Alan B. Whiting wrote a new paper on Applying Popper's Probability:
Professor Sir Karl Popper (1902-1994) was one of the most influential philosophers of science of the twentieth century, best known for his doctrine of falsifiability. His axiomatic formulation of probability, however, is unknown to current scientists, though it is championed by several current philosophers of science as superior to the familiar version. Applying his system to problems identified by himself and his supporters, it is shown that it does not have some features he intended and does not solve the problems they have identified.The paper starts by nicely explaining his best idea:
Professor Sir Karl Popper (1902-1994) is known to scientists as the authorThose who promote untestable concepts like string theory or multiverse theory hate this concept.
of the ‘doctrine of falsifiability,’ in which a statement is only admitted to be scientific if it can, in principle, be falsified. Although not strictly the originator of the idea, he can be credited with emphasizing it and it is a useful test for pseudoscientific statements. His clearest statement of this is from the Postscript to The Logic of Scientific Discovery:
... we adopt, as our criterion of demarcation, the criterion of falsifiability, i. e. of an (at least) unilateral or asymmetrical or one-sided decidability. According to this criterion, statements, or systems of statements, convey information about the empirical world only if they are capable of clashing with experience; or more precisely, only if they can be systematically tested, that is to say, if they can be subjected (in accordance with a ‘methodological decision’) to tests which might result in their refutation.
A lot of people think that Popper was a positivist because the above opinion is very similar to what the logical positivists were saying. They said that a statement is meaningful if there is some way to show that it is true or false.
It is not that profound. To mathematicians and scientists, the definition of a statement is something with a meaning that can be true or false.
Actually Popper wrote essays against positivism, and did not consider himself a positivist. Go figure. He mainly seems like a sensible positivist because the later philosophers of science were so anti-positivist, anti-science, and nutty.
Popper advocated what I call negativism. He believed that scientific theories are all provisional, and eventually get falsified. Some, like Newtonian mechanics, have already been falsified, and others, like relativity, are just waiting to be falsified. He was saying that you can only prove a negative, not a positive.
Sometimes you hear people say the opposite, and say you cannot prove a negative. Both views are false. Positives and negatives get proved all the time.
Newtonian mechanics has not been falsified. It is commonly used today, and it is valid within its domain of applicability. NASA uses it to calculate rocket trajectories. You could say that it is only an approximation, but all the data and observations are only approximate also. Newtonian mechanics correctly takes approximate data and gives approximate results, to acceptable accuracy. That is not what I would call falsified.