So you don't believe, then, that science tells us truths about the world?
I believe that the only way to collect useful ideas about how the world works is through experiencing it. I'm careful using the word truth, and I generally change "science" to "empiricism" (or experience). Most of my knowledge doesn't come from science. It comes from direct experience and the inductions I draw from it.
This is the dilemma of the strict empiricist, I suppose; that entities are observable, but terms, concepts, ideation etc are not.
Where's the dilemma? The objects and processes of experience are material and thus evident to the senses (evidence), and the abstractions (inductions) drawn from them are only found in minds. The faith-based thinker often broaches this topic as part of an argument for accepting the reality of gods absent empirical evidentiary support. He often next asks if one can hold or weigh love as part of an argument for accepting the reality of gods, which also cannot be experienced empirically. But the problem there is that love is an induction drawn from the experience of material objects and processes including one's own behavior toward objects of love. Unlike with gods and all other unfalsifiable claims of existence, the abstraction can't be pointed to, but what it refers to can.
So, given that empirical data is meaningless until it is interpreted, how do you arrive at any theories, axioms or assumptions at all?
By interpreting the data, by organizing it according to similarities and differences, and in so doing, generate useful inductions, meaning ideas that accurately predict outcomes. We should expect similar decisions made under similar circumstances to lead to similar outcomes. The measure of the value of a proposition lies in its capacity to produce expected results. If an idea is "true," it can be used in the real world to generate predictable consequences, and different ones if that idea turned out to be false. All we need to know is that we have desires and preferences, we make decisions, and we experience sensory perceptions of outcomes. If a man has belief B that some action A will produce desired result D, if B is "true," then doing A will achieve D, and B is added to one's fund of knowledge as a correct idea. If A fails to achieve D, then B is modified until it does or is discarded.
Are you saying then, that objective reality is unknowable in principle?
Yes, if by objective reality you mean whatever it is that exists outside of our minds before it is apprehended by a mind, which translates whatever that is into what we experience. You seem to have a good understanding of the philosophy here as your references to instrumentalism and positivism suggest. So you probably already know that you are referring to Kant's ding an sich, or noumenal reality. Yes, it is unknowable in principle, since the knowing immediately transforms whatever it is into the language and perspective of an individual consciousness.
And that we with our extensive libraries, our fathomless oceans of data, and our vast body of knowledge, are no closer to truths about the stars than the Egyptians who knew that when the Dog Star appeared in the sky, the Nile would flood?
Disagree there, but I suspect that you are using the word
truths here differently than I would, and maybe are more interested in the metaphysical realm underlying experience and outside of it than I am, calling THAT truth. That's the world of the unfalsifiable, where propositions are neither right nor wrong, but "not even wrong."
There's a pervasive view that that world outside of experience is more real than this one in here in the individual theater of consciousness- that in here is only a faint projection of that, and thus secondary to it, derivative and subordinate. But this attitude misses the fact that it doesn't really matter how accurate our understanding of what is out there is if the model we are using allows us to effectively navigate the experience of consciousness over time in a way that facilitates desirable outcomes and avoids undesirable ones. That is, if you one day discovered that your model of reality was an illusion - perhaps we are brains in vats, or Descartes' demon is manipulating our experience to appear that there is something else besides that demon outside of mind, nothing changes.
As an illustration, consider that it is literally true that you are in some matrix in some controlled mental state that you had always thought was your direct perception of a reality out there through the windows of the eyes and other senses, but you somehow suddenly learn that all of that is illusion. Now what? What do you do differently? Which of your rules for navigating your conscious experience need changing? Are you going to start doing what you previously thought was sticking an objectively real finger into an objectively real flame knowing that it hurt before? Probably not twice if it burns again. And you'll likely continue thinking in terms of objectively reality underlying the show playing in the theater of the mind. It's a heuristic now, but just as useful as before.
This is why I say that what goes on in here is primary and the metaphysical model we use to organize, understand, and control conscious experience only needs to work, working being leading to desired outcomes - not actually exist.