from Asad Zaman
Popper’s view on falsification appear plausible, and are widely accepted. Let me first summarize them, and then pose a puzzle.
1: A theory S is a scientific theory only if there exist some potential observations which can disconfirm it. If all observations are compatible with S, then S is a tautology, true by virtue of logic, and not an empirical scientific theory. In this case, theory S has nothing to say about empirical phenomena, since all phenomena are compatible with it.
2: A single observation in violation of the laws posited in S lead to falsification of S. All scientific theories are potentially falsifiable.
3: It is impossible to PROVE scientific theories — no matter how many confirming instances we observe, there always remains the possibility of a contrary observation tomorrow.
Prior to Popper, verificationists were searching for ways to validate scientific theories. However all efforts at proving the validity of induction failed. This led Popper to formulate the falsificationist view: Scientific theories can never be verified. Scientists attempt to falsify theories. If a theory resists strenuous efforts at falsification, this proves its robustness and suggests that the theory is good. The longer a theory survives, the better the theory.
Poppers views are also held in Statistical hypothesis testing, where we maintain that the Null Hypothesis can be rejected, but it cannot be accepted — in the sense of confirmation of truth. A sequence of trials may fail to reject the null hypothesis the a coin is fair (p=50%), but this failure to reject does not establish that the null hypothesis is true. For example, it may be that the null hypothesis is false, and p=50.01%, but this small difference was not detected in the trials.
The reason for this lengthy replication of what is well known is to ensure that we are all on the same page. Now to pose the logical puzzle:
A rejection of a theory S is logically equivalent to a confirmation — a proof of the negation of this theory. So rejection of S means affirmation of NOT S. SO certain types of theories can be proven. Similarly, certain types of null hypotheses can be proven true.
So a simple falsificationist view is logically impossible. If some theories can be proven false, then their negations can be proven true. To save Popper, we must consider different classes of theories, some of which cannot be proven true, while there are others which can. It is not at all clear how one would separate scientific theories into these two (possibly more) categories.