{"id":1025,"date":"2020-02-01T07:00:00","date_gmt":"2020-02-01T00:00:00","guid":{"rendered":"https:\/\/www.truyenthong.edu.vn\/?p=1025"},"modified":"2020-02-01T07:00:00","modified_gmt":"2020-02-01T00:00:00","slug":"dinh-ly-bat-toan-cua-godel-kham-pha-toan-hoc-so-1-trong-the-ky-20","status":"publish","type":"post","link":"https:\/\/truyenthong.edu.vn\/sanpham\/2020\/02\/01\/dinh-ly-bat-toan-cua-godel-kham-pha-toan-hoc-so-1-trong-the-ky-20\/","title":{"rendered":"\u0110\u1ecbnh l\u00fd B\u1ea5t to\u00e0n c\u1ee7a G\u00f6del: Kh\u00e1m ph\u00e1 To\u00e1n h\u1ecdc s\u1ed1 1 trong th\u1ebf k\u1ef7 20"},"content":{"rendered":"\n
\"Perry<\/a><\/figure><\/div>\n\n\n\n

\u201c\u0110\u1ecbnh l\u00fd B\u1ea5t to\u00e0n c\u1ee7a G\u00f6del: Kh\u00e1m ph\u00e1 To\u00e1n h\u1ecdc s\u1ed1 1 trong th\u1ebf k\u1ef7 20\u201d <\/strong>l\u00e0 m\u1ed9t b\u00e0i gi\u1ea3ng c\u1ee7a Perry Marshall.<\/strong> D\u01b0\u1edbi \u0111\u00e2y l\u00e0 b\u1ea3n l\u01b0\u1ee3c d\u1ecbch c\u1ee7a Ph\u1ea1m Vi\u1ec7t H\u01b0ng<\/strong>.<\/p>\n\n\n\n

Abstract:<\/strong> Gottfried Leibniz<\/strong> once said: \u201cWithout mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything.\u201d. Quoting Leibniz, Perry Marshall<\/strong> leads us to the world of Maths and Philosophy, where we can see more clearly the truth. That is the aim of his lecture: \u201cG\u00f6del\u2019s Incompleteness Theorem: The #1 Mathematical Discovery of the 20th Century<\/strong>\u201d.<\/p>\n\n\n\n\n\n\n\n

L\u1eddi d\u1eabn c\u1ee7a ng\u01b0\u1eddi d\u1ecbch:<\/strong>
Gottfried Leibniz<\/strong> c\u00f3 l\u1ea7n n\u00f3i: \u201cKh\u00f4ng c\u00f3 to\u00e1n h\u1ecdc ch\u00fang ta kh\u00f4ng th\u1ec3 \u0111i s\u00e2u v\u00e0o tri\u1ebft h\u1ecdc. Kh\u00f4ng c\u00f3 tri\u1ebft h\u1ecdc ch\u00fang ta kh\u00f4ng th\u1ec3 \u0111i s\u00e2u v\u00e0o to\u00e1n h\u1ecdc. Kh\u00f4ng c\u00f3 c\u1ea3 hai ch\u00fang ta kh\u00f4ng th\u1ec3 \u0111i s\u00e2u v\u00e0o b\u1ea5t c\u1ee9 th\u1ee9 g\u00ec\u201d. D\u1eabn l\u1eddi Leibniz, Perry Marshall<\/strong> \u0111\u01b0a ch\u00fang ta v\u00e0o th\u1ebf gi\u1edbi c\u1ee7a To\u00e1n h\u1ecdc v\u00e0 Tri\u1ebft h\u1ecdc, \u1edf \u0111\u00f3 ch\u00fang ta c\u00f3 th\u1ec3 th\u1ea5y r\u00f5 h\u01a1n ch\u00e2n l\u00fd, bi\u1ebft \u0111\u00e2u l\u00e0 s\u1ef1 th\u1eadt. \u0110\u00f3 l\u00e0 m\u1ee5c \u0111\u00edch b\u00e0i gi\u1ea3ng c\u1ee7a \u00f4ng: \u201c\u0110\u1ecbnh l\u00fd B\u1ea5t to\u00e0n c\u1ee7a G\u00f6del: Kh\u00e1m ph\u00e1 To\u00e1n h\u1ecdc s\u1ed1 1 c\u1ee7a th\u1ebf k\u1ef7 20\u201d<\/strong>\u2026.<\/p>\n\n\n\n

\u0110\u1ecaNH L\u00dd B\u1ea4T TO\u00c0N C\u1ee6A G\u00d6DEL: KH\u00c1M PH\u00c1 TO\u00c1N H\u1eccC S\u1ed0 I C\u1ee6A TH\u1ebe K\u1ef6 XX<\/strong><\/p>\n\n\n\n

B\u00e0i gi\u1ea3ng c\u1ee7a Perry Marshall<\/strong><\/em><\/p>\n\n\n\n

Gottfried Leibniz:<\/strong>
\u201cKh\u00f4ng c\u00f3 to\u00e1n h\u1ecdc ch\u00fang ta kh\u00f4ng th\u1ec3 \u0111i s\u00e2u v\u00e0o tri\u1ebft h\u1ecdc. Kh\u00f4ng c\u00f3 tri\u1ebft h\u1ecdc ch\u00fang ta kh\u00f4ng th\u1ec3 \u0111i s\u00e2u v\u00e0o to\u00e1n h\u1ecdc. Kh\u00f4ng c\u00f3 c\u1ea3 hai ch\u00fang ta kh\u00f4ng th\u1ec3 \u0111i s\u00e2u v\u00e0o b\u1ea5t c\u1ee9 th\u1ee9 g\u00ec\u201d.<\/em>
Galileo Galilei:<\/strong>
\u201cTo\u00e1n h\u1ecdc l\u00e0 ng\u00f4n ng\u1eef Ch\u00faa vi\u1ebft trong v\u0169 tr\u1ee5\u201d<\/em><\/p>\n\n\n\n

N\u0103m 1931, Kurt G\u00f6del gi\u00e1ng cho c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc trong th\u1eddi c\u1ee7a \u00f4ng m\u1ed9t \u0111\u00f2n n\u1eb7ng n\u1ec1
N\u0103m 1931, nh\u00e0 to\u00e1n h\u1ecdc tr\u1ebb Kurt G\u00f6del c\u00f3 m\u1ed9t kh\u00e1m ph\u00e1 mang t\u00ednh b\u01b0\u1edbc ngo\u1eb7t, g\u00e2y ra nh\u1eefng ch\u1ea5n \u0111\u1ed9ng l\u1edbn nh\u01b0 nh\u1eefng g\u00ec Albert Einstein \u0111\u00e3 l\u00e0m.
Kh\u00e1m ph\u00e1 c\u1ee7a G\u00f6del kh\u00f4ng ch\u1ec9 \u00e1p d\u1ee5ng cho to\u00e1n h\u1ecdc, m\u00e0 th\u1ef1c ra \u00e1p d\u1ee5ng cho t\u1ea5t c\u1ea3 c\u00e1c ng\u00e0nh c\u1ee7a khoa h\u1ecdc, logic v\u00e0 hi\u1ec3u bi\u1ebft c\u1ee7a con ng\u01b0\u1eddi n\u00f3i chung. N\u00f3 th\u1ef1c s\u1ef1 l\u00e0m rung chuy\u1ec3n tr\u00e1i \u0111\u1ea5t.
Nh\u01b0ng tr\u1edb tr\u00eau thay, kh\u00f4ng m\u1ea5y ai bi\u1ebft v\u1ec1 n\u00f3.
V\u1eady h\u00e3y cho ph\u00e9p t\u00f4i n\u00f3i v\u1edbi c\u00e1c b\u1ea1n c\u00e2u chuy\u1ec7n v\u1ec1 \u0111\u1ecbnh l\u00fd n\u00e0y.<\/p>\n\n\n\n

