We think the appeal to Redundancy is a powerful argument against the fundamental existence of most heaps, and so constitutes a serious challenge to Heapism.
However, some inorganic structures, including molecules, may be able to escape this argument from Redundancy. Quantum chemistry provides some indications of the emergent nature of whole molecules (Hendry 2006, 2010, Bishop 2005). Take for example, a water molecule, a molecule of H2O. Such molecules consist of a quantum system with 18 protons and electrons and (typically) eight neutrons. The quantum equation for such a system of particles is spherically symmetrical in shape. However, we always find water molecules to be asymmetrically organized in a V-shape, with approximately a 106o angle between the two chemical bonds, and the global behavior of water gives us reason to believe that this is so prior to observation (before, that is, the “collapse of the wave packet”). This asymmetric V-shape of the molecule appears to be an emergent property of the whole that has to be determined empirically. It cannot be deduced from the physical properties of the particles, even taken collectively. (At least, it's not deducible given our current knowledge of quantum chemistry.)
2. Occupation of space. The second objection to Fundamental Heapism concerns the problem of explaining how things occupy space. The key question is why is the location of a part of a thing is a part of the location of the whole thing. In fact, there are two facts that need explaining (in terms of metaphysical grounding):
Spatial Occupation Fact 1. If x is a material part of y, then the location of x is a part of the location of y.
Spatial Occupation Fact 2. If material body y is a sum of the x's, then the location of y is a sum of the location of the x's.
There are three possible explanations of these two facts:
They are metaphysically brute necessities or necessities imposed by the laws of nature.
The existence and location of the parts are fundamental, and the existence and location of the whole are wholly grounded by them. The location of the whole is always to be explained metaphysically in terms of the parts, in such a way as to make true the two Spatial Occupation Facts.
The existence and location of the whole are fundamental, and the existence and location of the parts are wholly grounded by them. When an extended material body has a region as its location, the body simultaneously has all of the parts of that region as partial locations. A material part of a fundamental body consists in the fact that the body has some region as a sub-location.
The first option is unattractive from the point of view of Ockham's Razor (PMeth 1.2), since it imposes a vast system of brute necessities between the locations and location-occupiers. Option 2 corresponds to the Priority of Spatial Proper Parts, and option 3 to the Non-Priority of Spatial Proper Parts:
22.3T Priority of Spatial Point-Parts. If x is a composite thing, then the location of x is wholly grounded in the point-locations of point-sized parts of x.
22.3A Non-Priority of Spatial Point-Parts. If x is a composite thing, then the location of x is not wholly grounded in the location of x's point-sized parts.
There is something very natural about the Priority of Spatial Point-Parts. It fits well with Spatial Pointillism (18.1T), the view that spatial points are the fundamental sort of location while spatial regions are something like constructions from spatial points. However, there are some powerful arguments against Spatial Pointillism (which we saw in detail in Chapter 18), and we have F.H. Bradley's argument against the universal priority of parts over wholes (Section 11.2.3), so we should take seriously the alternative position, the Non-Priority of Spatial Point-Parts. If spatial point-sized parts are not prior, then it is the region-filling location of extended bodies that must be metaphysically fundamental (assuming that we don't want both points and regions to be fundamental locations). If extended regions are the fundamental locations, what explains the fact that one region is a part of another? Given Spatial Anti-Pointillism (18.1A), we cannot give the simple answer that one region is a part of another just in case its points are a subset of the points of the other. We must instead either embrace composition as identity or take parthood to be a fundamental relation among regions.
The Non-Priority of Spatial Point-Parts requires a brute necessity linking fundamental material wholes with appropriate locations and sub-locations, in such a way that the derivative parthood relation among regional locations satisfies the axioms of mereology. In addition, it seems to require a brute necessity connecting dependent parts of fundamental wholes with corresponding sub-locations of those wholes. This is a theoretical cost of the view. We could lessen the cost somewhat by making the parts of fundamental bodies into derivative entities, entities whose very existence consists simply in certain facts about the location and nature of the whole body. The following picture emerges. The fundamental entities are certain extended, composite bodies. These fundamental entities have regional locations and sub-locations among their fundamental properties. The so-called ‘parts’ of these bodies are simply identical to the bodies' sub-locations. Each proper part of the location of a fundamental body is a potential proper part of the whole body. Thus, there is no need to explain the proper parts' locations. They simply are the locations, under a different guise.
