{"id":9755,"date":"2026-07-25T20:28:32","date_gmt":"2026-07-25T11:28:32","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=9755"},"modified":"2026-07-27T15:57:54","modified_gmt":"2026-07-27T06:57:54","slug":"math-abstraction-11-topography","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/mathematical-abstraction\/math-abstraction-11-topography\/","title":{"rendered":"\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \ubc29\ubc95\uacfc \ucca0\ud559"},"content":{"rendered":"<p><!-- \uc218\ud559\uc801 \ucd94\uc0c1\ud654 11\ud3b8: \ucd94\uc0c1\ud654\uc758 \uc9c0\ud615\ub3c4 --><\/p>\n<div class=\"math-abs-series\">\n<p><a href=\"..\/math-abstraction-10-optimal-generality\/\">10\ubd80<\/a>\uc758 \ub9d0\ubbf8\uc5d0\uc11c \uc6b0\ub9ac\ub294 \uc138 \uac00\uc9c0 \ubb35\uc9c1\ud55c \uc9c8\ubb38\uc744 \ub0a8\uacbc\ub2e4. \ucd94\uc0c1\ud654\uc640 \uc77c\ubc18\ud654, \uc774\uc0c1\ud654, \ud615\uc2dd\ud654\ub294 \uc5b4\ub5bb\uac8c \uad6c\ubd84\ub418\ub294\uac00? <a href=\"..\/\">\ubcf8 \uc5f0\uc7ac<\/a>\ub97c \ud1b5\ud574 \uc0b4\ud3b4\ubcf8 \uc5ec\uc12f \uac00\uc9c0 \ucd94\uc0c1\ud654 \uc870\uc791\uc740 \uc11c\ub85c \uc5b4\ub5bb\uac8c \uc5f0\uacb0\ub418\ub294\uac00? \uadf8\ub9ac\uace0 \uc774\ub7f0 \uc870\uc791\uc73c\ub85c \uaddc\uc815\ub41c \uc218\ud559\uc801 \ub300\uc0c1\uc740 \uc778\uac04\uc758 \uc0ac\uace0\uc640 \ub3c5\ub9bd\ud558\uc5ec \u2018\uc815\ub9d0\ub85c \uc874\uc7ac\ud558\ub294\uac00?\u2019 \uc774 \uae00\uc5d0\uc11c\ub294 \uc9c0\ub09c \uc5f4 \ud3b8\uc758 \uada4\uc801\uc744 \ud55c\uc790\ub9ac\uc5d0 \ubaa8\uc544 \uc774 \uc138 \uc9c8\ubb38\uc758 \uc9c0\ud615\ub3c4\ub97c \uadf8\ub824\ubcf8\ub2e4.<\/p>\n<h4>\uc77c\ubc18\ud654, \ucd94\uc0c1\ud654, \uc774\uc0c1\ud654, \ud615\uc2dd\ud654<\/h4>\n<p>\uc5f0\uc7ac\uc758 \uccab\uba38\ub9ac\uc5d0\uc11c \uc6b0\ub9ac\ub294 \ud3c9\uba74 \\(\\mathbb R^2\\)\uc758 \ub17c\uc758\ub97c \\(n\\)\ucc28\uc6d0 \uacf5\uac04 \\(\\mathbb R^n\\)\uc73c\ub85c \ub113\ud788\ub294 \uc77c\uacfc, \uad6c\uccb4\uc801\uc778 \\(\\mathbb R^n\\)\uc5d0\uc11c \ucd94\uc0c1 \ubca1\ud130\uacf5\uac04\uc73c\ub85c \ub118\uc5b4\uac00\ub294 \uc77c\uc744 \ub300\uc870\ud588\ub2e4. <!-- \uc774 \ub300\uc870\ub294 \uc720\uc6a9\ud558\uc9c0\ub9cc, \u2018\uc77c\ubc18\ud654, \ucd94\uc0c1\ud654, \uc774\uc0c1\ud654, \ud615\uc2dd\ud654\u2019\ub97c \uac00\ub974\ub294 \ud558\ub098\uc758 \ubcf4\ud3b8\uc801\uc774\uace0 \ubc30\ud0c0\uc801\uc778 \ud45c\uc900 \ubd84\ub958\uac00 \ud559\uacc4\uc5d0 \ud655\ub9bd\ub418\uc5b4 \uc788\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. --> \uac19\uc740 \uc791\uc5c5\uc774 \uad00\uc810\uc5d0 \ub530\ub77c \uc77c\ubc18\ud654\uc774\uba74\uc11c \ucd94\uc0c1\ud654\uc77c \uc218 \uc788\uace0, \ucd94\uc0c1\ud654\uc640 \uc774\uc0c1\ud654\ub3c4 \uc2e4\uc81c \uacfc\ud559\uc801 \ubaa8\ud615\uc5d0\uc11c\ub294 \uacb9\uce60 \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c \uc544\ub798 \uad6c\ubd84\uc740 \uc774 \uc5f0\uc7ac\uc758 \uc0ac\ub840\ub4e4\uc744 \uc815\ub9ac\ud558\uae30 \uc704\ud55c <em>\uc791\uc5c5\uc0c1\uc758 \uc9c0\ub3c4<\/em>\ub85c \uc774\ud574\ud574\uc57c \ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Michael Weisberg, Simulation and Similarity: Using Models to Understand the World, Oxford University Press, 2013.\" href=\"#ref-Weisberg2013\">[Weisberg2013]<\/a><\/p>\n<ul>\n<li><span class=\"defined\">\uc77c\ubc18\ud654<\/span>(generalization)\ub294 \uc5b4\ub5a4 \uba85\uc81c\ub098 \ubc29\ubc95\uc758 \uc801\uc6a9 \ubc94\uc704\ub97c \ub354 \ub113\uc740 \ub300\uc0c1\uad70\uc73c\ub85c \ud655\uc7a5\ud558\ub294 \uc77c\uc774\ub2e4. \\(\\mathbb R^2\\)\uc5d0\uc11c \\(\\mathbb R^n\\)\uc73c\ub85c\uc758 \ud655\uc7a5\uc774 \ud55c \uc608\ub2e4. \ubb3c\ub860, \uae30\uc874 \uc815\ub9ac\uac00 \uc5b8\uc81c\ub098 \ubb38\uad6c\uae4c\uc9c0 \uadf8\ub300\ub85c \uc720\uc9c0\ub418\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. \ucc28\uc6d0\uc5d0 \ub530\ub77c \uac00\uc815\uc744 \ubcf4\uac15\ud558\uac70\ub098 \uacb0\ub860\uc744 \ub2e4\uc2dc \uc368\uc57c \ud560 \uc218 \uc788\uace0, \ub113\uc5b4\uc9c4 \uc601\uc5ed\uc5d0\uc11c \uc815\ub9ac\ub97c \uc0c8\ub85c \uc99d\uba85\ud574\uc57c \ud55c\ub2e4.<\/li>\n<li><span class=\"defined\">\ucd94\uc0c1\ud654<\/span>(abstraction)\ub294 \ub2f9\uba74\ud55c \ubaa9\uc801\uacfc \ubb34\uad00\ud55c \ucc28\uc774\ub97c \ubb34\uc2dc\ud558\uac70\ub098 \ub3d9\uc77c\uc2dc\ud558\uace0, \uacf5\ud1b5 \uc131\uc9c8, \uad00\uacc4, \uc5f0\uc0b0\uc744 \uc804\uba74\uc5d0 \ub0b4\uc138\uc6b0\ub294 \uc77c\uc774\ub2e4. \\(\\mathbb R^n\\)\uc5d0\uc11c \ubca1\ud130\uacf5\uac04\uc73c\ub85c \ub118\uc5b4\uac00\uba74 \uc88c\ud45c \ud45c\ud604\uc740 \ud544\uc218 \uc790\ub8cc\uac00 \uc544\ub2c8\uac8c \ub418\uace0, \ub367\uc148\uacfc \uc2a4\uce7c\ub77c\uacf1\uc758 \uacf5\ub9ac\uac00 \uc911\uc2ec\uc774 \ub41c\ub2e4. \uadf8 \uacb0\uacfc \ub2e4\ud56d\uc2dd\uc774\ub098 \ud568\uc218\uc758 \uacf5\uac04\ub3c4 \uac19\uc740 \uc774\ub860 \uc544\ub798 \ub2e4\ub8f0 \uc218 \uc788\ub2e4. \uadf8\ub7ec\ub098 \ubaa8\ub4e0 \uc88c\ud45c\uacf5\uac04 \uc815\ub9ac\uac00 \uc784\uc758\uc758 \ubca1\ud130\uacf5\uac04\uc5d0 \uc790\ub3d9\uc73c\ub85c \uc62e\uaca8\uac00\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. \ucc28\uc6d0, \uc704\uc0c1, \ub0b4\uc801\ucc98\ub7fc \uc6d0\ub798 \uc99d\uba85\uc774 \uc0ac\uc6a9\ud55c \ucd94\uac00 \uad6c\uc870\uac00 \ubb34\uc5c7\uc778\uc9c0 \ub530\uc838\uc57c \ud55c\ub2e4.<\/li>\n<li><span class=\"defined\">\uc774\uc0c1\ud654<\/span>(idealization)\ub294 \ub9c8\ucc30 \uc5c6\ub294 \ud3c9\uba74, \uc810\uc785\uc790, \uc644\uc804 \uac15\uccb4\ucc98\ub7fc \ud604\uc2e4\uc758 \ub300\uc0c1\uc744 \uc758\ub3c4\uc801\uc73c\ub85c \ub2e8\uc21c\ud654\ud558\uac70\ub098 \ubb38\uc790 \uadf8\ub300\ub85c\ub294 \uc131\ub9bd\ud558\uc9c0 \uc54a\ub294 \uac00\uc815\uc744 \ub3c4\uc785\ud574 \ub2e4\ub8e8\uae30 \uc26c\uc6b4 \ubaa8\ud615\uc744 \ub9cc\ub4dc\ub294 \uc77c\uc774\ub2e4. \ud754\ud788 \ucd94\uc0c1\ud654\uac00 \ucc28\uc774\ub97c \uc0dd\ub7b5\ud558\ub294 \ub370, \uc774\uc0c1\ud654\uac00 \uc65c\uace1\uc774\ub098 \uadf9\ud55c\uc801 \uac00\uc815\uc744 \ub3c4\uc785\ud558\ub294 \ub370 \ucd08\uc810\uc744 \ub454\ub2e4\uace0 \uad6c\ubd84\ud558\uc9c0\ub9cc, \uc2e4\uc81c \ubaa8\ud615\uc5d0\uc11c\ub294 \ub450 \uacfc\uc815\uc774 \ud568\uaed8 \uc791\ub3d9\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Michael Weisberg, Simulation and Similarity: Using Models to Understand the World, Oxford University Press, 2013.\" href=\"#ref-Weisberg2013\">[Weisberg2013]<\/a><\/li>\n<\/ul>\n<p><span class=\"defined\">\ud615\uc2dd\ud654<\/span>(formalization)\ub294 \ud45c\ud604\uacfc \ucd94\ub860\uc744 \uba85\uc2dc\uc801\uc778 \uc5b8\uc5b4, \uacf5\ub9ac, \uaddc\uce59\uc73c\ub85c \ubd80\ud638\ud654\ud558\ub294 \uc77c\uc774\ub2e4. \ub77c\uc774\ud504\ub2c8\uce20\uac00 \uad6c\uc0c1\ud55c \ubcf4\ud3b8\uc801 \ud45c\uc0c1 \uc5b8\uc5b4\uc778 <i>characteristica universalis<\/i>\uc640 \uadf8 \ud45c\uc0c1\ub4e4\uc744 \uacc4\uc0b0\ud558\ub294 \ucd94\ub860\ubc95\uc778 <i>calculus ratiocinator<\/i>\uc758 \uc774\uc0c1\uc740 \uadf8 \uc911\uc694\ud55c \uc120\uad6c \uac00\uc6b4\ub370 \ud558\ub098\uc600\ub2e4.<a class=\"math-abs-series-ref\" title=\"Michael Beaney, \u201cAnalysis,\u201d supplement \u201cEarly Modern Conceptions of Analysis,\u201d Stanford Encyclopedia of Philosophy.\" href=\"#ref-BeaneyAnalysis\">[BeaneyAnalysis]<\/a> \ucda9\ubd84\ud788 \ud615\uc2dd\ud654\ub41c \uc99d\uba85\uc5d0\uc11c\ub294 \uac01 \ub2e8\uacc4\uac00 \uc815\ud574\uc9c4 \uad6c\ubb38 \uaddc\uce59\uc5d0 \ub9de\ub294\uc9c0 \uae30\uacc4\uc801\uc73c\ub85c \uac80\uc0ac\ud560 \uc218 \uc788\ub2e4. <!-- \ub2e4\ub9cc \ud615\uc2dd\ud654\ub41c \uae30\ud638\uc5f4\uc774 \uc544\ubb34 \uc758\ubbf8\ub3c4 \uac16\uc9c0 \uc54a\ub294\ub2e4\ub294 \ub73b\uc740 \uc544\ub2c8\ub2e4. --> \uc5b4\ub5a4 \ud615\uc2dd \uccb4\uacc4\ub3c4 \ub2e4\uc591\ud55c \ud574\uc11d\uacfc \ubaa8\ud615\uc744 \uac00\uc9c8 \uc218 \uc788\uc73c\uba70, \uad6c\ubb38\ub860\uacfc \uc758\ubbf8\ub860\uc744 \uad6c\ubcc4\ud558\ub294 \uac83\uacfc \uc758\ubbf8\ub860\uc744 \uc81c\uac70\ud558\ub294 \uac83\uc740 \uc11c\ub85c \ub2e4\ub978 \uc77c\uc774\ub2e4.<\/p>\n<p>\ud790\ubca0\ub974\ud2b8 \ud504\ub85c\uadf8\ub7a8\uc740 \uace0\uc804 \uc218\ud559\uc758 \ud615\uc2dd\ud654\ub97c \ucd94\uc9c4\ud558\uace0, \uadf8 \ud615\uc2dd \uccb4\uacc4\uc758 \ubb34\ubaa8\uc21c\uc131\uc744 \ub0b4\uc6a9\uc801\uc73c\ub85c \uc548\uc804\ud558\ub2e4\uace0 \uc5ec\uae34 \uc720\ud55c\uc8fc\uc758\uc801 \uba54\ud0c0\uc218\ud559\uc73c\ub85c \uc815\ub2f9\ud654\ud558\ub824\ub294 \uae30\ud68d\uc774\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Richard Zach, \u201cHilbert\u2019s Program,\u201d Stanford Encyclopedia of Philosophy.\" href=\"#ref-Zach2023\">[Zach2023]<\/a> 1931\ub144 \ucfe0\ub974\ud2b8 \uad34\ub378(Kurt G\u00f6del)\uc740 \ud6a8\uacfc\uc801\uc73c\ub85c \uacf5\ub9ac\ud654\ub418\uace0 \uc790\uc5f0\uc218 \uc0b0\uc220\uc744 \ud45c\ud604\ud560 \ub9cc\ud07c \uac15\ud55c \uc77c\uad00\ub41c \ud615\uc2dd \uccb4\uacc4\uc5d0\ub294 \uadf8 \uccb4\uacc4 \uc548\uc5d0\uc11c \uc99d\uba85\ud560 \uc218\ub3c4 \ubc18\uc99d\ud560 \uc218\ub3c4 \uc5c6\ub294 \ubb38\uc7a5\uc774 \uc788\uc74c\uc744 \ubcf4\uc600\ub2e4. <!-- \ubb38\uc7a5\uc744 \u2018\ucc38\uc774\uc9c0\ub9cc \uc99d\uba85 \ubd88\uac00\ub2a5\ud558\ub2e4\u2019\uace0 \ub9d0\ud560 \ub54c\uc5d0\ub294 \uc758\ub3c4\ub41c \uc790\uc5f0\uc218 \ud574\uc11d\uc774\ub098 \uc801\uc808\ud55c \uac74\uc804\uc131 \uac00\uc815\uc774 \ucd94\uac00\ub85c \ud544\uc694\ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Kurt G\u00f6del, \u201c\u00dcber formal unentscheidbare S\u00e4tze der Principia Mathematica und verwandter Systeme I,\u201d Monatshefte f\u00fcr Mathematik und Physik 38, 1931, pp. 173\u2013198.\" href=\"#ref-Godel1931\">[Godel1931]<\/a> --> [\uc774\uac83\uc774 \uc81c1 \ubd88\uc644\uc804\uc131 \uc815\ub9ac\uc758 \ud575\uc2ec\uc774\ub2e4. \uc774\uc5b4\uc9c0\ub294 \uc81c2 \ubd88\uc644\uc804\uc131 \uc815\ub9ac\ub294 \ucda9\ubd84\ud55c \uc0b0\uc220\uc744 \ud3ec\ud568\ud558\uace0 \ud45c\uc900\uc801\uc778 \ub3c4\ucd9c \uac00\ub2a5\uc131 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \uc77c\uad00\ub41c \ud6a8\uacfc\uc801 \uacf5\ub9ac\uacc4\uac00, \uadf8 \uccb4\uacc4\uc758 \ubb34\ubaa8\uc21c\uc131\uc744 \ud45c\ud604\ud558\ub294 \ud45c\uc900\uc801 \uba85\uc81c\ub97c \uc790\uae30 \uc548\uc5d0\uc11c \uc99d\uba85\ud560 \uc218 \uc5c6\ub2e4\uace0 \ub9d0\ud55c\ub2e4.]<\/p>\n<p><!-- \uad34\ub378\uc758 \uacb0\uacfc\ub294 \ud790\ubca0\ub974\ud2b8 \ud504\ub85c\uadf8\ub7a8\uc758 \uc6d0\ub798\uc758 \uad11\ubc94\uc704\ud55c \ubaa9\ud45c\ub97c \uacb0\uc815\uc801\uc73c\ub85c \uc81c\ud55c\ud588\uc9c0\ub9cc, \ubaa8\ub4e0 \ud615\uc2dd\ud654\ub098 \ubaa8\ub4e0 \ubb34\ubaa8\uc21c\uc131 \uc99d\uba85\uc744 \ubd88\uac00\ub2a5\ud558\uac8c \ub9cc\ub4e0 \uac83\uc740 \uc544\ub2c8\ub2e4. \uc81c\ud55c\ub41c \uccb4\uacc4\uc758 \uc0c1\ub300\uc801 \ubb34\ubaa8\uc21c\uc131\uc744 \ub354 \uac15\ud55c \uccb4\uacc4\uc5d0\uc11c \uc99d\uba85\ud560 \uc218 \uc788\uace0, \uc99d\uba85\uc774\ub860\uacfc \ud615\uc2dd \uac80\uc99d\uc740 \uc774\ud6c4\uc5d0\ub3c4 \ubc1c\uc804\ud588\ub2e4. -->\uad34\ub378\uc758 \ubc1c\uacac\uc73c\ub85c \uc778\ud574 \ud790\ubca0\ub974\ud2b8\uac00 \uafc8\uafe8\ub358 \uac70\ub300\ud55c \uacc4\ud68d\uc740 \ud070 \ubcbd\uc5d0 \ubd80\ub52a\ud614\ub2e4. \ud558\uc9c0\ub9cc \uadf8\ub807\ub2e4\uace0 \ud574\uc11c \uc218\ud559\uc758 \ud615\uc2dd\ud654 \uc790\uccb4\uac00 \uc758\ubbf8\ub97c \uc783\uc740 \uac83\uc740 \uc544\ub2c8\uc5c8\ub2e4. \uc624\ud788\ub824 \uc774\ub97c \uacc4\uae30\ub85c \uc81c\ud55c\ub41c \uccb4\uacc4 \uc548\uc5d0\uc11c\uc758 \ubb34\ubaa8\uc21c\uc131 \uc99d\uba85\uc774\ub098 \ud615\uc2dd \uac80\uc99d\uc740 \uc0c8\ub85c\uc6b4 \ubc29\ud5a5\uc73c\ub85c \uc9c4\ud654\ud574 \ub098\uac14\ub2e4.