modernism science and uncertainty
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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 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”
Karl Popper (1902 – 1994)
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.
“All sheep are white.”
“All sheep are white.”
“All sheep are white.”
verifica*on
falsifica*on
Moritz Schlick
Karl Popper
A. J. Ayer (1910 – 1989)
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
“Most sheep are white.”
Problem No. 2: The Problem of Induc*on
induc5ve reasoning: extrac*ng a generaliza*on from specific facts or cases.
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.
induc*ve reasoning
Kurt Gödel (1906 – 1978)
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.
In other words….
An arithme*c system, for instance a finite 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.”