This whole picture seems implausible if we apply it to heaps. How could the location of any heap be metaphysically fundamental and the location of its parts merely derivative? The heap has no being or nature over and above the being and nature of its parts. The dependency seems to run clearly in the other direction. Proper parts and their locations are fundamental, and the locations of heaps are dependent on them. If so, then we must embrace the Priority of Spatial Point-Parts, at least insofar as it applies to heaps:
22.3T.1 Priority of Spatial Point-Parts for Heaps. If x is a heap, then the location of x is wholly grounded in the locations of some proper parts of x.
If Priority of Spatial Point-Parts for Heaps is true, then we have a good reason to think that heaps are not metaphysically fundamental. If the location of the heap is grounded in the point-locations of its proper parts, then presumably the same thing is true of all of the properties of heaps, including their intrinsic qualities and their material composition. If so, then the only fundamental entities are the proper parts, and the heaps are merely derived entities. If a heap is heap-like all the way down to its point-sized parts, in the sense that all of its proper parts that are not point-sized are themselves mere heaps, then it is those point-sized parts that are metaphysically fundamental. Let's call such a heap a ‘thorough heap’.
Def D22.4 x is a thorough heap if and only if x is a heap and all of x's proper parts whose locations are larger than points are also heaps.
22.3T.2 Priority of Spatial Point-Parts for Thorough Heaps. If x is a thorough heap, then the location of x is wholly grounded in the locations of its point-sized parts.
This argument presupposes that all thorough heaps have point-sized parts. Suppose that all of the parts of a thorough heap were spatially extended. Then the Priority of Spatial Point-Parts would be obviously false, since there would be no point-sized parts to be the fundamental entities. The possibility that some thorough heaps might have no point-sized parts is closely related to the thesis that there is gunk, which we introduced in Chapter 11 and will take up again in Section 22.4.2 below, when we discuss the arguments for heaps.
Even if we dismiss the possibility of gunk, there is still one kind of thorough heap that can survive this argument: point-sized heaps. If a heap is point-sized, then its location has no proper parts. This means there is no need to explain the connection between proper parts of locations and proper parts of location-occupiers.
But can heaps be point-sized? How can a heap be composed of proper parts if it is the size of a point? Suppose that there are point-sized particles that can share exactly the same location (like photons). Several such particles could come to occupy exactly the same point, resulting in a point-sized heap.
3. Ontological economy. A t
heory of the world that denies the fundamental existence of heaps is simpler, both quantitatively and qualitatively, then one that includes heaps among its fundamental objects. Other things being equal, this gives us good reason to prefer Anti-Heapism, according to Ockham's Razor (PMeth 1.4).
UPSHOT OF OBJECTIONS TO HEAPS To sum up, there is just one kind of fundamental heap that can withstand scrutiny: point-sized bodies. This kind of heap could be exempt from the principle of Redundancy. Suppose, for instance, that several point-sized masses are fused together into a point-sized mass. In such a case, we might well suppose that the powers of the constituent masses themselves are fused together into a new set of powers, possessed only by the heap.
22..1 An argument in favor of fundamental heaps: The possibility of gunk
A more serious argument for Heapism relies on the possibility of gunk. If gunk is possible, then Heapists have a very powerful rebuttal to both the Redundancy argument and the spatial occupation argument. In addition, in a world containing gunk, heaps would have to exist, unless absolutely every bit of matter were filled with living organisms and artifacts. This possibility was embraced by Leibniz, but one which has seemed to nearly everyone else has thought it wildly unlikely. At any rate, we here explore the argument for Heapism from the possibility of gunk in some detail, and we therefore step back a bit to get clearer about what, exactly, gunk is.
