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How Tarski defined the undefinable How Tarski defined the undefinable

How Tarski defined the undefinable - PDF document

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How Tarski defined the undefinable - PPT Presentation

CEZARY CIELISKI Logic Department of the Institute of Philosophy University of Warsaw Email ccieslinskiuwedupl n r ID: 203595

 CEZARY CIELISKI Logic Department

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 How Tarski defined the undefinable CEZARY CIELISKI Logic Department of the Institute of Philosophy, University of Warsaw E-mail: c.cieslinski@uw.edu.pl   \n   \r       \n \n\n      \n  \n  \n \n      \n \r\n \r\r\n \n\r\n \n  \n\n\r\n\n\r \n\r\r \r\r!\n \n"#$%& \r\n'\r  \r!\n \n\r\r\r\n\r\n\n\n\r \r \r!\n \n\n \r\n\r \r\n\n\r\n\n\n\r  \n \r( \r\n \n) \n \r\r*\n+\n\r ,\n-.\r \r/\r \r-  $!\n \n 0\n\r \r\r \n \n  \r\n \r \r1\n\r\r\r!!\n"" \n \r\r 12\r \n\r34/\r\r\r \r \r5 / \r \r+\n\r ,\n-.\r \r6\r \n\r\n \r\r1\r 0\n\r\n   \r \r  / \r 7"\n\n -.\r \r / \n\r312  \n\r  5"\n \r  \n \n \r\n 12 -.\r \r/\r\n \n \r\n\n\n'\r  \r!\n \n\n \n\n\r  \n \r\n \n\r!\n \n+\r\r \n //\n\r\n \n\n\n\r \n\n \n \r!\n \n" 8 \n \r'+\n /\n\r'\r+\r9 \r\n \n \r \r\n\r\n 9 /\n \n \r \r0!!\n""  \n\r /\n:/\n\r\r\r\n \r \r\n\r\r\n \n\n; \n\n/\r \n\r\r\n\n\r \n\n\r \r\r; \r#8 \n \r\n \n/\r\r \r\r \r\n \n /\r  \r \r/\n\r\r  \r\r   \r \n\n\r/\n\r\r  \r\n  /\n\n\n"\n/\n/\r \r+\n;\n\n/ / \r\r /\r \n \n\n \n\n/ \r\n\r\r/\r \n\n \r\n\n\n\n      !  !"\r#$%&%'( \r#$%)*' \r    +\n (#),,-'    \r\n .\n\n/( % \r\r\n \r  \r  \n\n \n 3;\n\n$ \n \r/\n\n=5/  \r\n\r\r\n\n \r\n \n  /\r \r \r \n \n\n\n\n \n  \r\n4 \n\r  \r\n\n=\r\n\r*\n\r\n/\r\r \n\r \n\n  \n/\r / \n\r\r\n \r\r  \n \r(  \n\r \r\r\r  \r\r\r\r\r  \r\n\r \n \r\r  \r \n\n 3\n\r5\n\r \n\r\n//\n/\r\r   \r  \r \r\r\r\r\n\n\n\r\n\n\n\r\n\r\n\r\r\r /\n/\r  \r \n \r(  \r\n$\r\n\n\n \r\r\n \n \r\n / \r\n\n"\r\r\n  \n\r \n \r\n \n\r4\n  \n\n\n\r\n/\r \r\r\r4\r \n \r\n\r\r \n \n\r\r \r\n\r \r/ \r\n \r\n �\n/\n\r\r\n\r\r\n\r \r\n\r�"\n "\r\n \r ? \r \r\n \r\r\n \r \n \r(  \r \n \r \n+\r\n\r\r /\r / \n \n \r? \r \n\n-  \n\r \n \r\n? \n/\r \n/\n  • 3  \n\n\r \n\r\r \n\r \n\r\r \r \n \r \n\n\r \n\r\r \n\n\r \n\r\r \r 5\r  \n @A%A• 3B\r\n  \n\n?