C\u00e1c nh\u00e0 to\u00e1n h\u1ecdc v\u1ed1n th\u00edch ch\u1ee9ng minh m\u1ecdi th\u1ee9. V\u00ec th\u1ebf h\u1ecd n\u00f3ng l\u00f2ng v\u00e0 b\u0103n kho\u0103n trong su\u1ed1t nhi\u1ec1u th\u1ebf k\u1ef7 v\u00ec c\u00f3 m\u1ed9t s\u1ed1 \u0111\u1ecbnh \u0111\u1ec1 to\u00e1n h\u1ecdc h\u1ecd ngh\u0129 l\u00e0 \u0111\u00fang nh\u01b0ng kh\u00f4ng th\u1ec3 CH\u1ee8NG MINH.
Ch\u1eb3ng h\u1ea1n n\u1ebfu b\u1ea1n \u0111\u00e3 t\u1eebng h\u1ecdc H\u00ecnh h\u1ecdc \u1edf tr\u01b0\u1eddng trung h\u1ecdc, h\u1eb3n l\u00e0 b\u1ea1n \u0111\u00e3 l\u00e0m nh\u1eefng b\u00e0i t\u1eadp ch\u1ee9ng minh c\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a tam gi\u00e1c d\u1ef1a tr\u00ean m\u1ed9t s\u1ed1 \u0111\u1ecbnh l\u00fd c\u01a1 b\u1ea3n.
M\u00f4n h\u00ecnh h\u1ecdc \u0111\u00f3 \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng tr\u00ean 5 ti\u00ean \u0111\u1ec1 c\u1ee7a Euclid. M\u1ecdi ng\u01b0\u1eddi \u0111\u1ec1u th\u1ea5y nh\u1eefng ti\u00ean \u0111\u1ec1 \u0111\u00f3 l\u00e0 \u0111\u00fang, nh\u01b0ng sau 2500 n\u0103m v\u1eabn kh\u00f4ng c\u00f3 ai t\u00ecm ra c\u00e1ch ch\u1ee9ng minh ch\u00fang.
V\u00e2ng, d\u01b0\u1eddng nh\u01b0 ho\u00e0n to\u00e0n h\u1ee3p l\u00fd khi cho r\u1eb1ng m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 k\u00e9o d\u00e0i v\u00f4 t\u1eadn v\u1ec1 hai ph\u00eda, nh\u01b0ng kh\u00f4ng ai c\u00f3 th\u1ec3 CH\u1ee8NG T\u1ece \u0111i\u1ec1u \u0111\u00f3. Ch\u00fang ta ch\u1ec9 c\u00f3 th\u1ec3 b\u1ea7y t\u1ecf r\u1eb1ng \u0111\u00f3 l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p 5 ti\u00ean \u0111\u1ec1 h\u1ee3p l\u00fd, v\u00e0 th\u1ef1c t\u1ebf l\u00e0 c\u1ea7n thi\u1ebft.
Nh\u1eefng thi\u00ean t\u00e0i to\u00e1n h\u1ecdc cao ch\u00f3t v\u00f3t \u0111\u00e3 th\u1ea5t v\u1ecdng trong h\u01a1n 2000 n\u0103m b\u1edfi v\u00ec h\u1ecd kh\u00f4ng th\u1ec3 ch\u1ee9ng minh t\u1ea5t c\u1ea3 c\u00e1c \u0111\u1ecbnh l\u00fd c\u1ee7a h\u1ecd. C\u00f3 r\u1ea5t nhi\u1ec1u \u0111i\u1ec1u \u201cr\u00f5 r\u00e0ng\u201d l\u00e0 \u0111\u00fang nh\u01b0ng kh\u00f4ng ai c\u00f3 th\u1ec3 t\u00ecm ra c\u00e1ch ch\u1ee9ng minh.
Tuy nhi\u00ean, v\u00e0o nh\u1eefng n\u0103m \u0111\u1ea7u c\u1ee7a th\u1eadp ni\u00ean 1900, m\u1ed9t ni\u1ec1m l\u1ea1c quan to l\u1edbn b\u1eaft \u0111\u1ea7u ph\u00e1t tri\u1ec3n trong gi\u1edbi to\u00e1n h\u1ecdc. C\u00e1c nh\u00e0 to\u00e1n h\u1ecdc xu\u1ea5t s\u1eafc nh\u1ea5t th\u1ebf gi\u1edbi l\u00fac \u0111\u00f3 (nh\u01b0 Bertrand Russell, David Hilbert v\u00e0 Ludwig Wittgenstein) tin r\u1eb1ng h\u1ecd \u0111ang nhanh ch\u00f3ng ti\u1ebfn g\u1ea7n t\u1edbi m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p t\u1ed5ng h\u1ee3p cu\u1ed1i c\u00f9ng.
(H\u1ecd tin r\u1eb1ng) m\u1ed9t s\u1ef1 th\u1ed1ng nh\u1ea5t \u201cL\u00fd thuy\u1ebft v\u1ec1 m\u1ecdi th\u1ee9\u201d r\u1ed1t cu\u1ed9c s\u1ebd th\u00edt ch\u1eb7t c\u00e1c \u0111\u1ea7u m\u1ed1i l\u1ecfng l\u1ebbo. To\u00e1n h\u1ecdc s\u1ebd ki\u1ec7n to\u00e0n, \u0111\u1ea1n b\u1eafn kh\u00f4ng th\u1ee7ng, kh\u00f4ng c\u00f3 k\u1ebd h\u1edf cho kh\u00f4ng kh\u00ed l\u1ecdt v\u00e0o, v\u00e0 to\u00e1n h\u1ecdc s\u1ebd \u0111\u1eafc th\u1eafng.
(Nh\u01b0ng) n\u0103m 1931, nh\u00e0 to\u00e1n h\u1ecdc tr\u1ebb ng\u01b0\u1eddi \u00c1o, Kurt G\u00f6del, \u0111\u00e3 c\u00f4ng b\u1ed1 m\u1ed9t c\u00f4ng tr\u00ecnh CH\u1ee8NG MINH m\u1ed9t l\u1ea7n v\u00e0 m\u00e3i m\u00e3i r\u1eb1ng m\u1ed9t L\u00fd thuy\u1ebft Duy nh\u1ea5t v\u1ec1 M\u1ecdi th\u1ee9 th\u1ef1c ra l\u00e0 kh\u00f4ng th\u1ec3 c\u00f3 (impossible, b\u1ea5t kh\u1ea3).
Kh\u00e1m ph\u00e1 c\u1ee7a G\u00f6del \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u201c\u0110\u1ecbnh l\u00fd B\u1ea5t to\u00e0n\u201d.
N\u1ebfu b\u1ea1n d\u00e0nh cho t\u00f4i v\u00e0i ph\u00fat, th\u00ec t\u00f4i s\u1ebd gi\u1ea3i th\u00edch v\u1edbi b\u1ea1n \u0111\u1ecbnh l\u00fd \u0111\u00f3 n\u00f3i g\u00ec, G\u00f6del \u0111\u00e3 kh\u00e1m ph\u00e1 ra \u0111\u1ecbnh l\u00fd \u0111\u00f3 nh\u01b0 th\u1ebf n\u00e0o, v\u00e0 \u0111\u1ecbnh l\u00fd \u0111\u00f3 c\u00f3 \u00fd ngh\u0129a g\u00ec \u2013 t\u00f4i n\u00f3i b\u1eb1ng m\u1ed9t ng\u00f4n ng\u1eef m\u1ed9c m\u1ea1c, \u0111\u01a1n gi\u1ea3n \u0111\u1ebfn n\u1ed7i ai c\u0169ng hi\u1ec3u.<\/p>\n\n\n\n

