One of the most difficult things in philosophy to define and understand seems to me, oddly enough, to be matter. Understanding what it is that makes a thing "material," what exactly "matter" is, and what role it plays in schemes of understanding, is in practice monstrously difficult. If you put together all the different ideas of what matter is or has been in various philosophical systems, it's hard to see how we're even talking about the same thing.
The basic problem of matter is how you can have something left over when something dies or ceases to exist; as well as how something can pass over from one thing to another. Hence, the most basic idea of "matter" is simply material, in the sense of something out of which something else is made; if you make a statue out of marble, that marble remains distinct from the image you make in it, and you can later reuse that same marble to make something else. Yet "matter" in the philosophical sense is the attempt to describe a universal medium for all or at least a large class of objects--one in some way distinct from the regular, intelligible being of that object or, indeed, of that of any of the class of material objects.
The ancients and Medievals were all agreed, more or less, in seeing matter as a source of disorder and unintelligibility in things: whether Plato's material imposing necessity on the demiurge to Aristotle's pure potency receiving act. The basic idea in all these systems is the imposition of intelligible reality onto some more or less unintelligible material that delimits and conditions it. What exactly it does, and why and in what sense it even exists, is complex, and different in different systems. Even here, though, the basic problem is always to explain why this matter even has to exist, both as a means of explanation, and as a part of the cosmos; the other basic question is what relationship precisely it has with intelligible reality. These were all questions the ancients and Medievals were well aware of, and spent a lot of time trying to answer. I'm broadly a Thomist, and find the general Aristotelean-Scholastic account mostly satisfactory; but it still leaves me with a lot of questions, and I would have to study and think a lot more to really answer them. Perhaps I will write more on this topic at some point.
Starting in the modern period, we seem to move to a large-scale view that takes matter somehow both as the source of order, intelligibility, and even existence in things, and also as the realm of external knowledge and control opposed categorically to the mind as controller and knower. This meant that matter was often taken in a purely mathematical sense--to give a "material" account of an object is to give an account of it entirely in terms of quantitative relationships between discrete quality-less objects. By doing so, one exhausts the object entirely--nothing is left over besides subjective elements whose real origin is in the self. Yet if matter is simply mathematical, then it's hard to see what matter actually adds to mathematics; and since mathematics is itself an intelligible discourse of mind, matter as a discrete category opposed to mind ends up being rather slippery, to say the least. Hence, this idea of matter produced not only systems that made everything material, but also idealist systems that eliminated matter entirely.
As this account shows, the roots of this view are highly subjective, in the sense that they take the individual human self and its relationship with the world to be a constitutive element of philosophy. We move, essentially, from a more or less open account of things in themselves--usually with an explicit divine mind as governor or creator--to a view where the human mind itself takes the role formerly held by God, so that objects can be defined largely or entirely by their relation to the idealized individual self. It's not clear to me, in fact, if 'material' in the modern sense often means anything more or less than 'manipulable' or 'capable of systematization and control according to mathematical schema' or even simply 'external to the self.' Otherwise, it's hard to see what exactly 'matter' as a categorical phenomenon is contributing to these schema in terms of philosophical explanation.
Modern science here certainly provides important information; especially since the modern relativistic and quantum revolutions have succeeded in almost completely overturning the older, purely mathematical and deterministic ideas of matter I've talked about. Still, as always, pure science is very confusing, and highly in need of philosophical interpretation. I certainly believe an Aristotelean interpretation of modern physics is possible; and, indeed, such explanations are treated as increasingly attractive and persuasive by modern philosophers of science. Still, the question of how to fit matter in with *any* philosophical scheme remains, I believe, a difficult one.
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