\n\r\r \r56 \r \r\r\r 7 \n ?\r\n  \r\n "CD• 3 \r\n\r\r\r\n\n\r\r \n\r\r\r\r \r \n\n/ // 5"E\n\n\n\r\r FA$#G;#% \n\r \r ?\r\n \nE\n\n /\r\n\r /H/\n /\r\n\n\r\r\r  // \r6\r\r7\n\r H3\r53\n5 3 /5\r \n  \r\r\n\r\n \r\r\n\rH\r \r  \n \n /6\r\r7\r\n\r4\n\r ( \n\r  \n\r \r\r  /H\r  (0 (\n \r+#$%)-'1      \n23  \n \n 4     \n  + \n  3  \n    5    \r#$%**'4 \r#$%--' 8\r  \n /\n\r\r/ \r\r \n\n\n\n \n\r\r\n\r \r\n//\n\r  \n3\n\r 5\r \n  \r\n\r  \n3\n  5\r  \r\n  0\r\n ?\r\n \nE\n\n\n  /\n\r\r \n \r \r \r\r\n\r  /\r\r\r ?\r//\n\r/\n/\r /  \r \n//\n\n\n \r \n \r(   \n\r\r\n=/\n\n\r \r\n \r/ I\r   \n ? \r \n6\n 7\n \n /\n\r+ \n\r\r 6\r\r\r 7\n /\n \n\r/\n\n= !\n\r\r  \r  \r \r  \n \n"\r  /\r\n\r\r? \r   \n\nH6\n7!\n   \n /\n\r\r \r  �.07;ͥ " H\n \n$\n �.07;ͥ 67!\r\n \n\r\n //  \n\r\n /\n\r$\n �.07;ͥ 67!\n\r \n /\n\r�.07;ͥ B\n\r \n  \n\r ? \r6\n74/\r \r  \r\n\r\r   0\r\r \r \n\n\r*\r/ \n\r 4\r \n//\n\n:\r  3+\r \r5\nJ\n 3+\r \r 5 \n\r\n\r\r  \r 6\r  7\n\n\r\r\n   \r\n \n\n\r \n   \n\n \n /\r\n$\n 1/ \r\r\r  \n =/   \r  \n=/  \n// \r\r3+\r \r5\n3+\r \r 5=/  \n// \r\r6\n// \r\r\n \r \r7\n\r\r // \r\r   \r\r  \r\n \n\n\n \n +\r\n\n\r\n $\n  \r=\n/ \r \n / \r\n   \n\n\n/\n\r\n\r 6/\n/  \n\r\n\n\n\n \r \r7;\n\n \r\n\n=/\n\n\r\r /\r   $\n  ? \r67\r \r \n\r $\n / \n\r\n \n \n \n\n\r\n\r\r\r \n\n\n /\r\r�.07;ͥ "  0\r \r\n\n\n$\n \r/\r /  &\n\n\n//\n\n \r \r\n\r\n   /    \n I=\n/\r \n\nJ \r \n\r 3J \r 5 /\r \n6; \r/\n \r\n \n \r\n /\r /\r\n? \r \n\n\n 0\n\n=\n�.07;ᚒ耀7C \r67\r \n  !\n\r \n /\n\r\n\r $\n\n\n\r \nH\n// \r\r\n\n\n\r \r �.07;ᚒ耀"   \r\r\n\r ?\r0 \n// \r\r \n \r\r\n /\r\n�.07;ᚒ耀 /\r\r\n\n\r \r  /\n\r�.07;ᚒ耀\r\rKK\n/\r / /\r \n\r \r\r\n\r\r\n\n   \n\n? \r ;\n\n /\n\n  \n\r/\n\n= \n  \r \r\r\r \n \n \n\r \nL\n \n\r/\n\n= \n \r   \n 0 \r\n \n\r/\n\n= 0\r \n\r\n/\n\n=9 \r 6-7 \n\r\r  \n\r 6-7 H6-7\r \n " 6-7\n �.07;ᚒ耀 \r/\n \r \r  \n\n \r ? \r\r  \r\n!