And now, though I expect no one to read it, I’m going to paste in the paper. Its short.
If any actual people actually were to read this out of some kind of morbid curiosity, I should note: I’m quite happy with the first bit, but think its unimportant. I think the second (and last) bit is much more important and interesting, but I’m deeply unsatisfied with it. I insist to my self and others that I am on to something, though.
Also, there remain several infelicities due to the fact that this is less than half of the paper in its original form. (I had to shorten it for the conference.) I don’t think there’s anything glaring or confusing, but, for example, I mention several names without saying much about the views attached to those names. This is because in the longer version of the paper, I actually discuss those writers in some detail. I may try to find a way to take these references out.
Also, the footnotes are not being pasted into this post, but I think its basically okay without them.
And here it is.
A Way Out for Bundle Theories?
[Abstract] It is often argued that Bundle Theories (BT) of substance are false, on the basis of a purported fact that they are committed to the Principle of the Identity of Indiscernibles (PII), together with another purported fact that PII is false. In this paper, I take issue with the second claim. I argue that the usual way of arguing that PII is false, based on Max Black’s approach in The Identity of Indiscernibles, is inadequate. The possible existence of a special kind of property I will style “Q properties” renders invalid any argument which presupposes that there could be distinct objects which have all their non-relational properties in common. I also discuss some concerns that should arise in response to my way of defending BT.[/abstract]
Bundle theories are those which hold that the fundamental constituents of the world are attributes. Any given particular is just a bundle consisting of all of those attributes it has. In this paper I argue that a certain objection to Bundle Theories commonly taken to be decisive is not so decisive after all. On this basis I argue that Bundle Theories present a plausible theory of the constitution of the world. I further suggest, however, that though the means by which I rescue Bundle Theories from this objection are innocuously valid as arguments in metaphysics, at the same time, the very fact that the move counts as valid is itself a cause for worry.
It should be noted that there are both Trope and Realist versions of Bundle Theory. The Trope versions hold that objects are bundles of unrepeatable attributes. The Realist versions hold that objects are bundles of repeatable universals. The objection I’ll be discussing applies only to the Realist versions. So in this paper, I am discussing Realist, not Trope, versions of Bundle Theory.
It is common to argue against such Bundle Theories on the grounds that they are committed to a principle of the Identity of Indescernibles. This is the principle, tracing its origin to Leibniz, that there can not be distinct objects which share all of their properties. (It will be called hereinafter “PII.”) This works as an objection because PII is commonly taken to be false. The locus classicus for a recent refutation of the principle is to be found in Max Black’s The Identity of Indiscernibles. There he presents his famous example of the Two Spheres—a possible world in which there exist only two spheres, exactly alike in every way. Since they are alike in every way, Black argues, it follows that they share all their properties. Since they are distinct, it follows that it is possible for distinct objects to share all their properties, or in other words, that PII is false.
So the objection against Bundle Theories I am dealing with has this form:
- Bundle Theories imply PII.
- PII is false. (Justified by appeal to “Two Spheres” style counterexamples)
- Therefore, Bundle Theories are false.
In what follows, I will argue that this argument is not decisive, because premise 2 may well be false, “Two Spheres” style arguments notwithstanding. My strategy will be to develop a theory of a class of properties I will call Q properties. Q properties will serve as a basis upon which otherwise identical objects can be distinguished. The existence of this class of properties, or at least, the possibility of its existence, (indeed, the epistemic possibility of its existence) will save bundle theory from arguments of the form outlined above.
However in the end I will examine the notion that the mere epistemic possibility of the existence of a class of properties could do the kind of work I assign it here. I will find the notion worrisome, though not for all that something I can dismiss out of hand.
In this first section, I will briefly examine a representative contemporary argument against Bundle Theories of the “Two Spheres” style. In a longer version of this paper, I discuss this argument, and various strategies that might be used against it, much more extensively. For my present purpose, however, I will only briefly discuss and criticize it, with a view toward explaining how the idea of a “Q property” arises as a natural extension of the ongoing debate over Bundle Theory.
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Q Properties Defined and Discussed
There is a “Two Spheres” style of argument against Bundle Theories (BTs) to be found in Michael Loux’s Contemporary Introduction to Metaphysics. He argues that BT is committed to PII, and that PII is false.
