|Consistency, philosophy, logic: within a system, consistency may be demonstrated, but not beyond the boundaries of this system, since the use of the symbols and the set of possible objects are only defined for this system.|
Within mathematics, and only there applies that the mathematical objects, which are mentioned in consistent formulas, exist (Hilbert, Über das Unendliche, 1926). See also falsification, verification, existence, well-formed.
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Consistency/FeyerabendVsCoherence Theory/Coherence/Feyerabend: the consistency condition, according to which new hypotheses must coincide with accepted theories, is irrational. Diversity of theories is fruitful for science, uniformity paralyzes its critical power.
Theory/Physics/Absence of Contradiction/Duhem/Feyerabend: E.g. the theory of Newton contradicts the case law of Galileo and Kepler's laws. For example, statistical thermodynamics contradict 2nd law of thermodynamics. Wave optics, for example, contradict geometrical optics.
Important Point: this is a logical inconsistency. It is quite possible that the differences of the predictions are so small that they cannot be determined experimentally!
Moreover, the theories are not inconsistent in themselves.
Consistency Condition/Feyerabend: it is far less generous: it does not eliminate a theory because it contradicts the facts, but because it contradicts a different theory whose confirmed entities it shares. Thus, the still untested part of this theory is made the criterion. The only difference between this criterion and a more recent theory are age and habit!
A defendant of the consistency condition would say that the only real improvement would be the acquisition of new facts.
Wider den Methodenzwang Frankfurt 1997
Erkenntnis für freie Menschen Frankfurt 1979