\u0110\u1ecbnh l\u00fd B\u1ea5t to\u00e0n c\u1ee7a G\u00f6del n\u00f3i r\u1eb1ng:<\/strong>
\u201cB\u1ea5t c\u1ee9 \u0111i\u1ec1u g\u00ec m\u00e0 b\u1ea1n c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n bao quanh n\u00f3 s\u1ebd kh\u00f4ng th\u1ec3 t\u1ef1 gi\u1ea3i th\u00edch v\u1ec1 b\u1ea3n th\u00e2n n\u00f3 m\u00e0 kh\u00f4ng tham chi\u1ebfu \u0111\u1ebfn m\u1ed9t c\u00e1i g\u00ec \u0111\u00f3 \u1edf b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n \u2013 m\u1ed9t c\u00e1i g\u00ec \u0111\u00f3 m\u00e0 b\u1ea1n ph\u1ea3i th\u1eeba nh\u1eadn l\u00e0 \u0111\u00fang nh\u01b0ng kh\u00f4ng th\u1ec3 ch\u1ee9ng minh.\u201d<\/strong><\/p>\n\n\n\n

\"GODE1M\"<\/a><\/figure><\/div>\n\n\n\n

Xin nh\u1eafc l\u1ea1i \u0111i\u1ec1u n\u00f3i tr\u00ean b\u1eb1ng ng\u00f4n ng\u1eef ch\u00ednh th\u1ee9c c\u1ee7a khoa h\u1ecdc:
\u0110\u1ecbnh l\u00fd G\u00f6del n\u00f3i r\u1eb1ng: \u201cB\u1ea5t k\u1ef3 l\u00fd thuy\u1ebft n\u00e0o \u0111\u01b0\u1ee3c t\u1ea1o ra m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 \u0111\u1ee7 kh\u1ea3 n\u0103ng bi\u1ec3u di\u1ec5n s\u1ed1 h\u1ecdc s\u01a1 c\u1ea5p \u0111\u1ec1u kh\u00f4ng th\u1ec3 v\u1eeba nh\u1ea5t qu\u00e1n v\u1eeba \u0111\u1ea7y \u0111\u1ee7. \u0110\u1eb7c bi\u1ec7t, \u0111\u1ed1i v\u1edbi b\u1ea5t k\u1ef3 l\u00fd thuy\u1ebft h\u00ecnh th\u1ee9c n\u00e0o nh\u1ea5t qu\u00e1n, \u0111\u01b0\u1ee3c t\u1ea1o ra m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 cho ph\u00e9p ch\u1ee9ng minh m\u1ed9t s\u1ed1 ch\u00e2n l\u00fd s\u1ed1 h\u1ecdc c\u0103n b\u1ea3n, s\u1ebd c\u00f3 m\u1ed9t m\u1ec7nh \u0111\u1ec1 s\u1ed1 h\u1ecdc \u0111\u00fang nh\u01b0ng kh\u00f4ng th\u1ec3 ch\u1ee9ng minh trong l\u00fd thuy\u1ebft \u1ea5y.\u201d
Lu\u1eadn \u0111\u1ec1 Church-Turing n\u00f3i r\u1eb1ng m\u1ed9t h\u1ec7 v\u1eadt l\u00fd c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n s\u1ed1 h\u1ecdc s\u01a1 c\u1ea5p y nh\u01b0 con ng\u01b0\u1eddi, v\u00e0 r\u1eb1ng s\u1ed1 h\u1ecdc c\u1ee7a M\u00e1y Turing (computer) kh\u00f4ng th\u1ec3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c b\u00ean trong h\u1ec7 th\u1ed1ng \u0111\u00f3 v\u00e0 do \u0111\u00f3 computer c\u0169ng b\u1ea5t to\u00e0n.
B\u1ea5t k\u1ef3 h\u1ec7 v\u1eadt l\u00fd n\u00e0o c\u00f3 th\u1ec3 \u0111o l\u01b0\u1eddng \u0111\u1ec1u c\u00f3 kh\u1ea3 n\u0103ng bi\u1ec3u di\u1ec5n s\u1ed1 h\u1ecdc s\u01a1 c\u1ea5p (N\u00f3i c\u00e1ch kh\u00e1c, tr\u1ebb em c\u00f3 th\u1ec3 l\u00e0m to\u00e1n b\u1eb1ng c\u00e1ch \u0111\u1ebfm ng\u00f3n tay, n\u01b0\u1edbc ch\u1ea3y v\u00e0o th\u00f9ng s\u1ebd t\u1ea1o n\u00ean m\u1ed9t l\u01b0\u1ee3ng n\u01b0\u1edbc \u0111\u1ebfm \u0111\u01b0\u1ee3c, v\u00e0 c\u00e1c h\u1ec7 v\u1eadt l\u00fd lu\u00f4n lu\u00f4n \u0111ua ra c\u00e2u tr\u1ea3 l\u1eddi r\u00f5 r\u00e0ng).
Do \u0111\u00f3 v\u0169 tr\u1ee5 (th\u1ebf gi\u1edbi v\u1eadt l\u00fd) c\u00f3 kh\u1ea3 n\u0103ng bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c b\u1eb1ng s\u1ed1 h\u1ecdc s\u01a1 c\u1ea5p v\u00e0 gi\u1ed1ng nh\u01b0 b\u1ea3n th\u00e2n to\u00e1n h\u1ecdc v\u00e0 computer, v\u0169 tr\u1ee5 \u1ea5y l\u00e0 b\u1ea5t to\u00e0n.
L\u00fd lu\u1eadn tr\u00ean c\u00f3 th\u1ec3 t\u00f3m t\u1eaft b\u1eb1ng tam \u0111o\u1ea1n lu\u1eadn sau \u0111\u00e2y:
1. M\u1ecdi h\u1ec7 th\u1ed1ng \u0111\u1ee7 ph\u1ee9c t\u1ea1p c\u00f3 th\u1ec3 t\u00ednh to\u00e1n \u0111\u01b0\u1ee3c \u0111\u1ec1u b\u1ea5t to\u00e0n.
2. V\u0169 tr\u1ee5 l\u00e0 m\u1ed9t h\u1ec7 \u0111\u1ee7 ph\u1ee9c t\u1ea1p c\u00f3 th\u1ec3 t\u00ednh to\u00e1n \u0111\u01b0\u1ee3c.
3. Do \u0111\u00f3 v\u0169 tr\u1ee5 l\u00e0 b\u1ea5t to\u00e0n.
B\u1ea1n c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n xung quanh t\u1ea5t c\u1ea3 c\u00e1c kh\u00e1i ni\u1ec7m trong cu\u1ed1n s\u00e1ch h\u00ecnh h\u1ecdc trung h\u1ecdc c\u1ee7a b\u1ea1n. Nh\u01b0ng t\u1ea5t c\u1ea3 ch\u00fang \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng tr\u00ean 5 ti\u00ean \u0111\u1ec1 c\u1ee7a Euclid, nh\u1eefng ti\u00ean \u0111\u1ec1 n\u00e0y r\u00f5 r\u00e0ng l\u00e0 \u0111\u00fang nh\u01b0ng kh\u00f4ng th\u1ec3 ch\u1ee9ng minh. 5 ti\u00ean \u0111\u1ec1 \u0111\u00f3 n\u1eb1m ngo\u00e0i cu\u1ed1n s\u00e1ch, t\u1ee9c l\u00e0 b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n b\u1ea1n v\u1eeba v\u1ebd.
B\u1ea1n c\u0169ng c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n xung quanh m\u1ed9t chi\u1ebfc xe \u0111\u1ea1p nh\u01b0ng s\u1ef1 t\u1ed3n t\u1ea1i c\u1ee7a chi\u1ebfc xe \u0111\u1ea1p \u0111\u00f3 d\u1ef1a v\u00e0o m\u1ed9t nh\u00e0 m\u00e1y \u1edf b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n \u0111\u00f3. Chi\u1ebfc xe \u0111\u1ea1p kh\u00f4ng th\u1ec3 t\u1ef1 gi\u1ea3i th\u00edch s\u1ef1 t\u1ed3n t\u1ea1i c\u1ee7a b\u1ea3n th\u00e2n n\u00f3.
G\u00f6del ch\u1ee9ng minh r\u1eb1ng LU\u00d4N LU\u00d4N c\u00f3 nhi\u1ec1u c\u00e1i \u0111\u00fang h\u01a1n l\u00e0 c\u00e1i b\u1ea1n c\u00f3 th\u1ec3 ch\u1ee9ng minh. Trong b\u1ea5t k\u1ef3 h\u1ec7 th\u1ed1ng logic hay h\u1ec7 th\u1ed1ng s\u1ed1 n\u00e0o m\u00e0 c\u00e1c nh\u00e0 to\u00e1n h\u1ecdc \u0111\u00e3 t\u1eebng x\u00e2y d\u1ef1ng \u0111\u01b0\u1ee3c \u0111\u1ec1u lu\u00f4n lu\u00f4n t\u1ed3n t\u1ea1i \u00edt nh\u1ea5t m\u1ed9t v\u00e0i gi\u1ea3 \u0111\u1ecbnh kh\u00f4ng th\u1ec3 ch\u1ee9ng minh.
\u0110\u1ecbnh l\u00fd b\u1ea5t to\u00e0n c\u1ee7a G\u00f6del kh\u00f4ng ch\u1ec9 \u00e1p d\u1ee5ng cho to\u00e1n h\u1ecdc, m\u00e0 cho m\u1ecdi \u0111\u1ed1i t\u01b0\u1ee3ng tu\u00e2n th\u1ee7 c\u00e1c \u0111\u1ecbnh lu\u1eadt c\u1ee7a logic. B\u1ea5t to\u00e0n \u0111\u00fang trong to\u00e1n h\u1ecdc; n\u00f3 c\u0169ng \u0111\u00fang trong khoa h\u1ecdc hay ng\u00f4n ng\u1eef ho\u1eb7c tri\u1ebft h\u1ecdc.
V\u00e0: N\u1ebfu v\u0169 tr\u1ee5 mang t\u00ednh ch\u1ea5t to\u00e1n h\u1ecdc v\u00e0 logic th\u00ec t\u00ednh b\u1ea5t to\u00e0n c\u0169ng \u00e1p d\u1ee5ng cho v\u0169 tr\u1ee5.<\/p>\n\n\n\n