\n\n \r \r\r\n\n   /\n\n H\n \n6-7\r  \r\r =\n\n 6-7 \n  \r6-7 \n \n6-7\r \n \r \n6-7\r \r\n \n\r\r\r\n\n /\r\n6-7\r  H6-7\r \n  \r\r \n 6-7 \n \n \r6-7 \n \n6-7\r \n \r \n6-7\r \n \n\r\r\r\n\n /\r1\n\n= \r  \n /\n\r \n\r\r     \r\r\n/\n\n=\r \n\rJ /\r /:\r L\r \n \n\n \n\r\n\r \r\r \r\r6\n3\r\n/\n\n=57\n\r  \r\r  \n 3:/\r\r /\n\n=5"\n\r\n:/\r\r \n9\n \n \n\n9\n \n\n \r" \r�.07;ᚒ耀"\r \r\n\r /\r\r \n//\n \r\r\n\r:\r (\r\n\r   \r /\n\r \r "\n /\r\n\n +  \r   $ \n36  $ \r7(    $#   \r  '   \n\n \n 8      \r F9\n \n\n \r\n  \n\r\n\n\r\rH:/\r\r \r \n9\n\n\n\n\r\n /\r \n  M;\r   \n 9\n  \r \n:/\r\r \rN\n\r\r "\r  /\n \r\r \n\r\n  \r \r\n\n\n\r\r\r /" \r / \n\r\rKK\n \n \n\n  \r\r\r  /\r / \n/=/\n\r\r\r \n  \n\r\n\n \r \n \n \n\r\n \n \r\n /\r\r \r\n\r EJO/\rH9 8   \n  :;      \n\n  \n  \n\n  \n+\n\r 0\n\r \r/\r\r  \r\n\r\n\n \r\r\r/\n\r \n \r\r\r\r \r=/ \r 0\n \n\n /  \r\n/\n\r\n/ \r "9\n\n/(  H:= \r        2:;       \n\n :;  \n\n         \r\n     \n  \n \r(  \n\n \r\n\r/\n \r \r\r\n\r\r\n\r\r\n \n /\n \r\r\r/\n\r\r\r\n\r\n\r \r/\r6\n\n357  \n\n \n\r\r/\n\r "\n "\r \n \r\n  \n \r( \n//\n\n\r\r\n \n \r=/\r\r\r \n\r \n\n/\r\r\n\n\n\n \r :\r \r \n \r /\r\n35\r\n\n\n\n / \r \r \r 6\n \r\r\n/\n\n=7 \r \n\n\r*\n\r\r\n\n\n\n \r / \r4\n  \r \n\n\n\r*\n\r\n\n\n I\n \n \r\n\r \r\r\n\n\n\n\n\n\n\n"\r\r \n\n\r\n\n /\n \n"\n\r\n\n\r \r\r  \r +  �04?@\nA#),,*'$,B #$%-&'C D//\r \n\r\r\n  \r  \n\r\r\n\r/\r\n\r" \n\r  \r\n\n\n\r\r\r/\n\n\n0 / ;\r\n \n\n\n\r\r\r 6\r7 \r \n\r  \r \r \r\n\n\nH\n\n  /\n \n\n\n \n\n\r\r\n=\n/ \r\n \r\n\r\r  \r:\r \n//\r J\n   \n H : 0\n\n6\rJ\n7  3: 5\r 0\n\n\n6:\r 7  3: 5\r / 8 0\n\n\n6:\r 7"\n "\r\n \n\n\n\n\n\r \n \n=/ \r \n\n6\n \r\r ?\n\r\r 7'\r \r\n =\n/"\r\n \n \n\n\n\n\n\r \n\n\r 0\n  \n\n \n \n\n\n\n4 \n \r( \n//\n$\n \n  6? \r6\n7\r  \n\r7L /\r\r\n/\r\n35\r\n\n \n//\r  \n\r=\n\n\n\r \n\r\r  \n\r=/ \r 6\r\n \r/\n\r\n\n/\n  \r 3 57+\n \r\r\n   \r/\r\n\n\n\n  \n\r= \n\n\n\n \r :\r  /\r  \r\n\r H\n=/ \r3 :\r 5\r \r \n:\r =/ \rP\r\n \n \n \r\r \r\r \r\r\r\r  \n\r H\n\n/\n\r\r\r \n\n\n\r\n\n?\n• I\nH\r \n=/\r\r\r\r\r6\n\r\r\r3 \r \r\n\rQ57 \r/ \r \r \n\r/ \r \r• L\n\r\n\n?