Abstract
This is a response to a claim by Sven Ove Hansson to the effect that Poppers dictum that falsification lies at the heart of all pursuit of science has once and for all been falsified by his study of articles published in Nature during the year 2000. We claim that this is based on a misunderstanding of Poppers philosophy of science interpreting it too literally, and that alternative readings of those papers are fully compliant with falsification. We scrutinize Hansson’s arguments as well as giving an overview of Poppers falsification theory.
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Notes
In which he confuses the falsification of a fact with that of a theory!
Stating:The weakness of Popper’s argument is obvious. For scientists are not only interested in showing that certain theories are false...her arch-rival’s theory perhaps...But much more likely she is trying to convince people that her own theory is true. And goes on to claim that Popper purports to reject induction, which Okasha seems to confuse with verification.
Typically \(x\) which will ‘occur’ in the future and thus cannot be tested (verified) in the present. This accords a way of evading actual infinities.
Being rejected as scientific should only be seen as negative, when such claims are being central. Popper emphasizes that not being scientific does not mean being nonsense. In particular metaphysics could be valuable as an inspiration for a nascent science.
For Popper the content of a scientific theory is central, while Kuhn’s vision of paradigms, emphasizes the sociological aspects.
Hume (1739) relied on induction as much as anyone else, he only claimed that it was not rationally founded but based on passion in the form of habit.
Taken to the extreme, and as such potentially misleading, we may refer to the observation of William James to the effect that we have a passion for belief. If possible we would believe everything (James 1890, (II) p. 299).
It is different in mathematics, where a strong mathematician can in principle check anything he uses by himself. Otherwise this leads to specialization and the concomitant risks of alienation, as there is nothing more satisfying than to have complete control of your knowledge, and when large parts of that has to be jettisoned, the activity may no longer seem as meaningful.
Caesar was bald but that does not mean that he was entirely devoid so that makes it easier to count. Of course we may have to specify the question further to make it logically unambiguous.
Incidentally if there is no free will, unlimited time travel does not entail logical contradictions. If there is no free will one may argue that time has a reduced meaning, as Popper pointed out as to the role of time in Einstein’s special relativity. An example of the naivety of (Popper (2002c), p. 149).
Supposedly the Catholic church had no objection to the heliocentric worldview as long as it was merely an aid in computation.
Of course in recent decades distances to close celestial bodies such as the Moon has been done in direct ways assuming the velocity of light, which, however, originally was based on triangulated astronomical distances.
At the time no stellar parallax had been established, which indicated that the geometry was Euclidean (if that was the alternative choice) to a very high degree.
Our visual world is a sphere. The lower half of it is sensed as flat, as we can explore it tangibly moving around it, the upper half is sensed as a vault, only accessible by the eye. This made a split into the terrestrial world and the celestial. The first gave rise to flat Euclidean geometry, the second to the spherical one of astronomy. Ontologically the stars could be literally infinitely far away, making up an unbridgeable split between the two realms, but this extreme position seems never to have taken root, instead there seems to have been assumed that the celestial bodies were part of space, and hence had finite distances.
The latter discovered by Bradley can be given an elegant and suggestive formulation (Penrose, p. 428) as the parallax of the hyperbolic geometry of world-lines in Einstein’s theory of special relativity.
The most vocal critic—the astronomer Fred Hoyle, who incidentally coined the name with a disparaging intent, for a long time proposed an alternative theory involving the spontaneous creation of matter.
This is of course very commendable, there is a longstanding contention in philosophy that would only the concepts be clearly defined and the reasoning sufficiently strict the controversies that plague the subject would evaporate. In short, philosophy would be scientific and philosophical argument would turn into the form of calculations. We can compare with the remarks of Socrates in the dialogue Euthyphro (Plato), or with the vision of Leibniz pushing for a more precise language.
One may not take infinite literally of course, it can be argued that the infinite cannot be physically manifested, but is only an ideal construct of human thought. What is meant is that the statement holds for such large number of cases that it is not feasible to test them one by one, if for no other reasons that some of them are supposed to hold in the future.
