The Logic of Scientific Discovery (Routledge Classics) 2nd Edition, Kindle Edition
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First, Popper is often seen as advocating a skeptical way of life--the principle of falsification is made to mean that one should always try to falsify one's one own theories and worldview. There may be some support for this philosophy in the Open Society but not in the Logic of Scientific Discovery. Here, Popper is explicit that he is not proffering a philosophy of life but a methodology for science.
Another related misconception is that Popper does not contend that his logic is the way science has historically progressed. The Logic of Scientific Discovery is explicit that it is normative. It argues not how science has progressed but how it should progress. The fact that Popper was so personally authoritarian that the line among his students was that his other major work should have been called "The Open Society by One of Its Enemies" seems eerily consistent with a philosophy professor dictating to scientists how they should conduct their work.
And here is where I find the work someone dated. Popper argues against the inductivism epitomized by John Maynard Keynes but seems oblivious to the work of statisticians like Ronald Fisher. Fisher, with his method of randomized experimentation was able to show the validity of inductive causal inferences. In the 1970s statisticians like Rubin extended these inductive arguments to observational studies. Meta-analyses using Bayesian inference have also shown then value of induction. Obviously, Popper cannot be held responsible for not recognizing the Rubin causal model. His inattention to Fisher, however, is troubling since he was a contemporary.
Most social science continues to progress within the Fisher/Neyman framework along with Bayesian advances. To be honest, Popper's work in this domain can seem as passé as the inductivism of Keynes.
That the Logic is a work of genius is indubitable. I would argue, however, that falsification is not the one valid method for science. A fortiori it is not a philosophy of life all human beings must follow.
Of science that is inappropriate and more suitable for a religious faith not an open field of inquiry.