Comments

  • Popper and Turing: are they saying the exact same thing?
    Induction in the sense of mathematical induction, the only induction that gives the possibility of asserting something general given a set of examples, is not applicable in the vast majority of science. Popper says this.
    The only thing you can say is that the more positive examples you find, the more probable your theory is. This is statistical inference, a sort of induction: the more examples you have, the more precise you can be. This can be seen either from the positive part: the more positive examples you find, the better your theory is, but also on the other way round: as long as you don't find negative examples, your theory gets strength. The latter is what Popper says. But is equivalent to the former.

    I read this: "Thus Popper stresses that it should not be inferred from the fact that a theory has withstood the most rigorous testing, for however long a period of time, that it has been verified; rather we should recognise that such a theory has received a high measure of corroboration. and may be provisionally retained as the best available theory until it is finally falsified (if indeed it is ever falsified), and/or is superseded by a better theory." (http://plato.stanford.edu/entries/popper/), when I say "stronger" I mean "such a theory has received a high measure of corroboration".