G\u00f6del s\u00e1ng t\u1ea1o ra ch\u1ee9ng minh c\u1ee7a m\u00ecnh b\u1eb1ng c\u00e1ch kh\u1edfi \u0111\u1ea7u v\u1edbi \u201cNgh\u1ecbch l\u00fd K\u1ebb n\u00f3i d\u1ed1i\u201d (The Liar\u2019s Paradox) \u2013 \u0111\u00f3 l\u00e0 m\u1ec7nh \u0111\u1ec1:
\u201cT\u00f4i \u0111ang n\u00f3i d\u1ed1i.\u201d<\/strong> (I am lying)
M\u1ec7nh \u0111\u1ec1 \u201cT\u00f4i \u0111ang n\u00f3i d\u1ed1i\u201d l\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 t\u1ef1 m\u00e2u thu\u1eabn, b\u1edfi n\u1ebfu m\u1ec7nh \u0111\u1ec1 \u1ea5y ph\u1ea3n \u00e1nh \u0111\u00fang s\u1ef1 th\u1eadt, r\u1eb1ng t\u00f4i l\u00e0 m\u1ed9t k\u1ebb n\u00f3i d\u1ed1i, th\u00ec suy ra m\u1ec7nh \u0111\u1ec1 v\u1eeba n\u00f3i kh\u00f4ng \u0111\u00e1ng tin c\u1eady, t\u1ee9c l\u00e0 m\u1ec7nh \u0111\u1ec1 \u1ea5y m\u00e2u thu\u1eabn v\u1edbi ch\u00ednh n\u00f3; n\u1ebfu m\u1ec7nh \u0111\u1ec1 \u1ea5y sai, l\u1eadp lu\u1eadn t\u01b0\u01a1ng t\u1ef1 c\u0169ng \u0111i \u0111\u1ebfn m\u00e2u thu\u1eabn .
T\u01b0\u01a1ng t\u1ef1 nh\u01b0 v\u1eady, b\u1eb1ng m\u1ed9t trong nh\u1eefng bi\u1ebfn \u0111\u1ed5i kh\u00e9o l\u00e9o nh\u1ea5t trong l\u1ecbch s\u1eed to\u00e1n h\u1ecdc, G\u00f6del \u0111\u00e3 chuy\u1ec3n Ngh\u1ecbch l\u00fd K\u1ebb N\u00f3i D\u1ed1i th\u00e0nh m\u1ed9t c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc. \u00d4ng \u0111\u00e3 ch\u1ee9ng minh r\u1eb1ng b\u1ea5t k\u1ef3 m\u1ed9t m\u1ec7nh \u0111\u1ec1 n\u00e0o c\u0169ng \u0111\u00f2i h\u1ecfi m\u1ed9t quan s\u00e1t vi\u00ean b\u00ean ngo\u00e0i.
Kh\u00f4ng c\u00f3 m\u1ec7nh \u0111\u1ec1 n\u00e0o (m\u1ed9t s\u1ef1 tr\u00ecnh b\u00e0y n\u00e0o) c\u00f3 th\u1ec3 m\u1ed9t m\u00ecnh n\u00f3 t\u1ef1 ch\u1ee9ng minh n\u00f3 \u0111\u00fang.
\u0110\u1ecbnh l\u00fd b\u1ea5t to\u00e0n c\u1ee7a G\u00f6del l\u00e0 m\u1ed9t \u0111\u00f2n n\u1eb7ng n\u1ec1 gi\u00e1ng v\u00e0o \u201cch\u1ee7 ngh\u0129a th\u1ef1c ch\u1ee9ng\u201d trong th\u1eddi \u0111\u1ea1i \u0111\u00f3. G\u00f6del ch\u1ee9ng minh \u0111\u1ecbnh l\u00fd c\u1ee7a \u00f4ng m\u1ed9t c\u00e1ch r\u00f5 r\u00e0ng tr\u1eafng \u0111en \u0111\u1ebfn n\u1ed7i kh\u00f4ng ai c\u00f3 th\u1ec3 tranh c\u00e3i v\u1edbi logic c\u1ee7a \u00f4ng.
Tuy nhi\u00ean m\u1ed9t s\u1ed1 \u0111\u1ed3ng nghi\u1ec7p to\u00e1n h\u1ecdc c\u1ee7a \u00f4ng \u0111\u1ebfn l\u00fac ra \u0111i v\u1ec1 b\u00ean kia th\u1ebf gi\u1edbi v\u1eabn ph\u1ee7 nh\u1eadn \u00f4ng, tin r\u1eb1ng b\u1eb1ng c\u00e1ch n\u00e0y hay c\u00e1ch kh\u00e1c, tr\u01b0\u1edbc sau G\u00f6del ch\u1eafc ch\u1eafn ph\u1ea3i sai.
Nh\u01b0ng \u00f4ng kh\u00f4ng sai. \u0110\u1ecbnh l\u00fd c\u1ee7a \u00f4ng th\u1ef1c s\u1ef1 \u0111\u00fang. C\u00f3 nhi\u1ec1u c\u00e1i \u0111\u00fang h\u01a1n l\u00e0 c\u00e1i b\u1ea1n c\u00f3 th\u1ec3 ch\u1ee9ng minh.
M\u1ed9t \u201cl\u00fd thuy\u1ebft v\u1ec1 m\u1ecdi th\u1ee9\u201d \u2013 d\u00f9 trong to\u00e1n h\u1ecdc hay v\u1eadt l\u00fd, tri\u1ebft h\u1ecdc \u2013 s\u1ebd kh\u00f4ng bao gi\u1edd t\u00ecm th\u1ea5y. \u0110\u01a1n gi\u1ea3n v\u00ec n\u00f3 kh\u00f4ng th\u1ec3 t\u1ed3n t\u1ea1i (impossible, b\u1ea5t kh\u1ea3).
OK, v\u1eady \u0111i\u1ec1u n\u00e0y th\u1ef1c ra c\u00f3 \u00fd ngh\u0129a g\u00ec? T\u1ea1i sao v\u1ea5n \u0111\u1ec1 n\u00e0y l\u1ea1i l\u00e0 v\u00f4 c\u00f9ng quan tr\u1ecdng, thay v\u00ec ch\u1ec9 l\u00e0 m\u1ed9t chuy\u1ec7n phi\u1ebfm \u0111\u1ec3 mua vui?<\/p>\n\n\n\n

