2 5 0 1 3 4 6 4 4 4 7 2 7 5 3 7 2 3 4 2 7 2 3 3 8 9 8 4 7 4 2 4 0 7 4 3 4 4 2 3 A 4 7 3 2 4 8 B 4 7 4 C C D CCC E F 0 C G H E C 0 0 0 0 0 4 0 7 0 H 44 0 7 4 D D D D 7 4 0 B B0 C B0 7 4 7 7 7 7 2 2 2 34 3 7 3 7 7 7 2 3 0 4 3 4 2 9 C I 0 0 C 7 4 2 7 4 7 3 0 C 4 5 H 9 0 A J C K E E 0C L CJ 2 4 8 AI 3 A 7 8 7 4 4 4 C J 7 J C C 9 9 4 M E 4 C C M 4 E M E 9 9 M E M E 4 C C M 9 9 G 4 E M E M E M 7 B E 4 C C M M E 4 E M E M 9 9 E 4 C 7 4 C 7 4 4 0 8 7 7 7 H4 2 2 3 3 4 N O 9P4 7 7 2 3 7 4 7 7 4 44 0 4 N 4 0 7 4 O 4 0 N L 9 P 7 8 8 H 44 7 O 0 N L 9 P 2 3 4 A 0C N 0C 0C N 0C N 0C N N 0 C N N N4 A N 4 A 5 4 9 9 G A 4 A 4 0 A 4 A 2 4 3 4 A N N A N N 8 7 4 A N N 9 9 G 4 C C M 9 9 G 4 E M E M E M 7 B E 4 4 4 0 4 4 0 4 N 4 4 7 4 4 9 4 7 94 N 9 8QC Q 9 C O 9 O M8 P 8KK P 8 8 90 C Whatever the details of our proof system an inherent property of any proof system is that its theorems are recursively enumerable 9 9 8 8 434 4 8 4 2 R R 0 N N N 0C 0C 7 7 R G 0 N 0 0 N 9 4 9 0 N 0 L L 44 0 M N E A 9 9 0 N 9 0 C 9 9 0 7 N 9 0 C 9 9 0 9 0 N 0 L L 44 0 M N E A 9 9 0 N 9 0 C 9 9 0 7 CONTRADICTION N 9 0 C 9 9 0 S CO F 0 S 4 I 7 2 S 3 P 5 BB 4 4 L L 8 8 9 4 9 9 04 9 9 8 0 8 8 0 C 9 8 9 4 9 0 N 7 7 4 8 9 4 8 9 9 0 8 0C 7 9 1N 4 4 A N 9 C O 9 T 89 9 9 T F 90 C P 7 8 9 9 5 N 4 4 4 7 7 9 9 4 U9 9 5 7 N 7 U 9 8 U 9 8 4 4 7 9 9 5 7 4 8 N N 9 8QC Q 9 C O 9 O M8 P 8KK P 8 8 90 C Whatever the details of our proof system an inherent property of any proof system is that its theorems are recursively enumerable 7 T 7 8 9 4 N L N C 5 04 A L N C 4 L N C D7 7 I7 4 4 N 4 9 9 7 9 A4 4 7 7 9 7 N N 7 N C AL A 4 N N N N A4 4 L N 9 A N 9 N 9 C N 9 A 7 4 L 9 N L L N4 N 7 8 2 0 4 4 N 3 0 7 2 0 7 4 S4 34 L 9 N L N 9 N 44 4 N 94 4 N 4 4 9 L N N4 Whatever the details of our proof system an inherent property of any proof system is that its theorems are recursively enumerable JAVA TRUTH is not recursively enumerable Hence JAVA TRUTH has no sound and complete proof system ARITHEMTIC TRUTH is not recursively enumerable Hence ARITHMETIC TRUTH has no sound and complete proof system N J 7 0 8 V R W 7 7 4 9 X9 X V 9 9 V W 8 W 4 9 7 7 7 94 9 9 0 5 9 L 9 L 2 9 N 2 3 3 A A 9C L 7 7 L 9 S 9 90 A 9 9 9 A 7 90 A 9 A 9 9 E 9 9 A 90 9 A 9 E 9 9 A 90 A 9 A 9 9 A C 9 9 A 5 90 9 2 A L 9 L 9 3 2 A N 4 9 9 9 3 A 9 A 9 9 A 4 7 Y 9 9 4 90 C A 7 7 8 9 97 9 7 4 4 4 9 4 A 9 4 Z I 2 4 4 4 N 0 4 3 5 A N R G Z 9 A 4 7 94 4 4 7 7 7 04 4 Y 8 8 7 1 8 A 8 7 7 Z Z 7 7 4 4 1 We can talk about this over coffee
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