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A tale of two simples

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Abstract

A material simple is a material object that has no proper parts. Some philosophers have argued for the possibility of extended simples. Some have even argued for the possibility of heterogeneous simples or simples that have intrinsic variations across their surfaces. There is a puzzle, though, that is meant to show that extended, heterogeneous simples are impossible. Although several plausible responses have been given to this puzzle, I wish to reopen the case against extended, heterogeneous simples. In this paper, I briefly canvass responses to this puzzle which may be made in defense of extended, heterogeneous simples. I then present a new version of this puzzle which targets simples that occupy atomic yet extended regions of space. It seems that none of the traditional responses can be used to successfully save this particular kind of extended simple from the new puzzle. I also consider some non-traditional defenses of heterogeneous extended simples and argue that they too are unsuccessful. Finally, I will argue that a substantial case can be made against the possibility of extended heterogeneous simples of any kind.

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Notes

  1. An important difference between this puzzle and a more perfect analogue of the puzzle discussed by McDaniel and Hudson is that this puzzle does not spell out in detail the particular way in which the Statue Darnay is red whereas an analogue puzzle does. A more perfect analogue says that the statue, Darnay, is red in some particular region. The spatial aspect of this claim, along with the simplifying assumption that color properties are intrinsic, justifies the name given to this problem by McDaniel. That name is “The Problem of Spatial Intrinsics”. It seems that the problem of spatial intrinsics is just a special case of the problem presented above.

  2. The views canvassed in this section are discussed at length in Hudson (2006). Hudson presents them as responses to The Problem of Spatial Intrinsics, but they can be taken as responses to the puzzle presented above as well.

  3. See, for example, Markosian (1998, 2004a, b)

  4. See Parson (2000, 2004)

  5. Amati, Ciafaloni and Veneziano (1989); Bradden-Mitchell and Miller (2006); Green (2004); Gross and Mende (1988), and Rovelli and Smolin (1995).

  6. Why, one might ask, do we say that talk about regions less than one Planck length squared makes no sense rather than talk about regions less than one Planck length cubed. Well, it is compatible with the claim that talk about regions that are less than one Planck length squared makes no sense that talk about regions less than one Planck length cubed also makes no sense. But, there is also stronger reason to believe the first claim in addition to the second claim. For more on this see Green (2004).

  7. Such laws need not require that regions of space be substantival. They just need to have explicit quantification over regions of space.

  8. Again, for brief and accessible discussions please see Green (2004), Rovelli (2003) and Rovelli and Smolin (1995).

  9. The main competitor to Quantum Loop Gravity is String Theory. Currently, there seem to be far more scientists working on String Theory than Quantum Loop Gravity. In spite of this fact, there is some reason to believe that Quantum Loop Gravity is the more promising of the two views. For brief discussion of the case in favor of Quantum Loop Gravity see Rovelli (2003).

  10. Another plausible argument starts with the premise that possibly there are atomic regions no smaller than one Planck length. It also involves a premise that says there are no arbitrary cutoffs in modal space. If atomic regions of one Planck length are possible but atomic regions that are Statue Carton shaped are not, then there is an arbitrary cutoff in modal space. It follows from these premises that possibly, there are atomic regions that are Statue Carton shaped. For a defense of the kind of modal principles that bar arbitrary cutoffs in modal space see Bricker (1991).

  11. For that matter, if there were a perfectly symmetrical spherical simple that occupied a region with no proper subregions, then it seems difficult to say what the difference is between being stained in a way that makes it appear as if there is a red spot on the north face versus on the south face. Thanks to Earl Conee for this example.

  12. The arguments in this paragraph are variations on arguments found in Sider (2007)

  13. Here is a nice image that might help to make the view clear. Consider an overhead projector with an outline of Statue Carton drawn on a transparency that is being projected. Now, imagine several other transparencies that are partially colored and can be stacked on the original outline of Statue Carton. Some of these have red spots oriented so that when they are stacked on the outline, a red spot appears to be over Carton’s heart. Others have red spots that are oriented so that when they are stacked on the outline, a red spot will appear on Carton’s big toe and so on. Since the transparencies are only partially colored, we can stack several of them on top of the original outline. Thus, if we stack both the heart oriented transparency and the toe oriented transparency on our Statue Carton outline, then it will look as if Carton has a spot over his heart and on his big toe. These transparencies are like the fundamental distributional color properties several of which are exemplified by Statue Carton when they are “stacked” on the statue. Thanks to Kris McDaniel for this nice image of the situation.