\u0110\u00e2y l\u00e0 \u00fd ngh\u0129a c\u1ee7a \u0111\u1ecbnh l\u00fd:
\u25cf \u0110\u1ee9c tin v\u00e0 L\u00fd l\u1ebd kh\u00f4ng ph\u1ea3i l\u00e0 k\u1ebb th\u00f9 c\u1ee7a nhau.<\/strong> Th\u1ef1c ra \u0111i\u1ec1u ng\u01b0\u1ee3c l\u1ea1i m\u1edbi \u0111\u00fang! C\u00e1i n\u00e0y nh\u1ea5t thi\u1ebft c\u1ea7n c\u00e1i kia \u0111\u1ec3 t\u1ed3n t\u1ea1i. M\u1ecdi l\u00fd l\u1ebd r\u1ed1t cu\u1ed9c \u0111\u1ec1u quay tr\u1edf l\u1ea1i ni\u1ec1m tin v\u00e0o m\u1ed9t c\u00e1i g\u00ec \u0111\u00f3 m\u00e0 b\u1ea1n kh\u00f4ng th\u1ec3 ch\u1ee9ng minh.
\u25cf M\u1ecdi h\u1ec7 th\u1ed1ng \u0111\u00f3ng k\u00edn \u0111\u1ec1u ph\u1ee5 thu\u1ed9c v\u00e0o m\u1ed9t c\u00e1i g\u00ec \u0111\u00f3 \u1edf b\u00ean ngo\u00e0i h\u1ec7 th\u1ed1ng.<\/strong>
\u25cf B\u1ea1n lu\u00f4n lu\u00f4n c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n l\u1edbn h\u01a1n nh\u01b0ng s\u1ebd lu\u00f4n lu\u00f4n t\u1ed3n t\u1ea1i m\u1ed9t c\u00e1i g\u00ec \u0111\u00f3 b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n.<\/strong>
\u25cf L\u00fd l\u1ebd h\u01b0\u1edbng t\u1eeb m\u1ed9t v\u00f2ng tr\u00f2n l\u1edbn h\u01a1n v\u00e0o m\u1ed9t v\u00f2ng tr\u00f2n nh\u1ecf h\u01a1n l\u00e0 \u201cl\u00fd l\u1ebd suy di\u1ec5n\u201d<\/strong> (deductive reasoning). Th\u00ed d\u1ee5:
1. M\u1ecdi ng\u01b0\u1eddi \u0111\u1ec1u s\u1ebd ch\u1ebft.
2. Socrates l\u00e0 m\u1ed9t con ng\u01b0\u1eddi.
3. V\u1eady Socrates s\u1ebd ch\u1ebft.
\u25cf L\u00fd l\u1ebd h\u01b0\u1edbng t\u1eeb m\u1ed9t v\u00f2ng tr\u00f2n nh\u1ecf h\u01a1n ra m\u1ed9t v\u00f2ng tr\u00f2n l\u1edbn h\u01a1n l\u00e0 \u201cl\u00fd l\u1ebd quy n\u1ea1p\u201d<\/strong>. Th\u00ed d\u1ee5:
1. Khi t\u00f4i th\u1ea3 \u0111\u1ed3 v\u1eadt ra, ch\u00fang s\u1ebd r\u01a1i.
2. Do \u0111\u00f3 t\u1ed3n t\u1ea1i m\u1ed9t \u0111\u1ecbnh lu\u1eadt v\u1ec1 h\u1ea5p d\u1eabn chi ph\u1ed1i m\u1ecdi v\u1eadt th\u1ec3 r\u01a1i.
Ch\u00fa \u00fd r\u1eb1ng khi b\u1ea1n chuy\u1ec3n t\u1eeb v\u00f2ng tr\u00f2n nh\u1ecf h\u01a1n ra v\u00f2ng tr\u00f2n l\u1edbn h\u01a1n, b\u1ea1n ph\u1ea3i th\u1eeba nh\u1eadn r\u1eb1ng b\u1ea1n kh\u00f4ng th\u1ec3 ch\u1ee9ng minh 100%.
Ch\u1eb3ng h\u1ea1n b\u1ea1n kh\u00f4ng th\u1ec3 CH\u1ee8NG MINH l\u1ef1c h\u1ea5p d\u1eabn lu\u00f4n lu\u00f4n t\u1ed3n t\u1ea1i v\u00e0o m\u1ecdi l\u00fac. B\u1ea1n ch\u1ec9 c\u00f3 th\u1ec3 nh\u1eadn th\u1ea5y l\u1ef1c h\u1ea5p d\u1eabn t\u1ed3n t\u1ea1i v\u00e0o m\u1ed7i l\u00facc b\u1ea1n quan s\u00e1t. B\u1ea1n kh\u00f4ng th\u1ec3 CH\u1ee8NG MINH v\u0169 tr\u1ee5 l\u00e0 h\u1ee3p l\u00fd (rational, tu\u00e2n th\u1ee7 nh\u1eefng quy lu\u1eadt nh\u1ea5t \u0111\u1ecbnh). B\u1ea1n ch\u1ec9 c\u00f3 th\u1ec3 nh\u1eadn th\u1ea5y c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc, nh\u01b0 E = mc2 ch\u1eb3ng h\u1ea1n, d\u01b0\u1eddng nh\u01b0 m\u00f4 t\u1ea3 m\u1ed9t c\u00e1ch ho\u00e0n h\u1ea3o c\u00e1i m\u00e0 v\u0169 tr\u1ee5 ti\u1ebfn h\u00e0nh.
G\u1ea7n nh\u01b0 m\u1ecdi \u0111\u1ecbnh lu\u1eadt khoa h\u1ecdc \u0111\u1ec1u d\u1ef1a tr\u00ean l\u00fd l\u1ebd quy n\u1ea1p. Nh\u1eefng \u0111\u1ecbnh lu\u1eadt n\u00e0y \u0111\u1ec1u d\u1ef1a tr\u00ean m\u1ed9t gi\u1ea3 \u0111\u1ecbnh cho r\u1eb1ng v\u0169 tr\u1ee5 l\u00e0 logic v\u00e0 d\u1ef1a tr\u00ean nh\u1eefng \u0111\u1ecbnh lu\u1eadt c\u1ed1 \u0111\u1ecbnh c\u00f3 th\u1ec3 kh\u00e1m ph\u00e1 ra.
B\u1ea1n kh\u00f4ng th\u1ec3 CH\u1ee8NG MINH gi\u1ea3 \u0111\u1ecbnh \u0111\u00f3 ( B\u1ea1n kh\u00f4ng th\u1ec3 ch\u1ee9ng minh m\u1eb7t tr\u1eddi s\u1ebd m\u1ecdc v\u00e0o bu\u1ed5i s\u1edbm mai). Th\u1ef1c ra b\u1ea1n ph\u1ea3i ch\u1ea5p nh\u1eadn \u0111i\u1ec1u \u0111\u00f3 b\u1eb1ng ni\u1ec1m tin. Khoa h\u1ecdc \u0111\u01b0\u1ee3c x\u00e2y d\u1ef1ng tr\u00ean nh\u1eefng gi\u1ea3 \u0111\u1ecbnh tri\u1ebft h\u1ecdc m\u00e0 b\u1ea1n kh\u00f4ng th\u1ec3 ch\u1ee9ng minh b\u1eb1ng khoa h\u1ecdc. Th\u1eadt v\u1eady, ph\u01b0\u01a1ng ph\u00e1p khoa h\u1ecdc kh\u00f4ng th\u1ec3 ch\u1ee9ng minh, n\u00f3 ch\u1ec9 c\u00f3 th\u1ec3 g\u1ee3i \u00fd, ph\u1ecfng \u0111o\u00e1n (Khoa h\u1ecdc xu\u1ea5t ph\u00e1t t\u1eeb t\u01b0 t\u01b0\u1edfng nguy\u00ean th\u1ee7y r\u1eb1ng Ch\u00faa t\u1ea1o ra m\u1ed9t v\u0169 tr\u1ee5 c\u00f3 tr\u1eadt t\u1ef1 tu\u00e2n th\u1ee7 c\u00e1c \u0111\u1ecbnh lu\u1eadt c\u1ed1 \u0111\u1ecbnh c\u00f3 th\u1ec3 kh\u00e1m ph\u00e1 \u0111\u01b0\u1ee3c).<\/p>\n\n\n\n

