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Posted by Nathan Hays on September 29, 2003 23:41:06 UTC

"'[...] I hold that [epistemological] utility is all that can be demanded of a theory beyond empirical agreement'

What about Einstein's/Dirac's claim that theories should be 'beautiful'? How does symmetry play a role as a deciding factor in theory selection?"

Beauty and symmetry derive from reality and the theories should reflect that reality if they are to be valid. If the Universe is perversely unsymmetric (and the relative strengths of the forces demonstrate that all is not Platonic) then good theories must conform to that structure.

I don't think any theory is purely deductive in its origin or purely inductive in its origin. If that's correct, it becomes a matter of deciding whether a theory is more 'true' because it is more deductive than the other theory.

The scientific method incurs a tremendous amount of logical deduction as do the theories we operate with. The role deduction plays is to transfer the truth or falseness of one set of statements to another. Because of this, the deductive steps can be 'divided out' of the theory to yield the axioms and the testable statements. However, because the deductions link axioms to observable statements, if the axioms are not well founded, the observable statements may or may not be relevant to reality.

Once we have testable statements and begin to confirm the theory, we are forced, as described by Popper, to forego 100% affirmative surety and can only truly rely on refutations. This problem is whence the demand for unexpected predictions springs.

The relative amounts of deductive or inductive components of a theory do not bear on the theory's validity, I could take any deductive step and expand it with arbitrary complexity and not change the truth-transference one whit. The deductive part is nugatory and the inductive part denies irrefutable confirmation.

This sheds light on the primary shortcoming of the scientific method: the truth-transference function of the deductive component is run in reverse. The scientific method proposes a hypothesis and then attempts to validate its axioms through transference of the empirical results. But the instances of empirical results cannot confirm a categorical statement, any more than several billion dead ancestors can confirm the statement, "all humans are mortal".

"If rough approximation is a quality of truth, then simply by modifying the scale one can find truth in a lie."

It is important to distinguish between truth and approximation. Truth is something that holds at all scales, approximation is a purely utilitarian valuation. The utilitarian criteria for a theory's validity pertains to its suitability for prediction of a particular experiment at a particular scale and the theory's usefulness to engineering. In the first case we would not use quantum theory to predict hockey puck trajectories and in the second phlogiston is useful for predicting whether wood will burn in a campfire.

"[...] I place more importance [on] theoretical predictions and include those deductive merits of a theory as secondary."

If a theory extends a deductive chain to a more primal, general set of axioms but does not yield new predictions, then the theory may have a greater explanatory power and be more aesthetic. If those axioms are so fundamental that they cannot be doubted and the deductive chain holds to be valid, then the requirement for novel predictions is fallow.

- sfn

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