We know when we have made progress in science and our knowledge has grown, when we see the following..
(excerpts from Conjectures & Refutations, by Karl Popper)
(1) A theory (new theory.. that is) tells us more. It contains (explains) the greater amount of empirical information or content.
(2) It is logically stronger – Greater explanatory and predictive power
(3) And for reasons in (1) and (2), it can be (and is) more severely tested.
(4) It unifies/combines previous successful,but incompatible or scattered attempts,into a unified theory.
(5) The theory allows severe testing of its consequences, in short, it is highly refutable
(6) It has great explanatory power
(7) It has high degree of corroboration
(8) It leads to new problems of higher complexity and of higher dimensions, i.e. many of the new problems it generates leads to new tests which in turn make the theory even more refutable, but it does something very important…numerous consequences of this theory can only be tested via varied/multiple disciplines of Science.
Newton’s theory – logically stronger and better testable – superseded and unified theories of kepler and Galileo.
Maxwell’s theory did the same with theories of Fresnel’s and Faraday’s.
Einstein’s theory, in turn unified and superseded theories of Newton’s and Maxwell’s.
In each case the progress was towards a more informative and severely testable. This was because each progressive theory was severely testable, i.e. were more easily refutable.
A theory which is not in fact refuted by testing those new, bold and improbable predictions to which it gives rise can be said to be corroborated by these severe tests. Some illustrations of these severe tests….
(1) Galle’s discovery of Neptune
(2) Hertz’s discovery of Electromagnetic waves
(3) Eddington’s eclipse observations
(4) Elsasser’s interpretation of Davisson’s maxima as interference fringes of de Broglie waves
(5) Powell’s observations of the first Yukawa mesons
I would encourage readers to list those tests that led to falsification/refutation of a specific theory. Many of the chance-discoveries are in fact refutations of theories which were consciously or unconsciously held.
Columbus’s discovery of America, corroborate one theoy (of the spherical earth) while refuting at the same time another (the theory of the size of the earth, and with it, of the nearest way to India- from western Europe).