how does induction relate to falsifiability, and when does one trump the other?
Inductive Reasoning is the traditional tool of the Empiricism epistemology. Falsifiability or testability is Popper's criterion for demarcating scientific knowledge from everything else.
The latter relates to the former most famously in the writings of Popper, first in The Logic of Scientific Discovery, then in Conjectures and Refutations.
Popper suggests his own Epistemology, titled Critical Rationalism, according to which the advancement of our knowledge goes as follows: Using creativity, you come up with a hypothesis (hypothesis here means a falsifiable statement or theory), then, you try to refute it by aiming to find counter examples of deduced statements from said hypothesis. As long as no successful such refutations has been made, your hypothesis remains a Tentative Knowledge. The other kind of knowledge Popper acknowledges of is not scientific. i.e., for Popper, all scientific knowledge is tentative in that it can never be ultimately justified. The only thing we can do is endlessly minimize our error towards an accurate description of reality.
This works, according to Popper, because if "If A then B" then given "Not B" we get "Not A". Now A is the hypothesis at question, and B is a conclusion deduced from A; If we are convinced that the conclusion is false, then by Modus Tollens, the hypothesis is refuted.
Every failed serious attempt to refute a hypothesis is a further corroboration of it.
The methodology suggested by the classical Empiricist epistemology, employing induction alone, is to say that if "If A then B" then given "B" we get corroboration of A. Popper attacks this by reminding us that this is not logically valid. "B" could also be explained by infinite other theories other then A. The only logical way around this is to say that A could not be true if "Not B" is true.
According to induction alone, Newtonian physics is true just as anything else, including the Theory of Relativity. This is Popper's point: Only refutations progress our knowledge, and his canonical example is that of moving from Newton to Einstein. The newer theory replaced the old one (in terms of scientific explanation) only because it stood the tests of which the older one have failed.
It seems clear that in that case the induction should trump the
non-falsifiability of the statement of "I am mortal", since it's a
Note that for the claim "I am mortal", induction will do you zero good because for it to be supported inductively you will have to provide many observations of it and you so far have zero of those -- You don't have any observations demonstrating the particular demand of the hypothesis, according to which you are mortal. Going with induction here would only get us as far as claiming that the only relevant observation we do have is one where you are still alive, providing confirmation for the opposite of your mortality! :-0 How's that for common sense? ;-)
But what do we have when trying this the Popperian way? We treat the hypothesis of your mortality the following way:
- We notice the fact that, as you've mentioned, we are provided with the many refutations of immortality of all men dying up until this point. i.e. the claim that holds is "Men are mortal".
- In addition, we notice we have a background assumption included in our hypothesis, according to which you share with all these other men the characteristic of mortality/immortality.
- We conclude, by using critical rationalism and logic alone, that you are mortal.
While this is not conclusive, this is as good as you can get with Critical Rationalism and I think that, at least in this case, it is established that it brings you closer to your intuitive truth compared to induction, as demonstrated above.