A Serbian reader inquires,
I have read your latest post on truthmakers. Among other things, you mention [David] Armstrong's view on abstract objects. As I read elsewhere (not in Armstrong own works, I have not read anything by him yet) he was realist about universals and gives a very voluminous defense of his view. Does this view entail realism about abstract objects?
I think that Quine was realist about abstract objects and at the same time naturalist and also holds that his Platonism was consequence of his naturalized ontology. Moreover, I have the impression that several preeminent analytic philosophers hold realist views on abstract objects, mostly under influences from Quine and in a smaller degree from Putnam.
Do Armstrong's views about universals entail realism about abstract objects?
No, they do not. Rejecting extreme nominalism, Armstrong maintains that there are properties. (I find it obvious that there properties, a Moorean fact, though I grant that it is not entirely obvious what is obvious.) Armstrong further maintains that properties are universals (repeatables), not particulars (unrepeatables) as they would be if properties were tropes. But his is a theory of immanent universals. This means two things. First, it means that there are no unexemplified universals. Second, it means that universals are constituents of the individuals (thick particulars) that 'have' them. In Wolterstorff's terminology, Armstrong is a constituent ontologist as opposed to a relation ontologist. His universals are ontological parts of the things that 'have' them; they are not denizens of a realm apart only related by an asymmetrical exemplification tie to the things that have them.
So for Armstrong universals are immanent in two senses: (a) they cannot exist unexemplified, and (b) they enter into the structure of ordinary (thick) particulars. It follows that his universals are not abstract objects on the Quinean understanding of abstract objects as neither spatial nor temporal nor causally active/passive. For given (b), universals are where and when the things that have them are, and induce causal powers in these things. And yet they are universals, immanent universals: ones-in-many, not ones-over-many. Some philosophers, including Armstrong, who are not much concerned with historical accuracy, call them 'Aristotelian' universals.
Does Armstrong reject all abstract objects?
Yes he does. Armstrong is a thorough-going naturalist. Reality is exhausted by space-time and the matter that fills it. Hence there is nothing outside of space-time, whether abstract (causally inert) or concrete (causally active/passive). No God, no soul capable of disembodied existence, or embodied existence for that matter, no unexemplified universals, not even exemplified nonconstituent universals, no Fregean propositions, no numbers, no mathematical sets, and of course no Meinongian nonenties.
How do Armstrong and Quine differ on sets or classes?
For Quine, sets are abstract entities outside space and time. They are an addition to being, even in those cases in which the members of a set are concreta. Thus for Quine, Socrates' singleton is an abstract object in addition to the concrete Socrates. For Armstrong, sets supervene upon their members. They are not additions to being. Given the members, the class or set adds nothing ontologically. Sets are no threat to a space-time ontology. (See D. M. Armstrong, Sketch for a Systematic Metaphysics, Oxford UP, 2010, p. 8.)
What about the null set or empty class?
For Armstrong, there is no such entity. "It would be a strange addition to space-time!" he blusters. (Sketch, p. 8, n. 1). Armstrong makes a bad mistake in that footnote. He writes, "Wade Martin has reminded me about the empty class which logicians make a member of every class." Explain the mistake in the ComBox. Explain it correctly and I'll buy you dinner at Tres Banderas.
Are both Quine and Armstrong naturalists?
Yes. The Australian is a thorough-going naturalist: there is nothing that is not a denizen of space-time. The American, for reasons I can't go into, countenances some abstract objects, sets. It is a nice question, which is more the lover of desert landscapes.
Leave a Reply to Peter Lupu Cancel reply