<a class=\"math-abs-series-ref\" title=\"Richard Zach, \u201cHilbert\u2019s Program,\u201d Stanford Encyclopedia of Philosophy.\" href=\"#ref-Zach2023\">[Zach2023]<\/a> Lean\uacfc mathlib\uc5d0\uc11c\ub294 \uba85\uc81c\uc640 \uc99d\uba85\uc744 \ud615\uc2dd \uc5b8\uc5b4\ub85c \ud45c\ud604\ud558\uace0 \uc791\uc740 \uc2e0\ub8b0 \ud575\uc2ec\uc774 \uac01 \uc99d\uba85 \ud56d\uc744 \uac80\uc0ac\ud55c\ub2e4.<!-- \uc774\ub294 \ucef4\ud4e8\ud130\uac00 \uc778\uac04\uacfc \ub611\uac19\uc774 \uc758\ubbf8\ub97c \uc9c1\uad00\ud55c\ub2e4\ub294 \uc8fc\uc7a5\uacfc\ub294 \ub2e4\ub974\uc9c0\ub9cc, \ubcf5\uc7a1\ud55c \uc99d\uba85\uc758 \uaddc\uce59 \uc900\uc218\ub97c \uc138\ubc00\ud558\uac8c \uac80\uc99d\ud558\ub294 \uac15\ub825\ud55c \ubc29\ubc95\uc774\ub2e4. --><a class=\"math-abs-series-ref\" title=\"The mathlib Community, \u201cThe Lean Mathematical Library,\u201d Proceedings of CPP 2020, 2020, pp. 367\u2013381.\" href=\"#ref-MathlibCommunity2020\">[MathlibCommunity2020]<\/a><\/p>\n<p>\ud615\uc2dd\ud654\ub294 \uc77c\ubc18\ud654, \ucd94\uc0c1\ud654, \uc774\uc0c1\ud654\uc640 \uacb0\ud569\ud560 \uc218 \uc788\ub2e4. \uc77c\ubc18\ud654\ub41c \uc815\ub9ac, \ucd94\uc0c1 \ub300\uc218 \uad6c\uc870, \uc774\uc0c1\ud654\ub41c \ubb3c\ub9ac \ubaa8\ud615\uc744 \ubaa8\ub450 \ud615\uc2dd \uc5b8\uc5b4\ub85c \uae30\uc220\ud560 \uc218 \uc788\ub2e4. \uadf8\ub7ec\ub098 \ud615\uc2dd\ud654\uac00 \uc5b8\uc81c\ub098 \ub2e4\ub978 \uc791\uc5c5\uc774 \ub05d\ub09c \ub4a4 \ud45c\uba74\uc5d0\ub9cc \ub367\ubd99\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. \uba85\uc2dc\uc801 \ud615\uc2dd\ud654 \uacfc\uc815\uc5d0\uc11c \uc228\uc5b4 \uc788\ub358 \uac00\uc815\uc774 \ub4dc\ub7ec\ub098\uace0, \uadf8 \ubc1c\uacac\uc774 \ub2e4\uc2dc \uc815\uc758\uc640 \ucd94\uc0c1\ud654\uc758 \uc218\uc815\uc744 \uc774\ub04c\uae30\ub3c4 \ud55c\ub2e4.<\/p>\n<h4>\uc5ec\uc12f \uac00\uc9c0 \uc870\uc791<\/h4>\n<p>\ubcf8 \uc5f0\uc7ac\ub294 \uc218\ud559\uc801 \ucd94\uc0c1\ud654\uac00 \uc218\ud589\ub418\ub294 \uc5ec\ub7ec \ubc29\uc2dd\uc744 \ub2e4\uc74c \uc5ec\uc12f \uac00\uc9c0\ub85c \ubb36\uc5b4 \uc0b4\ud3b4\ubcf4\uc558\ub2e4.<!-- \uc774 \ubaa9\ub85d \uc5ed\uc2dc \ud45c\uc900 \ubb38\ud5cc\uc774 \uc2b9\uc778\ud55c \uc644\uc804\ud55c \ubd84\ub958\ud45c\ub77c\uae30\ubcf4\ub2e4, \uc5f0\uc7ac\uc5d0\uc11c \ub2e4\ub8ec \uc0ac\ub840\ub4e4\uc744 \uc870\uc9c1\ud558\uae30 \uc704\ud55c \uc800\uc790\uc758 \ubc29\ubc95\ub860\uc801 \uc9c0\ub3c4\ub2e4. \ud56d\ubaa9\ub4e4\uc740 \uc11c\ub85c \uacb9\uce58\uba70 \ub2e4\ub978 \ubc29\uc2dd\uc758 \ubd84\ub958\ub3c4 \uac00\ub2a5\ud558\ub2e4. --><\/p>\n<ul>\n<li><span class=\"defined\">\ub3d9\uce58\ub958\ub97c \uc0ac\uc6a9\ud55c \uc815\uc758<\/span>: \uc9c1\uc120\ub4e4\uc758 \u2018\uac19\uc740 \ubc29\ud5a5\u2019 \uad00\uacc4\ub098 \uc815\uc218\uc758 \uc21c\uc11c\uc30d \uad00\uacc4\ucc98\ub7fc \ubc18\uc0ac\uc131, \ub300\uce6d\uc131, \ucd94\uc774\uc131\uc744 \ub9cc\uc871\ud558\ub294 \uad00\uacc4\ub97c \uc815\ud558\uace0, \uc11c\ub85c \ub3d9\uce58\uc778 \ub300\uc0c1\ub4e4\uc744 \ud558\ub098\uc758 \ub3d9\uce58\ub958\ub85c \ubb36\ub294\ub2e4. \ubc29\ud5a5\uc758 \uacbd\uc6b0 \u2018\ud3c9\ud589\u2019\uc744 \uc11c\ub85c \ub2e4\ub978 \uc9c1\uc120\uc5d0\ub9cc \ud5c8\uc6a9\ud558\ub294 \uc5c4\uaca9\ud55c \uad00\uacc4\ub85c \uc4f0\uc9c0 \uc54a\uace0, \uac19\uc740 \uc9c1\uc120\ub3c4 \ud3ec\ud568\ud558\ub294 \uac19\uc740-\ubc29\ud5a5 \uad00\uacc4\ub85c \ud655\uc7a5\ud574\uc57c \ub3d9\uce58\uad00\uacc4\uac00 \ub41c\ub2e4.<\/li>\n<li><span class=\"defined\">\uacf5\ub9ac\ud654<\/span>: \ub300\uc0c1\uc758 \uc7ac\ub8cc\ubcf4\ub2e4 \uadf8 \ub300\uc0c1\uc774 \ub9cc\uc871\ud574\uc57c \ud560 \uba85\uc2dc\uc801 \uc870\uac74\uc744 \uc55e\uc138\uc6b4\ub2e4. \ud790\ubca0\ub974\ud2b8\uc758 \uae30\ud558\ud559 \uacf5\ub9ac\ud654\uc640 19\uc138\uae30 \uc5ec\ub7ec \uc218\ud559\uc790\ub97c \uac70\uce58\uba70 \ud615\uc131\ub41c \ucd94\uc0c1 \uad70 \uac1c\ub150\uc774 \ub300\ud45c\uc801\uc774\ub2e4. <!-- \uc774 \ubc1c\uc804\uc744 \ucf00\uc77c\ub9ac \ud55c \uc0ac\ub78c\uc774 \ud55c \ubc88\uc5d0 \uc644\uc131\ud588\ub2e4\uace0 \ub9d0\ud558\uae30\ubcf4\ub2e4\ub294, \uc21c\uc5f4\uad70, \ubcc0\ud658\uad70, \ucd94\uc0c1 \uc5f0\uc0b0 \uccb4\uacc4\uac00 \uc810\ucc28 \ubd84\ub9ac\ub41c \uc5ed\uc0ac\ub85c \ubcf4\ub294 \ud3b8\uc774 \uc815\ud655\ud558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Leo Corry, Modern Algebra and the Rise of Mathematical Structures, 2nd revised ed., Birkh\u00e4user, 2004.\" href=\"#ref-Corry2004\">[Corry2004]<\/a><a class=\"math-abs-series-ref\" title=\"Israel Kleiner, \u201cThe Evolution of Group Theory: A Brief Survey,\u201d Mathematics Magazine 59(4), 1986, pp. 195\u2013215.\" href=\"#ref-Kleiner1986\">[Kleiner1986]<\/a> --><\/li>\n<li><span class=\"defined\">\ubcf4\ud3b8 \uc131\uc9c8\uc744 \uc0ac\uc6a9\ud55c \uc815\uc758<\/span>: \uacf1 \ub300\uc0c1\uc744 \ud2b9\uc815 \uc21c\uc11c\uc30d\uc758 \uc9d1\ud569\uc73c\ub85c \uace0\uc815\ud558\uae30\ubcf4\ub2e4, \uc0ac\uc601 \uc0ac\uc0c1\ub4e4\uacfc \uc784\uc758\uc758 \ub2e4\ub978 \ub300\uc0c1\uc5d0\uc11c \ub4e4\uc5b4\uc624\ub294 \uc0ac\uc0c1\uc774 \ub9cc\uc871\ud574\uc57c \ud560 \ubcf4\ud3b8 \uc870\uac74\uc73c\ub85c \uaddc\uc815\ud55c\ub2e4. \uc774 \uc870\uac74\uc740 \ub300\uc0c1\uc744 \uc120\ud0dd\ud55c \ubc94\uc8fc \uc548\uc5d0\uc11c <em>\uc720\uc77c\ud55c \ub3d9\ud615\uc0ac\uc0c1\uae4c\uc9c0 \ud3ec\ud568\ud558\uc5ec<\/em> \ud2b9\uc9d5\uc9d3\ub294\ub2e4.<a class=\"math-abs-series-ref\" title=\"Saunders Mac Lane, Mathematics: Form and Function, Springer, 1986.\" href=\"#ref-MacLane1986\">[MacLane1986]<\/a><\/li>\n<li><span class=\"defined\">\uc0ac\ub840\uc758 \ud1b5\ud569<\/span>: \uc5f0\ub9bd\ubc29\uc815\uc2dd\uc758 \ud574, \uae30\ud558 \ubca1\ud130, \ub2e4\ud56d\uc2dd, \ud568\uc218\ucc98\ub7fc \uc7ac\ub8cc\uac00 \ub2e4\ub978 \uc0ac\ub840\uc5d0\uc11c \uacf5\ud1b5 \uc5f0\uc0b0 \ubc95\uce59\uc744 \ucd94\ucd9c\ud558\uc5ec \ubca1\ud130\uacf5\uac04 \uac19\uc740 \ud558\ub098\uc758 \uc774\ub860\uc73c\ub85c \ub2e4\ub8ec\ub2e4.<\/li>\n<li><span class=\"defined\">\uc815\ub9ac\uc5d0\uc11c \uc815\uc758\uc758 \ud6c4\ubcf4\ub97c \uc5bb\uae30<\/span>: \ub354 \uc881\uc740 \ub9e5\ub77d\uc5d0\uc11c \uc911\uc694\ud588\ub358 \uc815\ub9ac\uc758 \uc870\uac74\uc774\ub098 \uacb0\ub860\uc774 \ub354 \ub113\uc740 \uc774\ub860\uc5d0\uc11c \ud575\uc2ec \uc815\uc758\ub85c \ub2e4\ub4ec\uc5b4\uc9c0\ub294 \uacbd\uc6b0\ub2e4. \ucef4\ud329\ud2b8\uc131\uc740 \uc720\ud074\ub9ac\ub4dc \uacf5\uac04\uc5d0\uc11c\uc758 \ub2eb\ud798, \uc720\uacc4\uc131, \uc810\uc5f4\ucef4\ud329\ud2b8\uc131, \uc5f4\ub9b0 \ub36e\uac1c \uc131\uc9c8 \ub4f1\uc774 \uc5ec\ub7ec \ub2e8\uacc4\uc5d0 \uac78\uccd0 \ubd84\ub9ac\ub418\uace0 \ube44\uad50\ub418\uba70 \ud615\uc131\ub418\uc5c8\ub2e4. <!-- \ub530\ub77c\uc11c \ud558\uc774\ub124\u2013\ubcf4\ub810 \uc815\ub9ac\uc758 \uacb0\ub860\uc774 \uace7\ubc14\ub85c \uc77c\ubc18 \uc704\uc0c1\uacf5\uac04\uc758 \uc815\uc758\ub85c \u2018\uc2b9\uaca9\u2019\ub418\uc5c8\ub2e4\uace0 \ubcf4\ub294 \uac83\uc740 \uc2e4\uc81c \uc5ed\uc0ac\uc640 \ub17c\ub9ac \uad6c\uc870\ub97c \uc9c0\ub098\uce58\uac8c \uc555\ucd95\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Manya Raman-Sundstr\u00f6m, \u201cA Pedagogical History of Compactness,\u201d American Mathematical Monthly 122(7), 2015, pp. 619\u2013635.\" href=\"#ref-RamanSundstrom2015\">[RamanSundstrom2015]<\/a> --><\/li>\n<li><span class=\"defined\">\ub17c\uc7c1\uc744 \uacf5\ub9ac\uc801 \ud2c0\uacfc \ubd84\ub9ac\ud558\uae30<\/span>: \ucf5c\ubaa8\uace0\ub85c\ud504\ub294 \ud655\ub960\uacf5\uac04\uc744 \uc804\uccb4 \uc9c8\ub7c9\uc774 \\(1\\)\uc778 \uce21\ub3c4\uacf5\uac04\uc73c\ub85c \uacf5\ub9ac\ud654\ud558\uc5ec \ud655\ub960 \uacc4\uc0b0\uc758 \uacf5\ud1b5 \ud615\uc2dd\uc744 \uc81c\uc2dc\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"A. N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer, 1933; English trans., Foundations of the Theory of Probability.\" href=\"#ref-Kolmogorov1933\">[Kolmogorov1933]<\/a> \uc774\uac83\uc740 \uc11c\ub85c \ub2e4\ub978 \ud655\ub960 \ud574\uc11d\ub4e4\uc774 \uacf5\ud1b5\uc73c\ub85c \uacf5\uc720\ud560 \uc218 \uc788\ub294 \uc5c4\ubc00\ud55c \uc218\ud559\uc801 \uacc4\uc0b0 \ud2c0\uc744 \ubd84\ub9ac\ud574 \ub0b8 \uc131\uacfc\uc600\ub2e4.<!-- <a class=\"math-abs-series-ref\" title=\"Alan H\u00e1jek, \u201cInterpretations of Probability,\u201d Stanford Encyclopedia of Philosophy.\" href=\"#ref-Hajek2023\">[Hajek2023]<\/a> --><\/li>\n<\/ul>\n<p>\uc774 \uc870\uc791\ub4e4\uc740 \uc2e4\uc81c \uc791\uc5c5\uc5d0\uc11c \uc11c\ub85c \uc5bd\ud78c\ub2e4. \ud55c \uacf5\ub9ac\uacc4\uc758 \ubaa8\ud615\uc744 \uc81c\uc2dc\ud558\uba74 \uadf8 \uacf5\ub9ac\ub4e4\uc774 \ud568\uaed8 \ub9cc\uc871\ub420 \uc218 \uc788\uc74c\uc744 \ubcf4\uc774\uace0, \ucc44\ud0dd\ud55c \uba54\ud0c0\uc774\ub860\uc5d0 \ub300\ud55c \uc0c1\ub300\uc801 \ubb34\ubaa8\uc21c\uc131 \uadfc\uac70\ub97c \uc5bb\uc744 \uc218 \uc788\ub2e4. <!-- \ud558\uc9c0\ub9cc \ubaa8\ub4e0 \uacf5\ub9ac \uc774\ub860\uc774 \uc5f0\uad6c \uac00\uce58\ub098 \u2018\uc2e4\ud6a8\uc131\u2019\uc744 \uc5bb\uae30 \uc704\ud574 \uba3c\uc800 \uc758\ub3c4\ud55c \uad6c\uccb4 \ubaa8\ud615\uc744 \uac00\uc838\uc57c \ud558\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. --> \ub3d9\uce58\ub958 \uad6c\uc131\uc740 \uc815\uc218, \uc720\ub9ac\uc218, \uc2e4\uc218 \uac19\uc740 \ub300\uc0c1\uc758 \ubaa8\ud615\uc744 \ub9cc\ub4dc\ub294 \uac15\ub825\ud55c \uc218\ub2e8\uc774\uace0, \ubcf4\ud3b8 \uc131\uc9c8\uc740 \uacf5\ub9ac\uc801 \uc870\uac74\uc744 \uc0ac\uc0c1 \uc911\uc2ec\uc73c\ub85c \ud45c\ud604\ud558\ub294 \ud55c \ubc29\uc2dd\uc774\ub2e4. \uc0ac\ub840\uc758 \ud1b5\ud569\uc740 \uacf5\ub9ac\ud654\ub97c \ucd09\ubc1c\ud560 \uc218 \uc788\uc73c\uba70, \uae30\uc874 \uc815\ub9ac\uc5d0\uc11c \ucd94\ucd9c\ud55c \uc131\uc9c8\uc740 \uc0c8\ub85c\uc6b4 \uc815\uc758\uc758 \ud6c4\ubcf4\uac00 \ub420 \uc218 \uc788\ub2e4.<\/p>\n<p><!-- \uc5ec\uc12f \uc870\uc791 \ubaa8\ub450\ub97c \ud558\ub098\uc758 \ubcf8\uc9c8\ub85c \ud658\uc6d0\ud560 \ud544\uc694\ub3c4 \uc5c6\ub2e4. -->\ub3d9\uce58\ub958\ub294 \uc77c\uc815\ud55c \ucc28\uc774\ub97c \ub3d9\uc77c\uc2dc\ud558\uace0, \uacf5\ub9ac\ud654\ub294 \ud5c8\uc6a9\ub418\ub294 \uad6c\uc870\ub97c \uba85\uc2dc\ud558\uba70, \ubcf4\ud3b8 \uc131\uc9c8\uc740 \uc0ac\uc0c1 \uad00\uacc4\ub85c \ub300\uc0c1\uc744 \ud2b9\uc9d5\uc9d3\ub294\ub2e4. \uc774\ub4e4\uc774 \uacf5\uc720\ud558\ub294 \ub113\uc740 \uacbd\ud5a5\uc740 \ub300\uc0c1\uc758 \ubb3c\uc9c8\uc801 \uc7ac\ub8cc\ubcf4\ub2e4, \ud0d0\uad6c\uc5d0 \uad00\ub828\ub41c \ub3d9\uc77c\uc131 \uae30\uc900, \uc5f0\uc0b0, \uc870\uac74, \uad00\uacc4\ub97c \uba85\ub8cc\ud558\uac8c \ub4dc\ub7ec\ub0b8\ub2e4\ub294 \ub370 \uc788\ub2e4.<\/p>\n<h4>\uce35\uc704\uc758 \uc0ac\ub2e4\ub9ac<\/h4>\n<p>\u2018\ub300\uc0c1 \u2192 \uc5f0\uc0b0 \u2192 \ubc95\uce59 \u2192 \uad6c\uc870 \u2192 \uad00\uacc4\u2019\ub77c\ub294 \uc0ac\ub2e4\ub9ac\ub294 \uc774 \uc5f0\uc7ac\uc758 \ud750\ub984\uc744 \ub418\ub3cc\uc544\ubcf4\ub294 \uc720\uc6a9\ud55c \ube44\uc720\ub2e4. \ubb3c\ub860 \uc218\ud559\uc0ac\uac00 \uc774 \ub2e8\uacc4\ub4e4\uc744 \uce7c\ub85c \uc790\ub974\ub4ef \uc21c\uc11c\ub300\ub85c \ubc1f\uc544\uc628 \uac83\uc740 \uc544\ub2c8\ub2e4. \uc5ec\ub7ec \uce35\uc704\ub294 \uace0\ub300\ubd80\ud130 \uad50\ucc28\ud558\uba70 \ud568\uaed8 \ubc1c\uc804\ud574 \uc654\ub2e4.<\/p>\n<p>\uc148\ub3cc\uacfc \uc218 \ud45c\uae30\ub294 \uac1c\ubcc4 \uc0ac\ubb3c\uc5d0\uc11c \uc218\ub7c9\uc744 \ubd84\ub9ac\ud558\ub294 \ub370 \uae30\uc5ec\ud588\ub2e4. \ube44\uc5d0\ud2b8\uc758 \ubb38\uc790\ub300\uc218\ub294 \uc54c\ub824\uc9c4 \uc591\uacfc \ubbf8\uc9c0\uc758 \uc591\uc744 \ubb38\uc790\ub85c \uccb4\uacc4\uc801\uc73c\ub85c \ud45c\ud604\ud558\uc5ec \uac1c\ubcc4 \uc218\uce58 \uacc4\uc0b0\uc744 \uc77c\ubc18\uc801\uc778 \uc2dd\uc758 \uc870\uc791\uc73c\ub85c \ubc14\uafb8\uc5c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972; three-volume paperback ed., 1990.