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Tuesday, October 05, 2010


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Hello Bill,

Could you say a bit more about what you mean by an 'operator' in this context? You speak of the bundling operator B that takes some universals us and forms a particular p? You must mean something more than mere 'function' here for if x=Bus and y=Bus it would seem that x=y. There could be at most one particular derived from each plurality of universals, as the set formation example shows.

Hi David,

You may be alluding to the following objection to the bundle-of-universals theory of particulars.

1. It is possible that there be two particulars that share all universals.
2. But if a particular is just a bundle of universals, then there would be nothing to ground the numerical difference of the two particulars. Therefore,
3. A particular cannot be just a bundle of universals.

Is this what you are getting at?


I think the objection you cite in your reply is one David may intend. I was thinking of raising the same objection myself. An additional objection is this.

The bundling operation does not seem to allow for accidental properties. For if an individual is nothing but a bundle of universals, then each universal that is so bundled applies to the resulting individual. Moreover, it becomes an essential property of the said individual. But surely individuals have some of their properties accidentally.

Bill, Peter,

Yes, that comes into it. But if 'operating on some universals' meant the same as applying a function to some universals, then the operation that returns my desk lamp is clearly one that maps universals to a particular. Peter evidently thinks that 'unification of universals' is a more restricted notion than this. 'Bundling operation' suggests some sort of compounding in which the operands are present in the result, perhaps in a way analogous with the mereological sums we've been discussing recently (though uniqueness of summation would fail). This amounts to a restriction on the range of our putative bundling function. But is 'function' the right starting place for clarifying what you mean by 'operation'?


Actually, there are two problems, one temporal the other modal. If an ordinary particular is a bundle of universals, then it cannot gain or lose universals. This problem can be dealt with by adopting a bundle-bundle theory according to which an ordinary particular is a diachronic bundle of synchronic bundles of universals.

The modal problem is more difficult. To solve it, it looks like one would have to give up transworld identity and adopt a counterpart theory a la Lewis or a theory like that of Leibniz.


A function is too anemic to do the job that bundling does. As you say, bundling suggests some sort of compounding in which the operands are present in the result. That's right, and that is not the case with functions.

If B is the operator and U1,U2, . . . , Un are the operands, then the result of the operation is an entity that has the universals as 'parts.' But in the case of a function such as the propositional function 'x is mortal,' the value is T for Socrates as argument; but Socrates is not 'part' of the truth-value.

You could say that there is a function that maps each set of compossible universals onto a unique bundle which is their bundle. But that mapping presupposes that the bundle is altready on hand. The bundling operator gives us the bundle in the first place.

The idea is that you have some 'parts' -- universals -- that then have to be tied together into a 'whole' by an operator that does this job. But the 'whole' is not a mereological whole -- by the definitions and axioms of classical mereology -- because on classical mereology, the existence of the parts suffices for the existence of the whole. But that is not the case for bundles. So a bundle is not a mereological sum of its constituent universals.

Let me know if that's clear.


The following additional issues need to be addressed regarding the bundling of universals to create individuals in addition to the two issues raised so far by you, David, and myself;
(a) The problem of the possibility of numerically distinct but qualitatively identical individuals;
(b) The problem of contingent properties;

The additional issues:

(c) How many universals it takes to cook-up an individual? Is one universal sufficient? Are two? Etc.,

(d) It appears that the bundling operation presupposes the following Principle-of-Bundling (POB) that holds for every universal u bundled in order to create a given individual x:

(POB) u is *part* of individual x just in case u *applies* to x or u is *exemplified* by x.