‘Gunk’ is a term introduced by David Lewis (1991) for a hypothetical kind of stuff that has no atomic part. Each part of gunk can be further subdivided, without limit.
Def D22.5 Mereological Gunk. x is mereologically gunky if and only if x has no atomic parts.
What do we mean by ‘atomic parts’ or ‘atoms’? In a metaphysical context, we don't mean a complex entity like a hydrogen or oxygen atom. Chemical atoms have proper parts, namely, protons, neutrons, and electrons. By an ‘atom’, we mean something without any proper parts at all:
Def D22.6 Atom. x is an atom if and only if x has no proper parts.
22.4T Universal Atomism. Everything has an atomic part.
22.4A Existence of Mereological Gunk. Some things have no atomic part.
It is important, however, to distinguish between mereological gunk and spatial gunk. To be spatial gunk, a material body must have no point-sized masses as parts: each material part must have a proper part that is strictly smaller in extension.
Def D22.7 Spatial Gunk. x is spatially gunky if and only if x is mereological gunky and x has no point-sized parts.2
22.4A.1 Existence of Spatial Gunk. Something is spatially gunky.
Although there is a clear distinction between mereological and spatial gunk, spatial gunk seems to be the most plausible kind of gunk. If mereological gunk is possible, then it seems that spatial gunk would also be possible.
Suppose that a spatially gunky heap is possible. Then we cannot apply Redundancy for Composite Entities (PMeth 4) to eliminate all heaps from our theory. The active powers of a heap cannot be redundant if the heap has no atomic parts. Without atomic parts, there would be no final resting place, no ultimate bedrock for the fundamental powers of the heap. If we were tempted to say that the powers of a heap are always grounded in the powers of its smaller parts, then we would have to say that none of the powers of the heap or of any of its parts would be fundamental. All of the powers would ultimately be grounded in nothing. This is impossible.
If a spatially gunky heap were possible, what would be the fundamental bearers of the heap's powers? If we accept Strong Powerism, we must find some bearer for those powers. It would hardly be acceptable to suppose that the heap's powers are infinitely over-determined, with equivalent powers being fundamentally possessed by parts of the heap at every possible scale. Thus, Strong Powerism gives us good grounds for supposing gunk to be impossible. Similar arguments against spatial gunk could be made on the basis of Strong Hypotheticalism or Strong Nomism. Conversely, if spatial gunk is possible, then we have good grounds for rejecting all of these theories and embracing in their place Neo-Humeism.
In addition, the possibility of gunk provides a powerful response to the spatial occupation argument. If it were possible for a heap to be gunky, it would seem to be possible for a gunky heap to have no point-sized parts at all. If the heap has no point-sized parts, then it is obvious that the location of the heap could not be grounded in the location of its point-sized parts. What would then ground the location of the heap, and what could explain the fact that the location of any part of the heap must be a part of the location of the whole? Heapists could suppose that in each case it is the location of the part that is grounded in the location of the whole. Perhaps the only truly fundamental location-fact is the fact about the location of the entire material universe. Parts of the material universe then would derive their location somehow from the location of the whole. This seems counterintuitive, but the possibility of gunk seems to force us to some such conclusion.
If there is gunk, it seems virtually certain that that gunk or some part of it will be neither a living organism nor an artifact. Hence, the existence of gunk is incompatible with Anti-Heapism.
So, a lot turns on whether gunk is possible. It doesn't matter whether there is actually any gunky body. The mere metaphysical possibility of gunk would be enough to wreak havoc on the appeals to Redundancy and to the explanation of spatial occupation. What arguments are there for gunk's possibility?
