Abstract objects exist when instantiated. The “form of 2” does not exist in a world of forms somewhere, but 2 billiard balls is an instance of both ‘2’ and ‘billiard ball’.
I agree this is an ‘Other’ doctrine, and ‘nominalism’ is a bad name for the doctrine of concretism (i.e., everything is spatiotemporal). But isn’t Aristotelianism a form of ‘nominalism’ as defined here? Doesn’t your Aristotelianism deny, or refuse to affirm, any “object that does not correspond to any pattern of matter and energy in space-time”? Properties are not ordinarily thought of as objects, and even so if you think that all properties are instantiated, then they do seem to be spatiotemporal, though perhaps in an informational rather than ‘matter/energy’ sense. Hm.
In the loose sense of ‘form’ (cf. Physics I.7), I think objects could: a rabbit has the form of a rabbit, and if it’s white it has that form too. That’s also consistant with the relationship between primary and secondary substances and non-substances from Categories.
On the other hand, in Metaphysics, ‘form’ is pretty much restricted to the identity of a substance. Still I think Aristotle would be happy enough with polymorphism so long as you made a distinction between substance-forms and non-substance-forms.
Other: Aristotelianism.
Abstract objects exist when instantiated. The “form of 2” does not exist in a world of forms somewhere, but 2 billiard balls is an instance of both ‘2’ and ‘billiard ball’.
I agree this is an ‘Other’ doctrine, and ‘nominalism’ is a bad name for the doctrine of concretism (i.e., everything is spatiotemporal). But isn’t Aristotelianism a form of ‘nominalism’ as defined here? Doesn’t your Aristotelianism deny, or refuse to affirm, any “object that does not correspond to any pattern of matter and energy in space-time”? Properties are not ordinarily thought of as objects, and even so if you think that all properties are instantiated, then they do seem to be spatiotemporal, though perhaps in an informational rather than ‘matter/energy’ sense. Hm.
I’m not sure if Aristotle actually believed an object could be an instance of two forms. That’s pretty advanced polymorphism.
In the loose sense of ‘form’ (cf. Physics I.7), I think objects could: a rabbit has the form of a rabbit, and if it’s white it has that form too. That’s also consistant with the relationship between primary and secondary substances and non-substances from Categories.
On the other hand, in Metaphysics, ‘form’ is pretty much restricted to the identity of a substance. Still I think Aristotle would be happy enough with polymorphism so long as you made a distinction between substance-forms and non-substance-forms.
Sounds about right to me.