\nH\r \n/\n\r\r\r\r / \n \r\r\r / \n\n\r \r/\r  \n \r/\r\n\r\r\r\n\r \n  9\n\r  / / \r\r\r\r \n \r\n  \n\r\r\r\r\r \n\r\r \n\r\r\r/\r\n\n \r\n\n \r \n\r4\n\n\r\n\n?\n\r\r\n  \n\n \r \n \nI\r \r \n/\n\r\r\n\r\n \r\n3\n/5 \n\n\r�.07;ᚒ耀"\r \n\r /\r\n \n \r\n  \r \n  \n\r \n\n\r\n\n?\n/ \n\r\n\r\r\r\n?\r\n\n\r\n A\n\r  \n\n\nH\r\r\r6\r\n=\r \n\r\r\n\r \r\r\r7 \r/\n \n $  \r\n\r\r\r\n H\r \r\n\r\r\n\n\n\r \n\n   \r35\n\r     \r35-   =\n/  $  H3+\r \r5\r \r\n\r \r \r3%R%S&5\r \r\n%R%S&3 ?:\n\r \r 5\r \r\n\r?:\n\r \r  \r\r\r\r \n\r\n//\r\n\r \r \n \n \r\r ?\n\rH\n\n \r ?\r \n/\n\r\r    \r \r \n\r\r\r\r \r\r \n \r\n /  \r\r \n \r \r \r \n \n \r\n  \n\r \r\r\r\n \n\r\r\r\r\n \r \n \n\n   \n \n \n \r\r \n \n\r\r\n3 \n\r \n\r5+\n\r \n\r \r \n \n\n\r \r\n\n \n\n"   \n\r\n\r \r \n\n\r\n  0\r\n/\r\n\n\n\n \n  \r\n \n\n \n  9 \r\n\n\r\n\n\n\n\r\r\n \n=\n/  =/ \r \n \n\r\n \r\r \n\n\n\r 6\n\r 7 \n\r\n 6\r \n  \r 7\n?\n\r\r \r \n\n 35\n35 \r \r \n?\n\r\r\n\n 3 53\n5 \r =\r \r\n?\n\r\r\n\n 3 53\r 5 =/ \r \n=\n/ \n\r\r\n  H6\n76RS7676RS7 \n\r\r\n\n\n\rH6\n7\r \n \n\n\r \r  \n \n 67 \n\r \r  \n \n 6! \n \r\n\r  \r \r\r\n=\n/\n \r \n\n 7 92    \r\n    \n    \n   \n36D 7 \n \n  \n  8  \n\r?  #;6\n7\n67\n=\n/ \n\r\r\n   H \n \n\r\n\r  \r\r  /\r\r\r \n 6\r\r \n  \n\r\n\r /\n?\n\r\r7  6\r\r /=\r \r\n?\n\r\r7" \n \r\n\r \n\n\n  \n\r\n \n!\r\n?\n\r\r4\n \n\r\r\n=/ \r \n\n\n\r\n\n\r\r \n\r\n H67=R=S=! \n\n=/ \r67\r \n\n\n  \n \r \r\r \r\n H \n\r \n\r \r/"\r \n \n \n\r\n \n?\n\r\r\r\n\n\n\n?\n\r\r3\r 53 5\n\n67"\n  \n\n \r\n\r \n\r\n   \n\r\r\n\n\r* \n \r\r \r \n6 \n\r7\n\r \n\r \n\r\r \n 0/ \r\r \n\r\n 0\n ?  \r \r\r\r \r\n\r \n  9 \r\n\n\r \n\r\n 3\r \n\n59 \r ?6J7N \n\nH \n3\r \n\n5\r  \n\r \r ?6J7\r\n\r\r \n\nJ" \n\r\r / \r\n\r*\r \n\r\n\n \n\n\n =\n/\n\n\n\r  \n \r\n ?\n\n\n#\n\n\r\n 3T\nU5 \n \n\n \r \n\r \n\r\n\n=/\n\r\n  \r/\n6  \r/\n\r\n\n\r\n T\nU\n  /\n\n \n\r \r\n ?7 \n\rH\r  \n\r \r\r\n\rT\r  \n\r \r\nU\r  \n\r \r   \r  \n\n=\n\r\n\n \n\n\n \r \n\r \n\r\n\r\r \r \r\r  \n\r \n\r" \n\n \n\n\r  \n\r \r\r\n ?  \r   \n\r/ \n\r\n\n\r\r\r\r\r H\n(  \n\r \r\n\r\r\n\r  ?