  14. The argument here is not quite right. What we need to say is something like the following. If Statue Carton could be stained in a way that makes it appear as if there is a red spot over Carton’s heart, then it could be stained in a way that makes it appear as if there is a red spot over the right half of Carton’s heart and it could be stained in a way that makes it appear as if there is a red spot over the left half of Carton’s heart. Let’s say that an object that is possibly stained in either of these says is possibly half stained with respect to a way, w, of being stained. What we need to say to get the argument going is that for every way that Statue Carton could be stained, it is also possibly half stained.

  15. There is one more move that the defender of distributional, color properties can make. He can say that for every way that Statue Carton could be stained, there is a fundamental distributional, color property and that when an object is stained in a way that can be built out of some fundamental, distributional color properties it is exemplifying a non-fundamental distributional, color property alongside a fundamental one. This move, however, both multiplies entities beyond necessity and does not explain why there are sixteen basic distributive, color properties that can be exemplified by the statues manufactured at the factory when there are four basic designs.

  16. Josh Parsons suggested this view to me in conversation. It is also suggested in Parson (2000). One nice thing about this suggestion is that it is not subjected to the objections based on the claim that a distributional, color property cannot be fundamental if the color distribution it guarantees can be guaranteed by the exemplification of some other distributional, color properties.

  17. In a previous footnote, I introduced an example of a perfectly symmetrical spherical simple that occupied a region with no proper subregions. If such a simple were possible, given the views introduced above, there would be no difference between being stained in a way that makes it appear as if there is a red spot on the north face versus on the south face. Thanks, again, to Earl Conee for this example.

  18. Although I do believe in mirror images, I do not intend to be committed to mirror images here. I merely wish to use the reflective properties of mirrors to make vivid the dispositional properties that an object might have. The main points I want to make about dispositions can be said in a slightly more cumbersome way by talking about the colors reflected by mirrors rather than talking about mirror images.

  19. You might think that the name I have given to the image of Statue Carton implicitly conveys a thesis concerning the images of simples. But, I honestly have not come to any conclusions about whether or not the image of Statue Carton is a simple.

  20. Or, perhaps a bit more carefully, it could be that the closure of the region occupied by the hyper-mirror is continuous.

  21. Lewis (1986); Sider (2001) and Saucedo (Forthcoming) discuss principles of recombination. Such principles are quite popular and quite useful. If some principle of recombination is true, then certain epistemological puzzles concerning modality would be solved with some ease. This is just one benefit of such principles.

  22. It is important that the embedded claims are quantificational. I do not wish to make a de re claim about some region of space just above my table. I do not wish to do so because I do not wish to suggest that spacetime lacks certain structure. For example, if spacetime is Newtonian, then any region of space which is just above my table at one time would not remain there for a very long. Similar constraints are imposed by Galilean spacetime and Minkowski spacetime.

  23. If you do not like principles of recombination, then here is another argument for the desired conclusion. It is possible that (1) there are laws of nature that require regions of space and (2) those laws in conjunction with the claim that there is at some time a region, oriented a certain way, that is smaller than Darnay shaped entail a contradiction and (3) the conjunction of those laws with the claim that there are no point sized regions in any other orientation entails a contradiction. If that is possible, then it is possible that there is an atomic region into which Statue Darnay can fit and that all other regions are composed of points.

  24. I would like to thank audiences at the 2006 Creighton Club and the 2007 Pacific APA for very helpful questions and comments. I’d especially like to thank David Braun, Earl Conee, Greg Fowler, Mark Heller, Hud Hudson, David Leibesman, Kris McDaniel, Ned Markosian, Josh Parsons, Jonathan Shaffer, John Shoemaker, Ted Sider, Gabriel Uzquiano, and Andrew Wake for reading and commenting on earlier drafts of this paper and for extensively discussing these issues with me.

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Correspondence to Joshua Spencer.

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Spencer, J. A tale of two simples. Philos Stud 148, 167–181 (2010). https://doi.org/10.1007/s11098-008-9291-4

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