> Where does the concept of "falsification" come from? Karl Popper was a philosopher.
Karl Popper didn't invent falsifiability, he discovered it. This could have happened to anyone -- Popper happens to have been that one. The influence of the falsifiability idea eclipses its source. If we lose Popper, if he turns out to have some glaring personal defect that would end the career of a politician, falsifiability remains. The reason? Falsifiability is an idea, and ideas don't have parents.
Henry Ford invented efficient production-line methods. He was also a rabid anti-Semite. Does this character defect undermine the value of efficient production methods? Only if we try to associate ideas with their originators, or imagine some connection between the two.
This is how it works in the realm of ideas -- ideas are the focus, not those who express them.
In philosophy we talk about Popper or Foucault or Derrida. In science we talk about biology or evolution or physics.
There are an infinity of primes -- easily proven. Who first had this idea? Not important -- the idea stands on its own.
> You are right that most philosophical statements are not falsifiable, but that simply means they are not scientific according to a definition of science that assumes all scientific statements are falsifiable.
Yes, and that's how science is defined. No falsifiability, no science. But this requires us to imagine a world in which ideas have a life of their own.
> In short, you haven't really said anything ...
A perfect philosophical rejoinder. All ideas are constructed on a foundation of sand and no particular idea has more persuasiveness than another. Falsifiability is an idea. Therefore ...
Therefore why not take the next step and try to claim that all ideas are subjective, that we can't expect to meaningfully express and share ideas, or let reality-testing rank them in an objective way? In short, why not accept the postmodern thesis? The answer is that postmodernism contradicts the very idea of meaningful, productive conversation, conversation that might lead to a social good. To address the postmodern thesis is to fatally undermine the exchange in which it's introduced -- an exchange that requires the very thing postmodernism denies.
Meanwhile, outside philosophy, we have the recourse of testing our ideas against reality and letting reality rank the ideas for us. According to reality, natural selection shapes the biological world, and the identity of the people who stumbled on this idea is irrelevant. According to reality, there is no ether carrying light waves -- in spacetime theory, no medium is required -- and this idea's originator doesn't matter. When you understand the equations of relativity theory, you have learned the topic, and Einstein's having abandoned his first child can't undermine the idea or degrade its value.
But all that requires us to accept the idea that there is an objective, shared reality about which meaningful conversation is possible. As it happens, among philosophers this idea hasn't taken hold.