Over Sunday breakfast at Cindy's, a hardscrabble Mesa, Arizona eatery not unwelcoming to metaphysicians and motorcyclists alike, Peter Lupu fired a double-barreled objection at my solution to Deck's Paradox. The target, however, was not hit. My solution requires that (a) concrete particulars can be coherently 'assayed' (to use a favorite word of Gustav Bergmann), or given an ontological analysis in terms of constituents some or all of which are universals, and (b) modally contingent concrete particulars can be coherently assayed as composed of necessary beings.
Peter denies both of (a) and (b), without good reason as it seems to me. Let's begin with some definitions pithily presented.
Definitions
Abstract =df causally inert.
Concrete =df not abstract.
Universal =df repeatable (multiply exemplifiable).
Particular =df unrepeatable.
Modally contingent=df existent in some but not all broadly-logically possible worlds.
Modally necessary =df not modally contingent and not modally impossible.
Ad (a). One form of the question is: Could a concrete particular be coherently construed as a bundle universals? Peter thinks not: "But the unification of two universals U and V is another universal W, not a particular." (From a two page handout he brought to breakfast. How many people that you know bring handouts to breakfast?!) Now bundle-of-universals theories of particulars face various standard objections, but as far as I know no one in the literature has made Peter's objection. Presumably for good reason: it is a bad objection that confuses conjunction with the bundling relation.
We understand conjunction as a propositional connective. Given the propositions a is red and b is round we understand that the conjunction a is red & b is round is true iff both conjuncts are true. It is clear that a conjunction of propositions is itself a proposition. By a slight extension we can speak meaningfully of a conjunction of propositional functions, and from there we can move to talk of conjunctions of properties. Assuming that properties are universals, we can speak of conjunctions of universals. It is clear that a conjunction of universals is itself a universal. Thus the conjunction of Redness and Roundness is itself a universal, a multiply exemplifiable entity. I will use 'Konjunction' to single out conjunction of universals.
Now it should be obvious that a bundle of universals is not a conjunction of universals. Let K be the Konjunction operator: it operates upon universals to form universals. Let B be the bundling operator: it operates upon universals to form particulars. Bundling is not Konjunction. So far, then, Peter seems to have failed to make an elementary distinction.
Now suppose Peter objects that nothing could operate upon universals to form a particular. Universals in, universals out. Then I say that he is just wrong: the set-theoretical braces — { } — denote an operator that operates upon items of any category to form sets of those items. Now it should be obvious that a set of universals is not itself a universal, but a particular. A Konjunction of universals is a universal, but a set of universals is not a universal, but a particular. The Konjunction of Redness and Roundness is exemplifiable; but no set is exemplifiable.
Am I saying that a bundle of universals is a set of universals? No. I am saying that it is false to assume that any operation upon universals will result in a universal. What I have said so far suffices to refute Peter's first objection, which was that the unification of two universals yields a third universal. You can see that to be false by noting that the unification into a set of two or more universals does not yield a universal but a particular.
Ad (b). Our second question is whether a contingent particular could have as ontological constituents necessary beings. Peter thinks not. He thinks that anything composed of necessary beings will itself be a necessary being. And so, given that universals are necessary beings, and that concrete particulars are composed of universals, no concrete particular can be modally contingent.
This objection fares no better than the first. Suppose Redness and Roundness are compresent. (You will recall that Russell took the bundling relation to be the compresence relation. See An Inquiry into Meaning and Truth, 1940, Chapter 6.) Each of these universals, we are assuming, is a necessary being. But it doesn't follow that their compresence is necessary; it could easily be contingent. Here and now I see a complete complex of compresence two of whose constituent universals are Redness and Roundness. But surely there is no necessity that these two universals co-occur or be com-present. After all, Redness is often encountered compresent with shapes that are logically incompatible with Roundness. Compresence, then, is a contingent relation. It follows that complexes of compresence are contingent. Necessarily, Rednessexists. Necessarily, Roundness exists. But it does not follow that, necessarily, Redness and Roundness are compresent: surely there are possible worlds in which they are not.
Peter's argument for his conclusion commits the fallacy of composition:
1. Every universal necessarily exists.
2. Every concrete particular is composed of universals. Therefore,
3. Every concrete particular is composed of things that necessarily exist. Therefore,
4. Every concrete particular necessarily exists.
The move from (3) to(4) is the fallacy of composition. One cannot assume that if the parts of a whole have a certain property, then the whole has those properties.