\" href=\"#ref-Kline1972\">[Kline1972]<\/a> \ud53c\ucf55\uc758 \u2018\ud615\uc2dd \ubd88\uc5ed\uc758 \uc6d0\ub9ac\u2019\uc640 \ud574\ubc00\ud134\uc758 \uc0ac\uc6d0\uc218\ub294 \ub300\uc218 \ubc95\uce59\uc758 \uc801\uc6a9 \ubc94\uc704\ub97c \ud0d0\uc0c9\ud558\uace0, \uc0ac\uc6d0\uc218 \uacf1\uc148\uc5d0\uc11c\ub294 \uad50\ud658\ubc95\uce59\uc774 \uc131\ub9bd\ud558\uc9c0 \uc54a\ub294\ub2e4\ub294 \uc0ac\uc2e4\uc744 \ubc1b\uc544\ub4e4\uc774\uac8c \ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"George Peacock, A Treatise on Algebra, Vol. II: Symbolical Algebra and Its Applications to the Geometry of Position, Cambridge University Press, 1845.\" href=\"#ref-Peacock1845\">[Peacock1845]<\/a><a class=\"math-abs-series-ref\" title=\"William Rowan Hamilton, \u201cOn Quaternions,\u201d Proceedings of the Royal Irish Academy 3, 1847, pp. 1\u201316.\" href=\"#ref-Hamilton1847\">[Hamilton1847]<\/a> <!-- \uadf8\ub807\ub2e4\uace0 \ubc95\uce59\uc774 \uadfc\uac70 \uc5c6\uc774 \uc790\uc758\uc801\uc73c\ub85c \uc120\ud0dd\ub41c\ub2e4\ub294 \ub73b\uc740 \uc544\ub2c8\ub2e4. --> \uc0c8 \uc5f0\uc0b0\uc740 \uba85\uc2dc\ub41c \uacf5\ub9ac\uc640 \uae30\uc874 \uc774\ub860\uacfc\uc758 \uc815\ud569\uc131, \uadf8\ub9ac\uace0 \uadf8\uac83\uc774 \ud574\uacb0\ud558\ub294 \ubb38\uc81c\uc5d0 \uc758\ud574 \ud3c9\uac00\ub41c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Leo Corry, Modern Algebra and the Rise of Mathematical Structures, 2nd revised ed., Birkh\u00e4user, 2004.\" href=\"#ref-Corry2004\">[Corry2004]<\/a><\/p>\n<p><!-- \ud790\ubca0\ub974\ud2b8\uc758 \uacf5\ub9ac\uc801 \ubc29\ubc95\uc740 \uc810, \uc9c1\uc120, \ud3c9\uba74\uc744 \ubb34\uc815\uc758 \uc6a9\uc5b4\ub85c \ub450\uace0 \uadf8 \uad00\uacc4\ub97c \uacf5\ub9ac\ub85c \uaddc\uc728\ud588\uc9c0\ub9cc, \uacf5\ub9ac\uac00 \u2018\ub9f9\ubaa9\uc801\u2019\uc774\uac70\ub098 \uc544\ubb34 \uad6c\uc870\ub098 \ub9c8\uc74c\ub300\ub85c \ucc3d\uc870\ud55c\ub2e4\ub294 \ub73b\uc740 \uc544\ub2c8\ub2e4. -->\uc544\uc77c\ub80c\ubca0\ub974\ud06c\uc640 \ub9e4\ud074\ub808\uc778\uc740 1945\ub144\uc5d0 \uc790\uc5f0\uc801 \ub3d9\ud615\uc744 \uccb4\uacc4\ud654\ud558\ub294 \uacfc\uc815\uc5d0\uc11c \ubc94\uc8fc, \ud568\uc790, \uc790\uc5f0\ubcc0\ud658\uc744 \ub3c4\uc785\ud588\uace0, \ubc94\uc8fc\ub860\uc740 \uc120\ud0dd\ud55c \ubc94\uc8fc\uc5d0\uc11c \ub300\uc0c1\uacfc \uc0ac\uc0c1\uc744 \ud568\uaed8 \uc5f0\uad6c\ud558\ub294 \uc5b8\uc5b4\ub85c \ubc1c\uc804\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"Samuel Eilenberg and Saunders Mac Lane, \u201cGeneral Theory of Natural Equivalences,\u201d Transactions of the American Mathematical Society 58(2), 1945, pp. 231\u2013294.\" href=\"#ref-EilenbergMacLane1945\">[EilenbergMacLane1945]<\/a> <!-- \ubc94\uc8fc\ub860\uc774 \ub300\uc0c1\uc758 \ub0b4\ubd80\ub97c \uc5b8\uc81c\ub098 \uc644\uc804\ud788 \uc9c0\uc6b0\ub294 \uac83\ub3c4 \uc544\ub2c8\ub2e4. --><!-- \ubc94\uc8fc\ub860\uc5d0\uc11c \uc0ac\uc0c1\uc740 \ubcf4\uc874\ud558\uae30\ub85c \uc120\ud0dd\ud55c \uad6c\uc870\ub97c \ub2f4\uace0, \uc9d1\ud569\uc758 \uc6d0\uc18c\ub294 \uc608\ucee8\ub300 \ud55c \uc6d0\uc18c \uc9d1\ud569\uc5d0\uc11c \ub4e4\uc5b4\uc624\ub294 \uc0ac\uc0c1\uc73c\ub85c \ud45c\ud604\ud560 \uc218\ub3c4 \uc788\ub2e4.<a class=\"math-abs-series-ref\" title=\"Saunders Mac Lane, Mathematics: Form and Function, Springer, 1986.\" href=\"#ref-MacLane1986\">[MacLane1986]<\/a> --><\/p>\n<p>\ub530\ub77c\uc11c \uc774 \uc0ac\ub2e4\ub9ac\ub294 \uc5ed\uc0ac\uc801 \ud544\uc5f0\uc758 \uc21c\uc11c\uac00 \uc544\ub2c8\ub77c \uac15\uc870\uc810\uc758 \uc774\ub3d9\uc744 \ubcf4\uc5ec\uc8fc\ub294 \ubc1c\uacac\uc801 \ub3c4\uc2dd\uc774\ub2e4. \uc5ec\uc12f \uac00\uc9c0 \uc870\uc791\uc740 \uadf8 \uc774\ub3d9\uc5d0\uc11c \uc4f0\uc778 \ubc29\ubc95\ub4e4\uc758 \ubaa9\ub85d\uc774\uba70 \ub450 \ubd84\ub958\ub294 \uc77c\ub300\uc77c\ub85c \ub300\uc751\ud558\uc9c0 \uc54a\ub294\ub2e4. \uacf5\ub9ac\ud654\ub294 \uad6c\uc870 \uce35\uc704\uc5d0\uc11c \ub450\ub4dc\ub7ec\uc9c0\uace0 \ubcf4\ud3b8 \uc131\uc9c8\uc740 \uad00\uacc4 \uce35\uc704\ub97c \uc798 \ubcf4\uc5ec \uc8fc\uc9c0\ub9cc, \ub3d9\uce58\ub958 \uad6c\uc131\uc774\ub098 \uc0ac\ub840\uc758 \ud1b5\ud569\uc740 \uc5ec\ub7ec \uce35\uc704\uc5d0\uc11c \ubc18\ubcf5\ub41c\ub2e4.<\/p>\n<h4>\uc218\ud559\uc801 \ub300\uc0c1\uc740 \ubb34\uc5c7\uc73c\ub85c \uc544\ub294\uac00<\/h4>\n<p>\uc9c0\uae08\uae4c\uc9c0\ub294 \ucd94\uc0c1\ud654\uac00 \uc218\ud559\uc758 \uc5ed\uc0ac\uc5d0\uc11c \u2018\uc5b4\ub5bb\uac8c\u2019 \uc218\ud589\ub418\uc5b4 \uc654\ub294\uc9c0\ub97c \ub2e4\ub8e8\uc5c8\ub2e4. \uc774\uc81c \uc778\uac04\uc774 \uc18d\uc131\uc744 \ub35c\uc5b4 \ub0b4\uace0 \uad00\uacc4\ub97c \uc911\uc2ec\uc73c\ub85c \uaddc\uc815\ud55c \ucd94\uc0c1\uc801 \ub300\uc0c1\ub4e4\uc774 \uc778\uac04\uc758 \uc778\uc2dd\uacfc \ub3c5\ub9bd\ud558\uc5ec \uc874\uc7ac\ud558\ub294\uac00\ub77c\ub294 \ucca0\ud559\uc801 \uc9c8\ubb38\uc73c\ub85c \ub118\uc5b4\uac00 \ubcf4\uc790.<\/p>\n<p>\uc774 \ubb3c\uc74c\uc740 \ud3f0 \ub178\uc774\ub9cc\uc2dd \uc790\uc5f0\uc218\uc640 \uccb4\ub974\uba5c\ub85c\uc2dd \uc790\uc5f0\uc218\uc758 \ucc28\uc774\uc5d0\uc11c \uc774\ubbf8 \uc608\uace0\ub418\uc5c8\ub2e4. \ud3f4 \ubca0\ub098\uc138\ub77c\ud504(Paul Benacerraf)\ub294 1965\ub144 \ub17c\ubb38 \u300cWhat Numbers Could Not Be\u300d\uc5d0\uc11c, \ub450 \uc9d1\ud569\ub860\uc801 \uad6c\uc131\uc774 \uc0b0\uc220 \uad6c\uc870\ub85c\uc11c\ub294 \ub611\uac19\uc774 \uae30\ub2a5\ud558\uba74\uc11c\ub3c4 \u201c\\(1\\in3\\)\uc778\uac00?\u201d \uac19\uc740 \uc9d1\ud569\ub860\uc801 \ubd80\uac00 \uc9c8\ubb38\uc5d0\ub294 \uc11c\ub85c \ub2e4\ub978 \ub2f5\uc744 \uc900\ub2e4\ub294 \uc0ac\uc2e4\uc744 \uc9c0\uc801\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"Paul Benacerraf, \u201cWhat Numbers Could Not Be,\u201d The Philosophical Review 74(1), 1965, pp. 47\u201373.\" href=\"#ref-Benacerraf1965\">[Benacerraf1965]<\/a> \uc774\uac83\uc740 \ud55c \uc774\ub860 \uc548\uc758 \ub17c\ub9ac\uc801 \ubaa8\uc21c\uc774 \uc544\ub2c8\ub77c, \uc0b0\uc220\uc801\uc73c\ub85c \ub3d9\ud615\uc778 \uc5ec\ub7ec \uad6c\ud604 \uc0ac\uc774\uc758 \ucc28\uc774\ub2e4. \ubca0\ub098\uc138\ub77c\ud504\ub294 \uc774 \ube44\uace0\uc720\uc131\uc73c\ub85c\ubd80\ud130 \uc790\uc5f0\uc218\ub97c \uc5b4\ub290 \ud2b9\uc815\ud55c \uc9d1\ud569\uacfc \uc808\ub300\uc801\uc73c\ub85c \ub3d9\uc77c\uc2dc\ud560 \ube44\uc784\uc758\uc801 \uadfc\uac70\uac00 \uc5c6\ub2e4\uace0 \uc8fc\uc7a5\ud558\uace0, \uc218\ub97c \ud55c \uc9c4\ud589 \uad6c\uc870\uc5d0\uc11c \ub2e4\ub978 \uc218\ub4e4\uacfc \ub9fa\ub294 \uad00\uacc4\ub85c \uaddc\uc815\ub418\ub294 \u2018\uc704\uce58\u2019\ub85c \ubcf4\uc790\uace0 \uc81c\uc548\ud588\ub2e4.<!-- \ub2e4\ub9cc \uc774 \ub17c\ubb38\uc740 \ud6d7\ub0a0\uc758 \uc5ec\ub7ec \uad6c\uc870\uc8fc\uc758 \uc874\uc7ac\ub860\uc744 \uc644\uc131\ud55c \uc120\uc5b8\ubb38\uc774\ub77c\uae30\ubcf4\ub2e4 \uadf8 \ub17c\uc758\ub97c \ucd09\ubc1c\ud55c \ucd9c\ubc1c\uc810\uc5d0 \uac00\uae4c\uc6e0\ub2e4. --><\/p>\n<p>\ubca0\ub098\uc138\ub77c\ud504\ub294 1973\ub144 \ub17c\ubb38 \u300cMathematical Truth\u300d\uc5d0\uc11c \uc11c\ub85c \uae34\uc7a5\ud558\ub294 \ub450 \uc81c\uc57d\uc744 \uc81c\uc2dc\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"Paul Benacerraf, \u201cMathematical Truth,\u201d The Journal of Philosophy 70(19), 1973, pp. 661\u2013679.\" href=\"#ref-Benacerraf1973\">[Benacerraf1973]<\/a> \uccab\uc9f8\ub294 \uc218\ud559 \ubb38\uc7a5\uc758 \uc758\ubbf8\uc640 \ucc38\uc744 \ube44\uc218\ud559\uc801 \ubb38\uc7a5\uc5d0 \uc801\uc6a9\ub418\ub294 \uc77c\ubc18\uc801 \uc758\ubbf8\ub860\uacfc \ud3c9\ud589\ud558\uac8c \uc124\uba85\ud574\uc57c \ud55c\ub2e4\ub294 <span class=\"defined\">\uc758\ubbf8\ub860\uc801 \uc81c\uc57d<\/span>\uc774\ub2e4. \ud45c\uc900\uc801\uc778 \uc9c0\uc2dc\uc801 \uc758\ubbf8\ub860\uc744 \uadf8\ub300\ub85c \uc801\uc6a9\ud558\uba74 \ucc38\uc778 \uc218\ud559 \ubb38\uc7a5\uc758 \uc774\ub984\uacfc \uc591\ud654\uc0ac\ub294 \uc218\ub098 \uc9d1\ud569 \uac19\uc740 \ub300\uc0c1\uc5d0 \ub300\ud55c \uc874\uc7ac\ub860\uc801 \uad00\uc5ec\ub97c \ub0b3\ub294 \uac83\ucc98\ub7fc \ubcf4\uc778\ub2e4. \ub458\uc9f8\ub294 \uc218\ud559\uc801 \uc9c4\ub9ac\uc5d0 \ub300\ud55c \uc124\uba85\uc774 \uc6b0\ub9ac\uac00 \uc218\ud559\uc744 \uc5b4\ub5bb\uac8c \uc54c \uc218 \uc788\ub294\uc9c0\ub97c \ud574\uba85\ud558\ub294 \ud569\ub9ac\uc801\uc778 \uc77c\ubc18 \uc778\uc2dd\ub860\uacfc\ub3c4 \uc870\ud654\ub97c \uc774\ub8e8\uc5b4\uc57c \ud55c\ub2e4\ub294 <span class=\"defined\">\uc778\uc2dd\ub860\uc801 \uc81c\uc57d<\/span>\uc774\ub2e4. \uc218\ud559\uc801 \ub300\uc0c1\uc744 \uc2dc\uacf5\uac04 \ubc16\uc758 \uc778\uacfc\uc801\uc73c\ub85c \ubb34\ub825\ud55c \ucd94\uc0c1\uc801 \uc2e4\uc7ac\ub85c \uc774\ud574\ud558\uba74, \ub2f9\uc2dc \uc601\ud5a5\ub825 \uc788\ub358 \uc778\uacfc\uc801 \uc9c0\uc2dd\ub860\uacfc \uc9c0\uce6d\ub860 \uc544\ub798\uc5d0\uc11c\ub294 \uc778\uac04\uc774 \uadf8\uac83\uc744 \uc5b4\ub5bb\uac8c \uc54c\uac70\ub098 \uc9c0\uc2dc\ud558\ub294\uc9c0 \uc124\uba85\ud558\uae30 \uc5b4\ub824\uc6cc\uc9c4\ub2e4.<\/p>\n<p>\uc774 \uae34\uc7a5\uc744 \ud754\ud788 <span class=\"defined\">\ubca0\ub098\uc138\ub77c\ud504\uc758 \ub51c\ub808\ub9c8<\/span>(Benacerraf&#8217;s dilemma)\ub77c\uace0 \ubd80\ub978\ub2e4. \uc774 \ub51c\ub808\ub9c8\ub294 \uc5b4\ub290 \ud55c\ucabd\uc758 \uc77c\ubc29\uc801\uc778 \uc2e4\ud328\ub97c \uc120\uace0\ud588\ub2e4\uae30\ubcf4\ub2e4, \uc218\ud559\uc758 \ubcf8\uc9c8\uacfc \uc778\uac04\uc758 \uc778\uc2dd\uc774\ub77c\ub294 \ub450 \ub9c8\ub9ac \ud1a0\ub07c\ub97c \ubaa8\ub450 \uc7a1\ub294 \uc124\uba85\uc744 \ub0b4\ub193\uc73c\ub77c\ub294 \ubb34\uac70\uc6b4 \ucca0\ud559\uc801 \uacfc\uc81c\uc600\ub2e4. \ud615\uc2dd\uc8fc\uc758\ub098 \uad00\uc2b5\uc8fc\uc758\ub3c4 \uac1d\uad00\uc801 \uc9c4\ub9ac\ub97c \ud3ec\uae30\ud558\ub294 \uac83\uc740 \uc544\ub2c8\uc9c0\ub9cc, \uc99d\uba85 \uac00\ub2a5\uc131\uc774\ub098 \uaddc\uc57d\uc744 \ubb38\uc7a5\uc758 \uc758\ubbf8\uc640 \uc5f0\uacb0\ub41c \uc9c4\ub9ac\ub85c \uc5b4\ub5bb\uac8c \uc124\uba85\ud560 \uac83\uc778\uc9c0 \ub2f5\ud574\uc57c \ud55c\ub2e4.<\/p>\n<h4>\uad6c\uc870\uc8fc\uc758\uc758 \uac08\ub798<\/h4>\n<p>\ubca0\ub098\uc138\ub77c\ud504\uc758 1965\ub144 \ub17c\ubb38\uc740 \uc218\ud559\uc801 \ub300\uc0c1\uc744 \uace0\ub9bd\ub41c \uc2e4\uccb4\ubcf4\ub2e4 \uad6c\uc870 \uc548\uc758 \uc704\uce58\ub85c \uc774\ud574\ud558\ub824\ub294 \ud604\ub300 \uad6c\uc870\uc8fc\uc758 \ub17c\uc758\ub97c \ucd09\ubc1c\ud588\ub2e4. \uc774\ud6c4 \uad6c\uc870\uc8fc\uc758\ub294 \uad6c\uc870\uc640 \uadf8 \uc790\ub9ac\ub97c \ucd94\uc0c1\uc801 \ub300\uc0c1\uc73c\ub85c \uc778\uc815\ud558\ub294\uc9c0\uc5d0 \ub530\ub77c \ube44\uc81c\uac70\uc801 \uad6c\uc870\uc8fc\uc758\uc640 \uc81c\uac70\uc801 \uad6c\uc870\uc8fc\uc758 \ub4f1 \uc5ec\ub7ec \uc785\uc7a5\uc73c\ub85c \ubc1c\uc804\ud588\ub2e4. \uc154\ud53c\ub85c\uc758 ante rem \uad6c\uc870\uc8fc\uc758\uc640 \ud5ec\uba3c\uc758 \uc591\uc0c1 \uad6c\uc870\uc8fc\uc758\ub294 \ub300\ud45c\uc801\uc778 \ub450 \uc785\uc7a5\uc774\uc9c0\ub9cc, \uad6c\uc870\uc8fc\uc758 \uc804\uccb4\uac00 \uc774 \ub458\ub85c \uc18c\uc9c4\ub418\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Erich H. Reck and Georg Schiemer, \u201cStructuralism in the Philosophy of Mathematics,\u201d Stanford Encyclopedia of Philosophy.