Now consider the following universal: ‘u is exemplified by all and only those individuals that u is not a part of’. Let x be an individual and u* the universal just defined. Then if u* is bundled into x and, hence, is a part of x, then u* cannot apply to x; and, conversely, if u* does not apply to x, then u* is bundled to be part of x. Thus, u* is a counterexample to POB. Notice that u* is not a counterexample when POB does not hold; i.e., when individuals are not created by the bundling operation, for in such a world universals are not *part* of individuals to which they apply. Hence, in such a world my universal u* applies to all individuals. Therefore, u* is a legitimate universal, unless you object to universals that apply to all existing individuals. However, I do not think you will make such an objection for obvious reasons (e.g., 'is identical to itself').

(e) I think that the example of u* demonstrates the strangeness of thinking of universals in terms of the part-whole relationship that is required by the bundling operation, while at the same time distinguishing between universals and individuals in terms of the former potential for multiple application.

This is only a tiny bit off topic. I tried to justify a structure that necessarily exists, over at
does anybody think the ideas are salvagable?

Thank you,Bill, Yes. I'm trying to get the same picture in my head of bundling as you have, so I have a few more questions.

a) When we say 'x is a bundle of Us' the 'is' must be taken as the 'is' of constitution rather than description?

b) Do we have to see the bundling as taking place in space and time? Perhaps the bundling operator must act continuously at each point of spacetime to keep an individual in existence and to accommodate accidental change?

c) Could we have bundles without a bundling operator? Suppose the world were spatially two dimensional and the universals were stacked 'vertically' like the pages of a book with each page giving the spatial distribution of its universal. Then vertical ordinates through the book would give us the compresence relation and hence the individuals.

d) It's easy to think of colour universals as spatially distributed but don't some universals, particularly geometric ones like roundness and triangularity presuppose individuals? It doesn't make sense to speak of 'triangularity at a point'.

e) The picture I have so far seems to give a very good account of of my phenomenal world, but I have great difficulty in seeing it as an adequate account of any underlying reality. Is this fair or am I too prejudiced by my physicist mode of thought? I have the suspicion I'm not thinking at the right philosophical 'level' on this topic.


"It's easy to think of colour universals as spatially distributed but don't some universals, particularly geometric ones like roundness and triangularity presuppose individuals?"

Are you asking here whether the very existence of universals presupposes the existence of individuals or whether the instantiation of universals presupposes the *logically prior* existence of individuals?

Clearly, since some universals may not be instantiated at all, their existence (if you accept the existence of such universals at all) cannot presuppose their instantiation and therefore does not logically require the prior existence of individuals. However, the relation of *instantiation* of a universal by an individual seems to logically presuppose the prior existence of the individual which instantiates the given universal. At least such logical priority seems to be a reasonable constraint on the instantiation of universals. Bill needs to explain how this constraint can be either fulfilled by his account or bypassed by it.


Ad (a) Interesting question. Off the top of my head it is the 'is' of identity, not the 'is' of constitution/composition or the 'is' of predication. Thus Peter is identical to a particular bundle of universals. Of course, the universals have to be compossible both logically and nomologically, and they have to be complete, in a sense that I won't define but trust you understand.

But in 'x is the Us,' then I am inclined to say it is the 'is' of composition.

Ad (b). Depends on what the bundling relation is is. If it is compresence, then yes.

Ad (c). I would tend to say No.

Ad (d). I'm not sure you know what is meant by a universal here. Suppose redness (of a definite shade) and roundness are universals. Then they are wholly present in each red, round ball. They are ones-in-many. It's a further question whether they could exist unexemplified or only exemplified. But I may not be understanding you.

Ad (e). It may be that an an analysis like the above works only at the level of phenomenological ontology. But it is not clear to me why the microentities of physics could not also be thought of as bundles of universals.

Perhaps we can solve problems of transworld identity as follows. (If you remember, this transworld identity business is something I brought up against your constituent ontology, Bill, when all of us and Mike and Scott met in Tempe.)

An individual is a bundle but only of his essential properties. His accidental properties are not included in the bundle but rather the bundle acts in a manner analogous to a thin particular for those accidental properties, as sort of the object that the properties "attach" to.

Does Peter Simons make a suggestion along these lines?

I don't know.

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