ARGUMENTS FOR SPATIAL GUNK The strongest argument is a simple appeal to conceivability. We can imagine (in some broad sense) the Existence of Spatial Gunk, and no obvious contradiction appears in our conception of it. We might even feel a strong mental “pull” in the direction of believing it to be possible. These are not absolutely conclusive arguments, but they have to be given their due weight, as we have embodied in Imagination as Guide to Possibility (PEpist 1). In fact, we have already claimed that the possibility of gunk is a principle of natural philosophy (PNatPhil 1) on this basis.
ARGUMENTS AGAINST SPATIAL GUNK Besides the Redundancy and spatial occupation arguments, the best argument against spatial gunk is one that we have already encountered in another context: Hawthorne and Weatherson's (2004) supercutting argument.
This supercutting argument is based on a thought experiment of José Benardete's (1964: 184). We are to imagine that a block of material substance is subjected to an infinitary process of supercutting: after 1/2 second, it is cut into two pieces, in the next 1/4 second into four pieces, and so on, for each power of 2 (8, 16, 32, etc.) After one second has passed, the block will have been divided infinitely many times. The infinitely many slices will lack any depth, and the process can be described in such a way that, at the end of one second, the resulting set of slices are such that between any two slices, there is some completely unoccupied space, without requiring that any matter move at any point faster than the speed of light (Hawthorne and Weatherson 2004: 343). The distribution of slices will be dense (between any two slices there will always be others) and disconnected (between any two slices, there will always be some finitely wide, totally unoccupied space).
The supercutting process could be repeated along the two other dimensions of space, first dividing each of the slices into an infinite number of one-dimensional splinters, and then dividing each splinter into an infinite number of point-masses, each with zero volume. If matter is gunky and every piece of gunk occupies some finite volume, then the process of supercutting, when completed, will have annihilated all of the matter contained in the original block. It seems impossible for a process of mere dividing, even if repeated infinitely often, to annihilate any of the material substance being divided. The possibility of this supercutting is incompatible with the Existence of Spatial Gunk.
What are some of the assumptions of the Supercutting argument? First, we must assume that the process of supercutting does not simply annihilate the spatially gunky block:
PNatPhil 2 Independence of Motion and Substantial Change. Neither the movement of two extended things nor the div
ision of an extended thing into two parts can necessitate the creation or annihilation of material parts (not even point-masses).
Next, we have to assume that the parts of the block do not jump discontinuously at the very last moment into a new position.
PNatPhil 3 Continuity of Motion. It is impossible for any material thing to move discontinuously through spacetime.
Finally, we have to assume that if some body is spatially gunky, then all of the parts of the body must occupy connected regions of space.
Connected Occupation. If no part of a body is point-sized, then no part of the body occupies an isolated point—that is, if some part of the body occupies a point P, then there is a region, including P and extended in three dimensions, that that part occupies.
The Supercutting thought experiment shows that if we make these three assumptions and we assume that the process of supercutting, followed immediately by a period of stasis (the absence of motion) is possible, then spatial gunk must be impossible.
Can the Supercutting argument also be used as an argument against Aristotelian atoms, as well as against spatial gunk? Yes, since nothing turns on the fact that spatial gunk has actual, as opposed to merely potential parts.
Defenders of spatial gunk are going to have to object to the very possibility of supercutting. The most plausible argument against supercutting would depend on an assumption about the structure of time, namely, that it is impossible for any finite period of time to be divided into an infinity of actual parts. This requires Temporal Finitism (19.3T).
Summing up, we have one argument in favor of gunk (the appeal to conceivability) and several arguments against it (redundancy, spatial occupation, and supercutting). In order to avoid the arguments against gunk, those believing in gunk will have to embrace three positions: a Neo-Humeist account of causal powers (to avoid the Redundancy argument), the fundamentality of some but not all gunky heaps (to resist the spatial occupation argument), and an Aristotelian prohibition of processes with an actual infinity of parts (to counter the supercutting argument). This would be a very odd combination. Neo-Humeists are generally opposed to all Aristotelian prohibitions of a finitary nature. Thus, the appeal to gunk does not seem to provide a strong argument for Fundamental Heapism.
The Atlas of Reality Page 80