\" href=\"#ref-ReckSchiemer2021\">[ReckSchiemer2021]<\/a><\/p>\n<p>\uc2a4\ud29c\uc5b4\ud2b8 \uc154\ud53c\ub85c(Stewart Shapiro)\uc758 <span class=\"defined\">ante rem \uad6c\uc870\uc8fc\uc758<\/span>\ub294 \uad6c\uc870\uc640 \uad6c\uc870 \uc548\uc758 \uc790\ub9ac\ub97c \uad6c\uccb4\uc801\uc778 \uad6c\ud604\uccb4\uc640 \ub3c5\ub9bd\ud558\uc5ec \uc874\uc7ac\ud558\ub294 \ucd94\uc0c1\uc801 \ub300\uc0c1\uc73c\ub85c \uc778\uc815\ud558\ub294 \uc2e4\uc7ac\ub860\uc801 \uc785\uc7a5\uc774\ub2e4. [\uc774 \uc785\uc7a5\uc740 \uc154\ud53c\ub85c\uc758 1997\ub144 \uc800\uc11c \u300e<i>Philosophy of Mathematics: Structure and Ontology<\/i>\u300f\uc5d0\uc11c \uccb4\uacc4\uc801\uc73c\ub85c \uc804\uac1c\ub418\uc5c8\ub2e4.]<a class=\"math-abs-series-ref\" title=\"Stewart Shapiro, Philosophy of Mathematics: Structure and Ontology, Oxford University Press, 1997.\" href=\"#ref-Shapiro1997\">[Shapiro1997]<\/a> \uc154\ud53c\ub85c\uc5d0\uac8c \uc790\uc5f0\uc218 \uad6c\uc870\ub294 \ud3f0 \ub178\uc774\ub9cc\uc2dd \uccb4\uacc4\ub098 \uccb4\ub974\uba5c\ub85c\uc2dd \uccb4\uacc4\ucc98\ub7fc \uc5ec\ub7ec \ub3d9\ud615\uc778 \uad00\uacc4 \uccb4\uacc4\uac00 \uad6c\ud604\ud560 \uc218 \uc788\ub2e4\ub294 \uc810\uc5d0\uc11c\ub294 \ubcf4\ud3b8\uc790\uc640 \ube44\uc2b7\ud558\uc9c0\ub9cc, \ub3d9\uc2dc\uc5d0 \ud558\ub098\uc758 \ub300\uc0c1\uc73c\ub85c \uc9c0\uce6d\ud560 \uc218 \uc788\ub294 \ucd94\uc0c1\uc801 \uac1c\ubcc4\uc790\uc774\uae30\ub3c4 \ud558\ub2e4. \uad6c\uc870 \uc548\uc758 \uc790\ub9ac\ub3c4 \uc0ac\ub77c\uc9c0\ub294 \uac83\uc774 \uc544\ub2c8\ub77c, \uad6c\ud604\uccb4\uc758 \uc6d0\uc18c\uac00 \ucc28\uc9c0\ud560 \uc218 \uc788\ub294 \u2018\uc9c1\ucc45\u2019\uc778 \ub3d9\uc2dc\uc5d0 \uadf8 \uc790\uccb4\uc758 \ucd94\uc0c1\uc801 \ub300\uc0c1\uc73c\ub85c \uc774\ud574\ub41c\ub2e4. <!-- \uc5ec\uae30\uc11c <i>ante rem<\/i>\uc740 \uad6c\uc870\uac00 \uc2dc\uac04\uc801\uc73c\ub85c \uc6b0\uc8fc\ubcf4\ub2e4 \uba3c\uc800 \uc0dd\uacbc\ub2e4\ub294 \ub73b\uc774 \uc544\ub2c8\ub77c, \uc5b4\ub5a4 \uad6c\uccb4\uc801 \uad6c\ud604\uc5d0\ub3c4 \uc874\uc7ac\ub860\uc801\uc73c\ub85c \uc758\uc874\ud558\uc9c0 \uc54a\ub294\ub2e4\ub294 \ub73b\uc774\ub2e4. --> \uc774 \uc785\uc7a5\uc740 \uc218\ud559 \ub2f4\ub860\uc758 \uac1d\uad00\uc131\uacfc \uc9c0\uc2dc\uc801 \uc758\ubbf8\ub860\uc744 \ubcf4\uc874\ud558\uae30 \uc27d\uc9c0\ub9cc, \ucd94\uc0c1\uc801 \uad6c\uc870\uc5d0 \ub300\ud55c \uc9c0\uc2dd\uacfc \uad6c\uc870\uc801 \uc790\ub9ac\uc758 \ub3d9\uc77c\uc131\uc744 \uc5b4\ub5bb\uac8c \uc124\uba85\ud560\uc9c0\ub77c\ub294 \uacfc\uc81c\ub97c \uc548\ub294\ub2e4.<\/p>\n<p>\uc81c\ud504\ub9ac \ud5ec\uba3c(Geoffrey Hellman)\uc758 <span class=\"defined\">\uc591\uc0c1 \uad6c\uc870\uc8fc\uc758<\/span>(modal structuralism)\ub294 \uad6c\uc870\ub97c \ubcc4\uac1c\uc758 \ucd94\uc0c1\uc801 \ub300\uc0c1\uc73c\ub85c \uc778\uc815\ud558\uc9c0 \uc54a\ub294 \uc81c\uac70\uc801 \uad6c\uc870\uc8fc\uc758\uc758 \ub300\ud45c\uc801 \ud615\ud0dc\ub2e4. [\ud5ec\uba3c\uc740 1989\ub144 \uc800\uc11c \u300e<i>Mathematics without Numbers: Towards a Modal-Structural Interpretation<\/i>\u300f\uc5d0\uc11c \uc774 \uc785\uc7a5\uc744 \uccb4\uacc4\ud654\ud588\ub2e4.]<a class=\"math-abs-series-ref\" title=\"Geoffrey Hellman, Mathematics without Numbers: Towards a Modal-Structural Interpretation, Oxford University Press, 1989.\" href=\"#ref-Hellman1989\">[Hellman1989]<\/a> \uc774 \ud574\uc11d\uc5d0\uc11c \uc0b0\uc220 \uba85\uc81c \\(\\varphi\\)\ub294 \ub300\ub7b5<br \/>\n\\[<br \/>\n\\Box\\forall M\\bigl(\\mathrm{PA}(M)\\rightarrow\\varphi^M\\bigr)<br \/>\n\\]<br \/>\n\ucc98\ub7fc \u201c\ud544\uc5f0\uc801\uc73c\ub85c, \ubaa8\ub4e0 \uc801\uc808\ud55c \uad00\uacc4 \uccb4\uacc4 \\(M\\)\uc774 \ub370\ub370\ud0a8\ud2b8\u2013\ud398\uc544\ub178 \uacf5\ub9ac\ub97c \ub9cc\uc871\ud558\uba74 \\(\\varphi\\)\uac00 \\(M\\)\uc5d0\uc11c \uc131\ub9bd\ud55c\ub2e4\u201d\ub294 \uba85\uc81c\ub85c \ubc88\uc5ed\ub41c\ub2e4. \uc870\uac74\ubb38\uc774 \uacf5\ud5c8\ud558\uac8c \ucc38\uc774 \ub418\ub294 \uac83\uc744 \ub9c9\uae30 \uc704\ud574<br \/>\n\\[<br \/>\n\\Diamond\\exists M\\,\\mathrm{PA}(M)<br \/>\n\\]<br \/>\n\uc774\ub77c\ub294 \uac00\ub2a5\uc131 \ub610\ub294 \ube44\uacf5\ud5c8\uc131 \uc870\uac74\ub3c4 \ud568\uaed8 \ub454\ub2e4.<\/p>\n<p>\ud5ec\uba3c\uc740 \uac00\ub2a5\ud55c \uccb4\uacc4\ub97c \ub610 \ub2e4\ub978 \uadf8\ub9bc\uc790 \uac19\uc740 \uc2e4\uc7ac\ub85c \uac00\uc815\ud558\uc9c0 \uc54a\uace0, \uac00\ub2a5\uc131\uacfc \ud544\uc5f0\uc131\uc744 S5 \uc591\uc0c1\ub17c\ub9ac\uc758 \ubc95\uce59\uc73c\ub85c \uaddc\uc728\ub418\ub294 \ud658\uc6d0 \ubd88\uac00\ub2a5\ud55c \uae30\ubcf8 \uac1c\ub150\uc73c\ub85c \ubc1b\uc544\ub4e4\uc778\ub2e4. \uc774\ub85c\uc368 \ubcc4\ub3c4\uc758 \ucd94\uc0c1\uc801 \uad6c\uc870\uc5d0 \ub300\ud55c \uc874\uc7ac\ub860\uc801 \uad00\uc5ec\ub294 \ud53c\ud558\uc9c0\ub9cc, \uc5b4\ub5a4 \uc218\ud559\uc801 \uad6c\uc870\uc758 \uac00\ub2a5\uc131\uc744 \uc5b4\ub5bb\uac8c \uc815\ub2f9\ud654\ud558\uace0 \uadf8 \uc591\uc0c1\uc744 \uc5b4\ub5bb\uac8c \uc778\uc2dd\ud558\ub294\uc9c0\ub77c\ub294 \ubb38\uc81c\uac00 \ub0a8\ub294\ub2e4. <!-- \ub530\ub77c\uc11c \uc154\ud53c\ub85c\uc640 \ud5ec\uba3c\uc774 \ubca0\ub098\uc138\ub77c\ud504 \ub51c\ub808\ub9c8\uc758 \uc11c\ub85c \ub2e4\ub978 \ubfd4\uc744 \ud558\ub098\uc529 \ub2e8\uc21c\ud788 \uc120\ud0dd\ud588\ub2e4\uace0 \ubcf4\uae30\ub294 \uc5b4\ub835\ub2e4. --> \ub450 \uc785\uc7a5 \ubaa8\ub450 \uac1d\uad00\uc131\uacfc \uc9c0\uc2dd\uc744 \ud568\uaed8 \uc124\uba85\ud558\ub824 \ud558\ub418, \ud558\ub098\ub294 \ucd94\uc0c1 \uad6c\uc870\uc5d0 \ub300\ud55c \uc811\uadfc\uacfc \ub3d9\uc77c\uc131 \ubb38\uc81c\ub97c, \ub2e4\ub978 \ud558\ub098\ub294 \uc591\uc0c1\uacfc \ube44\uacf5\ud5c8\uc131\uc758 \uc815\ub2f9\ud654 \ubb38\uc81c\ub97c \ub5a0\uc548\ub294\ub2e4.<\/p>\n<h4>\uc2e0\ub17c\ub9ac\uc8fc\uc758\uc640 \ud744\uc758 \uc6d0\ub9ac<\/h4>\n<p>\uc774 \ub51c\ub808\ub9c8\uc5d0 \ub300\ud55c \ub610 \ub2e4\ub978 \uc751\ub2f5\uc740 \ud504\ub808\uac8c\uc758 \ub17c\ub9ac\uc8fc\uc758 \uae30\ud68d\uc73c\ub85c \uac70\uc2ac\ub7ec \uc62c\ub77c\uac04\ub2e4. \ud504\ub808\uac8c\ub294 1884\ub144\uc758 \u300e<i>Die Grundlagen der Arithmetik<\/i>\u300f\uc640 1893\ub144, 1903\ub144\uc5d0 \ub450 \uad8c\uc73c\ub85c \ucd9c\uac04\ud55c \u300e<i>Grundgesetze der Arithmetik<\/i>\u300f\uc5d0\uc11c \uc0b0\uc220\uc744 \ub17c\ub9ac\uc801 \ubc95\uce59\uacfc \uc815\uc758\ub85c\ubd80\ud130 \ub3c4\ucd9c\ud558\ub824 \ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"Gottlob Frege, Die Grundlagen der Arithmetik, Wilhelm Koebner, 1884, \ud2b9\ud788 \u00a7\u00a756, 63, 68.\" href=\"#ref-Frege1884\">[Frege1884]<\/a><a class=\"math-abs-series-ref\" title=\"Gottlob Frege, Grundgesetze der Arithmetik, Vols. I\u2013II, 1893\/1903; Philip A. Ebert and Marcus Rossberg (eds. and trans.), Basic Laws of Arithmetic, Oxford University Press, 2013.\" href=\"#ref-Frege1893\">[Frege1893]<\/a> \uadf8 \ud615\uc2dd \uccb4\uacc4\uc758 \ud575\uc2ec \uc6d0\ub9ac \uac00\uc6b4\ub370 \ud558\ub098\uc778 \uc81c5 \uae30\ubcf8\ubc95\uce59\uc740, \uac1c\ub150 \\(F\\)\uc640 \\(G\\)\uc758 \uc678\uc5f0\uc744 \uac01\uac01 \\(\\varepsilon F\\), \\(\\varepsilon G\\)\ub77c \ud560 \ub54c<br \/>\n\\[<br \/>\n\\varepsilon F=\\varepsilon G\\ \\Longleftrightarrow\\ \\forall x(Fx\\leftrightarrow Gx)<br \/>\n\\]<br \/>\n\ub77c\uace0 \uaddc\uc815\ud55c\ub2e4. \uc989 \ub450 \uac1c\ub150\uc758 \uc678\uc5f0\uc740 \uc815\ud655\ud788 \uac19\uc740 \ub300\uc0c1\ub4e4\uc774 \ub450 \uac1c\ub150 \uc544\ub798\uc5d0 \uc18d\ud560 \ub54c, \uadf8\ub9ac\uace0 \uadf8\ub54c\uc5d0\ub9cc \ub3d9\uc77c\ud558\ub2e4\ub294 \uc6d0\ub9ac\ub2e4. \ud504\ub808\uac8c\ub294 \uc678\uc5f0\uc744 \uc774\uc6a9\ud558\uc5ec \uc218\ub97c \uc815\uc758\ud558\uace0 \ud744\uc758 \uc6d0\ub9ac\ub97c \ub3c4\ucd9c\ud558\ub824 \ud588\ub2e4.<\/p>\n<p>\uadf8\ub7ec\ub098 \uc81c5 \uae30\ubcf8\ubc95\uce59\uc740 \ud504\ub808\uac8c\uac00 \ucc44\ud0dd\ud55c \uac15\ud55c \uc774\ucc28 \ub17c\ub9ac\uc758 \uac1c\ub150 \ud3ec\uad04 \uc6d0\ub9ac\uc640 \uacb0\ud569\ud560 \ub54c \ubaa8\uc21c\uc744 \ub0b3\ub294\ub2e4. \ub7ec\uc140\uc740 1901\ub144 \ubb34\ub835 \uc5ed\uc124\uc744 \ubc1c\uacac\ud558\uace0 1902\ub144 6\uc6d4 16\uc77c \ud504\ub808\uac8c\uc5d0\uac8c \uc54c\ub838\ub2e4. \ud604\ub300 \uc9d1\ud569\ub860\uc758 \uae30\ud638\ub85c \ud575\uc2ec\uc744 \ub098\ud0c0\ub0b4\uba74 \\(R=\\{x\\mid x\\notin x\\}\\)\ub97c \uac00\uc815\ud560 \ub54c \\(R\\in R\\Longleftrightarrow R\\notin R\\)\uac00 \ub418\uc5b4 \ubaa8\uc21c\uc774 \uc0dd\uae34\ub2e4. [\ud504\ub808\uac8c\ub294 \u300e<i>Grundgesetze der Arithmetik<\/i>\u300f \uc81c2\uad8c\uc774 \uc778\uc1c4\ub418\ub358 \uc911 \ub7ec\uc140\uc758 \ud3b8\uc9c0\ub97c \ubc1b\uc558\uc73c\uba70, 1903\ub144\uc5d0 \ucd9c\uac04\ub41c \uc81c2\uad8c \ud6c4\uae30\uc5d0\uc11c \ubaa8\uc21c\uc744 \uc804\uac1c\ud558\uace0 \uc81c5 \uae30\ubcf8\ubc95\uce59\uc758 \uc218\uc815\uc548\uc744 \uc81c\uc548\ud588\ub2e4. \uadf8\ub7ec\ub098 \uadf8 \uc218\uc815\uc548\uc740 \uc6d0\ub798\uc758 \uae30\ucd08 \uccb4\uacc4\ub97c \uad6c\ud558\uc9c0 \ubabb\ud588\ub2e4.]<a class=\"math-abs-series-ref\" title=\"Gottlob Frege, Grundgesetze der Arithmetik, Vols. I\u2013II, 1893\/1903; Philip A. Ebert and Marcus Rossberg (eds. and trans.), Basic Laws of Arithmetic, Oxford University Press, 2013.\" href=\"#ref-Frege1893\">[Frege1893]<\/a> \ub530\ub77c\uc11c \ubd95\uad34\ud55c \uac83\uc740 \uc81c5 \uae30\ubcf8\ubc95\uce59\uc744 \uac15\ud55c \ud3ec\uad04 \uc6d0\ub9ac\uc640 \uacb0\ud569\ud55c \ud504\ub808\uac8c\uc758 \uc804\uccb4 \uccb4\uacc4\uc774\ub2e4. <!-- \uc81c5 \uae30\ubcf8\ubc95\uce59 \uc790\uccb4\ub294 \ud3ec\uad04 \uc6d0\ub9ac\ub97c \uc81c\ud55c\ud55c \uc57d\ud55c \uccb4\uacc4\uc5d0\uc11c \uc815\ud569\uc801\uc778 \ub2e8\ud3b8\uc744 \uac00\uc9c8 \uc218 \uc788\uc73c\ubbc0\ub85c, \uc6d0\ub9ac \ud558\ub098\uac00 \uc544\ubb34 \uc870\uac74 \uc5c6\uc774 \u2018\uc790\uac00\ub2f9\ucc29\u2019\uc778 \uac83\uc740 \uc544\ub2c8\ub2e4. --><\/p>\n<p>20\uc138\uae30 \ud6c4\ubc18\uc5d0\ub294 \ud504\ub808\uac8c\uc758 \uae30\ud68d\uc744 \ud744\uc758 \uc6d0\ub9ac\ub97c \uc911\uc2ec\uc73c\ub85c \uc7ac\uad6c\uc131\ud558\ub824\ub294 <span class=\"defined\">\uc2e0\ub17c\ub9ac\uc8fc\uc758<\/span>(neo-logicism)\uac00 \ub4f1\uc7a5\ud588\ub2e4. [\ucc30\uc2a4 \ud30c\uc2a8\uc2a4(Charles Parsons)\ub294 1965\ub144\uc5d0 \ud744\uc758 \uc6d0\ub9ac\ub85c\ubd80\ud130 \uc0b0\uc220 \uacf5\ub9ac\ub97c \ub3c4\ucd9c\ud560 \uc218 \uc788\ub2e4\ub294 \uc810\uc744 \uc9c0\uc801\ud588\uace0, \ud06c\ub9ac\uc2a4\ud540 \ub77c\uc774\ud2b8(Crispin Wright)\uc758 1983\ub144 \uc800\uc11c \u300e<i>Frege\u2019s Conception of Numbers as Objects<\/i>\u300f\ub294 \uc774 \uae30\ud68d\uc744 \ubcf8\uaca9\uc801\uc73c\ub85c \ubd80\ud765\uc2dc\ud0a8 \ub300\ud45c\uc801 \ubb38\ud5cc\uc774 \ub418\uc5c8\ub2e4.]<a class=\"math-abs-series-ref\" title=\"Charles Parsons, \u201cFrege\u2019s Theory of Number,\u201d in Max Black (ed.), Philosophy in America, Allen &amp; Unwin, 1965, pp. 180\u2013203.\" href=\"#ref-Parsons1965\">[Parsons1965]<\/a><a class=\"math-abs-series-ref\" title=\"Crispin Wright, Frege\u2019s Conception of Numbers as Objects, Aberdeen University Press, 1983.\" href=\"#ref-Wright1983\">[Wright1983]<\/a> \ud504\ub808\uac8c \uc790\uc2e0\uc740 \u300e\uc0b0\uc220\uc758 \uae30\ucd08\u300f\uc5d0\uc11c \ud744\uc758 \uc6d0\ub9ac\ub97c \uc218\uc758 \uc644\uc804\ud55c \uc815\uc758\ub85c \uc0bc\uc744 \uc218 \uc788\ub294\uc9c0 \uac80\ud1a0\ud588\uc9c0\ub9cc, \uadf8\uac83\ub9cc\uc73c\ub85c\ub294 \u2018\uc728\ub9ac\uc6b0\uc2a4 \uce74\uc774\uc0ac\ub974\ub294 \uc218\uc778\uac00\u2019\uc640 \uac19\uc740 \ud63c\ud569 \ub3d9\uc77c\uc131 \ubb38\uc7a5\uc758 \ub2f5\uc744 \uc815\ud560 \uc218 \uc5c6\ub2e4\ub294 \ubb38\uc81c \ub54c\ubb38\uc5d0 \uc678\uc5f0\uc744 \ud1b5\ud55c \uba85\uc2dc\uc801 \uc815\uc758\ub85c \ub098\uc544\uac14\ub2e4. \uc2e0\ub17c\ub9ac\uc8fc\uc758\uc790\ub4e4\uc740 \ud744\uc758 \uc6d0\ub9ac\ub97c \uc0b0\uc220\uc758 \ucd9c\ubc1c\uc810\uc73c\ub85c \ub2e4\uc2dc \ucc44\ud0dd\ud55c\ub2e4. [\u2018Hume\u2019s Principle\u2019\uc774\ub77c\ub294 \uba85\uce6d\uc740 \uc870\uc9c0 \ubd88\ub85c\uc2a4(George Boolos)\uac00 1987\ub144\uc5d0 \ub3c4\uc785\ud588\ub2e4. \ud504\ub808\uac8c\ub294 \u300e\uc0b0\uc220\uc758 \uae30\ucd08\u300f \u00a763\uc5d0\uc11c \ub370\uc774\ube44\ub4dc \ud744\uc758 \u300e<i>A Treatise of Human Nature<\/i>\u300f \uc81c1\uad8c \uc81c3\ubd80 \uc81c1\uc808\uc744 \uc778\uc6a9\ud588\uc9c0\ub9cc, \uc790\uc2e0\uc740 \uc774 \uba85\uce6d\uc744 \uc0ac\uc6a9\ud558\uc9c0 \uc54a\uc558\ub2e4.]