I read your entire blog post about Laplace. Your reminder that Laplace’s solution was not perfect is well-taken. But even your critique of his math is only a complaint that his approximations make his solution imprecise, not that his proof was completely false. (I have never read Laplace’s original work and thus might be completely wrong.) In physics, it is normal to make simplifying assumptions that make our theory fail at some precision but is sufficient for most purposes. That doesn’t make the theory false.
In fact, the Laplace episode is still a good case study of God-of-the-gaps: even though Laplace was wrong to claim that God was completely unneeded at all (because his theory was imperfect), he did show that God was needed less. And subsequent developments in celestial mechanics (i.e. our knowledge of relativity, chaos theory, and numerical simulations) have made us able to model the solar system even better, showing that this kind of God is needed less and less.
Imagine if Newton did not hold to the idea that the stability of the solar system must only have a miraculous (i.e. intractable) explanation. Perhaps with his mathematical genius, he could have gone beyond his own theory and anticipated Laplace, Poincare, and others.
And I agree with you that strict methodological naturalism has not always been held throughout the history of science, as shown by Newton’s episode. I already said that in one of my above posts. But it is a natural outcome of what seems to work best.
It is not purely a philosophical question. How science is done, what scientists think science is about, and who does science has steadily evolved over the centuries. Philosophers of science are incredibly valuable in working out the logical, theoretical, and semantic issues. But any definition of science that seeks to be widely accepted must involve extensive collaboration with actual working scientists in the field.
Philosophers of science don’t regularly roll with scientists - they roll with other philosophers. I don’t see any philosophy of science grad students hanging around in our lab group meetings or even physics colloquia. They interact with science primarily through textbooks and papers - which are all idealized final products, not betraying the ugly, messy, possibly unanalyzable thought process that goes into that. As I said above, science is not merely something you can absorb by reading a set of propositional statements. Most people have to spend lots of time in the lab or thinking about physics before they can say something insightful.
Of course, the same is true about philosophy - which is why one cannot read bits of Aquinas’ Five Ways, think they don’t make any sense, and then proclaim that you’ve refuted him.
I have no illusions that science is free from political, personal, or social forces. But the same is true of the field of philosophy, probably even more so. There has been several instances of drama in academic philosophy, not all of which are purely logical arguments, but influenced greatly by politics and sociology.