What do these propositions have in common?
"Suppose that our astronomical observations were to show, from tomorrow on, that the velocity of the earth (which remains on its present geometrical path) was increasing, either in its daily or in its annual movement, while the other planets in the solar system proceeded as before. Or suppose that Mars started to move in a curve of the fourth power, instead of moving in an ellipse of power 2."
Firstly, they are both observation-statements proposed by Karl Popper, for which ‘the realisation of any of them would simply refute Newton's theory’. That is, in Popperian terms, falsify it. A theory is falsifiable if it is inconsistent with some observation-statement. Popper introduced the idea of falsificationism into the philosophy of science early in the 20th century as a method for demarcating science from pseudo-science, e.g. Marx and Freud.
Secondly, ‘it is blazingly obvious’ that neither of them is, in fact, inconsistent with—and thus a falsifier of—Newtonian physics. Indeed, any of these behaviours can be deduced from and explained by Newtonian physics in conjunction with the appropriate contingent assumptions, e.g. other masses and forces in operation. The discovery of Neptune is sufficient evidence for this fact. Observations of the orbit of Uranus had demonstrated that, without postulating anything other than currently known forces, Newton's theory did not predict the observed orbit. Is this a falsification of Newton? Of course not! It was Newton's theories, using the alleged anomalies in the orbit of Uranus, that allowed Le Verrier to predict the existence, mass, and location of Neptune!
One more for good measure: over the 20th century, there had been a growing recognition that the orbital velocities of stars around the centres of their galaxies did not match the naïve predictions of Newtonian mechanics. In response, some scientists proposed Modified Newtonian Dynamics (MOND). In 1980, Vera Rubin published a paper jumping the other way. She proposed, not that we needed to alter Newton, but that we postulate the existence of an invisible substance that, in conjunction with the original Newtonian Dynamics, would explain those stellar orbits. That substance she called 'dark matter' and it is now generally believed to account for up to 90% of the mass of the universe.
No law-statement is inconsistent with any observation-statement. You are free to take the observation as reason to revise your theory and equally free to use the conjunction of your theory and observation to infer the existence of something else altogether new. There is always that choice. That is the reason that falsificationism is bankrupt. For falsifiability to serve as the hallmark of true science, it must be, no matter how difficult in practice, at least, logically possible for a law-statement to be inconsistent with some observation-statement, but it isn't possible, even in principle, and, shockingly, Popper knew this all along.
No, really. David Stove explains:
[When considering law statements like] ‘The probability of a human birth being male is = .9’ ... Popper had fairly painted himself into a corner. For he had maintained (1) that some such propositions are scientific; (2) that none of them is falsifiable (i.e. inconsistent with some observation-statement); while he had also maintained (3) that only falsifiable propositions are scientific. (The reason why (2) is true is, of course, that [the statement above] is consistent even with, for example, the observation-statement E: ‘The observed relative frequency of males among births in human history so far is = .51’.)
Popper euphemistically refers to this as ‘the problem of decidability’, when really it is not a problem at all, but a contradiction. When faced with this ‘problem’, Popper says scientists act on a ‘methodological rule’ to decide whether a law-statement has been falsified.
No doubt they do. But obviously, as a solution to Popper's problem, this is of that kind for which old-fashioned boys' weeklies were once famous: 'With one bound Jack was free!' What will it profit a man, if he has caught himself in a flat contradiction, to tell us about something that scientists do, or about something non-scientists don't do, or anything of that sort? To a logical problem such as the inconsistency of (1), (2), and (3) there is of course— can it really be necessary to say this?—no solution.
The next time your friend challenges you that Christianity makes no falsifiable predictions, and, hence, is not worth investigating, before you dust off the 'finding the bones of Jesus' defence, how about try this first. Ask them to propose an observation that would falsify the theory that the earth spins on its axis once every 24 hours. Now, prepare yourself with infinite caveats about slowing clocks, invisible planets, magnetic fields, and the like, and let the fun begin.
 Karl Popper, ‘Replies to My Critics’. The Philosophy of Karl Popper ed. Schilpp (Open Court, 1974), pp1004f.
 Ibid., pp1004-1005.
 David Stove, Anything goes: origins of the cult of scientific irrationalism (Macleay Press, 1998), p174.
 Ibid., p65.
 Karl Popper, The Logic of Scientific Discovery (Hutchinson, 1959), p196.
 Ibid., p202, footnote.
 Stove, op.cit., p66.
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