The only really good way of understanding the variational principal in my experience as a physicist who has chewed on it informally since getting out of grad school is to recognize that <i>energy</i>, potential or kinetic, comes <i>after</i> the variational principal, not before it. In school we are taught to write down the kinetic and potential energies and then to form a lagrangian and turn the crank, but it is in fact the lagrangian formalism which determines which expression we write down for both terms. All the physics before, including the characterization of kinetic and potential energy as concepts, is fumbling towards that idea.<p>Really, if you look at Hamiltonian Mechanics this is more clear, since most of the ideas in Hamiltonian mechanics flow from the basic idea that p generates q AND either that paths in state space don't cross and/or that time evolution is unitary (depending on whether you want classical or quantum mechanics to shake out). These are more or less unavoidable assumptions which we <i>impose</i> or our efforts to understand reality and from these basic ideas we simply fiddle around with expressions until we find the mechanics that match our observations and from which we can sometimes identify objects which behave like the potential and kinetic energies we learn about in grade school.<p>Another way to appreciate this is the difficulty of coming up with a good totally fundamental definition of energy independent of a physical system. Energy is a handy way of thinking about how things will move. That is all.
It's important to contextualize Aristotle, farther of science, against Plato and Protagoras, fathers of philosophy. All of the worst impulses of a priori theorizing were in Plato and Protagoras -- from pure blind objectivity to pure blind subjectivity. Aristotle was working hard to defend a study of the world from both of them, delivering ingenuous arguments for realism which are no worse than any given since.<p>His philosophy is more-or-less a modern scientific realism: the world exists, it has essential properties, knowing the world is knowing these properties, these must be discovered, in general we do not know the accidental from the essential, etc.
Arguing against Aristotelian physics in 20th / 21st century is like pounding a rotten strawman.
Does anyone know a modern (influential) Aristotelian philosopher who holds views the writer is criticising?
HN has been surprisingly good today. Seen a couple of very high quality posts (at leasts posts that are to my liking), this one included. I thank OP for posting this.
> Anyway, I wanted to learn about this stuff, and I’m a firm believer that you can’t learn anything in physics without getting your hands dirty and solving some integrals.<p>If there's a better reason to remain entirely ignorant of all physics I can't think of it