<a class=\"math-abs-series-ref\" title=\"George Boolos, \u201cThe Consistency of Frege\u2019s Foundations of Arithmetic,\u201d in Judith Jarvis Thomson (ed.), On Being and Saying, MIT Press, 1987, pp. 3\u201320.\" href=\"#ref-Boolos1987\">[Boolos1987]<\/a><\/p>\n<p>\ud744\uc758 \uc6d0\ub9ac\ub294<br \/>\n\\[<br \/>\n\\#F=\\#G\\ \\Longleftrightarrow\\ F\\approx G<br \/>\n\\]<br \/>\n\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc5ec\uae30\uc11c \\(F\\approx G\\)\ub294 \\(F\\)\uc5d0 \uc18d\ud558\ub294 \ub300\uc0c1\ub4e4\uacfc \\(G\\)\uc5d0 \uc18d\ud558\ub294 \ub300\uc0c1\ub4e4 \uc0ac\uc774\uc5d0 \uc77c\ub300\uc77c \ub300\uc751\uc774 \uc874\uc7ac\ud55c\ub2e4\ub294 \ub73b\uc774\ub2e4. \uc774\uac83\uc740 \uc77c\ubc18\uc801\uc73c\ub85c<br \/>\n\\[<br \/>\n@a=@b\\ \\Longleftrightarrow\\ a\\sim b<br \/>\n\\]<br \/>\n\uaf34\ub85c \ud45c\ud604\ub418\ub294 <span class=\"defined\">\ucd94\uc0c1\ud654 \uc6d0\ub9ac<\/span>(abstraction principle)\uc758 \ub300\ud45c\uc801 \uc0ac\ub840\ub2e4. \uc9c1\uc120\uc758 \ubc29\ud5a5\ub3c4<br \/>\n\\[<br \/>\n\\mathrm{dir}(a)=\\mathrm{dir}(b)\\ \\Longleftrightarrow\\ a\\parallel b<br \/>\n\\]<br \/>\n\ucc98\ub7fc \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc5ec\uae30\uc11c \\(\\parallel\\)\ub294 \u2018\uac19\uc740 \ubc29\ud5a5\u2019\uc744 \ub098\ud0c0\ub0b4\ub294 \ub3d9\uce58\uad00\uacc4\uc774\ub2e4. [\ub2e8, \uc784\uc758\uc758 \uc9c1\uc120\uc740 \uc790\uae30 \uc790\uc2e0\uacfc \uac19\uc740 \ubc29\ud5a5\uc774\ub77c\uace0 \uc815\uc758\ud55c\ub2e4.] \ub2e4\ub9cc \ucd94\uc0c1\ud654 \uc6d0\ub9ac\uc640 \ub3d9\uce58\ub958 \uad6c\uc131\uc740 \uad6c\ubcc4\ud574\uc57c \ud55c\ub2e4. \ub3d9\uce58\ub958\ub294 \uc774 \ub3d9\uc77c\uc131 \uc870\uac74\uc744 \uc2e4\ud604\ud558\ub294 \ud55c \ubaa8\ud615\uc774\uc9c0\ub9cc, \uc2e0\ud504\ub808\uac8c\uc8fc\uc758\uc790\ub294 \\(\\#F\\)\ub97c \ub3d9\uce58\ub958\uc640 \ub3d9\uc77c\uc2dc\ud558\uc9c0 \uc54a\uace0 \uc6d0\ub9ac\uac00 \ub3d9\uc77c\uc131 \uc870\uac74\uc744 \ubd80\uc5ec\ud558\ub294 \ub3c5\uc790\uc801 \ucd94\uc0c1 \ub300\uc0c1\uc73c\ub85c \uc774\ud574\ud560 \uc218 \uc788\ub2e4.<\/p>\n<p>\ud744\uc758 \uc6d0\ub9ac\ub294 \ud45c\uc900\uc801\uc778 \uc774\ucc28 \ub17c\ub9ac\uc640 \ud568\uaed8 \ubaa8\ud615\uc744 \uac16\ub294\ub2e4. [\ubd88\ub85c\uc2a4\ub294 1987\ub144\uc5d0 \uc790\uc5f0\uc218\ub4e4\uacfc \ubcc4\ub3c4\uc758 \ub300\uc0c1 \ud558\ub098\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc601\uc5ed\uc744 \uc0ac\uc6a9\ud558\uc5ec, \uc720\ud55c \uac1c\ub150\uc5d0\ub294 \ud574\ub2f9 \uc790\uc5f0\uc218\ub97c, \ubb34\ud55c \uac1c\ub150\uc5d0\ub294 \uadf8 \ubcc4\ub3c4 \ub300\uc0c1\uc744 \ub300\uc751\uc2dc\ud0a4\ub294 \ubaa8\ud615\uc744 \uc81c\uc2dc\ud588\ub2e4. \uc774\ub294 \ud1b5\uc0c1\uc801\uc778 \uba54\ud0c0\uc774\ub860\uc744 \uc804\uc81c\ub85c \ud55c \uc0c1\ub300\uc801 \uc815\ud569\uc131 \uacb0\uacfc\uc774\uc9c0, \uc5b4\ub5a4 \ud615\uc2dd \uccb4\uacc4\uc758 \ubb34\uc870\uac74\uc801\uc778 \u2018\uc808\ub300 \uc815\ud569\uc131 \uc99d\uba85\u2019\uc740 \uc544\ub2c8\ub2e4.]<a class=\"math-abs-series-ref\" title=\"George Boolos, \u201cThe Consistency of Frege\u2019s Foundations of Arithmetic,\u201d in Judith Jarvis Thomson (ed.), On Being and Saying, MIT Press, 1987, pp. 3\u201320.\" href=\"#ref-Boolos1987\">[Boolos1987]<\/a> \uc774\ucc28 \ub17c\ub9ac\uc758 \ud544\uc694\ud55c \ud3ec\uad04 \uc6d0\ub9ac\uc640 \\(0\\), \ud6c4\uc18d\uc790, \uc790\uc5f0\uc218\uc5d0 \uad00\ud55c \uc815\uc758\uc5d0 \ud744\uc758 \uc6d0\ub9ac\ub97c \ub354\ud558\uba74 \ub370\ub370\ud0a8\ud2b8\u2013\ud398\uc544\ub178 \uacf5\ub9ac\ub4e4\uc744 \ub3c4\ucd9c\ud560 \uc218 \uc788\ub2e4. \uc774 \ud615\uc2dd\uc801 \uacb0\uacfc\ub97c <span class=\"defined\">\ud504\ub808\uac8c \uc815\ub9ac<\/span>(Frege&#8217;s theorem)\ub77c\uace0 \ubd80\ub978\ub2e4.<a class=\"math-abs-series-ref\" title=\"Edward N. Zalta, \u201cFrege\u2019s Theorem and Foundations for Arithmetic,\u201d Stanford Encyclopedia of Philosophy.\" href=\"#ref-ZaltaFregeTheorem\">[ZaltaFregeTheorem]<\/a><\/p>\n<p>[\u300e\uc0b0\uc220\uc758 \uae30\ucd08\u300f\uc5d0\ub294 \uc774 \ub3c4\ucd9c\uc758 \ube44\ud615\uc2dd\uc801 \uc804\ub7b5\uc774 \ub098\ud0c0\ub098\uace0 \u300e\uc0b0\uc220\uc758 \uadfc\ubcf8\ubc95\uce59\u300f\uc5d0\ub294 \uad00\ub828 \ud615\uc2dd\uc801 \uc99d\uba85\ub4e4\uc774 \uc804\uac1c\ub418\uc5b4 \uc788\ub2e4. \ud30c\uc2a8\uc2a4\uac00 1965\ub144\uc5d0 \uadf8 \uac00\ub2a5\uc131\uc744 \uc9c0\uc801\ud558\uace0 \ub77c\uc774\ud2b8\uac00 1983\ub144\uc5d0 \ub3c4\ucd9c\uc744 \uc7ac\uad6c\uc131\ud588\uc73c\uba70, \ub9ac\ucc98\ub4dc \ud5e5(Richard Heck)\uc740 1993\ub144\uc5d0 \ud504\ub808\uac8c\uac00 \ud744\uc758 \uc6d0\ub9ac\ub97c \uc5bb\uc740 \ub4a4 \uc218\ud589\ud55c \uc0b0\uc220\uc758 \ub3c4\ucd9c\uc774 \uc81c5 \uae30\ubcf8\ubc95\uce59\uc5d0 \ubcf8\uc9c8\uc801\uc73c\ub85c \uc758\uc874\ud558\uc9c0 \uc54a\ub294\ub2e4\ub294 \uc0ac\uc2e4\uc744 \ubcf4\uc600\ub2e4.]<a class=\"math-abs-series-ref\" title=\"Charles Parsons, \u201cFrege\u2019s Theory of Number,\u201d in Max Black (ed.), Philosophy in America, Allen &amp; Unwin, 1965, pp. 180\u2013203.\" href=\"#ref-Parsons1965\">[Parsons1965]<\/a><a class=\"math-abs-series-ref\" title=\"Crispin Wright, Frege\u2019s Conception of Numbers as Objects, Aberdeen University Press, 1983.\" href=\"#ref-Wright1983\">[Wright1983]<\/a><a class=\"math-abs-series-ref\" title=\"Richard G. Heck Jr., \u201cThe Development of Arithmetic in Frege\u2019s Grundgesetze der Arithmetik,\u201d Journal of Symbolic Logic 58(2), 1993, pp. 579\u2013601.\" href=\"#ref-Heck1993\">[Heck1993]<\/a> <!-- \ud504\ub808\uac8c\uac00 \ud744\uc758 \uc6d0\ub9ac\ub97c \ub2e8\uc21c\ud788 \u2018\ubc84\ub9b0\u2019 \ube44\uadf9\uc73c\ub85c\ub9cc \uc11c\uc220\ud558\uae30\ub3c4 \uc5b4\ub835\ub2e4. \uadf8\ub294 \ud744\uc758 \uc6d0\ub9ac\ub9cc\uc73c\ub85c \ud63c\ud569 \ub3d9\uc77c\uc131 \ubb38\uc81c\ub97c \ud574\uacb0\ud558\uae30 \uc5b4\ub835\ub2e4\uace0 \ubcf4\uc558\uae30 \ub54c\ubb38\uc5d0 \uc218\ub97c \uc678\uc5f0\uc73c\ub85c \uc815\uc758\ud558\ub824 \ud588\ub2e4. --><\/p>\n<p><!-- \ud504\ub808\uac8c \uc815\ub9ac\ub294 \uc911\uc694\ud55c \uc131\uacfc\uc9c0\ub9cc, \ud744\uc758 \uc6d0\ub9ac\uac00 \uc21c\uc218 \ub17c\ub9ac\uc774\uac70\ub098 \ubd84\uc11d\uc801 \uc9c4\ub9ac\ub77c\ub294 \ucca0\ud559\uc801 \uacb0\ub860\uae4c\uc9c0 \uc99d\uba85\ud558\uc9c0\ub294 \uc54a\ub294\ub2e4. -->\uc2e0\ub17c\ub9ac\uc8fc\uc758\uc758 \uad6c\uc0c1\uc740 \uc870\uac74\ubd80\uc774\ub2e4. \ud744\uc758 \uc6d0\ub9ac\uac00 \uc218 \uac1c\ub150\uc758 \uc815\ub2f9\ud55c \uc554\ubb35\uc801 \uc815\uc758\uc774\uace0 \ubd84\uc11d\uc801\uc73c\ub85c \ucc38\uc774\ub77c\uba74, \uadf8 \uc6d0\ub9ac\uc640 \ub17c\ub9ac\uc5d0\uc11c \ub3c4\ucd9c\ub418\ub294 \uc0b0\uc220\uc5d0\ub3c4 \uc120\ud5d8\uc801 \uc815\ub2f9\ud654\ub97c \ubd80\uc5ec\ud560 \uc218 \uc788\ub2e4\ub294 \uac83\uc774\ub2e4. \uc774\ub294 \uc218\uc5d0 \ub300\ud55c \uc9c0\uc2dd\uc744 \uc778\uacfc\uc801 \uc811\ucd09\ubcf4\ub2e4 \ub17c\ub9ac\uc640 \uac1c\ub150\uc758 \uc774\ud574\ub85c \uc124\uba85\ud558\ub824\ub294 \ubca0\ub098\uc138\ub77c\ud504 \ubb38\uc81c\uc758 \ud55c \uc751\ub2f5\uc774\ub2e4. \uadf8\ub7ec\ub098 \ud744\uc758 \uc6d0\ub9ac\uac00 \uc2e4\uc81c\ub85c \ub17c\ub9ac\uc801 \ub610\ub294 \ubd84\uc11d\uc801\uc778\uc9c0, \ub610 \uadf8\uac83\uc774 \ubb34\ud55c\ud788 \ub9ce\uc740 \uc218\uc758 \uc874\uc7ac\ub97c \uc815\ub2f9\ud558\uac8c \ub3c4\uc785\ud558\ub294\uc9c0\ub294 \ub17c\uc7c1 \uc911\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"George Boolos, \u201cIs Hume\u2019s Principle Analytic?\u201d, in Richard G. Heck Jr. (ed.), Language, Thought, and Logic, Oxford University Press, 1997, pp. 245\u2013261.\" href=\"#ref-Boolos1997\">[Boolos1997]<\/a><\/p>\n<p>\ub354 \uc77c\ubc18\uc801\uc73c\ub85c, \uac19\uc740 \ubb38\ubc95 \ud615\uc2dd\uc744 \uc9c0\ub2cc \ucd94\uc0c1\ud654 \uc6d0\ub9ac\ub77c\uace0 \ud574\uc11c \ubaa8\ub450 \uc815\ub2f9\ud55c \uac83\uc740 \uc544\ub2c8\ub2e4. \uc5b4\ub5a4 \uc6d0\ub9ac\ub294 \uadf8 \uc790\uccb4\ub85c \ubaa8\uc21c\uc744 \ub0b3\uace0, \uac1c\ubcc4\uc801\uc73c\ub85c \ubaa8\ud615\uc744 \uac16\ub294 \uc6d0\ub9ac\ub4e4\uc774 \ub2e4\ub978 \ucd94\uc0c1\ud654 \uc6d0\ub9ac\uc640 \uacb0\ud569\ud560 \ub54c \ud568\uaed8 \ub9cc\uc871\ub420 \uc218 \uc5c6\ub294 \uc0ac\ub840\ub3c4 \uc788\ub2e4. \uc774\ub97c <span class=\"defined\">\ub098\uc05c \ub3d9\ub8cc \ubb38\uc81c<\/span>(bad company problem)\ub77c\uace0 \ud55c\ub2e4. \ubcf4\uc218\uc131, \uc548\uc815\uc131, \uacf5\ub3d9 \ub9cc\uc871 \uac00\ub2a5\uc131 \ub4f1 \uc5ec\ub7ec \uc120\ubcc4 \uae30\uc900\uc774 \uc81c\uc548\ub418\uc5c8\uc9c0\ub9cc, \ud744\uc758 \uc6d0\ub9ac\ub97c \ube44\uc21c\ud658\uc801\uc73c\ub85c \uc815\ub2f9\ud654\ud558\uba74\uc11c \ubaa8\ub4e0 \ub098\uc05c \uc6d0\ub9ac\ub97c \ubc30\uc81c\ud558\ub294 \ud558\ub098\uc758 \uae30\uc900\uc5d0 \ud569\uc758\uac00 \uc774\ub8e8\uc5b4\uc9c4 \uac83\uc740 \uc544\ub2c8\ub2e4.<a class=\"math-abs-series-ref\" title=\"Edward N. Zalta, \u201cFrege\u2019s Theorem and Foundations for Arithmetic,\u201d Stanford Encyclopedia of Philosophy.\" href=\"#ref-ZaltaFregeTheorem\">[ZaltaFregeTheorem]<\/a><\/p>\n<h4>\ud604\uc2e4 \uc138\uacc4\uc5d0 \ub4e4\uc5b4\ub9de\ub294 \uc774\uc720<\/h4>\n<p>\uc218\ud559\uc758 \uc874\uc7ac\ub860\uc744 \uc7a0\uc2dc \uc606\uc73c\ub85c \ub450\ub354\ub77c\ub3c4 \ud070 \ubb3c\uc74c \ud558\ub098\uac00 \ub0a8\ub294\ub2e4. \ud604\uc2e4\uc758 \uad6c\uccb4\uc131\uc744 \ub9ce\uc774 \ub35c\uc5b4 \ub0b8 \uc218\ud559\uc801 \uad6c\uc870\uac00 \uc65c \ubb3c\ub9ac \uc138\uacc4\ub97c \uadf8\ud1a0\ub85d \uc798 \uae30\uc220\ud558\ub294\uac00?<\/p>\n<p>\uc720\uc9c4 \uc704\uadf8\ub108(Eugene Wigner)\ub294 1960\ub144 \uc5d0\uc138\uc774 \u300cThe Unreasonable Effectiveness of Mathematics in the Natural Sciences\u300d\uc5d0\uc11c \uc774 \ubb3c\uc74c\uc744 \uc720\uba85\ud558\uac8c \uc81c\uae30\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"Eugene P. Wigner, \u201cThe Unreasonable Effectiveness of Mathematics in the Natural Sciences,\u201d Communications on Pure and Applied Mathematics 13(1), 1960, pp. 1\u201314.\" href=\"#ref-Wigner1960\">[Wigner1960]<\/a> \uadf8\uac00 \ub17c\ud55c \uc0ac\ub840\uc5d0\ub294 \ubcf5\uc18c\uc218, \ubcf5\uc18c \ud790\ubca0\ub974\ud2b8 \uacf5\uac04, \uc5f0\uc0b0\uc790\uc640 \ud589\ub82c\uc5ed\ud559\uc774 \ud3ec\ud568\ub41c\ub2e4. \ub2e4\ub9cc \uc218\ud559\uc774 \uc591\uc790\uc5ed\ud559\uc758 \u2018\uc720\uc77c\ud558\uace0 \uc644\ubcbd\ud55c \uc5b8\uc5b4\u2019\ub77c\uace0 \uacb0\ub860 \ub0b4\ub9b0 \uac83\uc740 \uc544\ub2c8\ub2e4. \uc704\uadf8\ub108\ub294 \uc218\ud559 \uac1c\ub150\uc774 \uacbd\ud5d8 \ubc95\uce59\uc744 \ub180\ub784 \ub9cc\ud07c \uc815\ud655\ud558\uac8c \ud45c\ud604\ud558\uace0 \uc0c8\ub85c\uc6b4 \uc608\uce21\uae4c\uc9c0 \uac00\ub2a5\ud558\uac8c \ud558\ub294 \ud604\uc0c1\uc744 \u2018\ubd80\ub2f9\ud560 \ub9cc\ud07c\u2019 \ud6a8\uacfc\uc801\uc774\ub77c\uace0 \ubd80\ub974\uba70 \uadf8 \uc131\uacf5\uc758 \ubc94\uc704\uc640 \uc774\uc720\ub97c \uc218\uc218\uaed8\ub07c\ub85c \ub0a8\uacbc\ub2e4.