One often says that history is no science, because it deals in particulars, not generalities. That might be true to some extent, but one can reason about the past, using more or less hidden universal statements, such as there were no airplanes in the seventeenth century. The same thing goes for natural history, we may with great confidence assert that no humans walked the earth during the era of dinosaurs. However, would human fossils be found together with those of dinosaurs, we would in principle be forced to reconsider the actual course of evolution, but using the general principle of Occam’s razor, we would be rather convinced it was a hoax. Collingwood makes an important distinction between natural history, as an unfolding of a spectacle, and human history, in which the reconstruction of thought plays a crucial role, just as motive does in forensic investigations. This adds another element akin to universal statements into the picture.
Although it is of course not as straightforward as non-mathematicians may suppose.
We may also think of the statement every human has a mother as of being in that form. Is it unscientific, because not being formally falsifiable? It hinges of course what we mean by the statement ‘x’ has a mother? Is it something that cannot be falsified, as it would in principle involve an infinite search? If so yes, it is not falsifiable, it means it is actually of the logical form \(P(x,y)\) where you for each \(x,y\) have to ascertain whether \(y\) is a mother of \(x\). But if you take a more pragmatic view? Also, note that the sharpening every human has a human mother is in contradiction with the Darwinian interpretation of the evolutionary record. Anyway the statement in its vaguer form is something we all believe in, and do not need science to inform us of.
When the movement of Uranus did not adhere to Newtonian theory, this was not seen as a falsification, instead it was explained by an ad hoc assumption of a previously unknown planet, later vindicated by the discovery of Neptune (Popper 2002c, p. 45).
Of course we may make as our hypothesis that a universal law is not true, then of course it is possible to verify it, falsifying the law. But this is just a trivial play with words, signifying nothing.
This may be thought of as a universal statement, and thus contradicting everything I am maintaining. But in logic as well as in mathematics, universal statements are allowed based on intuition. You may of course question intuition, but then logic as we know it disintegrates and we are in strange territory indeed. Less drastically I can simple challenge him to come up with such statements.
But of course in any empirical undertaking, there is trial and error, and in the applications of the general laws, there are bound to be small guesses, to be tested and occasionally rejected, too technical to survive in the write-up. Thus there is indeed a kind of fractal structure, trial and error used at all levels.
Although that this does not contradict the fact that individual scientists may not be concerned with the big picture, but caught up in their technicalities. Popper is concerned about science as a whole, not the individual practitioners.
It is not my intention to dismiss those examples in bulk, psychoanalysis and marxism do contain very interesting ideas.
But not as hard to make sense of as I presume a paper in mathematics would be to the layman.
Here I am afraid I do not differ much from members at hiring committees, reduced to rely on formal authority.
The present Polar Star is actually more accurate as such than it was during antiquity.
Standard caveats are to be supplied. We assume that the time-period is short enough to assume that the proper motions of stars are uniform and that the speed of the precession as well as its axis, do not change significantly, something that can be safely assumed for historical periods.
The hypothesis that every parent of a human being is a human being has been confirmed literally billions of times and not a single concrete counterexample has ever been found. Yet the conclusion would in one blow destroy the theory of Evolution, the key being that the notion of Human being is not specific enough for the larger question but of course sufficient in everyday life.
The setting of those confidence intervals are more or less arbitrary. It is symptomatic that those are set to be much stricter in medicine than in the social sciences. Often those are set to acknowledge uncertainty, but that uncertainty is quantified. We claim that with such and such probability this is true. Popper, wisely refrains from making such quantitative statements as in a sense they tend to be circular.
It is far from obvious which theories will be at fault, cf. the case of debugging a program!
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Acknowledgments
I thank an anonymous referee for a valuable admonishment, leading to a major revision.
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Persson, U. Is Falsification Falsifiable?. Found Sci 21, 461–475 (2016). https://doi.org/10.1007/s10699-015-9420-4
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DOI: https://doi.org/10.1007/s10699-015-9420-4