Posts on: Mereology
Here's an attractive picture. All there really is, at a fundamental
level, are fields in spacetime (or something like that). The world as we
know it, with its rocks and chairs and cats and people, somehow emerges
from this basis: all truths about rocks and chairs etc. are made true by
truths about fields in spacetime. But how? To explain this, it would
help if we could locate the familiar objects – rocks and chairs etc. –
in the physical description of reality. With the help of classical
mereology, which is plausibly analytic, this
seems possible: ordinary objects can be identified with aggregates of
spacetime points. They are regions in spacetime. With this, we can
explain how simple facts involving ordinary objects can emerge. For
example, what makes it true that my chair has steel legs is that its
region has a certain kind of subregion with high-amplitude excitations
of quark and electron fields in a certain arrangement.
I used to agree with Lewis that classical mereology, including
mereological universalism, is "perfectly understood, unproblematic,
and certain". But then I fell into a dogmatic slumber in which it seemed
to me that the debate over mereology is
somehow non-substantive: that there is no fact of the
matter. I was recently awakened from this slumber by a footnote in
Ralf Busse's forthcoming article "The
Adequacy of Resemblance Nominalism" (you should read the whole
thing: it's terrific). So now I once again think that Lewis was right. Let
me describe the slumber and the awakening.
Here's an odd passage from Armstrong's A Combinatorial Theory of Possibility, p.116:
[Hume's Distinct Existences Principle], as we shall uphold it, may be stated thus:
If A and B are wholly distinct existences, then it is possible for A to exist while no part of B does (and vice versa).
The principle applies straightforwardly to individuals, properties and relations. [...]
It is interesting to notice that the converse of Hume's principle also seems to be true:
If meaning is largely determined by use and inferential connections, then if a word is used very differently in two groups of people and if the two groups accept very different inferential connections, then the word does not mean the same thing in those groups.
On this account, mereological nihilists don't mean the same by mereological vocabulary as I (a universalist) do: they reject all ordinary examples of parthood, overlap etc.; they reject some of the most central theoretical principles governing these notions; and they ask unintelligible quesions, like:
A structural property is a property that belongs to things in virtue of their constituents' properties and interrelations. For instance, the property being a methane molecule necessarily belongs to all and only things consisting of suitably connected carbon and hydrogen atoms.
There is two-way dependence: Necessarily, if something instantiates a structural property, then it has proper parts that instantiate certain other properties; conversely, if the proper parts of a thing instantiate those other properties then, necessarily, the thing itself instantiates the structural property.
I've written a little paper about the difference between theories on which ordinary things are fusions of parts located at various places, times, and worlds, and theories on which they instead have counterparts there. The dull conclusion is that there is no difference. I'm not sure I believe anything in there, and it's all quite rough, so comments are welcome: Parts and Counterparts (PDF).
Update 2005-03-08: Robbie Williams points out that my translation between Counterpart and Fusion Theory does not handle fission cases correctly. I should at least (following Lewis's translation scheme) say that names in the fusion language are indeterminate between all maximal eligible fusions of the corresponding counterparts from the counterpart language. But this is only a partial fix. I hope to come up with something better soon, though as I'm on the road for the next couple of days, that will probably have to wait until the weekend.
Ordinary objects - persons, planets, rivers and tables - are unextended atoms. They occupy only one point of space at only one time at only one world.
At first sight, this might sound absurd. Don't ordinary things
obviously exist at many different places, times and worlds? Isn't the
Yangtze clean in Geladandong and dirty in Shanghai? Wasn't it clean in Shanghai in 1500? And isn't it clean in Shanghai now at some other possible world?
Fortunately, Atomism need not deny any of this. For even though the
Yangtze is an unextended atom that strictly speaking only occupies a
single point, it has many counterparts at other points. And
these counterparts make all those statements true.
Suppose there are at least proper-class many possibilia. Does it follow that some fusions of possibilia are not members of any set? For the last two years or so I thought it does. My reasoning was that if some of the possibilia correspond one-one with all the sets, then some atoms of possibilia also correspond one-one with all the sets (for there cannot be proper-class many fusions of set-many atoms); but since there are always more fusions of atoms than atoms, it follows that there must be more fusions of atoms of possibilia than sets, and hence that some (in fact, most) of these fusions lack a singleton. This does not take into account atomless possibilia, but I always thought the reasoning would easily carry over, by something like the fact that even with gunk
Brian points to Gabriel Uzquiano's Cardinality Puzzle about Mereology and Set Theory (PDF), which he (Gabriel) introduced a while ago in the now-deceased Philosophy from the 617 weblog. I still don't know enough set theory and mereology to competently discuss the matter, but anyway, it seems to me that perhaps the puzzle can be strengthened, as follows.
