What are the best examples of genuine progress in philosophy?
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Replying to @keithfrankish
Hilbert’s switch to constructivism (computationalism) in the wake of Gödel and Turing demonstrating the undecidability of stateless mathematical semantics. Solomonoff induction as a proposed general principle of unified understanding.
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Replying to @Plinz @keithfrankish
Isn't Solmonoff induction a variation on Occam's razor? Is Occam's razor valid?
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Replying to @IntuitMachine @keithfrankish
No, it’s more complicated. Optimizing for low Kolmogoroff complexity of a model is only part of it (and the criterion is not a heuristic).
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Replying to @Plinz @keithfrankish
Kolmogorov complexity is a measure based on the instruction length of the generating function. It follows the same logic of Ockham's razor. That is the Law of Parsimony. But this logic is a heuristic that is related more to the likelihood of causality than complexity.
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Taking this further, the proof of Fermat's Last Theorem is extremely long yet its formulation can be scribbled in the margins of a book. The problem with many measures of complexity is that few of them are useful.
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All models are wrong, but some are useful. Can we say the same about models of complexity? All are wrong, but which ones are useful?
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We have to be wary about the 'Law of Parsimony'. It's an intrinsic human cognitive bias to prefer short models of reality.
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Replying to @IntuitMachine @keithfrankish
In practice, the computational cost of dealing with a model has to be accounted for, but the principle of Solomonoff induction goes for optimality. It does not introduce a bias, it looks for the shortest among the best models.
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How do we come up with the best candidate models in the first place? Also via the solomonoff principle?
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That is precisely the problem. For domains of unbounded complexity, Solomonoff induction is not computable. A rational agent may approximate it but must compare the cost of modeling to the expected benefit of having a better model, which in turn usually depends on lossy models.
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