Falsification: Difference between revisions

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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.


It that isn’t possible, even in theory, then the theory is consistent with all possible facts, does not limit any possible outcomes, makes no predictions, and is not science.
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, in which 2 +2 ≠ 4.
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.