B\u00e2y gi\u1edd h\u00e3y xem x\u00e9t \u0111i\u1ec1u g\u00ec s\u1ebd x\u1ea9y ra khi ch\u00fang ta v\u1ebd v\u00f2ng tr\u00f2n l\u1edbn nh\u1ea5t c\u00f3 th\u1ec3 c\u00f3<\/strong> \u2013 v\u00f2ng tr\u00f2n bao quanh to\u00e0n th\u1ec3 v\u0169 tr\u1ee5 (n\u1ebfu c\u00f3 \u0111a v\u0169 tr\u1ee5 th\u00ec v\u1ebd m\u00f4t v\u00f2ng tr\u00f2n ch\u1ee9a t\u1ea5t c\u1ea3 nh\u1eefng v\u0169 tr\u1ee5 \u0111\u00f3):
\u25cf Ph\u1ea3i c\u00f3 m\u1ed9t c\u00e1i g\u00ec \u0111\u00f3 b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n \u0111\u00f3.<\/strong> M\u1ed9t c\u00e1i g\u00ec \u0111\u00f3 m\u00e0 ch\u00fang ta ph\u1ea3i th\u1eeba nh\u1eadn l\u00e0 kh\u00f4ng th\u1ec3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c.
\u25cf V\u0169 tr\u1ee5 m\u00e0 ch\u00fang ta bi\u1ebft l\u00e0 h\u1eefu h\u1ea1n<\/strong> \u2013 h\u1eefu h\u1ea1n v\u1eadt ch\u1ea5t, h\u1eefu h\u1ea1n n\u0103ng l\u01b0\u1ee3ng, kh\u00f4ng gian h\u1eefu h\u1ea1n v\u00e0 th\u1eddi gian l\u00e0 13.7 t\u1ef7 n\u0103m tu\u1ed5i.
\u25cf V\u0169 tr\u1ee5 \u1ea5y mang t\u00ednh ch\u1ea5t to\u00e1n h\u1ecdc.<\/strong> B\u1ea5t k\u1ef3 h\u1ec7 v\u1eadt l\u00fd n\u00e0o c\u00f3 th\u1ec3 \u0111o \u0111\u1ea1c \u0111\u1ec1u c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n b\u1edfi s\u1ed1 h\u1ecdc (B\u1ea1n kh\u00f4ng c\u1ea7n bi\u1ebft to\u00e1n h\u1ecdc \u0111\u1ec3 l\u00e0m ph\u00e9p c\u1ed9ng \u2013 b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng b\u00e0n t\u00ednh g\u1ea9y tay \u0111\u1ec3 t\u00ecm c\u00e2u tr\u1ea3 l\u1eddi v\u00e0o m\u1ecdi l\u00fac).
\u25cf V\u0169 tr\u1ee5<\/strong> (t\u1ea5t c\u1ea3 m\u1ecdi v\u1eadt ch\u1ea5t, n\u0103ng l\u01b0\u1ee3ng, kh\u00f4ng gian, th\u1eddi gian) kh\u00f4ng th\u1ec3 t\u1ef1 gi\u1ea3i th\u00edch cho n\u00f3<\/strong>.
\u25cf B\u1ea5t k\u1ec3 c\u00e1i g\u00ec \u1edf b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n l\u1edbn nh\u1ea5t \u0111\u1ec1u l\u00e0 v\u00f4 h\u1ea1n.<\/strong> Theo \u0111\u1ecbnh ngh\u0129a, kh\u00f4ng th\u1ec3 v\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n bao quanh n\u00f3 .
\u25cf N\u1ebfu ch\u00fang ta v\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n bao quanh m\u1ecdi v\u1eadt ch\u1ea5t, n\u0103ng l\u01b0\u1ee3ng, kh\u00f4ng gian v\u00e0 th\u1eddi gian v\u00e0 \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd G\u00f6del, ch\u00fang ta s\u1ebd th\u1ea5y c\u00e1i g\u00ec \u1edf ngo\u00e0i v\u00f2ng tr\u00f2n \u0111\u00f3 s\u1ebd kh\u00f4ng ph\u1ea3i l\u00e0 v\u1eadt ch\u1ea5t, kh\u00f4ng ph\u1ea3i n\u0103ng l\u01b0\u1ee3ng, kh\u00f4ng ph\u1ea3i kh\u00f4ng gian v\u00e0 c\u0169ng kh\u00f4ng ph\u1ea3i th\u1eddi gian. \u0110\u00f3 l\u00e0 th\u1ebf gi\u1edbi phi v\u1eadt ch\u1ea5t.<\/strong>
\u25cf B\u1ea5t k\u1ec3 c\u00e1i g\u00ec \u1edf b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n l\u1edbn nh\u1ea5t \u0111\u1ec1u kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t h\u1ec7 th\u1ed1ng<\/strong> \u2013 ngh\u0129a l\u00e0 kh\u00f4ng ph\u1ea3i m\u1ed9t t\u1eadp h\u1ee3p bao g\u1ed3m c\u00e1c th\u00e0nh ph\u1ea7n. N\u00f3i c\u00e1ch kh\u00e1c, n\u1ebfu ch\u00fang ta c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n bao quanh v\u1eadt ch\u1ea5t, n\u0103ng l\u01b0\u1ee3ng, kh\u00f4ng-th\u1eddi-gian th\u00ec c\u00e1i n\u1eb1m ngo\u00e0i v\u00f2ng tr\u00f2n \u1ea5y l\u00e0 kh\u00f4ng th\u1ec3 ph\u00e2n chia \u0111\u01b0\u1ee3c.
\u25cf B\u1ea5t k\u1ec3 c\u00e1i g\u00ec \u1edf b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n l\u1edbn nh\u1ea5t \u0111\u1ec1u l\u00e0 nguy\u00ean nh\u00e2n kh\u00f4ng c\u00f3 nguy\u00ean nh\u00e2n<\/strong>, b\u1edfi v\u00ec b\u1ea1n lu\u00f4n lu\u00f4n c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n bao quanh m\u1ed9t k\u1ebft qu\u1ea3.<\/p>\n\n\n\n

