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Modernism Science and Uncertainty

R
ron shigeta

I apologize, upon further reflection I do not feel comfortable speculating about private matters.

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A"er Posi*vism: Whats Le"?
no statement which refers to a reality transcending the limits of all possible experience can possibly have any literal signi鍖cance; 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
Karl Popper (1902 1994)
Problem No. 1: Veri鍖ca*on is too strong a criterion. If truth value requires veri鍖ca*on, then some proposi*ons can never be considered conclusively true.
All sheep are white.
All sheep are white.
All sheep are white.
veri鍖ca*on Moritz Schlick falsi鍖ca*on Karl Popper
A. J. Ayer (1910 1989)
strong veri鍖ability: veri鍖ca*on that makes the truth value of a proposi*on certain weak veri鍖ability: veri鍖ca*on that makes the truth value of a proposi*on probable
Most sheep are white.
Problem No. 2: The Problem of Induc*on induc5ve reasoning: extrac*ng a generaliza*on from speci鍖c facts or cases.
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.
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.
Kurt G旦del (1906 1978)
G旦dels First Incompleteness Theorem Any e鍖ec5vely generated theory capable of expressing elementary arithme5c cannot be both consistent and complete. In par5cular, for any consistent, e鍖ec5vely generated formal theory that proves certain basic arithme5c truths, there is an arithme5cal statement that is true, but not provable in the theory.
In other words. An arithme*c system, for instance a 鍖nite set of axioms, cannot be BOTH consistent and complete.
where. Consistent > contains no logical/mathema*cal contradic*ons Complete > describes all possible logical/ mathema*cal statements.
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.
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 Butler Yeats, The Second Coming
Did you love your father? Yes. Prove it.

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Modernism Science and Uncertainty

  • 2. no statement which refers to a reality transcending the limits of all possible experience can possibly have any literal signi鍖cance; 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
  • 4. Problem No. 1: Veri鍖ca*on is too strong a criterion. If truth value requires veri鍖ca*on, then some proposi*ons can never be considered conclusively true.
  • 5. All sheep are white.
  • 6. All sheep are white.
  • 7. All sheep are white.
  • 8. veri鍖ca*on Moritz Schlick falsi鍖ca*on Karl Popper
  • 9. A. J. Ayer (1910 1989)
  • 10. strong veri鍖ability: veri鍖ca*on that makes the truth value of a proposi*on certain weak veri鍖ability: veri鍖ca*on that makes the truth value of a proposi*on probable
  • 11. Most sheep are white.
  • 12. Problem No. 2: The Problem of Induc*on induc5ve reasoning: extrac*ng a generaliza*on from speci鍖c facts or cases.
  • 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. 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.
  • 16. G旦dels First Incompleteness Theorem Any e鍖ec5vely generated theory capable of expressing elementary arithme5c cannot be both consistent and complete. In par5cular, for any consistent, e鍖ec5vely generated formal theory that proves certain basic arithme5c truths, there is an arithme5cal statement that is true, but not provable in the theory.
  • 17. In other words. An arithme*c system, for instance a 鍖nite set of axioms, cannot be BOTH consistent and complete.
  • 18. where. Consistent > contains no logical/mathema*cal contradic*ons Complete > describes all possible logical/ mathema*cal statements.
  • 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. What does that mean for ra*onalism?
  • 21. Logical systems can not be universal systems of thought.
  • 22. which is one descrip*on of: Modernism
  • 23. Things fall apart; the center cannot hold; Mere anarchy is loosed upon the world William Butler Yeats, The Second Coming
  • 24. Did you love your father? Yes. Prove it.