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Karl Popper’s idea that, since the only way to rule out a scientific theory is with evidence that contradicts its predictions, it is a necessary condition of a bona fide scientific theory that it must be, in theory falsifiable. There must be evidence you could present that, if you could find it, would falsify the theory.

If it isn’t possible to formulate counter-evidence, even in theory, then the theory must consistent with any possible facts, does not limit any possible outcomes, makes no predictions, as no explanatory power, and is not science.

Mathematical axioms, for example, are statements of logic and not fact. They can’t be falsified. There are no possible circumstances[1] in which 2 + 2 ≠ 4.

Therefore the mathematical statement, 2 + 2 = 4 is not scientific.

This isn’t as controversial as it might seem if you have never heard it before and it has just slapped you in the face. How can mathematics — the very language of science — not itself be scientific? But that is the key to it: it is a language in which falsifiable scientific statements may be made; its own internal logic is not, of itself, a matter of science. The rules of English grammar make no statements about the world either. 2 + 2 = 4 is logically true, not empirically true. You don’t need evidence to prove it.

Far more controversial is the contention that evolution by natural selection, for exactly the same reason, isn’t scientific either.

Kuhn vs. Popper celebrity death match

Following the publication of his The Structure of Scientific Revolutions, Thomas Kuhn famously debated Karl Popper over what counts as science and the way in which science develops over time. Popper had, in his earlier book The Logic of Scientific Discovery, made the invaluable observation that “verification” as a standard for a theory to qualify as “scientific” is too high since, logically, no argument based on induction (“since the sun has risen on every day in recorded history, therefore it will rise tomorrow”) can be proven true. For all our folksy expectations, current cosmology predicts that there will be a point in the distant future when the sun will explode, and therefore will not rise tomorrow. We are but turkeys, only Christmas hasn’t arrived just yet.

In lieu of verification as the scientific gold standard, Popper asserted that a valid scientific theory could be assessed only by the lack of any falsifying evidence among the data. Thus, to be useful, a scientific theory must be “falsifiable”: it must narrow down from the list of all possible outcomes a set of predicted ones, and rule the rest out. Theories which cannot be falsified by any conceivable evidence don’t do that, so fail at science’s fundamental task. They are not science.

Thomas Kuhn’s tremendous insight was to offer the historian’s perspective that, while that might be theory, that’s just not what science has ever done in practice. Scientific theories are never thrown out the moment contradictory evidence is observed: the dial is tapped, the experiment re-run, and “numerous articulations and ad hoc modifications of their theory” are devised to eliminate apparent conflict. When the data won’t do what they’re meant to, sometimes it is the question which is rejected as being irrelevant, and not the answer predicted by the theory.

See also


  1. all right, pedants: at least, not within the paradigm of Euclidian geometry.