\"kurt<\/a><\/figure><\/div>\n\n\n\n

Ch\u00fang ta c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng l\u00fd l\u1ebd quy n\u1ea1p t\u01b0\u01a1ng t\u1ef1 cho ngu\u1ed3n g\u1ed1c c\u1ee7a th\u00f4ng tin:<\/strong>
\u25cf Trong l\u1ecbch s\u1eed v\u0169 tr\u1ee5, ch\u00fang ta c\u0169ng \u0111\u00e3 bi\u1ebft s\u1ef1 xu\u1ea5t hi\u1ec7n c\u1ee7a th\u00f4ng tin<\/strong>, v\u00e0o kho\u1ea3ng 3.5 t\u1ef7 n\u0103m tr\u01b0\u1edbc. N\u00f3 xu\u1ea5t ph\u00e1t t\u1eeb m\u00e3 c\u1ee7a H\u1ec7 Di truy\u1ec1n (Genetic code), m\u1ed9t th\u1ee9 phi v\u1eadt ch\u1ea5t mang t\u00ednh bi\u1ec3u t\u01b0\u1ee3ng .
\u25cf Th\u00f4ng tin ph\u1ea3i xu\u1ea5t ph\u00e1t t\u1eeb b\u00ean ngo\u00e0i<\/strong>, b\u1edfi v\u00ec th\u00f4ng tin \u0111\u01b0\u1ee3c bi\u1ebft kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t \u0111\u1eb7c tr\u01b0ng v\u1ed1n thu\u1ed9c v\u1ec1 v\u1eadt ch\u1ea5t, n\u0103ng l\u01b0\u1ee3ng v\u00e0 kh\u00f4ng gian ho\u1eb7c th\u1eddi gian.
\u25cf M\u1ecdi m\u00e3 m\u00e0 ch\u00fang ta bi\u1ebft ngu\u1ed3n g\u1ed1c \u0111\u1ec1u \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf b\u1edfi nh\u1eefng th\u1ef1c th\u1ec3 c\u00f3 \u00fd th\u1ee9c<\/strong>.
\u25cf Do \u0111\u00f3 b\u1ea5t k\u1ec3 c\u00e1i g\u00ec \u1edf b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n l\u1edbn nh\u1ea5t c\u0169ng ph\u1ea3i l\u00e0 m\u1ed9t th\u1ef1c th\u1ec3 c\u00f3 \u00fd th\u1ee9c.<\/strong>
N\u00f3i c\u00e1ch kh\u00e1c, khi ch\u00fang ta b\u1ed5 sung th\u00f4ng tin v\u00e0o trong ph\u01b0\u01a1ng tr\u00ecnh, ch\u00fang ta c\u00f3 th\u1ec3 k\u1ebft lu\u1eadn r\u1eb1ng c\u00e1i \u1edf b\u00ean ngo\u00e0i v\u00f2ng tr\u00f2n l\u1edbn nh\u1ea5t kh\u00f4ng ch\u1ec9 v\u00f4 h\u1ea1n v\u00e0 phi v\u1eadt ch\u1ea5t, m\u00e0 c\u00f2n c\u00f3 \u00fd th\u1ee9c.
Ch\u1eb3ng ph\u1ea3i th\u00fa v\u1ecb hay sao khi nh\u1eefng v\u1ea5n \u0111\u1ec1 n\u00e0y nghe c\u00f3 v\u1ebb \u0111\u00e1ng ng\u1edd v\u1ef1c nh\u01b0 nh\u1eefng g\u00ec m\u00e0 c\u00e1c nh\u00e0 th\u1ea7n h\u1ecdc \u0111\u00e3 m\u00f4 t\u1ea3 Ch\u00faa trong h\u00e0ng ng\u00e0n n\u0103m nay?
V\u00ec th\u1ebf s\u1ebd ch\u1eb3ng c\u00f3 g\u00ec \u0111\u00e1ng ng\u1ea1c nhi\u00ean khi th\u1ea5y 80-90% d\u00e2n ch\u00fang tr\u00ean th\u1ebf gi\u1edbi tin v\u00e0o Th\u01b0\u1ee3ng \u0111\u1ebf theo m\u1ed9t c\u00e1ch n\u00e0o \u0111\u00f3. Th\u1eadt v\u1eady, \u0111\u00f3 l\u00e0 tr\u1ef1c gi\u00e1c \u0111\u1ed1i v\u1edbi ph\u1ea7n l\u1edbn c\u00e1c d\u00e2n t\u1ed9c. Nh\u01b0ng \u0111\u1ecbnh l\u00fd G\u00f6del ch\u1ec9 ra r\u1eb1ng \u0111\u00f3 c\u0169ng l\u00e0 logic t\u1ed1i cao. Th\u1ef1c ra \u0111\u00f3 l\u00e0 l\u1eadp tr\u01b0\u1eddng duy nh\u1ea5t m\u00e0 ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 n\u1eafm l\u1ea5y v\u00e0 \u0111\u1ee9ng tr\u00ean \u0111\u00f3 trong v\u01b0\u01a1ng qu\u1ed1c c\u1ee7a l\u00fd l\u1ebd v\u00e0 logic.
Ng\u01b0\u1eddi n\u00e0o t\u1ef1 ph\u1ee5 tuy\u00ean b\u1ed1 \u201cB\u1ea1n l\u00e0 ng\u01b0\u1eddi c\u1ee7a \u0111\u1ee9c tin, c\u00f2n t\u00f4i l\u00e0 ng\u01b0\u1eddi c\u1ee7a khoa h\u1ecdc\u201d th\u00ec ng\u01b0\u1eddi \u1ea5y kh\u00f4ng hi\u1ec3u g\u1ed1c r\u1ec5 c\u1ee7a khoa h\u1ecdc ho\u1eb7c b\u1ea3n ch\u1ea5t c\u1ee7a tri th\u1ee9c!
M\u1ed9t kh\u00eda c\u1ea1nh th\u00fa v\u1ecb kh\u00e1c\u2026
N\u1ebfu b\u1ea1n c\u00f3 d\u1ecbp th\u0103m m\u1ed9t trang m\u1ea1ng v\u00f4 th\u1ea7n l\u1edbn nh\u1ea5t th\u1ebf gi\u1edbi c\u00f3 t\u00ean l\u00e0 Infidels, b\u1ea1n s\u1ebd th\u1ea5y tr\u00ean trang ch\u1ee7 l\u1eddi tuy\u00ean b\u1ed1 sau \u0111\u00e2y:
\u201cCh\u1ee7 ngh\u0129a duy t\u1ef1 nhi\u00ean (naturalism) l\u00e0 gi\u1ea3 thuy\u1ebft cho r\u1eb1ng th\u1ebf gi\u1edbi t\u1ef1 nhi\u00ean l\u00e0 m\u1ed9t h\u1ec7 \u0111\u00f3ng, ng\u1ee5 \u00fd r\u1eb1ng kh\u00f4ng c\u00f3 c\u00e1i g\u00ec kh\u00f4ng ph\u1ea3i l\u00e0 th\u00e0nh ph\u1ea7n c\u1ee7a th\u1ebf gi\u1edbi t\u1ef1 nhi\u00ean m\u00e0 l\u1ea1i \u1ea3nh h\u01b0\u1edfng l\u00ean n\u00f3<\/strong>\u201d
N\u1ebfu b\u1ea1n bi\u1ebft \u0111\u1ecbnh l\u00fd G\u00f6del, b\u1ea1n s\u1ebd th\u1ea5y r\u1eb1ng m\u1ecdi h\u1ec7 logic ph\u1ea3i ph\u1ee5 thu\u1ed9c v\u00e0o m\u1ed9t c\u00e1i g\u00ec \u0111\u00f3 \u1edf b\u00ean ngo\u00e0i h\u1ec7 th\u1ed1ng. V\u1eady theo \u0111\u1ecbnh l\u00fd b\u1ea5t to\u00e0n c\u1ee7a G\u00f6del, tuy\u00ean b\u1ed1 c\u1ee7a trang m\u1ea1ng Infidels kh\u00f4ng th\u1ec3 ch\u00ednh x\u00e1c. N\u1ebfu v\u0169 tr\u1ee5 l\u00e0 logic, n\u00f3 ph\u1ea3i c\u00f3 m\u1ed9t nguy\u00ean nh\u00e2n b\u00ean ngo\u00e0i.
Do \u0111\u00f3 ch\u1ee7 ngh\u0129a v\u00f4 th\u1ea7n vi ph\u1ea1m c\u00e1c \u0111\u1ecbnh lu\u1eadt c\u1ee7a l\u00fd l\u1ebd v\u00e0 logic.
\u0110\u1ecbnh l\u00fd B\u1ea5t to\u00e0n c\u1ee7a G\u00f6del ch\u1ee9ng minh m\u1ed9t c\u00e1ch d\u1ee9t kho\u00e1t r\u1eb1ng khoa h\u1ecdc kh\u00f4ng bao gi\u1edd c\u00f3 th\u1ec3 l\u1ea5p k\u00edn nh\u1eefng l\u1ed7 h\u1ed5ng c\u1ee7a ch\u00ednh n\u00f3. Ch\u00fang ta kh\u00f4ng c\u00f3 l\u1ef1a ch\u1ecdn n\u00e0o kh\u00e1c l\u00e0 nh\u00ecn ra b\u00ean ngo\u00e0i khoa h\u1ecdc \u0111\u1ec3 t\u00ecm c\u00e2u tr\u1ea3 l\u1eddi.
T\u00ednh B\u1ea5t to\u00e0n c\u1ee7a v\u0169 tr\u1ee5 kh\u00f4ng ph\u1ea3i l\u00e0 ch\u1ee9ng minh cho vi\u1ec7c Ch\u00faa t\u1ed3n t\u1ea1i. Nh\u01b0ng\u2026 \u0111\u00f3 L\u00c0 ch\u1ee9ng minh cho nh\u1eadn \u0111\u1ecbnh r\u1eb1ng \u0111\u1ec3 ki\u1ebfn t\u1ea1o n\u00ean m\u1ed9t m\u00f4 h\u00ecnh v\u0169 tr\u1ee5 h\u1ee3p l\u00fd th\u00ec ni\u1ec1m tin v\u00e0o Ch\u00faa kh\u00f4ng ch\u1ec9 logic 100%\u2026 m\u00e0 \u0111\u00f3 l\u00e0 \u0111i\u1ec1u c\u1ea7n thi\u1ebft.
5 ti\u00ean \u0111\u1ec1 c\u1ee7a Euclid kh\u00f4ng th\u1ec3 ch\u1ee9ng minh m\u1ed9t c\u00e1ch h\u00ecnh th\u1ee9c v\u00e0 Ch\u00faa c\u0169ng kh\u00f4ng th\u1ec3 ch\u1ee9ng minh m\u1ed9t c\u00e1ch h\u00ecnh th\u1ee9c . Nh\u01b0ng\u2026 gi\u1ed1ng nh\u01b0 b\u1ea1n kh\u00f4ng th\u1ec3 x\u00e2y d\u1ef1ng m\u1ed9t h\u1ec7 th\u1ed1ng h\u00ecnh h\u1ecdc ch\u1eb7t ch\u1ebd m\u00e0 kh\u00f4ng c\u00f3 5 ti\u00ean \u0111\u1ec1 c\u1ee7a Euclid, b\u1ea1n c\u0169ng kh\u00f4ng th\u1ec3 x\u00e2y d\u1ef1ng m\u1ed9t l\u00fd thuy\u1ebft m\u00f4 t\u1ea3 v\u0169 tr\u1ee5 ch\u1eb7t ch\u1ebd m\u00e0 kh\u00f4ng c\u00f3 Nguy\u00ean nh\u00e2n Ban \u0111\u1ea7u v\u00e0 m\u1ed9t C\u1ed9i Ngu\u1ed3n c\u1ee7a tr\u1eadt t\u1ef1.
Do \u0111\u00f3 \u0111\u1ee9c tin v\u00e0 khoa h\u1ecdc kh\u00f4ng ph\u1ea3i l\u00e0 k\u1ebb th\u00f9 c\u1ee7a nhau, m\u00e0 li\u00ean minh v\u1edbi nhau. \u0110i\u1ec1u \u0111\u00f3 \u0111\u00e3 \u0111\u00fang trong h\u00e0ng tr\u0103m n\u0103m, nh\u01b0ng \u0111\u1ebfn n\u0103m 1931 th\u00ec nh\u00e0 to\u00e1n h\u1ecdc tr\u1ebb g\u1ea7y \u1ed1m Kurt G\u00f6del \u0111\u00e3 ch\u1ee9ng minh \u0111i\u1ec1u \u0111\u00f3.
Kh\u00f4ng c\u00f3 th\u1eddi k\u1ef3 n\u00e0o trong l\u1ecbch s\u1eed nh\u00e2n lo\u1ea1i \u0111\u1ee9c tin v\u00e0o Ch\u00faa l\u1ea1i tr\u1edf n\u00ean c\u00f3 l\u00fd h\u01a1n, logic h\u01a1n, ho\u1eb7c ho\u00e0n h\u1ea3o h\u01a1n b\u1eb1ng khi n\u00f3 \u0111\u01b0\u1ee3c h\u1ed7 tr\u1ee3 b\u1edfi khoa h\u1ecdc v\u00e0 to\u00e1n h\u1ecdc.<\/p>\n\n\n\n

