Popper and Turing: are they saying the exact same thing?

MadMage

Dear all philosophers,
in a discussion of some days ago, it happened that I remember the though of K. Popper, in particular his arguments against the induction in the scientific method. For all computer scientists like me, this argument is obvious and it is related to the computability and semi-decidible sets, formalized by Alan Turing: there are many problems that are semi-decidible, that is, if you find a negative solution, the answer is "no", but you can go forever in finding positive solutions and never be sure that you will not find, eventually, a negative one.

This leads me to three thoughts:
1) they seem to say the exact same thing, so why are they not citing each other? the answer can be that there are only some years of difference between the two and they belong to very different areas (philosophy and mathematics); is this correlation been noticed by someone else (I assume yes): who and when?

2) thinking with the computability in mind, Popper says to be against induction, but also says that you (or others) can go on looking for negative examples for your theory and that the longer your theory lasts, the stronger it is: this is actually again induction!

3) the current scientific method is much more similar to Popper's idea than to Galileo's one: actually Popper changed Galileo's method:
- observe similar cases
- induce a law
- describe the model
- test your model with other cases

with this:
- find a law, in whatever way you prefer, being it induction, dreaming, intuition or other means
- describe the model
- test your model and make other people test it so that your theory become stronger

It seems that it extended Galileo's method, more than going against it. Can we say that the current scientific method is the Popper's extension of the original Galileo's method?

Thanks to all.

tom

2) thinking with the computability in mind, Popper says to be against induction, but also says that you (or others) can go on looking for negative examples for your theory and that the longer your theory lasts, the stronger it is: this is actually again induction! — MadMage

That certainly is not induction, which Popper showed to be a myth. Deducing singular statements from an existing theory for the purpose of testing has nothing to do with induction!

- find a law, in whatever way you prefer, being it induction, dreaming, intuition or other means
- describe the model
- test your model and make other people test it so that your theory become stronger — MadMage

Except, that for Popper, your theory doesn't become "stronger", whatever you might mean by that.

It's a travesty that "induction" is still taught to school kids!

I'm not sure what semi-decidable sets has to do with Popper (don't forget LSD was published in 1934). The asymmetry between verification and falsification that he exploits in his method is the asymmetry between the impossible and useless and the (tentatively) possible and productive.

wuliheron

Popper is actually the quintessential academic clown bravely taking a pie-in-the-face literally for the cause of causality. You have to respect a popular philosopher of science who can promote a contradiction that even flies in the face of empirical evidence in the name of growth and progress and being reasonable. His philosophy is related to that of Niels Bohr who famously shouted, "Shut up and calculate!" The assumption being that, all nonsense aside, any academic slapstick will all be revealed in good time by merely accumulating more evidence!

Everything being context dependent means even whether you consider a pet rock conscious just depends upon the situation. Already experts as attempting to produce a super Von Neumann architecture, but mother nature having a sense of humor that rivals her beauty means consciousness itself can be considered merely another aspect of the original creative impetus of the Big Bang still expanding to this day.

tom

His philosophy is related to that of Niels Bohr who famously shouted, "Shut up and calculate!" — wuliheron

Except that Popper completely disagreed with Bohr, and Bohr never said that.

Janus

↪tom

Don't you mean "we have no good reason to believe that Bohr ever said that"? Then the question becomes: 'if we reject induction what good reason could we ever have for believing either that Bohr did, or did not, say that'?

wuliheron

Bohr said it in another quantum universe and I'm sure it just caught up with him.

MadMage

↪tom

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".

Popper and Turing: are they saying the exact same thing?

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