\u71ac\uff0c \u52a0\u4e0a\u8bba\u9898\u672c\u8eab\u7684\u8270\u5de8\uff0c \u4ee5\u53ca\u7f57\u7d20\u6096\u8bba\u7684 \u201c\u62e6\u8def\u201d\uff0c \u4f7f\u7f57\u7d20\u64b0\u5199\u300a\u6570\u5b66\u539f\u7406\u300b\u7684\u8fc7\u7a0b\u7531\u8270\u82e6\u53d8\u4e3a\u75db\u82e6\u3002 \u8fd9\u79cd\u75db\u82e6\u5728 1903 \u548c 1904 \u5e74\u7684\u590f\u5929\u8fbe\u5230\u4e86\u9ad8\u5cf0\u3002 \u90a3\u6bb5\u65e5\u5b50\u88ab\u4ed6\u79f0\u4e3a \u201c\u5f7b\u5e95\u7684\u667a\u529b\u50f5\u5c40\u201d (complete intellectual deadlock)\u3002 \u5728\u90a3\u6bb5\u65e5\u5b50\u91cc\uff0c \u4ed6\u6bcf\u5929\u65e9\u6668\u62ff\u51fa\u4e00\u5f20\u767d\u7eb8\uff0c \u9664\u5348\u996d\u5916\uff0c \u6574\u5929\u5c31\u5bf9\u7740\u767d\u7eb8\u67af\u5750\uff0c \u5374\u5f80\u5f80\u4e00\u4e2a\u5b57\u4e5f\u5199\u4e0d\u51fa\uff0c \u751a\u81f3\u7126\u8651\u5730\u62c5\u5fc3\u81ea\u5df1\u4e00\u8f88\u5b50\u90fd\u8981\u5bf9\u7740\u767d\u7eb8\u4e00\u4e8b\u65e0\u6210\u4e86\u3002<\/p>\n<p>\u90a3\u4e9b\u5e74\uff0c \u7f57\u7d20\u5e38\u5230\u725b\u6d25\u9644\u8fd1\u4e00\u5ea7\u8de8\u8d8a\u94c1\u8def\u7684\u6865\u4e0a\u53bb\u770b\u706b\u8f66\uff0c \u5728\u60c5\u7eea\u60b2\u89c2\u65f6\uff0c \u770b\u7740\u4e00\u5217\u5217\u706b\u8f66\u9a76\u8fc7\uff0c \u4ed6\u6709\u65f6\u4f1a\u751f\u51fa\u53ef\u6015\u7684\u5ff5\u5934\uff1a \u4e5f\u8bb8\u660e\u5929\u5e72\u8106\u5367\u8f68\u4e86\u7ed3\u6b64\u751f\u3002 \u4e0d\u8fc7\u8fd9\u65f6\u5019\uff0c \u4f7f\u4ed6\u60b2\u89c2\u538c\u4e16\u7684\u300a\u6570\u5b66\u539f\u7406\u300b\u5374\u53c8\u53d8\u6210\u4e86\u8ba9\u4ed6\u6d3b\u4e0b\u53bb\u7684\u52a8\u529b\uff0c \u56e0\u4e3a\u6bcf\u5f53\u9ece\u660e\u6765\u4e34\uff0c \u4ed6\u53c8\u4f1a\u91cd\u65b0\u71c3\u8d77\u5e0c\u671b\uff1a \u6d3b\u4e0b\u53bb\uff0c \u201c\u4e5f\u8bb8\u67d0\u4e00\u5929\u80fd\u5b8c\u6210\u300a\u6570\u5b66\u539f\u7406\u300b\u201d\u3002<\/p>\n<p>1906 \u5e74\u4e4b\u540e\uff0c \u300a\u6570\u5b66\u539f\u7406\u300b\u6240\u9047\u5230\u7684\u6280\u672f\u74f6\u9888\u5f00\u59cb\u88ab\u7a81\u7834\uff0c \u5199\u4f5c\u5f97\u4ee5\u52a0\u901f\u3002 \u90a3\u65f6\u5019\uff0c \u6000\u7279\u6d77\u56e0\u6559\u4e66\u5de5\u4f5c\u7684\u7f81\u7eca\u65e0\u6cd5\u82b1\u8db3\u591f\u7684\u65f6\u95f4\u5728\u300a\u6570\u5b66\u539f\u7406\u300b\u4e0a\uff0c \u7f57\u7d20\u5f00\u59cb\u4ee5\u6bcf\u5929 10-12 \u5c0f\u65f6\uff0c \u6bcf\u5e74 8 \u4e2a\u6708\u5de6\u53f3\u7684\u65f6\u95f4\u6295\u5165\u5199\u4f5c\u3002 \u4f46\u70e6\u607c\u5e76\u672a\u5c31\u6b64\u8fdc\u79bb\uff0c \u968f\u7740\u624b\u7a3f\u6570\u91cf\u7684\u589e\u591a\uff0c \u4ed6\u53c8\u9677\u5165\u4e86\u8fd1\u4e4e\u675e\u4eba\u5fe7\u5929\u7684\u62c5\u5fe7\u4e4b\u4e2d\uff0c \u5bb3\u6015\u624b\u7a3f\u4f1a\u56e0\u623f\u5b50\u5931\u706b\u800c\u88ab\u6bc1\u3002<\/p>\n<p>\u6574\u6574\u5341\u5e74\uff0c \u75db\u82e6\u3001 \u7126\u8651\u3001 \u60b2\u89c2\u3001 \u62c5\u5fe7\u7ec8\u4e8e\u90fd\u88ab\u71ac\u8fc7\u3002 1910 \u5e74\uff0c \u300a\u6570\u5b66\u539f\u7406\u300b\u7684\u521d\u7a3f\u5b8c\u6210\u3002 \u5728\u7ed9\u670b\u53cb\u7684\u4fe1\u4e2d\uff0c \u7f57\u7d20\u5f88\u4e0d\u5409\u5229\u5730\u628a\u5f53\u65f6\u7684\u5fc3\u60c5\u5f62\u5bb9\u4e3a\uff1a \u4e00\u4e2a\u56e0\u7167\u987e\u91cd\u75c5\u60a3\u800c\u7cbe\u75b2\u529b\u5c3d\u7684\u4eba\uff0c \u770b\u5230\u53ef\u6076\u7684\u75c5\u60a3\u7ec8\u4e8e\u6b7b\u53bb\u65f6\u7684\u90a3\u79cd\u5982\u91ca\u91cd\u8d1f\u7684\u611f\u89c9\u3002<\/p>\n<p>\u7531\u4e8e\u7bc7\u5e45\u6d69\u7e41\uff0c \u7f57\u7d20\u5c06\u624b\u7a3f\u88c5\u4e86\u4e24\u4e2a\u7bb1\u5b50\uff0c \u96c7\u4e86\u56db\u8f6e\u9a6c\u8f66\u8fd0\u5230\u5251\u6865\u5927\u5b66\u51fa\u7248\u793e (Cambridge University Press)\u3002 \u51fa\u7248\u793e\u5bf9\u51fa\u7248\u8fd9\u90e8\u5de8\u8457\u7684 \u201c\u5229\u6da6\u201d \u8fdb\u884c\u4e86\u8bc4\u4f30\uff0c \u5f97\u51fa\u4e00\u4e2a\u5f88\u4e0d\u9f13\u821e\u4eba\u5fc3\u7684\u7ed3\u679c\uff1a \u8d1f 600 \u82f1\u9551\u3002 \u5f53\u7136\uff0c \u5251\u6865\u5927\u5b66\u51fa\u7248\u793e\u5e76\u975e\u552f\u5229\u662f\u56fe\u7684\u5730\u65b9\uff0c \u4ed6\u4eec\u613f\u610f\u4e3a\u8fd9\u6837\u7684\u5de8\u8457\u8d54\u4e0a\u4e00\u4e9b\u94b1\uff0c \u95ee\u9898\u662f 600 \u82f1\u9551\u5728\u5f53\u65f6\u5b9e\u5728\u662f\u4e00\u4e2a\u4e0d\u5c0f\u7684\u6570\u76ee\uff0c \u4ed6\u4eec\u53ea\u80fd\u627f\u62c5\u4e00\u534a\u5de6\u53f3\u2014\u2014\u5373\u7ea6 300 \u82f1\u9551\u3002 \u5269\u4e0b\u7684 300 \u82f1\u9551\u600e\u4e48\u529e\u5462\uff1f \u5728\u7f57\u7d20\u4e0e\u6000\u7279\u6d77\u7684\u7533\u8bf7\u4e0b\uff0c \u7687\u5bb6\u5b66\u4f1a\u6177\u6168\u89e3\u56ca\uff0c \u8d5e\u52a9\u4e86 200 \u82f1\u9551\u3002 \u4f46\u6700\u540e\u7684 100 \u82f1\u9551\u5b9e\u5728\u662f\u6ca1\u529e\u6cd5\u7b79\u63aa\u4e86\uff0c \u53ea\u80fd\u644a\u6d3e\u5230\u7f57\u7d20\u548c\u6000\u7279\u6d77\u8fd9\u4e24\u4f4d\u4f5c\u8005\u5934\u4e0a\uff0c \u6bcf\u4eba 50 \u82f1\u9551 (\u76f8\u5f53\u4e8e 2006 \u5e74\u7684 7,000 \u591a\u7f8e\u5143)\u3002 \u5bf9\u4e8e\u8fd9\u4e00\u7ed3\u679c\uff0c \u7f57\u7d20\u5728\u81ea\u4f20\u4e2d\u611f\u6168\u5730\u5199\u9053\uff1a \u6211\u4eec\u7528 10 \u5e74\u7684\u5de5\u4f5c\u6bcf\u4eba\u8d5a\u4e86\u8d1f 50 \u82f1\u9551\u3002<\/p>\n<p>\u5927\u4e66\u51fa\u7248\u4e86\uff0c \u5927\u94b1\u8d54\u6389\u4e86[\u6ce8\u516d]\uff0c \u4f46\u7f57\u7d20\u628a\u5927\u4e66\u7684\u5b8c\u6210\u6bd4\u55bb\u4e3a\u91cd\u75c5\u60a3\u7684\u6b7b\u53bb\u5e76\u4e0d\u6070\u5f53\uff0c \u4e66\u4e4b\u4e8e\u4f5c\u8005\u5176\u5b9e\u66f4\u50cf\u5b69\u5b50\u4e4b\u4e8e\u7236\u6bcd\uff0c \u4e66\u7684\u51fa\u7248\u597d\u6bd4\u5b69\u5b50\u7684\u964d\u751f\uff0c \u672a\u5fc5\u662f\u4e00\u4e2a\u80fd\u8ba9\u7236\u6bcd\u5982\u91ca\u91cd\u8d1f\u7684\u65f6\u523b\u3002 \u4e8b\u5b9e\u4e0a\uff0c \u7f57\u7d20\u56e0\u8fd9\u90e8\u5927\u4e66\u800c\u53d7 \u201c\u5927\u7f6a\u201d \u7684\u5386\u53f2\u5e76\u672a\u5c31\u6b64\u7ec8\u7ed3\u3002<\/p>\n<p>\u7f57\u7d20\u548c\u6000\u7279\u6d77\u7684\u8fd9\u90e8\u5927\u4e66\u987e\u540d\u601d\u4e49\uff0c \u662f\u7814\u7a76\u6570\u5b66\u57fa\u7840\u7684\u3002 \u8fd9\u7c7b\u7814\u7a76\u6709\u51e0\u4e2a\u4e3b\u8981\u6d41\u6d3e\uff0c \u6bd4\u5982\u4ee5\u5fb7\u56fd\u6570\u5b66\u5bb6\u5e0c\u5c14\u4f2f\u7279 (David Hilbert) \u4e3a\u4ee3\u8868\u7684\u5f62\u5f0f\u4e3b\u4e49 (Formalism)\u3001 \u4ee5\u8377\u5170\u6570\u5b66\u5bb6\u5e03\u52b3\u5a01\u5c14 (L. E. J. Brouwer) \u4e3a\u4ee3\u8868\u7684\u76f4\u89c9\u4e3b\u4e49 (Intuitionism)\uff0c \u7b49\u7b49\u3002 \u7f57\u7d20\u548c\u6000\u7279\u6d77\u8fd9\u90e8\u300a\u6570\u5b66\u539f\u7406\u300b\u4e5f\u5c5e\u4e8e\u4e00\u4e2a\u8457\u540d\u6d41\u6d3e\uff0c \u53eb\u505a\u903b\u8f91\u4e3b\u4e49 (Logicism)\uff0c \u4e3b\u5f20\u6570\u5b66\u53ef\u4ee5\u7ea6\u5316\u4e3a\u903b\u8f91\u3002 \u300a\u6570\u5b66\u539f\u7406\u300b\u4e0d\u662f\u903b\u8f91\u4e3b\u4e49\u7684\u5960\u57fa\u4e4b\u4f5c\uff0c \u5374\u662f\u5b83\u7684\u9ad8\u5cf0\u3002 \u5728\u300a\u6570\u5b66\u539f\u7406\u300b\u4e2d\uff0c \u6570\u5b66\u5927\u53a6\u7684\u4e00\u90e8\u5206\u88ab\u4ece\u903b\u8f91\u51fa\u53d1\u76f4\u63a5\u6784\u7b51\u4e86\u51fa\u6765\u3002 \u7f57\u7d20\u548c\u6000\u7279\u6d77\u5bf9\u6b64\u6df1\u611f\u81ea\u8c6a\uff0c \u5728\u5411\u7687\u5bb6\u5b66\u4f1a\u7533\u8bf7\u8d5e\u52a9\u7684\u4fe1\u91cc\uff0c \u7279\u522b\u5f3a\u8c03\u4e86\u8fd9\u90e8\u4e66\u7684\u7cbe\u786e\u6027 (exactness)\u3001 \u63a8\u7406\u7684\u7f1c\u5bc6\u6027 (particularity of reasoning) \u4ee5\u53ca\u5185\u5bb9\u7684\u5b8c\u5907\u6027 (completeness)\u3002<\/p>\n<p>\u4f46\u662f\uff0c \u8fd9\u4e00\u5207\u5e76\u975e\u6ca1\u6709\u4ee3\u4ef7\uff0c \u90a3\u4ee3\u4ef7\u5c31\u662f\u63a8\u7406\u7684\u6781\u5ea6\u66f2\u6298\u548c\u5197\u957f\u3002 \u6bd4\u65b9\u8bf4\uff0c \u201c1\u201d \u8fd9\u4e2a\u5c0f\u5b66\u6570\u5b66\u7b2c\u4e00\u8bfe\u7684\u5185\u5bb9\u5728\u300a\u6570\u5b66\u539f\u7406\u300b\u4e2d\u76f4\u5230\u7b2c 363 \u9875\u624d\u88ab\u5b9a\u4e49\uff1b 1+1 \u8fd9\u4e2a\u6700\u7b80\u5355\u7684\u5c0f\u5b66\u7b97\u672f\u9898\u76f4\u5230\u7b2c 379 \u9875\u624d\u6709\u7b54\u6848\u3002 \u6bd4\u8fd9\u79cd\u66f2\u6298\u548c\u5197\u957f\u66f4\u7cdf\u7cd5\u7684\uff0c \u662f\u300a\u6570\u5b66\u539f\u7406\u300b\u867d\u7136\u662f\u903b\u8f91\u4e3b\u4e49\u7684\u9ad8\u5cf0\uff0c \u5374\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u80cc\u79bb\u4e86\u903b\u8f91\u4e3b\u4e49\u7684\u521d\u8877\uff0c \u5373\u501f\u52a9\u903b\u8f91\u6240\u5177\u6709\u7684\u81ea\u660e\u6027 (self-evidence) \u6765\u6784\u7b51\u6570\u5b66\u3002 \u5728\u300a\u6570\u5b66\u539f\u7406\u300b\u4e2d\uff0c \u7f57\u7d20\u548c\u6000\u7279\u6d77\u5f15\u8fdb\u4e86\u51e0\u6761\u4e0d\u4ec5\u4e0d\u81ea\u660e\uff0c \u751a\u81f3\u672a\u5fc5\u80fd\u7b97\u903b\u8f91\u7684\u516c\u7406\uff0c \u6bd4\u5982\u65e0\u7a77\u516c\u7406 (axiom of infinity)\u3001 \u9009\u62e9\u516c\u7406 (axiom of choice)\uff0c \u4ee5\u53ca\u53ef\u5316\u5f52\u6027\u516c\u7406 (axiom of reducibility)\u3002 \u8fd9\u5176\u4e2d\u65e0\u7a77\u516c\u7406\u548c\u9009\u62e9\u516c\u7406\u5728\u96c6\u5408\u8bba\u4e2d\u4e5f\u91c7\u7528\uff0c \u5012\u8fd8\u7f62\u4e86\uff0c \u53ef\u5316\u5f52\u6027\u516c\u7406\u5219\u5b8c\u5168\u662f\u53e6\u7c7b\u3002 \u300a\u6570\u5b66\u539f\u7406\u300b\u7684\u8fd9\u4e00\u7279\u70b9\u2014\u2014\u5c24\u5176\u662f\u53ef\u5316\u5f52\u6027\u516c\u7406\u2014\u2014\u906d\u5230\u4e86\u731b\u70c8\u6279\u8bc4\uff0c \u6279\u8bc4\u8005\u5305\u62ec\u7b2c\u4e00\u6d41\u7684\u6570\u5b66\u5bb6\u3001 \u903b\u8f91\u5b66\u5bb6\u548c\u54f2\u5b66\u5bb6\uff0c \u51e0\u4e4e\u662f\u6570\u5b66\u57fa\u7840\u7814\u7a76\u7684\u4e00\u4e2a\u660e\u661f\u9635\u5bb9\u3002<\/p>\n<p><img src=\"https:\/\/i01piccdn.sogoucdn.com\/f29e42e76cd44c2c\" \/><\/p>\n<p>\u25b3\u300a\u6570\u5b66\u539f\u7406\u300b\u5bf9 \u201c1\u201d \u7684\u5b9a\u4e49<\/p>\n<p>\u6bd4\u5982\u8457\u540d\u5fb7\u56fd\u6570\u5b66\u5bb6\u5916\u5c14 (Hermann Weyl) \u5c31\u8d28\u7591\u9053\uff0c \u6709\u4efb\u4f55\u5177\u5907\u73b0\u5b9e\u5934\u8111\u7684\u4eba\u6562\u8bf4\u81ea\u5df1\u76f8\u4fe1\u8fd9\u6837\u4e00\u4e2a\u4e0d\u81ea\u7136\u7684\u4f53\u7cfb\u5417\uff1f \u7f57\u7d20\u7684\u5b66\u751f\uff0c \u8457\u540d\u54f2\u5b66\u5bb6\u7ef4\u7279\u6839\u65af\u5766 (Ludwig Wittgenstein) \u4e5f\u6beb\u4e0d\u5ba2\u6c14\u5730 \u201c\u53db\u53d8\u201d \u4e86\uff0c \u8868\u793a\u6570\u5b66\u7684\u771f\u6b63\u57fa\u7840\u662f\u50cf \u201c1\u201d \u90a3\u6837\u6765\u81ea\u7b97\u672f\u5b9e\u8df5\u7684\u4e1c\u897f\uff0c \u800c\u4e0d\u662f\u7528\u51e0\u767e\u9875\u7bc7\u5e45\u624d\u80fd\u63a8\u51fa \u201c1\u201d \u6765\u7684\u300a\u6570\u5b66\u539f\u7406\u300b\uff0c \u7406\u7531\u5f88\u7b80\u5355\uff1a \u4e00\u65e6\u300a\u6570\u5b66\u539f\u7406\u300b\u4e0e\u90a3\u4e9b\u7b97\u672f\u5b9e\u8df5\u76f8\u77db\u76fe\uff0c \u6211\u4eec\u7acb\u523b\u5c31\u77e5\u9053\u662f\u300a\u6570\u5b66\u539f\u7406\u300b\u800c\u4e0d\u662f\u7b97\u672f\u5b9e\u8df5\u9519\u4e86\u3002 \u786e\u5b9e\uff0c \u50cf \u201c1\u201d \u548c \u201c1+1=2\u201d \u90a3\u6837\u7684 \u201c\u5c0f\u5b66\u6570\u5b66\u201d \u679c\u771f\u9700\u8981\u50cf\u53ef\u5316\u5f52\u6027\u516c\u7406\u90a3\u6837\u7684\u516c\u7406\u53ca\u51e0\u767e\u9875\u7684\u903b\u8f91\u63a8\u7406\u4e3a \u201c\u57fa\u7840\u201d \u5417\uff1f \u8fd9\u5bf9\u903b\u8f91\u4e3b\u4e49\u582a\u79f0\u662f\u81f4\u547d\u95ee\u9898[\u6ce8\u4e03]\u3002<\/p>\n<p>\u5728\u8fd9\u4e00\u95ee\u9898\u524d\u9996\u5148\u5012\u4e0b\u7684\u5f53\u7136\u5c31\u662f\u5df2\u6210\u4f17\u77e2\u4e4b\u7684\u7684\u53ef\u5316\u5f52\u6027\u516c\u7406\u3002 \u7f57\u7d20\u81ea\u5df1\u540e\u6765\u4e5f\u4e0d\u5f97\u4e0d\u627f\u8ba4\uff0c \u201c\u6ca1\u6709\u4efb\u4f55\u7406\u7531\u76f8\u4fe1\u53ef\u5316\u5f52\u6027\u516c\u7406\u662f\u903b\u8f91\u4e0a\u5fc5\u8981\u7684\u201d\uff0c \u201c\u628a\u8fd9\u4e00\u516c\u7406\u5f15\u8fdb\u4f53\u7cfb\u662f\u4e00\u4e2a\u7f3a\u9677\u201d\u3002 \u4f46\u53e6\u4e00\u65b9\u9762\uff0c \u7f57\u7d20\u4e5f\u4e0d\u65e0\u611f\u6168\u5730\u610f\u8bc6\u5230\uff0c \u5f88\u591a\u56f0\u96be\u4f3c\u4e4e\u53ea\u6709\u7528 \u201c\u5e76\u4e0d\u6f02\u4eae\u7684\u7406\u8bba\u201d \u624d\u80fd\u89e3\u51b3\uff0c \u800c\u53ef\u5316\u5f52\u6027\u516c\u7406\u5c31\u662f\u8fd9\u79cd \u201c\u5e76\u4e0d\u6f02\u4eae\u7684\u7406\u8bba\u201d 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\u8fd8\u4e0d\u6b62\u4e00\u6b21\u9047\u5230\u6709\u4eba\u8bd5\u56fe\u91cd\u590d\u89e3\u51b3\u65e9\u5df2\u88ab\u300a\u6570\u5b66\u539f\u7406\u300b\u89e3\u51b3\u6389\u7684\u95ee\u9898\u3002<\/p>\n<p>\u5199\u4e86\u4e00\u90e8\u5927\u4e66\u5374\u8bfb\u8005\u5be5\u5be5\u65e0\u51e0\uff0c \u8fd9\u662f\u4e0d\u5e78\u3002 \u6bd4\u8fd9\u66f4\u4e0d\u5e78\u7684\uff0c \u662f\u90a3\u5be5\u5be5\u65e0\u51e0\u7684\u8bfb\u8005\u4e4b\u4e2d\uff0c \u5374\u6709\u4e00\u4eba\u6345\u51fa\u4e86\u5a04\u5b50\u3002 \u6b64\u4eba\u540d\u53eb\u54e5\u5fb7\u5c14 (Kurt G\u00f6del)\uff0c 1931 \u5e74\uff0c \u4ed6\u53d1\u8868\u4e86\u4e00\u7bc7\u5212\u65f6\u4ee3\u7684\u8bba\u6587\uff0c \u9898\u4e3a \u201c\u8bba\u300a\u6570\u5b66\u539f\u7406\u300b\u53ca\u76f8\u5173\u4f53\u7cfb\u4e2d\u7684\u5f62\u5f0f\u4e0a\u4e0d\u53ef\u5224\u5b9a\u547d\u9898\u201d (On Formally Undecidable Propositions of Principia Mathematica and Related Systems)[\u6ce8\u516b]\u3002 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