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A"er	  Posi*vism:	  What’s	  Le"?	  
“…no	  statement	  which	  refers	  to	  a	  ‘reality’	  transcending	  the	  limits	  of	  all	  possible	  experience	  ...
Karl	  Popper	  (1902	  –	  1994)	  
Problem	  No.	  1:	  “Verifica*on”	  is	  too	  strong	  a	  criterion.	  If	  truth	  value	  requires	  verifica*on,	  the...
“All	  sheep	  are	  white.”	  
“All	  sheep	  are	  white.”	  
“All	  sheep	  are	  white.”	  
verifica*on	  Moritz	  Schlick	                           falsifica*on	                                             Karl	  P...
A.	  J.	  Ayer	  (1910	  –	  1989)	  
strong	  verifiability:	  verifica*on	  that	  makes	  the	  truth	  value	  of	  a	  proposi*on	  certain	  weak	  verifiabi...
“Most	  sheep	  are	  white.”	  
Problem	  No.	  2:	            The	  Problem	  of	  Induc*on	  induc5ve	  reasoning:	  extrac*ng	  a	    generaliza*on	  f...
induc*ve	  reasoning	  1.  In	  the	  past,	  most	  sheep	  have	      been	  white.	  2.  Today,	  most	  sheep	  are	  ...
induc*ve	  reasoning	  1.  In	  the	  past,	  the	  future	  has	      resembled	  the	  past.	  2.  Today,	  the	  future...
Kurt	  Gödel	  (1906	  –	  1978)	  
Gödel’s	  First	  Incompleteness	  Theorem	  	  Any	  effec5vely	  generated	  theory	  capable	  of	        expressing	  e...
In	  other	  words….	  An	  arithme*c	  system,	  for	  instance	  a	  finite	  set	  of	    axioms,	  cannot	  be	  BOTH	 ...
where….	  Consistent	  –>	  contains	  no	  logical/mathema*cal	    contradic*ons	  Complete	  –>	  describes	  all	  poss...
In	  other	  words….	  …there	  is	  an	  arithme*c	  statement	  that	  is	  true,	   but	  not	  provable	  by	  the	  t...
What	  does	  that	  mean	  for	  ra*onalism?	  
Logical	  systems	  can	  not	  be	  universal	              systems	  of	  thought.	  
…which	  is	  one	  descrip*on	  of:	       Modernism	  
Things	  fall	  apart;	  the	  center	  cannot	  hold;	  Mere	  anarchy	  is	  loosed	  upon	  the	  world…	  	  William	 ...
“Did	  you	  love	  your	  father?”	  “Yes.”	  “Prove	  it.”	  
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Modernism Science and Uncertainty


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Modernism Science and Uncertainty

  1. 1. A"er  Posi*vism:  What’s  Le"?  
  2. 2. “…no  statement  which  refers  to  a  ‘reality’  transcending  the  limits  of  all  possible  experience  can  possibly  have  any  literal  significance;  from  which  it  must  follow  that…  those  who  have  striven  to  describe  such  a  reality  have  all  been  devoted  to  the  produc*on  of  nonsense.”   Alfred  Jules  Ayer,   “The  Elimina*on  of  Metaphysics”  
  3. 3. Karl  Popper  (1902  –  1994)  
  4. 4. Problem  No.  1:  “Verifica*on”  is  too  strong  a  criterion.  If  truth  value  requires  verifica*on,  then   some  proposi*ons  can  never  be   considered  conclusively  true.    
  5. 5. “All  sheep  are  white.”  
  6. 6. “All  sheep  are  white.”  
  7. 7. “All  sheep  are  white.”  
  8. 8. verifica*on  Moritz  Schlick   falsifica*on   Karl  Popper  
  9. 9. A.  J.  Ayer  (1910  –  1989)  
  10. 10. strong  verifiability:  verifica*on  that  makes  the  truth  value  of  a  proposi*on  certain  weak  verifiability:  verifica*on  that  makes  the  truth  value  of  a  proposi*on  probable  
  11. 11. “Most  sheep  are  white.”  
  12. 12. Problem  No.  2:   The  Problem  of  Induc*on  induc5ve  reasoning:  extrac*ng  a   generaliza*on  from  specific  facts  or   cases.    
  13. 13. induc*ve  reasoning  1.  In  the  past,  most  sheep  have   been  white.  2.  Today,  most  sheep  are  white.  3.  Therefore,  in  the  future  most   sheep  will  probably  be  white.  
  14. 14. induc*ve  reasoning  1.  In  the  past,  the  future  has   resembled  the  past.  2.  Today,  the  future  resembles   the  past.  3.  Therefore,  in  the  future,  the   future  will  probably  resemble   the  past.  
  15. 15. Kurt  Gödel  (1906  –  1978)  
  16. 16. Gödel’s  First  Incompleteness  Theorem    Any  effec5vely  generated  theory  capable  of   expressing  elementary  arithme5c  cannot  be   both  consistent  and  complete.    In  par5cular,  for  any  consistent,  effec5vely   generated  formal  theory  that  proves  certain   basic  arithme5c  truths,  there  is  an   arithme5cal  statement  that  is  true,  but  not   provable  in  the  theory.  
  17. 17. In  other  words….  An  arithme*c  system,  for  instance  a  finite  set  of   axioms,  cannot  be  BOTH  consistent  and   complete.  
  18. 18. where….  Consistent  –>  contains  no  logical/mathema*cal   contradic*ons  Complete  –>  describes  all  possible  logical/ mathema*cal  statements.  
  19. 19. In  other  words….  …there  is  an  arithme*c  statement  that  is  true,   but  not  provable  by  the  theory.  Finite  lists  of  axioms  cannot  describe  a  system   where  all  statements  are  shown  to  be  true/ false.  
  20. 20. What  does  that  mean  for  ra*onalism?  
  21. 21. Logical  systems  can  not  be  universal   systems  of  thought.  
  22. 22. …which  is  one  descrip*on  of:   Modernism  
  23. 23. Things  fall  apart;  the  center  cannot  hold;  Mere  anarchy  is  loosed  upon  the  world…    William  Butler  Yeats,  “ The  Second  Coming”  
  24. 24. “Did  you  love  your  father?”  “Yes.”  “Prove  it.”