I started this as a comment on Brian Weatherson's latest posting. But it grew so long that I decided to post it here instead and test my trackback implementation on it.
Imagine a world in which there are nothing but two atoms.
This is ambiguous. Does it mean I should imagine a world in which there are two atoms and nothing else, not even the fusion of these atoms? Or is "nothing but" restricted to things distinct from the two atoms? I can follow the instruction on the latter interpretation but not on the former: a world with two atoms and nothing that is not identical to one of them is inconceivable to me.
In my last post,
I said that I do not believe that every extended thing must have parts. Sam disgrees, arguing that whenever something is extended over length h, we can restrict our attention to a part of it with length h/n for any n < h.
I do agree that all ordinary extended things have parts. And I do agree that extended things without parts are really very strange. I'm just not sure that they are impossible.
There are lots of distinctions between perdurantism and endurantism (or better, between different perdurantisms and endurantisms). Here I want to talk about the following perdurantist claim:
1) Some things (that are not events) have temporal parts.
This does not imply that ordinary things like buildings and persons have temporal parts. And even if one believes the latter, it is still perfectly coherent to reject any account of intrinsic change in terms of temporal parts, or reject an account of personal identity in terms of (properties of) temporal parts, or reject an account of persistence in terms of temporal parts, or reject whatever else temporal parts are used to account for. It is also okay to accept only some of these accounts and reject others. (I for example am a perdurantist who rejects the account of persistence in terms of temporal parts: not only can I say what it is to persist through time without mentioning temporal parts, I even believe that it is possible for a thing to exist through time without having temporal parts.) That's how we get so many perdurantisms and endurantisms. (I think it would be very helpful if people discussing this matter exactly said what they say on each of these issues rather than vaguely asserting that, e.g., things are 'wholly present at different times'.)
So I don't see any means to escape the conclusion that given mereological universalism, some things trivially move faster than light. Lots of things, in fact. Perhaps that's less troublesome than I thought because these things don't actually violate any physical laws.
For instance, I guess the principle that physics looks the same for all things that move with constant speed relative to each other has to be restricted to things with speed < c anyway. (At least Lorentz transformation doesn't make much sense if v = c.) If so, the exclusion of faster-than-light fusions from the principle is already built in and we don't need to worry about e.g. what such a fusion's proper time might be.
Let A and C be two distinct objects such that C exists at a later time and a
different place than A.
Let F be the mereological fusion of A and C. Question: Does F move from
the location of A to the location of C? I don't think so. If a thing moves
from one location to another, there should be a continuous path from the one location
to the other along which the thing moves.
So let B1, B2, ... be (continuum many) further objects (perhaps spacetime points, if nothing else is around)
that lie on a continuous spacetime path
between A and C, and let F be the fusion of A, B1, B2, ..., C. Does F now move? I'm not sure.
Maybe when a thing moves the later stages should depend causally on the earlier
stages. Or maybe the concept of movement is not applicable to gerrymandered fusions like F.
It is sometimes (e.g. in David Sanford, 'Fusion Confusion', Analysis 63,
2003) said that some things are not fusions of all their parts: cats
and fusions of cat-parts for instance seem to differ in tensed and modal
properties. It may be noteworthy that on the standard definition of
'fusion', this position is outright inconsistent: X is the fusion of
Y1,Y2,... iff all of Y1,Y2,... are parts of X and no part of X is
distinct from all of Y1,Y2,.... Hence if X is not the fusion of
Y1,Y2,... then either one of Y1,Y2,... is not a part of X or some part of
X does not overlap Y1,Y2,.... So nothing can possibly fail to be the
fusion of all its parts.
In her paper 'Logical
Parts', forthcoming in the december issue of Nous, L.A. Paul presents a nice
theory of objects according to which things are mereologically composed of
their properties. Here are a couple of potential problems.
First, the theory seems to conflict with Unrestricted Composition and
incompatible properties. For suppose that P and Q are incompatible
properties, like being square and being round. By Unrestricted
Composition, there is a fusion of P and Q (or, if you prefer, of P and Q
and Paul's red cup). This fusion has both P and Q as parts, hence, on
Paul's theory, it is both P and Q. But if P and Q are incompatible, nothing
can be both P and Q.
First: Are fundamental particles mereological atoms?
Fundamental particles are 'the ultimate constituents of the world',
those upon whose properties and relations everything else supervenes. Many
of us believe that the instrinsic properties of complex things supervene
upon the properties and relations of their consituents. Then maybe the
fundamental particles can be identified with the ultimate constituents of
the world, if there are any. In fact, when we find that some things are
composed out of smaller things, we will usually not call the complex things
'fundamental particles'. I think it is in this sense that fundamental particles are supposed to be
indivisible -- not because we lack the means to break them into parts, nor
because it is impossible 'in principle' to break them, but simply because
they lack (proper) parts.