Perry Marshall<\/strong><\/p>\n\n\n\n

Link: https:\/\/viethungpham.com\/2014\/08\/29\/dinh-ly-bat-toan-cua-godel-kham-pha-toan-hoc-so-1-trong-the-ky-20\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

\u201c\u0110\u1ecbnh l\u00fd B\u1ea5t to\u00e0n c\u1ee7a G\u00f6del: Kh\u00e1m ph\u00e1 To\u00e1n h\u1ecdc s\u1ed1 1 trong th\u1ebf k\u1ef7 20\u201d l\u00e0 m\u1ed9t b\u00e0i gi\u1ea3ng c\u1ee7a Perry Marshall. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 b\u1ea3n l\u01b0\u1ee3c d\u1ecbch c\u1ee7a Ph\u1ea1m Vi\u1ec7t H\u01b0ng. Abstract: Gottfried Leibniz once said: \u201cWithout mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,13],"tags":[70,142,191],"class_list":["post-1025","post","type-post","status-publish","format-standard","hentry","category-sinh-menh","category-vu-tru","tag-godel","tag-suy-luan","tag-vu-tru-7"],"_links":{"self":[{"href":"https:\/\/truyenthong.edu.vn\/sanpham\/wp-json\/wp\/v2\/posts\/1025","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/truyenthong.edu.vn\/sanpham\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/truyenthong.edu.vn\/sanpham\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/truyenthong.edu.vn\/sanpham\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/truyenthong.edu.vn\/sanpham\/wp-json\/wp\/v2\/comments?post=1025"}],"version-history":[{"count":0,"href":"https:\/\/truyenthong.edu.vn\/sanpham\/wp-json\/wp\/v2\/posts\/1025\/revisions"}],"wp:attachment":[{"href":"https:\/\/truyenthong.edu.vn\/sanpham\/wp-json\/wp\/v2\/media?parent=1025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/truyenthong.edu.vn\/sanpham\/wp-json\/wp\/v2\/categories?post=1025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/truyenthong.edu.vn\/sanpham\/wp-json\/wp\/v2\/tags?post=1025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}