Albert Einstein famously believed that, given some general principles, there is essentially a unique way to construct a consistent, functioning universe.That is much of the rationale behind string theory. Ignore experiment, follow abstract principles, and devise laws of nature.
Put another way, he believed in a top-down approach, instead of a bottom-up approach. See recent postings by Allanach, Lumo, and Bee. They would all like to believe in the top-down approach, but they differ in the extent that they are willing to reconsider their beliefs in the face of contrary LHC evidence.
Sabine Hossenfelder (aka Dr. Bee) has a new book, Lost in Math, that critcizes various purely mathematical approaches to theoretical physics that have failed to get any empirical results. I have not read it.
Some people think that Einstein did this top-down approach with relativity. That is, he just adopted some philosophically attractive postulates, and derived special relativity.
That is not exactly what happened. Maxwell developed his electromagnetic theory from experiments by Faraday and others, and noticed a paradox about the motion of the Earth. The Michelson-Morley experiment tested Maxwell's ideas, and found a symmetry of nature that was not obviously apparent in his equations. Lorentz found a way to reconcile the theory and experiment. Poincare showed that the Lorentz transformations generated a symmetry group for 4-dimensional spacetime, and that Maxwell’s equations could be understood geometrically on spacetime. Einstein adopted two of Lorentz's theorems as postulates, and showed how they could be used to derive the Lorentz transformations. Minkowski elaborated on the non-Euclidean geometry of Poincare’s spacetime, and formulated the version of special relativity that became popular at the time.
There are philosophers who say that getting relativity from experiment is just positivist propaganda. They say Einstein ignored the Michelson-Morley and other experiments, and applied non-empirical thinking. Polyanhi even said that special relativity was proposed "on the basis of pure speculation, rationally intuited by Einstein before he had ever heard about it."
So Einstein’s 1905 special relativity paper is widely praised, but some praise it for being positivist, and some for it being anti-positivist!
It was not really either, because it was just an exposition of the ideas of others. The theory was created by Lorentz, Poincare, and Minkowski, and they all explicitly relied on empirical findings in their papers, and did their work independently from Einstein.
I don’t think physics has ever had substantial advances from anti-positivist thinking.
But if there were to be an anti-positivist invention of relativity in some alternate universe, what would it look like? That is what I wish to propose in several subsequent posts.