Hume was *wrong* in certain crucial respects.

[David Wolpert]

Um, to just make one last statement before leaving well enough alone (at
least, so I hope).

This thread is dismayingly full of word arguments rather than formal math.
Relying on such arguments can be very dangerous. For example, even the
arguments of Hume, being word arguments, are wrong in the conclusions they
reach in certain important respects. (Or they are at best misleadingly
incomplete - being word arguments, who can even be 100% sure what they
say?)

Mathematically proven ways in which one *can* justify "induction", without
making any assumptions, are discussed in the following article. This
article also relates these results to the other respects in which Hume was
exactly correct. (All is subtlety - far more than mere words can convey.)

David H. Wolpert, "The existence of a priori distinctions between learning
algorithms", Neural Computation, vol. 7, p. 1391, 1996.

Interested readers are encouraged to read subsequent articles in Neural
Computation by Zhu and many others, extending the analysis to time-series
analysis, the estimation of noise levels, etc.




Signing off for now,

David Wolpert