For Loux, BT is the doctrine that “necessarily, for any concrete a, if any entity b is a constituent of a, then b is an attribute.” PII (acc. to Loux) says that “necessarily, for any concrete objects a and b, if for any attribute f f is an attribute of a if an only if f is an attribute of b then a is numerically identical with b.” (107) Loux introduces another principle of constituent identity (PCI) which says that “necessarily, for any complex objects a and b, if for any entity c c is a constituent of a if and only if c is a constituent of b, then a is numerically identical with b.” (ibid.) BT and PCI together entail PII. Since PCI is true, and PII false, it follows that BT is false.
As a basis for the the claim that PII is false, Loux relies, as I’ve said, on a “Two Spheres” style of argument. (108) In doing so, he introduces the notion of a pure attribute. This is an attribute which does not “presuppose” the existence of any concrete particular(s). Examples of impure properties would be ones such as “identical to a” or “on top of b.” Loux argues that Bundle theorists should not allow such properties to count as constitutive of bundles. His basis for this limitation is an observation that Bundle Theorists are reductivists when it comes to concrete particulars, and that since this is so, it would be illegitimate for them to allow for a reductive account of some concrete particular in which some other concrete particular occurs essentially. So, on Loux’s account, a Bundle theory must only allow for pure properties to be constitutive of its bundles. “Being to the left of c” can not be constitutive of any particular object, though “Having a charge of +1 electron-volt” might be.
In the longer version of this paper mentioned above, I argue that Loux’s considerations against the use of impure properties are not adequate. However, for the purpose of this shorter paper, I can grant to Loux that the Bundle Theorist must limit himself to pure properties. In any case, it is usual for Bundle Theorists to agree to something like this stipulation, and to try to work around it. I will follow that tradition herein.
From this limitation to pure properties, Loux deduced that the Bundle Theorist is committed to the following:
BT*: Necessarily, if a is a constituent of b then a is a pure property
PII*: Necessarily, distinct objects differ in at least one pure property.
PII* follows from BT* given PCI. Loux argues that even if there is some question about PII, PII* is certainly false, and so BT* is false. (110-111) But Loux is wrong—PII* is not certainly false, and in fact may well be true. Imagine the following kind of property, which I call a Q property. Q properties are a class of properties Q1, Q2, Q3… such that
necessarily, everything that exists has some property Q1, Q2, Q3,…
necessarily, for any n, at most one object has Qn, and
necessarily, if x has Qn, then in some possible world, some object y ≠ x has
Qn.
I see no reason to think that a Q property has to be an impure property. (I see no reason, in fact, to think that any Q property ever is impure.) And Q-properties are uncontroversially universals, since, per the third clause of the definition, they can be instantiated by distinct objects. A Q property is therefore allowable, on the present account, to a Bundle Theorist as a potential constitutive property.
Yet it follows from the definition of Q properties that, if they exist, then necessarily, distinct objects differ in at least one pure property (which is just what PII* says) since, as per the first and second clauses in the definition, every object has some Q property, and no two things in the same world could have the same Q property.
On the assumption that Q properties exist, then, PII* is true, and Bundle Theory is in the clear (at least as far as this kind of argument goes). The task for a Bundle Theorist, then, is to find some account of what the Q properties could actually be such that they satisfy the desiderata I’ve given regarding them.
I would argue that this is exactly what many have tried to do on behalf of Bundle Theory, though to my knowledge no one has explicated the nature of the task at hand explicitly as I have here.
To begin to set up an example of this, I’ll point out that one sort of property that would fit the bill for a set of Q properties would correspond to an absolute space-time , if such a thing existed. I’ll call this the set of L-properties. Each worldline in absolute space and time corresponds to a distinct L property. L properties are pure properties. Also, we can see that each concrete particular has a single L property , and that no two things in a single world share their L properties. Furthermore, given a concrete particular a and its L property L1, in some other possible world a distinct concrete particular b has that L property. From this we can see that L-properties are universals, and that any distinct objects must differ in at least one pure property since they must differ at least in their L-properties
L properties, in such a scenario, are just like Q properties. If space behaves as I have described it here, then a Bundle Theory can work to describe the metaphysics of the world contained in that space. But, of course, most people do not think space is actually absolute. My example also makes use of controversial assumptions regarding the possibility of identity of points in space across possible worlds. So the illustration, while useful, can’t serve as an explication as to what Q properties actually could be.