<\/p>\n<p>\ub9ac\ub9cc\uc758 \uae30\ud558\ud559\uacfc \uc77c\ubc18\uc0c1\ub300\uc131\uc774\ub860\uc758 \uc5f0\uacb0\ub3c4 \ud55c \uc0ac\ub78c\uc758 \uc21c\uc218 \uc774\ub860\uc774 \ubc18\uc138\uae30 \ub4a4 \uadf8\ub300\ub85c \ubb3c\ub9ac\ud559\uc774 \ub41c \ub2e8\uc120\uc801 \uc774\uc57c\uae30\ub294 \uc544\ub2c8\ub2e4. \ub9ac\ub9cc \uc774\ud6c4 \ud06c\ub9ac\uc2a4\ud1a0\ud3a0, \ub9ac\uce58, \ub808\ube44\uce58\ube44\ud0c0 \ub4f1\uc774 \ud150\uc11c \uacc4\uc0b0\uacfc \ubbf8\ubd84\uae30\ud558\ub97c \ubc1c\uc804\uc2dc\ucf30\uace0, \uadf8\ub85c\uc2a4\ub9cc\uacfc \uc544\uc778\uc288\ud0c0\uc778\uc740 \uc774 \ub3c4\uad6c\ub4e4\uc744 \uc911\ub825 \uc774\ub860\uc5d0 \ub9de\uac8c \ud65c\uc6a9\ud588\ub2e4.<a class=\"math-abs-series-ref\" title=\"John D. Norton, \u201cHow Einstein Found His Field Equations: 1912\u20131915,\u201d Historical Studies in the Physical Sciences 14(2), 1984, pp. 253\u2013316.\" href=\"#ref-Norton1984\">[Norton1984]<\/a> \uadf8\ub7fc\uc5d0\ub3c4 \ubb3c\ub9ac\uc801 \ub3d9\uae30\uc640 \ub3c5\ub9bd\ud558\uc5ec \ubc1c\uc804\ud55c \uc218\ud559\uc774 \ud6d7\ub0a0 \ud575\uc2ec \ubaa8\ub378 \uc5b8\uc5b4\uac00 \ub41c\ub2e4\ub294 \uc810\uc740 \uc704\uadf8\ub108\uc758 \ubb38\uc81c\ub97c \uc798 \ubcf4\uc5ec \uc900\ub2e4.<\/p>\n<p>\ub2e4\uc74c\uc740 \uc774 \ubb38\uc81c\uc5d0 \uc81c\uc548\ub41c \uc5ec\ub7ec \uc124\uba85\uc758 \uacc4\uc5f4\uc774\ub2e4. \ubaa8\ub450 \uc704\uadf8\ub108 \uc790\uc2e0\uc774 \ub124 \uac00\uc9c0 \ub2f5\uc73c\ub85c \uc5f4\uac70\ud55c \uac83\uc740 \uc544\ub2c8\uba70, \uc11c\ub85c \ubc30\ud0c0\uc801\uc774\uc9c0\ub3c4 \uc54a\ub2e4.<\/p>\n<ul>\n<li><span class=\"defined\">\uc120\ud0dd \ud6a8\uacfc<\/span>: \uc778\uac04\uc740 \ubb3c\ub9ac \uc138\uacc4\uc5d0\uc11c \ubc18\ubcf5\ub418\ub294 \ud615\ud0dc\ub97c \uace8\ub77c \ubb38\uc81c\ub85c \uc0bc\uace0, \uac1c\ubc1c\ub41c \uc218\ud559 \uac00\uc6b4\ub370 \uc801\uc6a9\uc5d0 \uc131\uacf5\ud55c \ubd80\ubd84\uc744 \ud2b9\ud788 \uae30\uc5b5\ud558\uace0 \ud655\uc7a5\ud55c\ub2e4. \ud574\ubc0d(Richard Hamming)\uc740 \uc6b0\ub9ac\uac00 \ubb38\uc81c\uc640 \uc218\ud559 \ub3c4\uad6c\ub97c \uc120\ud0dd\ud55c\ub2e4\ub294 \uc810\uc744 \ubd80\ubd84\uc801 \uc124\uba85\uc73c\ub85c \ub4e4\uc5c8\uc9c0\ub9cc, \uadf8\uac83\ub9cc\uc73c\ub85c \ub0a8\ub294 \ub180\ub77c\uc6c0\uc744 \ubaa8\ub450 \ud574\uc18c\ud558\uc9c0\ub294 \ubabb\ud55c\ub2e4\uace0 \ubcf4\uc558\ub2e4.<a class=\"math-abs-series-ref\" title=\"Richard W. Hamming, \u201cThe Unreasonable Effectiveness of Mathematics,\u201d American Mathematical Monthly 87(2), 1980, pp. 81\u201390.\" href=\"#ref-Hamming1980\">[Hamming1980]<\/a><\/li>\n<li><span class=\"defined\">\uc9c4\ud654 \u00b7 \uc778\uc9c0\uc801 \uc124\uba85<\/span>: \uc778\uac04\uc758 \uc9c0\uac01\uacfc \ucd94\ub860 \ub2a5\ub825\uc774 \ubb3c\ub9ac \ud658\uacbd\uacfc \uc0c1\ud638\uc791\uc6a9\ud558\uba70 \ud615\uc131\ub418\uc5c8\uc73c\ubbc0\ub85c, \uadf8 \ub2a5\ub825\uc5d0\uc11c \ucd9c\ubc1c\ud55c \uc218\ud559\uc774 \uc138\uacc4\uc758 \uc77c\ubd80 \uaddc\uce59\uc131\uacfc \ub9de\ub294 \uac83\uc740 \uc804\ud600 \uc6b0\uc5f0\ub9cc\uc740 \uc544\ub2c8\ub77c\ub294 \uacac\ud574\ub2e4. \uadf8\ub7ec\ub098 \ud604\ub300 \uace0\ub4f1\uc218\ud559\uc758 \uba3c \uc804\uc774\uae4c\uc9c0 \uc774\uac83\ub9cc\uc73c\ub85c \uc124\uba85\ub418\ub294\uc9c0\ub294 \ubcc4\ub3c4 \ubb38\uc81c\ub2e4.<\/li>\n<li><span class=\"defined\">\uc218\ud559\uc801 \uc6b0\uc8fc \uac00\uc124<\/span>: \ubb3c\ub9ac \uc138\uacc4\uac00 \ub2e8\uc9c0 \uc218\ud559\uc73c\ub85c \uae30\uc220\ub418\ub294 \uac83\uc744 \ub118\uc5b4 \uadf8 \uc790\uccb4\uac00 \uc218\ud559\uc801 \uad6c\uc870\ub77c\ub294 \ud14c\uadf8\ub9c8\ud06c(Max Tegmark)\uc758 \uac15\ud55c \ud615\uc774\uc0c1\ud559\uc801 \uc81c\uc548\uc774\ub2e4. \uc774\ub294 \ub110\ub9ac \ud569\uc758\ub41c \uacb0\ub860\uc774 \uc544\ub2c8\ub77c \ub17c\uc7c1\uc801\uc778 \uac00\uc124\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Max Tegmark, \u201cThe Mathematical Universe,\u201d Foundations of Physics 38, 2008, pp. 101\u2013150.\" href=\"#ref-Tegmark2008\">[Tegmark2008]<\/a><\/li>\n<li><span class=\"defined\">\ubaa8\ud615\ud654\uc640 \uadfc\uc0ac\uc758 \uad00\uc810<\/span>: \uc801\uc6a9\uc218\ud559\uc740 \ud604\uc2e4\uc744 \uadf8\ub300\ub85c \ubcf5\uc0ac\ud558\uc9c0 \uc54a\ub294\ub2e4. \ubaa9\uc801\uc5d0 \ub9de\ub294 \ubcc0\uc218\ub97c \uc120\ud0dd\ud558\uace0, \uc774\uc0c1\ud654, \uadfc\uc0ac, \ubcf4\uc815\uc744 \uac70\uccd0 \uc81c\ud55c\ub41c \ubc94\uc704\uc5d0\uc11c \uc4f8 \uc218 \uc788\ub294 \ubaa8\ud615\uc744 \ub9cc\ub4e0\ub2e4. \uc774 \uad00\uc810\uc5d0\uc11c\ub294 \uc131\uacf5\uc758 \uc77c\ubd80\uac00 \uc218\ud559\uc758 \uae30\uc801\uc774\ub77c\uae30\ubcf4\ub2e4 \uc138\uc2ec\ud55c \ubaa8\ud615 \uc120\ud0dd\uacfc \uc870\uc815\uc758 \uacb0\uacfc\ub2e4.<a class=\"math-abs-series-ref\" title=\"Michael Weisberg, Simulation and Similarity: Using Models to Understand the World, Oxford University Press, 2013.\" href=\"#ref-Weisberg2013\">[Weisberg2013]<\/a><\/li>\n<\/ul>\n<p><!--\n\n\n<p>\uc774 \uc124\uba85\ub4e4\uc740 \uc218\ud559\uc758 \uc801\uc6a9 \uac00\ub2a5\uc131\uc744 \uc11c\ub85c \ub2e4\ub978 \uac01\ub3c4\uc5d0\uc11c \ube44\ucd94\uc9c0\ub9cc, \uc5b4\ub290 \ud558\ub098\uac00 \ubb38\uc81c\ub97c \uc885\uacb0\ud588\ub2e4\uace0 \ubcf4\uae30\ub294 \uc5b4\ub835\ub2e4.<\/p>\n\n\n--><\/p>\n<h4>\uc815\ud655\ud568\uc73c\ub85c\uc11c\uc758 \ucd94\uc0c1<\/h4>\n<p>\uc774\uc81c \uc5f0\uc7ac\uc758 \ucd9c\ubc1c\uc810\uc73c\ub85c \ub3cc\uc544\uac00 \ubcf4\uc790. \uc77c\uc0c1\uc5b4\uc5d0\uc11c \u2018\ucd94\uc0c1\uc801\u2019\uc774\ub77c\ub294 \ub9d0\uc740 \ub54c\ub54c\ub85c \ub9c9\uc5f0\ud568\uc744 \ub73b\ud558\ub294\ub370, \uc218\ud559\uc801 \ucd94\uc0c1\ud654\ub294 \uc65c \uc815\ubc00\ud568\uc744 \ub0b3\ub294\uac00?<\/p>\n<p>\uc774 \uc5f0\uc7ac\uac00 \uc81c\uc548\ud55c \ud55c \uac00\uc9c0 \ub2f5\uc740, \uc218\ud559\uc801 \ucd94\uc0c1\ud654\uac00 \uc5b4\ub5a4 \ucc28\uc774\ub294 \ubb34\uc2dc\ud558\uace0 \uc5b4\ub5a4 \uad6c\uc870\ub294 \ubcf4\uc874\ud560\uc9c0\ub97c \uba85\uc2dc\ud558\ub294 \uc791\uc5c5\uc774\ub77c\ub294 \uac83\uc774\ub2e4. \ucd94\uc0c1\ud654\ub294 \ub2e8\uc21c\ud55c \ube84\uc148\ub9cc\uc774 \uc544\ub2c8\ub77c \uc0c8 \ud45c\ud604\uc744 \ub3c4\uc785\ud558\uace0, \ub300\uc0c1\uc744 \ub3d9\uc77c\uc2dc\ud558\uace0, \uc5ec\ub7ec \uc0ac\ub840\ub97c \ud1b5\ud569\ud558\ub294 \uc77c\ub3c4 \ud3ec\ud568\ud55c\ub2e4.<\/p>\n<ul>\n<li><span class=\"defined\">\ub3d9\uce58\ub958\ub97c \uc0ac\uc6a9\ud55c \uc815\uc758<\/span>\ub294 \uc5b4\ub5a4 \ucc28\uc774\ub97c \ubb34\uc2dc\ud560\uc9c0\ub97c \ub3d9\uce58\uad00\uacc4\uc758 \ubc18\uc0ac\uc131, \ub300\uce6d\uc131, \ucd94\uc774\uc131\uc73c\ub85c \uaddc\uc728\ud55c\ub2e4.<\/li>\n<li><span class=\"defined\">\uacf5\ub9ac\ud654<\/span>\ub294 \ud5c8\uc6a9\ub418\ub294 \uad6c\uc870\uac00 \ub9cc\uc871\ud574\uc57c \ud560 \uc870\uac74\uc744 \uba85\uc2dc\ud55c\ub2e4. \uacf5\ub9ac\ub9cc\uc73c\ub85c \uc874\uc7ac\uac00 \uc790\ub3d9 \ubcf4\uc7a5\ub418\ub294 \uac83\uc740 \uc544\ub2c8\uba70, \ubaa8\ud615\uc744 \uc81c\uc2dc\ud558\uba74 \uadf8 \uc870\uac74\ub4e4\uc758 \uacf5\ub3d9 \ub9cc\uc871 \uac00\ub2a5\uc131\uc744 \ubcf4\uc77c \uc218 \uc788\ub2e4.<\/li>\n<li><span class=\"defined\">\ubcf4\ud3b8 \uc131\uc9c8\uc744 \uc0ac\uc6a9\ud55c \uc815\uc758<\/span>\ub294 \ub2e4\ub978 \ub300\uc0c1\ub4e4\uacfc\uc758 \uc0ac\uc0c1 \uad00\uacc4\ub97c \ud1b5\ud574 \ub300\uc0c1\uc744 \uc720\uc77c\ud55c \ub3d9\ud615\uc0ac\uc0c1\uae4c\uc9c0 \ud3ec\ud568\ud558\uc5ec \ud2b9\uc9d5\uc9d3\ub294\ub2e4.<\/li>\n<li><span class=\"defined\">\uc0ac\ub840\uc758 \ud1b5\ud569<\/span>\uc740 \uc11c\ub85c \ub2e4\ub978 \uc0ac\ub840\uac00 \uacf5\uc720\ud558\ub294 \uc5f0\uc0b0\uacfc \ubc95\uce59\uc744 \ucd94\ucd9c\ud558\ub418, \ud1b5\ud569 \uacfc\uc815\uc5d0\uc11c \ubb34\uc5c7\uc774 \ucd94\uac00\ub85c \uac00\uc815\ub418\ub294\uc9c0\ub3c4 \ub4dc\ub7ec\ub0b8\ub2e4.<\/li>\n<li><span class=\"defined\">\uc815\ub9ac\uc5d0\uc11c \uc815\uc758\uc758 \ud6c4\ubcf4\ub97c \uc5bb\uae30<\/span>\ub294 \uae30\uc874 \uc815\ub9ac\uc758 \uc870\uac74\uc774\ub098 \uacb0\ub860\uc744 \ub354 \ub113\uc740 \ub9e5\ub77d\uc5d0 \ub9de\uac8c \uc218\uc815\ud558\uace0 \ube44\uad50\ud558\uc5ec \uc0c8\ub85c\uc6b4 \uac1c\ub150\uc73c\ub85c \ub2e4\ub4ec\ub294\ub2e4.<\/li>\n<li><span class=\"defined\">\ub17c\uc7c1\uc744 \uacf5\ub9ac\uc801 \ud2c0\uacfc \ubd84\ub9ac\ud558\uae30<\/span>\ub294 \uc5ec\ub7ec \ud574\uc11d\uc774 \uacf5\uc720\ud560 \uacc4\uc0b0 \uaddc\uce59\uc744 \uace0\ub9bd\uc2dc\ud0a8\ub2e4. \uc989 \ub17c\uc7c1\uc744 \uacf5\ub9ac\uc801 \ud2c0\uacfc \ubd84\ub9ac\ud558\uae30\ub294 \uc5ec\ub7ec \ud574\uc11d\uc774 \uacf5\uc720\ud560 \uc218 \uc788\ub294 \ubcf4\ud3b8\uc801 \uacc4\uc0b0 \uaddc\uce59\uc744 \uba85\ud655\ud788 \uc815\ub9bd\ud574 \uc900\ub2e4.<\/li>\n<\/ul>\n<p>\uadf8\ub7ec\ubbc0\ub85c \u201c\ubb34\uc5c7\uc744 \ubc84\ub838\uace0 \ubb34\uc5c7\uc774 \ub0a8\uc558\ub294\uac00?\u201d\ub77c\ub294 \uc9c8\ubb38\uc740 \uc5ec\uc804\ud788 \uc720\uc775\ud558\uc9c0\ub9cc, \ub54c\ub85c\ub294 \u201c\ubb34\uc5c7\uc744 \uc0c8\ub85c \ub3c4\uc785\ud588\uace0 \ubb34\uc5c7\uc744 \ub3d9\uc77c\uc2dc\ud588\ub294\uac00?\u201d\ub3c4 \ud568\uaed8 \ubb3c\uc5b4\uc57c \ud55c\ub2e4.<\/p>\n<p>\uc148\ub3cc\uc5d0\uc11c\ub294 \uc0ac\ubb3c\uc758 \uc7ac\uc9c8\uacfc \uc218\ub7c9\uc774 \ubd84\ub9ac\ub418\uace0, \ubb38\uc790\ub300\uc218\uc5d0\uc11c\ub294 \ud2b9\uc815 \uc218\uce58 \ub300\uc2e0 \uc77c\ubc18\uc801\uc778 \uad00\uacc4\uac00 \ud45c\ud604\ub418\uc5c8\ub2e4. \uacf5\ub9ac\uc801 \ubc29\ubc95\uc5d0\uc11c\ub294 \ub300\uc0c1\uc758 \uc9c1\uad00\uc801 \ud574\uc11d\uacfc \uacf5\ub9ac\ub85c \ubcf4\uc874\ud560 \uad6c\uc870\uac00 \uad6c\ubcc4\ub418\uc5c8\ub2e4. \ubc94\uc8fc\ub860\uc5d0\uc11c\ub294 \ub0b4\ubd80 \uc6d0\uc18c\uac00 \uc5b8\uc81c\ub098 \u2018\ubaa8\uc870\ub9ac \uc9c0\uc6cc\uc9c0\ub294\u2019 \uac83\uc774 \uc544\ub2c8\ub77c, \uc120\ud0dd\ud55c \uc0ac\uc0c1\ub4e4\uc774 \ubcf4\uc874\ud558\ub294 \uad6c\uc870\uc640 \ub300\uc0c1 \uc0ac\uc774\uc758 \uad00\uacc4\uac00 \uc911\uc2ec\uc5d0 \ub193\uc600\ub2e4.<a class=\"math-abs-series-ref\" title=\"Saunders Mac Lane, Mathematics: Form and Function, Springer, 1986.\" href=\"#ref-MacLane1986\">[MacLane1986]<\/a> \uc704\uc0c1\uc218\ud559\uc740 \uc2e4\uc9c1\uc120\uc758 \uac70\ub9ac\ub9cc\uc744 \ubc84\ub9ac\uace0 \u2018\uc5f4\ub9bc \ud558\ub098\u2019\ub9cc \ub0a8\uae34 \uc774\ub860\uc774\ub77c\uae30\ubcf4\ub2e4, \uc5f4\ub9b0\uc9d1\ud569\uc774\ub098 \uadfc\ubc29\uc744 \uae30\ubcf8 \uc790\ub8cc\ub85c \uc0bc\uc544 \uc5f0\uc18d\uc131\uc744 \uc6d0\uc0c1\uc758 \uc5f4\ub9b0\uc131\uc73c\ub85c \uc77c\ubc18\ud654\ud55c\ub2e4. \ud655\ub960\ub860\uc5d0\uc11c\ub3c4 \\(P(\\Omega)=1\\) \ud558\ub098\ub9cc \ub0a8\ub294 \uac83\uc774 \uc544\ub2c8\ub77c, \uac00\uc0b0 \uac00\ubc95\uc131\uc744 \uac16\ub294 \ud655\ub960\uce21\ub3c4 \\(P\\) \uc804\uccb4\uac00 \ud615\uc2dd \uad6c\uc870\ub97c \uc774\ub8ec\ub2e4.<a class=\"math-abs-series-ref\" title=\"A. N. Kolmogorov, Grundbegriffe der Wahrscheinlichkeitsrechnung, Springer, 1933; English trans., Foundations of the Theory of Probability.\" href=\"#ref-Kolmogorov1933\">[Kolmogorov1933]<\/a><\/p>\n<p>\u2018\ucd94\uc0c1(\u62bd\u8c61, \uc0c1\uc744 \ubf51\uc544\ub0c4)\u2019\uacfc \u2018\uc0ac\uc0c1(\u6368\u8c61, \uc0c1\uc744 \ubc84\ub9bc)\u2019\uc758 \ub300\ube44\ub294 \uc774 \uacfc\uc815\uc744 \uc0dd\uac01\ud558\ub294 \uc778\uc0c1\uc801\uc778 \ucca0\ud559\uc801 \ube44\uc720\ub2e4. [\ub2e4\ub9cc \uc11c\ub85c \ub2e4\ub978 \ud55c\uc790\uc5b4\uc758 \ud480\uc774\uac00 \uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uc720\uc77c\ud55c \uc5ed\uc0ac\uc801 \uc815\uc758\ub97c \ud655\uc815\ud558\ub294 \uac83\uc740 \uc544\ub2c8\ub2e4. \uc218\ud559\uc758 \uc815\ud655\ud568\uc740 \uc5b4\uc6d0\ubcf4\ub2e4, \ub3d9\uc77c\uc131 \uae30\uc900, \uacf5\ub9ac, \uc0ac\uc0c1, \uc99d\uba85 \uaddc\uce59\uc744 \uacf5\uac1c\uc801\uc73c\ub85c \uba85\uc2dc\ud558\uace0 \uadf8 \uacb0\uacfc\ub97c \uac80\ud1a0\ud560 \uc218 \uc788\ub2e4\ub294 \ub370\uc11c \ub098\uc628\ub2e4.]