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As in any line of scientific inquiry, methods determine theories, and vice versa.
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That is why, in practice, simplicity seems to determine theory choice univocally.
Yet experimental results that conform to rationally determined theory confirm it.
For if the criterion of ontological commitment is to be applied only to true theories, then one would have to determine which theories are true prior to applying the criterion.
The story you choose for the Results and Discussion sections will determine which theories and past research or methodologies need to be presented in the Introduction.
One would have to determine which theories one takes to be true prior to applying the criterion.
The suspicion is that if featuring in best science is the mark of credibility, it should be scientific standards that ultimately determine mathematical theories' acceptability.
Thus, the need arises to find a criterion of ontological commitment: a test or method that can be applied to theories in a neutral way to determine the theory's ontological commitments.
The strong inference approach involves developing and contrasting alternative theories including null theories, which will not give rise to emergent properties to determine the theory most amenable to reproducing the observed patterns [ 28].
The next step is taking the research to the lab bench, to determine if theory can be converted into reality.
We determine theK-theory of the resultingC*-algebras for large classes of examples.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com