HighwoodFool wrote:Physics cannot be reduced as pure mathematics
HighwoodFool wrote:logic and philosophy would be purer than mathematics
I like to treat the root elements of the various disciplines as a two-branch system based off of physics on the one hand (with a chain of abstracted disciplines similar to that depicted in the comic) and, loosely speaking, "economics" on the other hand. More closely, I'd say the other branch is grounded in game theory, that being an application of mathematical models to strategic, goal-seeking purposes, akin to physics as an application of mathematical models to theoretic or explanatory purposes; though the title "game theory" alone doesn't carry any ethical connotations with it the way "physics" carries certain metaphysical and epistemological connotations of naturalism. (I'm tempted for aesthetic and etymological purposes to call the second branch the "ethical sciences", in reflection of the "physical sciences", but that would be confusing given the modern connotations of "ethics").
More to the point of this thread, both of these branches are grounded, as already obvious from the above, in mathematics, so the comic's depiction of it as "most pure" is still accurate in my book; but as HighwoodFool here points out, physics is not entirely reducible to mathematics, and logic and philosophy have their own claim as the "purest" as well.
My answer to that is that both physics and the root of the "ethical sciences" (whatever we are to call it) are grounded not only in mathematics but equally in philosophy. Mathematics provides the tools for building theoretic and strategic models, but philosophy provides the guides for how to judge one model as superior to another. We've got general consensus in the case of physical models that that criterion is consistency with empirical observation, but... well, the ethical side of things is still contentious, though we seem to be coming slowly closer over the centuries to agreement that it's some kind of altruistic hedonism (i.e. the happiness/well-being of everybody in this world, rather than any transcendent/otherworldly [on the one hand] or egotistic [on the other hand] standard).
I'd say that there is also a third "purest" root, along with mathematics and philosophy: art, encompassing writing and music as well. Whereas mathematics is purely analytic, breaking ideas apart into their more base structures, the arts are synthetic, as in creative, putting things together into new combinations. When you throw this into the mix, you get another branch of disciplines parallel to the sciences: engineering. Engineering is, very loosely speaking, taking the "parts" sorted and identified by the sciences, and combining them together into new things. On the physical side of things these fields are well-known as engineering fields - mechanical engineering, genetic engineering, etc - but I see faint parallels on the other side in fields such as political economics, and I hope that some day, when the ethical side of philosophy has settled down as much as the physical side has, we might see similar levels of mathematical rigor applied to fields in that domain as well.