Monday, June 21, 2004

Bundles of Joy

Most of my metaphysics posts so far have concentrated on the universals debate, so now I'll move on to considering particulars instead. (I've an exam on Friday, so I'm basically just using this opportunity to revise, plus it's kinda fun anyway.)

Concrete particulars are simply those things which we call "objects" in everyday life. Now, the big question is whether these objects can be analysed in terms of anything simpler (their constituent parts). Austere nominalists suggest not, but the metaphysical realist will want to analyse objects in terms of its attributes/properties/universals.

The (reductionist) Bundle Theory suggests that particulars are simply "bundles" of attributes which happen to be co-present. For example, if you have a ball with properties: {is spherical, has a 10 cm diameter, is made of rubber, is red, etc...}, then the ball simply is the bundle of those properties. Those are its only constituents, there's nothing more to it than that. (But note that any object probably has an infinite number of such properties, e.g. "being green or not-green", or "not being the number 42", etc.)

Substratum Theory, by contrast, insists that there is something else, something which possesses those properties, a special something at the core of an object. They call this special something a 'bare particular', or 'substratum'. It functions as a sort of empty shell, which gets filled in by all the properties the object possesses.

Now, many philosophers have objected to the substratum theory on the grounds that it is bizarre, stupid, and borderline incoherent. All good reasons to reject a theory, I suppose. (Actually, the main reason is just good old Ockham's Razor - why invent substrata if we don't need to?) Anyhoo, Bundle Theory is certainly the default choice, so let's see if it will work.

Objections to Bundle Theory:
(1) It renders subject-predicate discourse tautological.
Recall the ball described above, and consider the sentence "the ball is red". According to bundle theory, this sentence is really saying "the bundle of attributes {is spherical, has a 10 cm diameter, is made of rubber, is red, etc...} includes the attribute of being red". In other words, "this red thing is red" - an obviously empty claim!

However, this objection is easily overcome if we distinguish metaphysics from epistemology, i.e. the difference between what exists, and what we know to exist. It is entirely possible to refer to an object, despite being in a position of ignorance regarding its attributes - rather like it's possible for Lois to refer to Clark Kent, without knowing that he is Superman. So although referring to the ball means referring (metaphysically) to the property of redness, the speaker does not necessarily know this. He can refer to the ball, without knowingly (i.e. epistemologically) referring to redness. So the sentence "the ball is red" will indeed contain epistemologically (though not metaphysically) meaningful information.

(2) It is ultra-essentialist.
Bundle Theory implies that objects have the properties they do essentially - i.e. necessarily, if the object had any different properties, it would be a different object. This seems counterintuitive. A book is sitting on my computer desk. But if instead it were sitting on a bookshelf, surely it would still be the same particular book, not a different one. Ultimately, the bundle theorist just has to bite the bullet and insist that our intuitions there are, strictly speaking, mistaken. I plan to post more about strict vs common-sense identity soon.

I should mention though, that the opposite extreme of substratum theory is similarly implausible in this regard. Substratum theory is anti-essentialist: all that matters for identity is the substrata, you could change any of the properties and it wouldn't matter. You would still be the same object, even if you were a beetle, or a rock, or even the number 7. Riight...

(3) It implies a false principle - the Identity of Indiscernibles
This is the strongest objection against Bundle Theory, since it actually, erm... works. Here's the problem.

According to the Principle of Constituent Identity (PCI): If any two objects are made of all the same constituent parts, then they are the same object. But, according to Bundle Theory (BT): The only constituents are attributes. These 2 principles together imply a third, the Identity of Indiscernibles (II): If any two objects have all the same attributes, then they are the same object.

However, II seems to be a false principle. We can imagine a perfectly symmetrical universe with exactly 2 objects in it, e.g. two golden spheres, which exactly resemble each other. They have all the same attributes. But then II implies that they are the same object, which they're not! So II is false. Thus BT must be false.

