Selection from Eleonore Stump: Aquinas, pp. 38-39
Substantial and accidental forms
Aquinas takes it that the forms of material objects can be divided into two sorts, substantial forms (that is, the substantial forms of primary substances) and accidental forms. (Immaterial things can also have both substantial and accidental forms, but in the discussion which follows, for the sake of simplicity, my focus will be just on that part of Aquinas’s theory of things which has to do with things made of matter). For present purposes we can understand his distinction between these two sorts of forms roughly in this way. The difference between the substantial and the accidental forms of material objects is a function of three things: (1) what the form organizes or configures; (2) what the configuration effects; and (3) what kind of change is produced by the advent of the configuration.
Regarding (1): a substantial form of a material thing configures prime matter. An accidental form, on the other hand, configures something which is an actually existing complete thing, a matter-form composite. Or to put the same point in a different way, if we conceptually strip away a substantial form from a material thing (and don’t immediately replace it with another substantial form of some sort), what is left cannot exist in actuality. Nothing that is actual consists only of prime matter plus accidental properties. But if we strip away any particular accidental form, what is left is still an actually existing complete thing, and it remains the same complete thing it was before the accidental form was stripped away. (On the other hand, it is not possible to strip away all accidental forms from a material thing. It is necessary to a material thing that it have accidental forms, even if it is not necessary that it have one rather than another accidental form.)
Regarding (2): for this reason, configuration by a substantial form brings it about that a thing which was not already in existence comes into existence. Since any thing that comes into existence exists as a member of a kind, the substantial form of a thing is thus also responsible for a thing’s belonging to a particular primary kind or lowest species. On Aquinas’s views, every substance is a member of exactly one lowest species or primary kind, although species can be ordered hierarchically under genera, which can themselves be ordered hierarchically under higher genera until one comes to the highest genus, which is substance. Configuration by an accidental form, on the other hand, brings it about only that an already existing thing comes to have a certain property, without ceasing to be the thing (or the kind of thing) it was. Accidental forms are thus responsible for the non-essential properties of a thing; the addition or removal of an accidental form does not alter the species to which the whole belongs or the identity of the whole.
Regarding (3): the change produced by the advent of a substantial form is therefore a generation of a thing. The change produced by the advent of an accidental form, by contrast, is only an alteration of one and the same thing.
It is clear from these claims that any material thing which exists has a substantial form. But Aquinas’s claims about substantial form also imply that no existing material thing has more than one substantial form. A composite which consists of prime matter configured by a substantial form could not itself be one component among others of a larger whole configured by yet another substantial form. That is because a substantial form of a material thing configures prime matter; but if a substantial form were to configure what is already configured by a substantial form, then it would be configuring a matter-form composite, not prime matter. (Of course, the new substantial form might simply replace the previous one, but in that case the composite would still be configured by only one substantial form.)
Furthermore, Aquinas’s claims about substantial forms limit the way in which already existing things can be combined into a composite substance. Barnacles have a substantial form, and so do starfish. If a barnacle attaches itself very firmly to the back of a starfish, that attaching will not constitute a generation of a substance. If it did, there would be one thing — the barnacle-starfish composite — which had more than one substantial form, the form of the barnacle and the form of the starfish. So what the attachment of the barnacle to the starfish effects, on Aquinas’s views, is just that two complete things come to have a property or properties which they did not have before, as, for example, the property of being fastened together. The new configuration of the barnacle attached to the starfish will thus be an accidental one. Any case in which two already existing material things come together into some kind of composite without ceasing to exist as the things they were before they came together will similarly be a case of alteration rather than generation, and the new composite will be configured with an accidental, rather than a substantial, form.
Any ordinary artifact is configured only with an accidental form. The production of an artifact, such as an axe with a metal blade attached to a wooden handle, brings together already existing things — a metal thing and a wooden thing — which in the new composite still remain the things they were before being conjoined. An artifact is thus a composite of things configured together into a whole but not by a substantial form. Since only something configured by a substantial form is a substance, no artifact is a substance.
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Eleonore Stump, Aquinas (New York: Routledge, 2003), 38-39.