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Induction

Page history last edited by olivier 14 years, 1 month ago
  • Naive Inductivism

 

    • Objective observation of the facts regarding a phenomenon under investigation.
    • Inductive generalization from the facts, producing a universal theory of the phenomenon.
    • Empirical justification of the theory, producing a quantitative measure of certainty.
    • Reliable prophesy.

 

  • Einstein

 

"Physics constitutes a logical system of thought which is in a state of evolution, whose basis cannot be distilled, as it were, from experience by an inductive

method, but can only be arrived at by free invention." -Physics and Reality

 

  • Einstein

"Altogether I do not like the now fashionable positivistic tendency of clinging to what is observable..., and I think (like you by the way) that theory cannot be fabricated out of the results of observation, but that it can only be invented."

-In a letter to Karl Popper

 

  • Gödel

Incompleteness Theorems:Every nontrivial reasoning system contains questions that cannot be answered within that system

 

  • Turing

Turing Machines and the Halting Problem:

No procedure to answer arbitrary questions given perfect information can exist. No logical principle of induction can exist.

 

  • Algorithmic Information Theory:Knowledge development is compression. Uncertainty is fundamental, and the truth is almost always beyond full comprehension.

 

  • Critical Rationalism

 

"... science grows, and may even approach the truth, not by amassing supporting evidence, but through an unending cycle of problems, tentative solutions --unjustifiable conjectures--and error elimination; i.e., the vigorous testing of deductive consequences and the refutation of conjectures that fail.... More generally, criticism is installed as the hallmark of rationality, and the traditional justificationist insistence on proof, conclusive or inconclusive, on confirmation, and on positive argument, is repudiated"

 

  • The Morals of the Story
    • No principle of induction has ever been furnished. It turns out that no such principle can possibly exist.
    • The single answer is not inevitable in principle given sufficient information. Providing the same facts simply does not produce ‘shared understanding’ and thereby enable ‘self-synchronization’.
    • Uncertainty is proven to be fundamental, it is not a mere residue of insufficient information.
    • The truth might be out there, but it almost always lies beyond full comprehension. It often lies beyond any comprehension at all.
    • We are left to simplify, approximate, for the truth is almost always beyond full comprehension. We normally cannot even know if one of our simplifications is closer to the truth than another.

 

 

But as for certain truth, no man has known it

Nor will he know it; neither of the gods,

Nor yet of all the things of which I speak.

And if by chance he were to utter

The final truth, he would himself not know it:

For all is but a woven web of guesses.

-Xenophanes

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