The Bundle Theory and the Identity of Indiscernibles

I have been defending the bundle-of-universals theory of concrete particulars (BT) against various weak objections over a series of posts, here,  here, here, and here. Now I consider a very powerful objection, one that many will consider decisive.  The objection can be cast in the mold of modus tollendo tollens:  If BT is true, then the Identity of Indiscernibles is a necessary truth.  But the Identity of Indiscernibles is not a necessary truth. Ergo, BT is not true.

1. The Identity of Indiscernibles (IdIn) is the converse of the Indiscernibility of Identicals (InId) and not to be confused with it.  InId is well-nigh self-evident, while IdInis not.  Roughly, the latter is the principle that if x and y share all properties, then x = y.  It is a strictly ontological principle despite the epistemological flavor of 'indiscernible.' As just stated, it is more of a principle-schema than a principle.  We will get different principles depending on what we count as a property.  To arrive at a plausible nontrivial principle we must first rule out haecceity properties.  If, for any x,there is a property of identity-with-x, then no two things could share all properties, and the principle would be trivially true due to the falsehood of the antecedent.  Haecceity properties are creatures of darkness in any case as I argue elsewhere.

A plausible, nontrivial, principle results if we allow as properties all and only relational and  nonrelational pure properties.  A pure property is one that makes no reference to any specific individual.   Being married would then be an example of a pure relational property: to be married is to be married to someone, but not to any specified individual.  Being married to Xanthippe, however, is an impure relational property.  Being obese would be an example of a nonrelational property.  Here then is a plausible version of the Identity of Indiscernibles:

Necessarily, for any x, for any y, and for any relational or nonrelational pure property P, if (x has P iff y has P) then x = y.

2.  It is obvious, I think, that BT entails IdIn in the above form.  Consider a concrete particular, an iron sphere say, at a time.  On BT it is nothing but a bundle of universals. This implies that it is not possible that there be a second iron sphere that shares with the first  all relational and nonrelational pure properties.  This is not possible on BT because on BT a concrete particular is nothing more than a bundle of universals.  Thus there is no ontological ingredient in a concrete particular that could serve to differentiate it from another particular having all the same relational and nonrelational pure properties.  And if it is not possible that there be two things that differ numerically without differing property-wise, then the Identity of Indiscernibles as above formulated is necessarily true.

I am assuming that BT, if true, is necessarily true.  This is a special case of the assumption that the propositions of metaphysics, if true, are necessarily true.  If this assumption is granted, then BT entails IdIn.

3.  But is IdIn true?  Since it is necessarily true if true, all it takes to refute it is a possible counterexample.  Imagine a world consisting of two iron spheres and nothing else.  (The thought experiment was proposed in a 1952 Mind article by Max Black.) They are the same size, shape, volume, chemical composition and so on.  They agree in every nonrelational respect.  But they also agree in every relational respect.  Thus, each has the property of being ten meters from an iron sphere.   What Black's example seems to show is that there can be numerical difference without property-difference.  But then IdIn is false, whence it follows that BT is false.

4.  This is a powerful objection, but is it fatal?  Here are three ways to resist the argument, fit topics for further posts.  He who has the will to blog will never be bereft of topics.

a. Maintain that BT is a contingent truth.  If so, then BT does not entail IdIn as formulated above.

b. Grant that BT entails IdIn, but deny that scenarios such as Black's are really possible.  Admit that they are conceivable, but deny that conceivability entails possibility.

c.  An immanent universal can be wholly present at different places at once.  So why can't a bundle of universals be wholly present in different places at once?  Argue that Black's world can be interpreted, not as two particulars sharing all universals, but as one particular existing in two places at the same time.  From that infer that Black's Gedankenexperiment does show that IdIn is false.

Any other paths of resistance?

Comments

[aresh v.]

"What Black's example seems to show is that there can be numerical difference without property-difference"
Say, we name the 2 spheres A and B (and use these names rigidly). Now there is at least one property they don't share "being 10 meters distant from B". Am I wrong?

[Bill Vallicella]

Thanks for your comment, but to answer your question, Yes.

First of all, the spheres are not labeled, and there are no observers or language users in Black's world. If they were labeled, then of course there would be a property difference.

Second, being 10 meters from B is an impure property.

[aresh v.]

I may be a bit confused. If you can say "each has the property of being ten meters from an iron sphere"
while "each" stands for a single sphere why can't I use A and B rigidly in the same way? If we are not observers inhabiting Black's world, we are still observers of Black's possible world and we can refer to its insividuals rigidly, i.e. without involving us as observers.
Then you say "being 10 meters from B" is an impure property. Agreed, but why shouldn't I cansider also "being 10 meters from an iron sphere" an impure property or something that presupposes an impure property? After all isn't true that the sentence "A is 10 meters from B and B is 10 meters from A" and the sentence "each has the property of being ten meters from an iron sphere" are made true by the same portion of reality?

[Bill Vallicella]

But 'each' does not refer to one sphere rather than the other.

Ex hypothesi, the spheres are not labeled, and there is no one to label them. Being ten meters from an iron sphere is common to both, and so can't distinguish them.