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.