I don't think scientific theories give us truth per se, they meet a certain standard and if those standards are met we have an adequate theory. On the other hand, that's not to say that there is no truth to our theories, it is just not an issue for science to consider (in my view).
Beauty and symmetry derive from reality and the theories should reflect that reality if they are to be valid.
Maybe so, however reality also seems to have a liking to apparent randomness and asymmetry as well.
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".
I say the situation would not change if science were an entirely deductive process. Deduction relies on axiom, and even if the predictions derived from those axioms matched perfectly with our observations and gave us unspeakable amounts of insight, we would still be left wondering on whether we had all the axioms or all of them as correctly stated. For example, if we had the axioms that successfully led to the conclusion that "all humans are mortal", who's to say that one of our axioms is incorrect or just an approximation? In the end, we can have just as much confidence in an deductive/inductive approach as we could have of any pure axiomatic approach to reality. The difference is that in a successful deductive/inductive approach we know we are talking about models and not reality, whereas in a successful axiomatic approach we would probably sleep well thinking we 'knew' ultimate reality, but do we?
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.
The problem I have with this is that bottom line we cannot say science has ever produced truthful theory. The history of science is one of seeing our theories become seen as 'just approximations'. If that is so, then why associate truth with science even for future theories? Why not just say that a theory is adequate for the scales on which we observe, and not bother with reference to truth, at least as to how it pertains as a scientific concept.
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.
I have to disagree. If a theory adds primal axioms to a formerly confirmed theory, but does not provide novel predictions (or those predictions are not testable), then the competition of the two competing theories is, in my mind, undecidable from a scientific point of view - unless the latter more primal theory can directly derive the former less primal theory. That is, as long as both theories are adequate from a theoretical perspective (e.g., overall logico-mathematically consistent, etc), then two competing theories are undecidable if there are no novel predictions that favor one and dispute the other. Giving primacy to the latter theory simply because it is deducible from 'undoubtable' axioms is not good enough from a science perspective, in my opinion. I know of changes that could be made to discarded theories having 'good' axioms (i.e., axioms having undoubted reliablity to the timeperiod they were considered undeniable), and if those theoretical changes were made at the time (to save this old theory), then the discarded theory would never have been supplanted by the new theory. For example, I recently read that there were alternatives to Planck's blackbody theory that had they been considered, would have been a much more pleasing alternative than to suggest that energy comes in units of quanta. Now, let's say that someone had replied to Planck with that competing approach to energy quanta, then the history of quantum physics might have been entirely different with perhaps a longer period before quantum physics becomes accepted. The point is that this is a situation which could have happened which would have favored "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", however such a theory would have been eventually shown to be inadequate. In the case of a TOE, we might sooner or later be unable to experimentally determine between competing TOEs, and therefore science will need to be agnostic about their adequacy - even if one has more primal properties than the other.