Notwithstanding this unfortunate fact, it is quite usual for Bundle Theorists to attempt to appeal to intuitions about spatial locatedness in order to account for the possibility of distinction between qualitatively identical objects. Russell, in An Inquiry into Meaning and Truth, appealed to location in space and time as itself indicative of a set of qualities that go into bundles just like the other qualitative properties. In The Identity of Indicernibles, Max Black’s character A (defending BT) continuously appeals to the possibility of distinction based on spatial separation. Contemporary writers such as John Hawthorne and Gonzalo Rodriguez-Pereyra arguably are trying to find ways to allow spatial location to serve as a distinction-maker between otherwise identical objects.
But all these writers believe that space is relational and not absolute. And since relational spatial properties are “impure” in Loux’s sense, there is a general feeling that there is something troubling or even illegitimate about trying to appeal to such properties in giving a full Bundle theoretic account.
So, for example, in trying to work around this relationality, in An Inquiry, Russell begins, at one point to call a quality’s coordinates in the visual field, themselves, (non-relational) qualities. (99) He seems to hope to define away relational spatial properties in terms of absolute coordinate properties as measured against the visual field. He soon says, though, that, at least as long as we’re trying to reconstruct physics out of our perceptual data, to call the location of a thing, whether its location relative to earth or its location relative to a visual field or whatever, a “quality” can only be thought of as a “harmless avoidance of circumlocution.” (100) In reality, on the account of that passage, it seems locations are not themselves qualities—at least, not “directly observed qualities,” but are nevertheless “definable in terms of qualities.” (ibid.) He does not here make clear what he means by saying locations are “definable in terms of qualities,” and I do not want here to take up that gauntlet. I just mean to note that Russell exemplifies the point I’ve just made—that location seems a very tempting candidate for a “distinction making” property for a bundle theorist, but that there are problems with using locations for this purpose.
Notice also that Russell proposes that there are real properties (“qualities”) in some sense underlying facts about location, allowing locations to be somehow thought of as though they were qualities. I suggest that something like this could be said about Q properties. Q properties are not properties of locatedness, or at least, can’t be for a Bundle Theorist since this would render them impure. But if we can imagine a set of pure properties somehow underlying spatial relations, we may have imagined what Q properties could be like. What I have in mind is something like this. Suppose there were two spheres whose color was continually shifting. Suppose also that, as their respective colors shift, so too does the distance between them grow and shrink. Say the distance between them is determined by the colors each has taken on, and say, indeed, that the distance depends on the colors they take on. Now suppose we are able to observe their distance, but not their color. We might, in such a case, hypothesize that, at any point in time, there is some property had by one of the spheres, and some property had by the other sphere, such that their having these two properties somehow underlies the fact that they hold the distance relation which they do. Were we to make this hypothesis, I would say we would thereby have caught a glimpse of the set of color properties, even though we were unable to observe the spheres’ colors directly. We would have hypothesized, correctly, the existence of a set of pure properties underlying the relational properties we can actually observe.
I suspect that Q properties, if they exist, work something like that. By my illustration, I don’t mean to imply something as strong as that we are necessarily blind to Q properties. But I am trying to illustrate what it could mean to say there is such a set of properties, even if I haven’t been able to successfully point one out directly.
While I have not by any means shown that Q properties in fact exist, still, I have eked out a clear logical space for their possibility. Based on the definition of Q property which I have given, we can certainly at least build models which include Q properties, and see that such models represent coherent arrays of possible worlds. The question has to be whether the array of possible worlds we actually inhabit is one which includes Q properties. To that end, I’ll make some concluding remarks in the following section. I want to reiterate, however, that by showing that the existence of Q properties is a real conceptual possibility, I have undercut the force of Two Spheres objections to Bundle theories. Such objections, at least as they have been formulated to date, rely at least implicitly on claims such as Loux’s that PII* is clearly false. And as long as it remains epistemologically possible for us that there are Q properties, such claims remain undemonstrated.
Part 2 (final part) is in the next post