There are a couple of ways to argue that the spheres actually have different attributes:

a) The spheres occupy different areas of space. This requires that we conceive of space as being absolute, an object in itself, rather than a mere relation between objects. (For clearly the spheres are in the same relation to each other!) But then we are in danger of regress, for how are we to identify one portion of space as different from the other? This response then begs the question, by assuming what we have set out to prove.

b) Haecceity / Impure Properties. Call one sphere 'A', and the other one 'B'. Then we can say that A has the property of "being identical to A", which B does not! However, recall that we are attempting an analysis of what particular objects consist of. It would clearly be circular to appeal to the concept of a particular object as part of this analysis/definition. Yet that is precisely what this response does, by appealing to 'impure properties' (properties which already involve the notion of a particular object). Thus, we really should update the BT and II principles mentioned above, by replacing each mention of "attributes" with "pure attributes" instead.

c) Trope theory. This is the Bundle Theorist's only real option. If you understand attributes/properties as being multiply-exemplifiable universals, then counterexamples to II are possible. However, this can be avoided by adopting Trope theory instead. If we understand attributes as tropes, then no two distinct objects (not even the golden spheres) will ever have any (let alone all) of the same attributes - they can have exactly resembling tropes, but they are nevertheless numerically distinct.

I have to say, I think properties are a load of bunk, so trying to analyse concrete objects in terms of these fictional entities isn't gonna do a lot of good. But for those who think differently, the best option is definitely bundle theory with tropes. Substratum Theory is ontologically bloated, but Bundle Theory won't work with universals, because of the II objection. Alternatively, there's Aristotelian 'substance theory', which I haven't mentioned here, but that's pretty lame anyway. (Ha, yeah, not much of an argument, I know, but I'm lazy. Sue me.)


  1. [Copied from old comments thread]

    While does absolute space necessarily entail substantial spacetime? I know that Sklar argues that substantial spacetime is the best view within physics - but I'm partial enough to Leibniz to hope a purely relativistic spacetime is possible.

    In anycase, one can argue that position is an absolute property without arguing that there must be a substantial space to make position make sense. i.e. it's just a value like charge, spin, etc. Within QM I think this makes sense, even if QM assumes a substantial spacetime. (Although one hopes the GUT theorists who are influenced by Leibniz can get us out of that predictament)
    clark | Email | Homepage | 22nd Jun 04 - 11:21 am | #


    That's an interesting possibility.

    As I understand it, spatial properties 'tie' an object to something else. As an absolute property, this tie would link objects to a spatial position (rather than to other objects).

    Now, if I understand you correctly, you're suggesting that we need not understand this 'position' as an object in itself. Instead, it could just be a sort of mathematical value, a number, perhaps like co-ordinates on a cartesian grid.

    So the spheres are positioned at different co-ordinates. The co-ordinates are NOT to be understood as distinct objects in themselves, but rather, as properties that spatial objects possess. The uniqueness of each co-ordinate-based property is then taken as a basic, unanalysable fact.

    Hmm. Yeah. I don't see why that wouldn't work. I might email my lecturer and ask him about it. Thanks for the pointer.
    Richard | Email | Homepage | 22nd Jun 04 - 2:47 pm | #


    But spatial properties tie an object to something else only because we perceive it as such on a macro scale. Whether we adopt a relative space/time or an absolute one of the sort I suggest space as we perceive it is still an emergent property/feature. Of course most still favor the "container" model of space for pretty good reasons. As I mentioned Sklar's _Space, Time, and Spacetime_ give most of the fairly persuasive arguments for this. (A good read for those who think Einstein achieved more of Leibniz' project than he actually did)
    Clark | Email | Homepage | 23rd Jun 04 - 5:12 pm | #

  2. at the end of your objection 2 to the bundle theory, right was spelt with 2 i's but other than that this is a great resource.

  3. I can't remember for sure, but I imagine I did that intentionally, to signal a long drawn out sarcastic tone ("riiiiight").

    But thanks. Glad you found it helpful.

  4. A wondefully concise and light-hearted account of some of the problems BT is presented with. I found this really helpful and easy to digest, thank you :)


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