<\/p>\n<h4>\uc555\ucd95\uacfc \uc21c\uc11c<\/h4>\n<p>\uc218\ud559\uad50\uc721\uc758 \uad00\uc810\uc5d0\uc11c \ucd94\uc0c1\ud654\ub97c <span class=\"defined\">\uc555\ucd95<\/span>(compression)\uc73c\ub85c \ubcf4\ub294 \uac83\uc740 \uc720\uc6a9\ud55c \uad00\uc810 \uc911 \ud558\ub098\uc774\ub2e4. \ubcf5\uc7a1\ud55c \uacfc\uc815\uc774 \uc775\uc219\ud574\uc9c0\uba74 \ud558\ub098\uc758 \uac1c\ub150\uc801 \ub2e8\uc704\ub85c \ub2e4\ub904\uc9c0\uace0, \uadf8 \ub2e8\uc704\uac00 \ub354 \ub192\uc740 \uc0ac\uace0\uc758 \uc7ac\ub8cc\uac00 \ub41c\ub2e4. \ub370\uc774\ube44\ub4dc \ud1a8(David Tall)\uc740 \uc218\ud559\uc801 \uc0ac\uace0\uc758 \ubc1c\ub2ec\uc5d0\uc11c \uc555\ucd95, \uc5f0\uacb0, \uac1c\ub150\uc758 \ub300\uc0c1\ud654\ub97c \uc911\uc694\ud55c \uacfc\uc815\uc73c\ub85c \ub2e4\ub8ec\ub2e4.<a class=\"math-abs-series-ref\" title=\"David Tall, How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics, Cambridge University Press, 2013.\" href=\"#ref-Tall2013\">[Tall2013]<\/a> <!-- \uadf8\ub7ec\ub098 \ucd94\uc0c1\ud654 \uc804\uccb4\uac00 \uace7 \uc555\ucd95\uc774\ub77c\ub294 \ub3d9\uc77c\uc131 \uba85\uc81c\uc774\uac70\ub098, \ubaa8\ub4e0 \ud559\uc2b5\uc790\uac00 \uac19\uc740 \uacbd\ub85c\ub97c \ubc1f\ub294\ub2e4\ub294 \ub73b\uc740 \uc544\ub2c8\ub2e4. --><\/p>\n<p>1960\ub144\ub300\uc758 \uc0c8\uc218\ud559 \uc6b4\ub3d9\uc740 \uc644\uc131\ub41c \uc9d1\ud569, \uad6c\uc870 \uc5b8\uc5b4\ub97c \ud559\uad50\uad50\uc721\uc5d0 \uc55e\uc138\uc6e0\ub2e4\ub294 \ube44\ud310\uc744 \ubc1b\uc558\uace0 \uc5ec\ub7ec \uc9c0\uc5ed\uc5d0\uc11c \uac15\ud55c \ubc18\ubc1c\uacfc \uc218\uc815\uc744 \uacaa\uc5c8\ub2e4. <!-- \ub2e4\ub9cc \uadf8\uac83\uc740 \uad6d\uac00, \uad50\uc721\uacfc\uc815, \ud559\ub144\ub9c8\ub2e4 \ubaa8\uc2b5\uc774 \ub2ec\ub790\ub358 \uad6d\uc81c\uc801 \uac1c\ud601\ub4e4\uc758 \ubb36\uc74c\uc774\uc5c8\uc73c\uba70, \uc138\uacc4 \uc804\uccb4\uac00 \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \uc2e4\ud328\ud55c \ub2e8\uc77c \uc2e4\ud5d8\uc740 \uc544\ub2c8\uc5c8\ub2e4. --> \uc774\ud6c4 \ud559\uad50\uc218\ud559\uc758 \ub0b4\uc6a9\uacfc \uc5b8\uc5b4\uc5d0 \ub0a8\uae34 \uc601\ud5a5\ub3c4 \uc801\uc9c0 \uc54a\ub2e4.<a class=\"math-abs-series-ref\" title=\"Jeremy Kilpatrick, \u201cThe New Math as an International Phenomenon,\u201d ZDM Mathematics Education 44, 2012, pp. 563\u2013571.\" href=\"#ref-Kilpatrick2012\">[Kilpatrick2012]<\/a><\/p>\n<p>\uc774 \uc5f0\uc7ac\ub294 \ubca1\ud130\uacf5\uac04, \uc704\uc0c1\uacf5\uac04, \uce21\ub3c4\uacf5\uac04\uc744 \uc644\uc131\ub41c \uacf5\ub9ac\ubd80\ud130 \uc81c\uc2dc\ud558\uae30\ubcf4\ub2e4, \uad6c\uccb4\uc801 \ubb38\uc81c\uc640 \uc5ed\uc0ac\uc801 \ub3d9\uae30\ub97c \uac70\uccd0 \uacf5\ub9ac\ub85c \ub098\uc544\uac00\ub294 \ubc29\uc2dd\uc73c\ub85c \uc11c\uc220\ud588\ub2e4. \ub17c\ub9ac\uc801 \uc804\uac1c \uc21c\uc11c, \uc2e4\uc81c \uc5ed\uc0ac\uc758 \uc21c\uc11c, \ud559\uc2b5\uc5d0 \ud6a8\uacfc\uc801\uc778 \uc21c\uc11c\ub294 \uc11c\ub85c \ub2e4\ub97c \uc218 \uc788\ub2e4.<!-- \uadf8\ub7ec\ub098 \ubaa8\ub4e0 \uac1c\ub150\uc774 \ubc18\ub4dc\uc2dc \u2018\ubaa8\uc21c\uc744 \uba3c\uc800 \uacaa\uc740 \ub4a4 \uacf5\ub9ac\uac00 \ud0c4\uc0dd\ud558\ub294\u2019 \ub3d9\uc77c\ud55c \uc5ed\uc0ac\uc801 \ub3c4\uc2dd\uc744 \ub530\ub978\ub2e4\uace0 \ub2e8\uc815\ud560 \uc218\ub294 \uc5c6\ub2e4. \ub3c5\uc790\uc758 \ubc30\uacbd\uacfc \ud559\uc2b5 \ubaa9\ud45c\uc5d0 \ub530\ub77c \uc0ac\ub840\uc640 \uc815\uc758 \uc0ac\uc774\ub97c \uc624\uac00\ub294 \uad6c\uc131\uc774 \ub354 \uc801\uc808\ud560 \uc218 \uc788\ub2e4. --><a class=\"math-abs-series-ref\" title=\"David Tall, How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics, Cambridge University Press, 2013.\" href=\"#ref-Tall2013\">[Tall2013]<\/a><\/p>\n<p><!--\n\n\n<h4>\ub354 \uc77d\uc744\uac70\ub9ac<\/h4>\n\n\n\n\n\n<p>\uc774 \uc5f0\uc7ac\uc5d0\uc11c \ub2e4\ub8ec \ub0b4\uc6a9\uc744 \ub354 \uae4a\uace0 \ub113\uac8c \ud0d0\uad6c\ud558\uace0 \uc2f6\uc740 \ub3c5\uc790\uc5d0\uac8c \ub2e4\uc74c \ubb38\ud5cc\uc744 \uad8c\ud55c\ub2e4.<\/p>\n\n\n\n\n\n<ul>\n    \n\n<li>\ubaa8\ub9ac\uc2a4 \ud074\ub77c\uc778(Morris Kline)\uc758 \u300e<b>Mathematical Thought from Ancient to Modern Times<\/b>\u300f: \uace0\ub300\ubd80\ud130 20\uc138\uae30 \ucd08\uae4c\uc9c0 \uc218\ud559\uc758 \uc8fc\uc694 \uac1c\ub150\uacfc \ubb38\uc81c\ub97c \ud3ed\ub113\uac8c \uc11c\uc220\ud55c \ud1b5\uc0ac\ub2e4.<a class=\"math-abs-series-ref\" title=\"Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1972; three-volume paperback ed., 1990.\" href=\"#ref-Kline1972\">[Kline1972]<\/a><\/li>\n\n\n    \n\n<li>\ub808\uc624 \ucf54\ub9ac(Leo Corry)\uc758 \u300e<b>Modern Algebra and the Rise of Mathematical Structures<\/b>\u300f: \ud604\ub300 \ub300\uc218\ud559\uc5d0\uc11c \u2018\uad6c\uc870\u2019 \uac1c\ub150\uc774 \ud615\uc131\ub418\ub294 \uacfc\uc815\uc744 \ud310\ub370\ub974\ubc14\ub974\ub358\uacfc \ubd80\ub974\ubc14\ud0a4 \ub4f1\uc744 \uc911\uc2ec\uc73c\ub85c \ubd84\uc11d\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Leo Corry, Modern Algebra and the Rise of Mathematical Structures, 2nd revised ed., Birkh\u00e4user, 2004.\" href=\"#ref-Corry2004\">[Corry2004]<\/a><\/li>\n\n\n    \n\n<li>\uc190\ub354\uc2a4 \ub9e4\ud074\ub808\uc778(Saunders Mac Lane)\uc758 \u300e<b>Mathematics: Form and Function<\/b>\u300f: \ubc94\uc8fc\ub860\uc758 \uacf5\ub3d9 \ucc3d\uc2dc\uc790\uac00 \uc218\ud559\uc758 \ud615\uc2dd\uacfc \uae30\ub2a5, \uac1c\ub150\uc758 \uc870\uc9c1 \ubc29\uc2dd\uc744 \uc131\ucc30\ud55c \ucc45\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"Saunders Mac Lane, Mathematics: Form and Function, Springer, 1986.\" href=\"#ref-MacLane1986\">[MacLane1986]<\/a><\/li>\n\n\n    \n\n<li>\uc81c\ub7ec\ubbf8 \uadf8\ub808\uc774(Jeremy Gray)\uc758 \u300e<b>The Real and the Complex: A History of Analysis in the Nineteenth Century<\/b>\u300f: \ub77c\uadf8\ub791\uc8fc\uc640 \ud478\ub9ac\uc5d0\uc5d0\uc11c \uc9d1\ud569\ub860\uacfc \uae30\ucd08\ub860\uc5d0 \uc774\ub974\uae30\uae4c\uc9c0 19\uc138\uae30 \uc2e4\ud574\uc11d\uacfc \ubcf5\uc18c\ud574\uc11d\uc758 \uc804\uac1c\ub97c \ucd94\uc801\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Jeremy Gray, The Real and the Complex: A History of Analysis in the 19th Century, Springer, 2015.\" href=\"#ref-Gray2015\">[Gray2015]<\/a><\/li>\n\n\n    \n\n<li>\ub370\uc774\ube44\ub4dc \ud1a8\uc758 \u300e<b>How Humans Learn to Think Mathematically<\/b>\u300f: \uc218\ud559\uc801 \uc0ac\uace0\uc758 \ubc1c\ub2ec, \uc555\ucd95, \uc5f0\uacb0, \uac1c\ub150\uc758 \ub300\uc0c1\ud654\ub97c \uc885\ud569\uc801\uc73c\ub85c \ub2e4\ub8ec\ub2e4.<a class=\"math-abs-series-ref\" title=\"David Tall, How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics, Cambridge University Press, 2013.\" href=\"#ref-Tall2013\">[Tall2013]<\/a><\/li>\n\n\n    \n\n<li>\uc2a4\ud29c\uc5b4\ud2b8 \uc154\ud53c\ub85c\uc758 \u300e<b>Thinking about Mathematics<\/b>\u300f: \ud50c\ub77c\ud1a4\uc8fc\uc758, \ud615\uc2dd\uc8fc\uc758, \uad6c\uc870\uc8fc\uc758, \ub17c\ub9ac\uc8fc\uc758 \ub4f1 \ud604\ub300 \uc218\ub9ac\ucca0\ud559\uc758 \uc8fc\uc694 \uc785\uc7a5\uc744 \uc548\ub0b4\ud55c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Stewart Shapiro, Thinking about Mathematics: The Philosophy of Mathematics, Oxford University Press, 2000.\" href=\"#ref-Shapiro2000\">[Shapiro2000]<\/a><\/li>\n\n\n    \n\n<li>\uc70c\ub9ac\uc5c4 \uc11c\uc2a4\ud134(William Thurston)\uc758 \u300c<b>On Proof and Progress in Mathematics<\/b>\u300d\uc640 \ud2f0\uba38\uc2dc \uac00\uc6cc\uc2a4(Timothy Gowers)\uc758 \u300c<b>The Two Cultures of Mathematics<\/b>\u300d: \uc99d\uba85, \uc774\ud574, \ubb38\uc81c \ud574\uacb0, \uc774\ub860 \uad6c\ucd95\uc744 \uc5f0\uad6c\uc790\uc758 \uad00\uc810\uc5d0\uc11c \uc131\ucc30\ud55c \uae00\uc774\ub2e4.<a class=\"math-abs-series-ref\" title=\"William P. Thurston, \u201cOn Proof and Progress in Mathematics,\u201d Bulletin of the American Mathematical Society 30(2), 1994, pp. 161\u2013177.\" href=\"#ref-Thurston1994\">[Thurston1994]<\/a><a class=\"math-abs-series-ref\" title=\"Timothy Gowers, \u201cThe Two Cultures of Mathematics,\u201d in Mathematics: Frontiers and Perspectives, American Mathematical Society, 2000, pp. 65\u201378.\" href=\"#ref-Gowers2000\">[Gowers2000]<\/a><\/li>\n\n\n<\/ul>\n\n\n--><\/p>\n<h4>\ub9fa\uc73c\uba70<\/h4>\n<p>\uc774 \uc5f0\uc7ac\ub294 \u201c\uc65c \uc218\ud559\uc5d0\uc11c \u2018\ucd94\uc0c1\uc801\u2019\uc774\ub77c\ub294 \ub9d0\uc740 \ub9c9\uc5f0\ud568\uacfc \ubc18\ub300\ub85c \uc815\ubc00\ud568\uc744 \ub73b\ud558\ub294\uac00?\u201d\ub77c\ub294 \uc9c8\ubb38\uc5d0\uc11c \ucd9c\ubc1c\ud588\ub2e4. \uc6b0\ub9ac\ub294 \uc218\ucc9c \ub144\uc758 \uc218\ud559\uc0ac\uc5d0\uc11c \uc0ac\ubb3c\uacfc \uc218\ub7c9\uc758 \ubd84\ub9ac, \uadf8\ub9bc\uacfc \uc99d\uba85\uc758 \uad6c\ubcc4, \ubb38\uc790\ub300\uc218, \uacf5\ub9ac\uc801 \uad6c\uc870, \ubc94\uc8fc\uc640 \uc0ac\uc0c1, \ubca1\ud130\uacf5\uac04, \uc704\uc0c1\uacf5\uac04, \ud655\ub960\uacf5\uac04\uc774 \ud615\uc131\ub418\ub294 \uc5ec\ub7ec \uc7a5\uba74\uc744 \uc0b4\ud3b4\ubcf4\uc558\ub2e4.<\/p>\n<p>\uadf8 \uc7a5\uba74\ub4e4\uc744 \ud558\ub098\uc758 \uacf5\uc2dd\uc73c\ub85c \ud658\uc6d0\ud560 \uc218\ub294 \uc5c6\ub2e4. \uc5b4\ub5a4 \ucd94\uc0c1\ud654\ub294 \uc18d\uc131\uc744 \ub35c\uc5b4 \ub0b4\uace0, \uc5b4\ub5a4 \ucd94\uc0c1\ud654\ub294 \uc11c\ub85c \ub2e4\ub978 \ub300\uc0c1\uc744 \ub3d9\uc77c\uc2dc\ud558\uba70, \uc5b4\ub5a4 \ucd94\uc0c1\ud654\ub294 \uacf5\ud1b5 \uad6c\uc870\ub97c \uc0c8 \uc5b8\uc5b4\ub85c \ub3c4\uc785\ud55c\ub2e4. \uacf5\ud1b5\uc810\uc774 \uc788\ub2e4\uba74 \ub300\uc0c1\uc758 \uc7ac\ub8cc\ub9cc \ubb3b\uc9c0 \uc54a\uace0, \uc5b4\ub5a4 \ucc28\uc774\ub97c \ubb34\uc2dc\ud558\uba70 \uc5b4\ub5a4 \ub3d9\uc77c\uc131, \uc5f0\uc0b0, \uad00\uacc4, \ubc95\uce59\uc744 \ubcf4\uc874\ud560\uc9c0\ub97c \uba85\uc2dc\ud55c\ub2e4\ub294 \ub370 \uc788\ub2e4.<\/p>\n<p>\uc544\ub9ac\uc2a4\ud1a0\ud154\ub808\uc2a4\ub294 \uc218\ud559\uc801 \ub300\uc0c1\uc744 \uac10\uac01\uc801 \uc0ac\ubb3c\uc5d0\uc11c \ud2b9\uc815 \uc18d\uc131\uc744 \ub5bc\uc5b4 \ub0b4\uc5b4 \uace0\ucc30\ud558\ub294 \uac83\uacfc \uad00\ub828\ud574 \u2018\uc81c\uac70\uc5d0\uc11c \ub098\uc628 \uac83\ub4e4\u2019(<i>ta ex aphairese\u014ds<\/i>)\uc774\ub77c\ub294 \ud45c\ud604\uc744 \uc0ac\uc6a9\ud588\ub2e4. <!-- \uadf8\ub7ec\ub098 \uadf8\uac00 \uc624\ub298\ub0a0\uc758 \uc218\ud559\uc801 \ucd94\uc0c1\ud654 \uac1c\ub150\uc744 \ud63c\uc790 \ubc1c\uba85\ud558\uace0 \ud558\ub098\uc758 \uace0\uc815\ub41c \ubc29\ubc95\ub860\uc73c\ub85c \uba85\uba85\ud588\ub2e4\uace0 \ub2e8\uc815\ud574\uc11c\ub294 \uc548 \ub41c\ub2e4.<a class=\"math-abs-series-ref\" title=\"Henry Mendell, \u201cAristotle and Mathematics,\u201d Stanford Encyclopedia of Philosophy.\" href=\"#ref-Mendell2016\">[Mendell2016]<\/a> --> \uc774\ud6c4\uc758 \uc218\ud559\uc740 \uc774 \uc624\ub798\ub41c \uad00\uc810\uc744 \uacf5\ub9ac, \uad6c\uc870, \uc0ac\uc0c1, \ud615\uc2dd \uc99d\uba85\uc774\ub77c\ub294 \ub9e4\uc6b0 \ub2e4\uc591\ud55c \ubc29\ubc95\uc73c\ub85c \ud655\uc7a5\ud588\ub2e4.<\/p>\n<p>\ubb34\uc5c7\uc744 \uad6c\ubcc4\ud558\uace0 \ubb34\uc5c7\uc744 \ub3d9\uc77c\uc2dc\ud560\uc9c0, \ubb34\uc5c7\uc744 \uac00\uc815\ud558\uace0 \ubb34\uc5c7\uc744 \uc99d\uba85\ud560\uc9c0\ub97c \uacf5\uac1c\uc801\uc778 \uc5b8\uc5b4\ub85c \uba85\uc2dc\ud558\ub294 \uc77c\uc740 \uc218\ud559\uc758 \uc5c4\ubc00\uc131\uacfc \uc774\ub3d9 \uac00\ub2a5\uc131\uc744 \ub0b3\ub294 \uc911\uc694\ud55c \uc6d0\ucc9c\uc774\ub2e4. <!