“… (1) Newton’s theory is exceedingly well corroborated. (2) Einstein’s theory is at least equally well corroborated. (3) Newton’s and Einstein’s theories largely agree with each other; nevertheless, they are logically inconsistent with each other because, as for instance in the case of strongly eccentric planetary orbits, they lead to conflicting predictions. (4) Therefore, corroboration cannot be a probability (in the sense of the calculus of probabilities).
“… The proof is simple. If corroboration were a probability, then the corroboration of ‘Either Newton or Einstein’ would be equal to the sum of the two corroborations, for the two logically exclude each other. But as both are exceedingly well corroborated, they would both have had a greater probability than ½ (½ would mean: no corroboration). Thus, their sum would be greater than 1, which is impossible. It follows that corroboration cannot be a probability.
“… It would be interesting to hear what the theoreticians of induction … who identify the degree of corroboration (or the ‘degree of rational belief’) with a degree of probability — would have to say about this simple refutation of their theory.” (Popper, Karl. 2009. The Two Fundamental Problems of the Theory of Knowledge, xxivn. New York: Routledge.)