/ \r/\n\r6/ \r ?7 \n\r\n \r\r \n9 \r\n3\r \n\r\r\n\r50\r\r \n\r \r ? \r\n\r\r\n\r\n \r \n \r\r \n \r\n\n\r\r\n \n\r\n \r/\r"\n \n 6\r\r 0\r0\n\n\r \n\r\n 7 ?\n \n  \r/\r \n  3J\r \n\n5\r  \n\r \r\n \n\r\n ?0 \n6P\n2\n\rJ\n70\r\n\rJ\r \n\n:  ?\n\r\r \n  \r\n \n\r  \n\r\n \r/ \r\r/\n\r"\r\r\r\r\n\n/H \r \r\n\r\r\r  \n\r \r\n " \n\n\r\r\r \r\r \n \n\r \r \n\n\n\r\n\n?\n\r\r \n \n /\n \r\r\r/\n\nM \n\n\r \n  \n!/\n\r 6-7 \n\r\r \n \r\r\n \r \r\n/\n\n=N\r \n \r\n/\r\n\n\n\n\n \n\n\rH\r 6-7\n �-\r \n \r\n/\r\n\n\n \r\n 6-7\r  \r\n  \n\rH6-7\r \r"\n\n*\n \r6-7\n \r  \n\r H6-7 \n\n%+6-7\r \r8 6-7"  \n6-7\r \r %4  \r \n6-7\n\r  \n \r\n/\r\n\r \n\n\r\n /\r \n\r \n\r=/ \r \r   \n\r\r \n ! \r\n\r\r\n  \n\n\n/\r\n\r 6-7\r\r \r6 %\n 7+\r\n( \n6-7 \n \r /8\n6-7\r \n/\r \n\r \n\n 6-7\r \r\r\r 0\r\n\n\n6-7 \n  \r\n\n\n\r M \r /\n\r  \r " \n \r( \n \n\r \r\n6-7\r \r"\n6-7\n\n  \r /8\r \r0\n  \n\r  \n\n\n\r\n6-7 "\r \n\n\r\r\r \n \r\r\r\r\n6-7\n\r\n\r \r  \r \r\r\r\n=/  \r \n \r\n\n H\n\r\n/\r\n\r\n\n\n\n\n$=\r\r/\r\n\n/\n \r" \r= \n\r/ \r \n\n\n\n \n\n\n\r\r  \n: \n  6-7\r\n \r\r\r  /\r\n= \r \n \r\n\r\n   \n\n\n \n \r \r/ \n \n\n \r\n\r\r6\r\r\r\n\r \n?\r 3 \n \r( 57"\n\r\n  \n \n\r \r\n! \n \n \n \r/ \r\n\r\r\r \n\r\n\r\r\n \r \n \r�.07;ဩ \n \r \r\n\n\n\r \n \r( "\n\n  \r \n \n\n\r\r\n\n\r\r\n\r\rL\n\r \n \n\n\n\n\r\n \n \n\r\n \r\r \n\r\n\n\r " H\r\n\r\n\n\r\n \r\n\n\r " \n \r   \n\r\r\r\r\n\r\n!\n\r \r\n\n=/\n\n\r\r\r /\n/H\r\n\r\n\n\n\r\r\n\r\n \n \r \r \r\r\r\n\r\n\n\n \n\n\n\n \n35 \n \r   \n\n  //\n\nN\n\r\n+\r9\r9\n6N9N7\r \r2:9$%GG;G+G8VW;\n\n+\n \n \r6%&73+\nX/ \r\r   /\r /\n\r  /\r  5#\r\n D//%&&$%AA V%W9\n\n/P6&\r \n \n 9\n\rL\n \n  \n \n'\r  \r 1 V8WI\n\nI\n+6%&7' (\n%\n\n 9\n\r'\r  \r1 9\n\rV&WJOE6%87 (  "B4='\r  \r1 4=VFW \n \r6%8734\n*\r/\r\r  \r52\n\r \n\r/\r \r1*YI\r*Z* %D//D#0#:\r \n \n\r\n//\n \r6 \n \r#87//0%8\r34/\r\r\r \r \r5 VDW \n \r688731[\r/\n[* \n\n  5 \n* N\n !\n *\n \r \n \n!\n 3 /\r\n\r*\n\n 5\r \n \r6#87//F%$%A# VAW \n \r6&&73  \n\r/\r\n\n\r  \n\r 5\n \n   &//8&08ADV#W \n \r6#87\n ) \n )\n % *+*+,6\n \n\r !7\n 1\r \r9/\n"\r\n\n/\r "\r\n\nVW!\ \r6#7\n \n \n--./  E\n\r1\r 2

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