The problem of falsifiability consists of weather something could conceivably be shown to be false. For example the following claim is not falsifiable: “there is exists an ether, permeating space everywhere, that can’t be measured or detected in any way”. What experiement could be performed to prove this hypothesis false? None!
But why is falsifiability important? If something makes perfect sense in my mind, why should I care about falsifiability? It all comes down to the problem of induction. Induction is the process of extrapolating a particular case to general one, examples:
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All matter we know is made of atoms (particular), therefore all matter in the universe is made of atoms (general);
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I’ve seen 10.000 swans and they were all white (particular), therefore all swans are white (general).
Unless you have some interest in physics you are probably fine with induction number 1, but anyone over the age of 10 will quickly point out that indeed there are black swans and number 2 is wrong.
So there are good and bad inductions, we would like a way to tell them apart. We would like a method \( M() \) that given an inductive hypothesis \( h \) can output weather it’s true or false \( M(h) = True | False \).
Of course we want our method \( M() \) to work on all hypothesis but, again of course, we don’t want to have to test it on all possible hypothesis because that’s impossible. And there lies the problem, the method \( M() \) has to extrapolate to the general case (all possible inductive hypothesis) from a set of particular cases. That is, the method \( M() \) is itself an inductive hypothesis and any such method we come up with will lead to circular reasoning \( M(M(M(…))) \).
The first person to notice this problem was David Hume and the first to come up with a satisfactory solution was Karl Popper. Unfortunately no one ever told me this at school and the problem of induction caused me years of anxiety.
Karl Popper noticed that while having an induction method would be “based and redpilled”, we don’t really need it. All we need is to be able to find and correct errors. If a hypothesis \( h \) is found not to work (if it’s falsified) under certain conditions, we simply come up with a new and more complete hypothesis. No claim is ever made on weather a hypothesis will always work everywhere. But given multiple hypothesis to choose from, one would normally pick the one that’s easier to falsify because it will take the least effort to find out if it doesn’t work.
Positivism is the name given to any philosophy of science that proposes some kind of induction method \( M() \).
Some people criticize falsifiability and Karl Popper’s philosophy on the basis that the term “science” has meant different things in past, in particular it has meant positivism. From there it’s argued that some kind of positivism is an equally valid form of “science”. Of course this ignores the problem of induction and the fact that falsifiability is important for doing away with it, not because it receives the label “science”. No one cares, or no one should care, about the word “science” specifically but about the problem that candidates to “science” solve. This is called a persuasive definition fallacy.