Perhaps Patrick Toner could tell me whether whether I understand the different uses of 'matter' in Aristotelian-Scholastic (A-S) philosophy. Here are some of the distinctions as I understand and interpret them.
1. For starters, we can and do use 'matter' to refer to material particulars, a horse, a statue, a man, and indeed any hylomorphic compound, any compound of matter (in a different sense!) and form. When we speak of the material world, we mean these material things some of which are primary substances.
2. Then there is matter as individual proximate matter: what a material thing is immediately made of. Take a nice Southwest example, a quesadilla, the individual proximate matter of which is a tortilla and some melted cheese.
3. Individual nonproximate matter. The individual proximate matter of the melted cheese is some cheese. But this cheese and its material components, while individual, are not the proximate matter of the quesadilla.
4. Matter as specific proximate matter: the various kinds of space-filling stuff. Cheese and tortillas for example.
5. Matter as matter in general. This is materia prima, prime matter, absolutely indeterminate and bare of any and all forms and, as such, pure potency to any and all forms.
On this scheme, (2) and (3) are designated matter (materia signata) while (4) is undesignated matter: the matter that can be referred to in a definition. For example, if I eat a quesadilla, the matter I consume is designated matter whereas if I define 'quesadilla,' the matter entering the definition is undesignated and inedible: 'A quesadilla is a common item of Mexican cuisine consisting of a corn or flour tortilla folded over melted cheese and sometimes other ingredients in the shape of a half-moon.'
Now what about secondary matter, materia secunda? This contrasts with materia prima. 'Secondary matter' is an umbrella term covering both (2) and (3) and (4). Or that's how I understand it. Note that proximate matter is not the same as secondary matter. The proximate matter of a meat ball is the meat (assuming it is made of meat only), but protein is part of its secondary matter without being proximate matter. The concept of proximate matter is relative; the concept of secondary matter is not.
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