## Tuesday, October 12, 2010

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Hi Bill

You mean: "So from the fact that sphericality is bundled with rubberness, and rubberness with cubicality, it does not follow that sphericality is bundled with CUBICALITY".

But what explains transivity in a BT? There is maybe a similar way to see the problem: assume we have 2 red things, A and B, and transitivity holds, now since the universal property red is the same one which is bound with all the other properties of A and B, it follows that all the properties of A would be bound with all the properties of B. But how can we count A and B as 2 distinct objects? If one replies: thanks to time and space. Then my objections would be: how? In fact if time and space were also properties then A's time-space properties would be connected to B's time and space properties by transitivity again.

Aresh,

Thanks for the correction. Yes, that's what I meant.

But I don't understand what the rest of of your comment means.

I've got a question for you. Suppose there were no red objects in existence. Then, you imagine a red car. Does "redness" exist in the universe in this case?

According to your argument, if one accepted that "bundling" were not only symmetrical but also transitive the consequence would be e.g. that "the ball has as constituents both sphericality and cubicality, universals that are not compossible". This may happen when we consider a whole individual and its part. My point is that this problem can arise also between individual and individual: in fact if according to a BT theory of universals 2 complete individuals must be at least disntinguishable in virtue of space and time and again space and time were properties, it follows that
all the properties of one individual would be bundled with all the properties of the other individual, included space and time properties by transitivity. And this result makes me wonder why then we talk about 2 individuals (e.g. 2 red apples existing in different time/space) instead of one individual (which is the bundle of all the properties the 2 apples share along with the properties they don't share since the latter are bundled together by means of the former). Sorry for my bad english.

Paul asks: " Suppose there were no red objects in existence. Then, you imagine a red car. Does "redness" exist in the universe in this case?"

Are you assuming that universals exist only if exemplified? I think you are, and that's a possible view. Another view is that universals can exist unexemplified. If universals exist only if exemplified, and there are no red particulars, then redness does not exist. Now if there never were any red particulars, then I don't think one could imagine a red car or a red anything. So let's suppose that there were some red particulars and I remember one or more of them. Then I presumably could now imagine a red car even if now there is nothing outside the mind that is a red particular.

Your question, then, is this: given that universals exist only if exemplified, and the only red particular is an object of imagination, would the universal redness then exist?

I would say no. For those who maintain that universals exist only if exemplified mean that they exist only if exemplified by particulars that exist 'outside' the mind.

A,

That the bundling relation cannot be transitive is obvious if you think about it. All you need to do is find a possible case in which three universals satisfy these conditions: U1 is bundled with U2; U2 is bundled with U3; U1 is not bundled with U3. I gave an example above.

This is not controversial. All agree that the bundling relation is nontransitive.

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