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Posted by Nathan Hays on September 30, 2003 19:25:05 UTC

I think you are right about what things science can or cannot achieve. I am also adamant that theory be empirically verified.

The role of a theory in predicting outcomes makes the theory useful as a tool, particularly for engineering. The explanatory power of a theory is another thing. We have theories of QED, the Standard Model, GR, etc... that seem to explain a lot. We think we understand the Universe a little better with than without them. And yet there are these nagging assumptions about wave collapse, e/m ratio, and Cosmological Constants, not to mention their disjoint applicability. So we search for TOEs that have a greater explanatory power, but do not necessarily predict the novel outcome. Sure it would be grand to have new grist for the engineer's mill, but it may not be forthcoming.

I joined the thread because it was asserted that a theory must make novel predictions. I tried to show that the satisfaction obtained from novel explanatory power can have equal if not greater merit than novel prediction. Novel predictions are like miracles in that they force us to accept the world is not as we thought. Theorems in mathematics are similar, but have no empirical analogue. When confronted with Goedel's Undecidability theorem, we are forced to reevaluate our understanding of logical systems.

In the extreme case of a comprehensive, closed, and consistent theory of reality deduced from irrefutable axioms, we may find that truth that science can never categorically confirm. How will we take that? As a mathematician or a Missourian?

- sfn

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