-- \uc774\uac83\uc774 \uc218\ud559\uc801 \ucd94\uc0c1\ud654\ub97c \ubaa8\ub4e0 \ud559\ubb38\uc758 \uc720\uc77c\ud55c \u2018\uc808\ub300 \uc9c4\ub9ac\u2019\ub85c \ub9cc\ub4dc\ub294 \uac83\uc740 \uc544\ub2c8\uc9c0\ub9cc, \uc11c\ub85c \ub2e4\ub978 \ub300\uc0c1\uc5d0\uc11c \uac19\uc740 \uad6c\uc870\ub97c \ubc1c\uacac\ud558\uace0 \uadf8 \uacb0\uacfc\ub97c \uac80\uc99d \uac00\ub2a5\ud558\uac8c \uc804\ub2ec\ud558\ub294 \uac15\ub825\ud55c \ud798\uc744 \uc124\uba85\ud574 \uc900\ub2e4. --><\/p>\n<h4>\ucc38\uace0\ubb38\ud5cc<\/h4>\n<ul>\n<li id=\"ref-Weisberg2013\">[Weisberg2013] Michael Weisberg, <i>Simulation and Similarity: Using Models to Understand the World<\/i>, Oxford University Press, 2013. <a href=\"https:\/\/global.oup.com\/academic\/product\/simulation-and-similarity-9780199933662\">https:\/\/global.oup.com\/academic\/product\/simulation-and-similarity-9780199933662<\/a>.<\/li>\n<li id=\"ref-BeaneyAnalysis\">[BeaneyAnalysis] Michael Beaney, \u201cAnalysis,\u201d supplement \u201cEarly Modern Conceptions of Analysis,\u201d <i>Stanford Encyclopedia of Philosophy<\/i>, Leibniz \uc808. <a href=\"https:\/\/plato.stanford.edu\/entries\/analysis\/s4.html\">https:\/\/plato.stanford.edu\/entries\/analysis\/s4.html<\/a>.<\/li>\n<li id=\"ref-Zach2023\">[Zach2023] Richard Zach, \u201cHilbert\u2019s Program,\u201d <i>Stanford Encyclopedia of Philosophy<\/i>. <a href=\"https:\/\/plato.stanford.edu\/entries\/hilbert-program\/\">https:\/\/plato.stanford.edu\/entries\/hilbert-program\/<\/a>.<\/li>\n<li id=\"ref-Godel1931\">[Godel1931] Kurt G\u00f6del, \u201c\u00dcber formal unentscheidbare S\u00e4tze der Principia Mathematica und verwandter Systeme I,\u201d <i>Monatshefte f\u00fcr Mathematik und Physik<\/i> 38, 1931, pp. 173\u2013198. <a href=\"https:\/\/doi.org\/10.1007\/BF01700692\">DOI: 10.1007\/BF01700692<\/a>.<\/li>\n<li id=\"ref-MathlibCommunity2020\">[MathlibCommunity2020] The mathlib Community, \u201cThe Lean Mathematical Library,\u201d <i>Proceedings of CPP 2020<\/i>, 2020, pp. 367\u2013381. <a href=\"https:\/\/doi.org\/10.1145\/3372885.3373824\">DOI: 10.1145\/3372885.3373824<\/a>.<\/li>\n<li id=\"ref-Corry2004\">[Corry2004] Leo Corry, <i>Modern Algebra and the Rise of Mathematical Structures<\/i>, 2nd revised ed., Birkh\u00e4user, 2004. <a href=\"https:\/\/doi.org\/10.1007\/978-3-0348-7917-0\">DOI: 10.1007\/978-3-0348-7917-0<\/a>.<\/li>\n<li id=\"ref-MacLane1986\">[MacLane1986] Saunders Mac Lane, <i>Mathematics: Form and Function<\/i>, Springer, 1986. <a href=\"https:\/\/doi.org\/10.1007\/978-1-4612-4872-9\">DOI: 10.1007\/978-1-4612-4872-9<\/a>.<\/li>\n<li id=\"ref-RamanSundstrom2015\">[RamanSundstrom2015] Manya Raman-Sundstr\u00f6m, \u201cA Pedagogical History of Compactness,\u201d <i>American Mathematical Monthly<\/i> 122(7), 2015, pp. 619\u2013635. <a href=\"https:\/\/doi.org\/10.4169\/amer.math.monthly.122.7.619\">DOI: 10.4169\/amer.math.monthly.122.7.619<\/a>.<\/li>\n<li id=\"ref-Kolmogorov1933\">[Kolmogorov1933] A. N. Kolmogorov, <i>Grundbegriffe der Wahrscheinlichkeitsrechnung<\/i>, Springer, 1933; English trans., <i>Foundations of the Theory of Probability<\/i>. <a href=\"https:\/\/doi.org\/10.1007\/978-3-642-49888-6\">DOI: 10.1007\/978-3-642-49888-6<\/a>.<\/li>\n<li id=\"ref-Hajek2023\">[Hajek2023] Alan H\u00e1jek, \u201cInterpretations of Probability,\u201d <i>Stanford Encyclopedia of Philosophy<\/i>. <a href=\"https:\/\/plato.stanford.edu\/entries\/probability-interpret\/\">https:\/\/plato.stanford.edu\/entries\/probability-interpret\/<\/a>.<\/li>\n<li id=\"ref-Benacerraf1965\">[Benacerraf1965] Paul Benacerraf, \u201cWhat Numbers Could Not Be,\u201d <i>The Philosophical Review<\/i> 74(1), 1965, pp. 47\u201373. <a href=\"https:\/\/doi.org\/10.2307\/2183530\">DOI: 10.2307\/2183530<\/a>.<\/li>\n<li id=\"ref-Benacerraf1973\">[Benacerraf1973] Paul Benacerraf, \u201cMathematical Truth,\u201d <i>The Journal of Philosophy<\/i> 70(19), 1973, pp. 661\u2013679. <a href=\"https:\/\/doi.org\/10.2307\/2025075\">DOI: 10.2307\/2025075<\/a>.<\/li>\n<li id=\"ref-ReckSchiemer2021\">[ReckSchiemer2021] Erich H. Reck and Georg Schiemer, \u201cStructuralism in the Philosophy of Mathematics,\u201d <i>Stanford Encyclopedia of Philosophy<\/i>. <a href=\"https:\/\/plato.stanford.edu\/entries\/structuralism-mathematics\/\">https:\/\/plato.stanford.edu\/entries\/structuralism-mathematics\/<\/a>.<\/li>\n<li id=\"ref-Shapiro1997\">[Shapiro1997] Stewart Shapiro, <i>Philosophy of Mathematics: Structure and Ontology<\/i>, Oxford University Press, 1997. <a href=\"https:\/\/doi.org\/10.1093\/0195139305.001.0001\">DOI: 10.1093\/0195139305.001.0001<\/a>.<\/li>\n<li id=\"ref-Hellman1989\">[Hellman1989] Geoffrey Hellman, <i>Mathematics without Numbers: Towards a Modal-Structural Interpretation<\/i>, Oxford University Press, 1989. <a href=\"https:\/\/doi.org\/10.1093\/0198240341.001.0001\">DOI: 10.1093\/0198240341.001.0001<\/a>.<\/li>\n<li id=\"ref-Frege1884\">[Frege1884] Gottlob Frege, <i>Die Grundlagen der Arithmetik<\/i>, Wilhelm Koebner, 1884, \ud2b9\ud788 \u00a7\u00a756, 63, 68. <a href=\"https:\/\/www.gutenberg.org\/ebooks\/48312\">https:\/\/www.gutenberg.org\/ebooks\/48312<\/a>.<\/li>\n<li id=\"ref-Frege1893\">[Frege1893] Gottlob Frege, <i>Grundgesetze der Arithmetik<\/i>, Vols. I\u2013II, 1893\/1903; Philip A. 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Hamming, \u201cThe Unreasonable Effectiveness of Mathematics,\u201d <i>American Mathematical Monthly<\/i> 87(2), 1980, pp. 81\u201390. <a href=\"https:\/\/doi.org\/10.1080\/00029890.1980.11994966\">DOI: 10.1080\/00029890.1980.11994966<\/a>.<\/li>\n<li id=\"ref-Tegmark2008\">[Tegmark2008] Max Tegmark, \u201cThe Mathematical Universe,\u201d <i>Foundations of Physics<\/i> 38, 2008, pp. 101\u2013150. <a href=\"https:\/\/doi.org\/10.1007\/s10701-007-9186-9\">DOI: 10.1007\/s10701-007-9186-9<\/a>.<\/li>\n<li id=\"ref-Tall2013\">[Tall2013] David Tall, <i>How Humans Learn to Think Mathematically: Exploring the Three Worlds of Mathematics<\/i>, Cambridge University Press, 2013. <a href=\"https:\/\/doi.org\/10.1017\/CBO9781139565202\">DOI: 10.1017\/CBO9781139565202<\/a>.<\/li>\n<li id=\"ref-Kilpatrick2012\">[Kilpatrick2012] Jeremy Kilpatrick, \u201cThe New Math as an International Phenomenon,\u201d <i>ZDM Mathematics Education<\/i> 44, 2012, pp. 563\u2013571. <a href=\"https:\/\/doi.org\/10.1007\/s11858-012-0393-2\">DOI: 10.1007\/s11858-012-0393-2<\/a>.<\/li>\n<li id=\"ref-Kline1972\">[Kline1972] Morris Kline, <i>Mathematical Thought from Ancient to Modern Times<\/i>, Oxford University Press, 1972; three-volume paperback ed., 1990. <a href=\"https:\/\/global.oup.com\/academic\/product\/mathematical-thought-from-ancient-to-modern-times-volume-1-9780195061352\">https:\/\/global.oup.com\/academic\/product\/mathematical-thought-from-ancient-to-modern-times-volume-1-9780195061352<\/a>.<\/li>\n<li id=\"ref-Gray2015\">[Gray2015] Jeremy Gray, <i>The Real and the Complex: A History of Analysis in the 19th Century<\/i>, Springer, 2015. <a href=\"https:\/\/doi.org\/10.1007\/978-3-319-23715-2\">DOI: 10.1007\/978-3-319-23715-2<\/a>.<\/li>\n<li id=\"ref-Shapiro2000\">[Shapiro2000] Stewart Shapiro, <i>Thinking about Mathematics: The Philosophy of Mathematics<\/i>, Oxford University Press, 2000. <a href=\"https:\/\/global.oup.com\/academic\/product\/thinking-about-mathematics-9780192893062\">https:\/\/global.oup.com\/academic\/product\/thinking-about-mathematics-9780192893062<\/a>.<\/li>\n<li id=\"ref-Thurston1994\">[Thurston1994] William P. 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Norton, \u201cHow Einstein Found His Field Equations: 1912\u20131915,\u201d <i>Historical Studies in the Physical Sciences<\/i> 14(2), 1984, pp. 253\u2013316. <a href=\"https:\/\/doi.org\/10.2307\/27757535\">DOI: 10.2307\/27757535<\/a>.<\/li>\n<li id=\"ref-Peacock1845\">[Peacock1845] George Peacock, <i>A Treatise on Algebra<\/i>, Vol. II: <i>Symbolical Algebra and Its Applications to the Geometry of Position<\/i>, Cambridge University Press, 1845, \ud2b9\ud788 p. 59. <a href=\"https:\/\/books.google.co.uk\/books?id=1OcGAAAAYAAJ\">https:\/\/books.google.co.uk\/books?id=1OcGAAAAYAAJ<\/a>.<\/li>\n<li id=\"ref-Hamilton1847\">[Hamilton1847] William Rowan Hamilton, \u201cOn Quaternions,\u201d <i>Proceedings of the Royal Irish Academy<\/i> 3, 1847, pp. 1\u201316. <a href=\"https:\/\/www.maths.tcd.ie\/pub\/HistMath\/People\/Hamilton\/Quatern2\/Quatern2.pdf\">https:\/\/www.maths.tcd.ie\/pub\/HistMath\/People\/Hamilton\/Quatern2\/Quatern2.pdf<\/a>.<\/li>\n<li id=\"ref-EilenbergMacLane1945\">[EilenbergMacLane1945] Samuel Eilenberg and Saunders Mac Lane, \u201cGeneral Theory of Natural Equivalences,\u201d <i>Transactions of the American Mathematical Society<\/i> 58(2), 1945, pp. 231\u2013294. <a href=\"https:\/\/doi.org\/10.1090\/S0002-9947-1945-0013131-6\">DOI: 10.1090\/S0002-9947-1945-0013131-6<\/a>.<\/li>\n<li id=\"ref-Kleiner1986\">[Kleiner1986] Israel Kleiner, \u201cThe Evolution of Group Theory: A Brief Survey,\u201d <i>Mathematics Magazine<\/i> 59(4), 1986, pp. 195\u2013215. <a href=\"https:\/\/doi.org\/10.2307\/2690312\">DOI: 10.2307\/2690312<\/a>.<\/li>\n<\/ul>\n<h4>\uc800\uc791\uad8c<\/h4>\n<p>\uc774\uc2ac\ube44, 2026. designeralice\uff20daum.net.<\/p>\n<div class=\"math-abs-series-contents\">\n<p class=\"math-abs-series-menu-title\"><a href=\"..\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654<\/a><\/p>\n<ol class=\"math-abs-series-menu-list\">\n        <!-- \ud604\uc7ac \ud398\uc774\uc9c0\uc5d0 \ud574\ub2f9\ud558\ub294 li \ud0dc\uadf8\uc5d0 class=\"math-abs-series-current-page\" \uc18d\uc131 \ucd94\uac00 --><\/p>\n<li><a href=\"..\/math-abstraction-01-essence\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uae30\ubcf8 \uac1c\ub150<\/a><\/li>\n<li><a href=\"..\/math-abstraction-02-implicit-era\/\">\ucd08\uae30 \uc218\ud559\uc5d0\uc11c\uc758 \uc554\ubb35\uc801 \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-03-algebraic-symbols\/\">\ub300\uc218\uc801 \uae30\ud638\uc640 \uc5f0\uc0b0 \ubc95\uce59<\/a><\/li>\n<li><a href=\"..\/math-abstraction-04-axiomatic-method\/\">\uacf5\ub9ac\uc801 \ubc29\ubc95\uc5d0 \uc758\ud55c \ucd94\uc0c1\ud654<\/a><\/li>\n<li><a href=\"..\/math-abstraction-05-mathematical-structures\/\">\uc218\ud559\uc801 \uad6c\uc870\uc640 \ubc94\uc8fc\ub860<\/a><\/li>\n<li><a href=\"..\/math-abstraction-06-vector-spaces\/\">\ubca1\ud130\uacf5\uac04\uacfc \uc120\ud615 \uad6c\uc870<\/a><\/li>\n<li><a href=\"..\/math-abstraction-07-topological-spaces\/\">\uac70\ub9ac\uacf5\uac04\uacfc \uc704\uc0c1\uacf5\uac04<\/a><\/li>\n<li><a href=\"..\/math-abstraction-08-measure-spaces\/\">\uce21\ub3c4\uacf5\uac04\uacfc \ud655\ub960\uacf5\uac04<\/a><\/li>\n<li><a href=\"..\/math-abstraction-09-cognitive-process\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \uc778\uc9c0\uc640 \ud559\uc2b5<\/a><\/li>\n<li><a href=\"..\/math-abstraction-10-optimal-generality\/\">\ud604\ub300 \uc218\ud559 \uc5f0\uad6c\uc5d0\uc11c\uc758 \ucd94\uc0c1\ud654<\/a><\/li>\n<li class=\"math-abs-series-current-page\"><a href=\"..\/math-abstraction-11-topography\/\">\uc218\ud559\uc801 \ucd94\uc0c1\ud654\uc758 \ubc29\ubc95\uacfc \ucca0\ud559<\/a><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p><!-- class=\"math-abs-series\" --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>10\ubd80\uc758 \ub9d0\ubbf8\uc5d0\uc11c \uc6b0\ub9ac\ub294 \uc138 \uac00\uc9c0 \ubb35\uc9c1\ud55c \uc9c8\ubb38\uc744 \ub0a8\uacbc\ub2e4. \ucd94\uc0c1\ud654\uc640 \uc77c\ubc18\ud654, \uc774\uc0c1\ud654, \ud615\uc2dd\ud654\ub294 \uc5b4\ub5bb\uac8c \uad6c\ubd84\ub418\ub294\uac00? 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