I have a unique philosophy of science project (although I feel it's just giving voice to the implicit philosophy of many theoretical physicists). However I despise academia so I stealth published it in '15 in the form of a more accessible brass-tacks zine, humaniterations.net/2015/08/18/sci…
Some of the conclusions: Math is a subset of science (the purest expression of science). And the best science and the best philosophy exists at crossroads of the two. Science is radical (high fidelity reductionist) model construction, the best philosophy operates similarly.
Small kolmogorov complexity structures that perfectly or with high fidelity unfold into more complex structures is the essence of radicalism/reductionism. And the trick to Science As Radicalism is seeing empirical data AND models as the same general category of structures.
There is no "pure" data (unmediated phenomenology), everything is models all the way down, but also all models are themselves data. You can do science (radicalism/reductionism) on all of this. The wider the scope and the higher the compression and fidelity, the more scientific.
It's legitimate science to work purely on collapsing one model into a more compressed model or finding tools (eg dualities, relationships) that facilitate this in general, but the drive for wider scope reproduces the empirical inclinations (and corrections) of science.
If you're doing pure math then you're doing science (& there are empirical leakages into the 'purity' of any math), but ultimately the reductionist/radical project of science is infinitely greedy in scope, so it has to contact with all other models including the more data-y ones.
Anyway, this definition of science makes math very sciencey and a lot of social sciences extremely un-sciencey (which is more accurate to the history of all this). One consequence is that a ton of philosophy is immediately obviously *trivially* science.
All of which is to say, like Liam, I really enjoyed the hell out of this paper:
philsci-archive.pitt.edu/18972/1/Pradeu…
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