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{{author|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 falsifi''able''. There must be evidence you ''could'' present that, if you could find it, ''would'' falsify the theory. | {{author|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 falsifi''able''. 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, can’t be falsified. There are no possible circumstances, at least within the [[paradigm]] of Euclidian geometry | Mathematical axioms, for example, are statements of logic and not fact. They can’t be falsified. There are no possible circumstances<ref>all right, pedants: at least, not within the [[paradigm]] of Euclidian geometry.</ref> 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 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 2 + 2 = 4 is ''logically'' true, not ''empirically'' true. You don’t need evidence to prove it. | 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. | Far more controversial is the contention that [[evolution by natural selection]], for exactly the same reason, isn’t scientific either. |