Wednesday, September 27, 2006

Gunk in Discrete Space

So suppose that space is discrete at w. Does this rule out the possibility that there is gunk in w? It would surely be weird to suppose there were--for then it seems there would be objects that exactly occupy a region though no proper parts of those objects exactly occupy any region. Though this is weird, it does not seem contradictory or incoherent. So is gunk compatible with discrete space?


Blogger Joshua said...

I am not sure why it would follow that there would be a filled region of space such that no object exactly occupies that region, if space were discrete and there were some material gunk. Could you explain that more.

Also, could you tell me what you mean by 'discrete space'. For example, are you thinking of a space that is dense or not. I ask because I don't think I understand how there could be gunk in a non-dense space.

7:43 PM  
Blogger Chris Tillman said...

Oops, I misspoke. I was thinking about this as sort of the "inverse case" of an extended simple in continuous space. I was thinking that if that is possible, it's no weirder than gunk in discrete space. I was thinking a principal weirdness of extended simples in continuous space is that there seems there would be filled regions of space not exactly occupied by any object. What I meant to say in the gunk-in-discrete-space-case was that there would be objects that exactly occupy a region though none of its proper parts exactly occupy any region (and this condition is not trivially satisfied).

By 'discrete' I mean not continuous. So not dense. (I think that follows but I'm not sure.) I think we can understand there being gunk in such a space if we deny that every object has to be located and deny that no object is such that it can exactly occupy a region while none of its proper parts occupy any region.

Gunk in discrete space seems as intelligible to me as extended simples in continuous space. So I was mostly wondering whether their intelligibility stood or fell together; whether there was some special problem for supposing that gunk occupies discrete space with no analogous problem for supposing that extended simples occupy continuous space. Sorry for the think-o and I apologize for any remaining unclarities.

7:58 AM  
Blogger Joshua said...

I am still a bit confused. Let me describe three cases and note some parallels between them.

First case: Extended simples in continuous space. One feature of such a view is that there are some matter filled regions that are not exactly occupied by objects.

Second case, Extended simples in discrete (but pointy) space. This is a situation in which space is discrete, but no atomic region is extended. In this case we seem to be committed to the claim that there are some matter filled regions that are not exactly occupied by objets. This case is the perfect discrete space analogue of the first case.

Third case, Gunk in discrete space. In this situation, we would not say that there are some matter filled regions that don't have objects in them. Rather, it looks like we would have to say that there are some objects that do not exactly occupy any region whatsoever (although they may in some sense be in a region).

So, first, I agree with you that someone might hold that Gunk in discrete space is possible if they deny that every material object has to be located. I think I agree that they have to say that some material objects exactly occupy a region while none of their parts exactly occupy regions. But I fail to see the parallel between this case and the case of simples.

Finally, I want to say that someone who believes that discrete space with extended atomic regions is possible and believes that such space is compossible with Gunk need not deny that the Gunk has some proper parts that are not located. Rather he could say that they are located, but they are not exactly located. Perhaps there are parts that are in a region without filling the region.

Maybe this is all a restatement of what you were thinking. If so, then I think we are on the same page.

11:58 AM  
Blogger Chris Tillman said...

We were mostly on the same page, except that I assumed that lacking an exact location implies lack of a location. But I see that that need not be the case (in some weird sense of "need".) So is there any combination of topological properties that space could have that would rule out there being gunk in that space without adding in further constraints, like "every object that is exactly located is such that every proper part of it is exactly located" or "if o is located then o exactly occupies some region"? It seems to me that the answer is 'no'.

9:50 AM  
Blogger Joshua said...

I think you are correct. I don't think we can rule out material gunk based on topological constraints alone.

The one idea that I had was this. Is it possible for there to be a space with no regions? If so, and if it is necessary that anything material is located, then we can rule out material gunk. I am not sure if the claim that necessarily, anything material is located counts as an extra assumption or not.

Moreover, I think it is probably impossible for there to be space with no regions.


8:17 PM  

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