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Presentations

Biosemiotics
Free Will
Mental Causation
James Symposium
 
Composition (Parts and Wholes)

Debates about the relation of parts to wholes is a major part of modern metaphysics. Many puzzles have to do with different persistence conditions of the "parts" of a composited whole.

Mereological universalism or extensional mereology is an abstract idea, defined in 1937 by Stanislaw Leśniewski and later by Henry Leonard and Nelson Goodman (1940). It claims that any collection of things, for example the members of a set in symbolic logic, can be considered as the parts of a whole, a "fusion" or "mereological sum," and thus can compose an object. Critics of this idea says that such arbitrary collections are just "scattered objects." A mind-independent connection between objects is needed for them to be integral "parts."

Mereological essentialism is Roderick Chisholm's radical idea that every whole has its parts necessarily and in every possible world. This goes too far. No physical object can maintain its parts indefinitely and freeze its identity over time. Our third axiom of identity is

Id3. Everything is identical to itself in all respects at each instant of time, but different in some respects from itself at any other time.

Mereological nihilists, such as Peter van Inwagen and the early Peter Unger denied the existence of composites, seeing them as simples (partless entities) arranged to look like a composite object. For him, a table is "simples arranged table-wise."

Van Inwagen made an exception for living objects. Surprisingly, he based the composite nature of biological entities on the Cartesian dualist view that humans are thinking beings. Van Inwagen then could see no obvious demarcation level at which even the simplest living things should not be treated as composite objects.

Information philosophy and metaphysics ask who or what is doing the arranging? Information provides a more fundamental reason than van Inwagen's for treating living things as integrated composites and not simply mereological sums of scattered objects. Furthermore, it extends a true composite nature to artifacts and to groupings of living things because they share a teleonomic property – a purpose. And it shows how some "proper parts" of these composites can have a holistic relation with their own parts, enforcing transitivity of part/whole relations.

A process that makes a composite object an integrated whole we call teleonomic (following Colin Pittendrigh, Jacques Monod, and Ernst Mayr) to distinguish it from a teleological cause with a "telos" pre-existing all life. We will show that teleonomy is the explanatory force behind van Inwagen's "arrangement" of simple parts.

Biological parts, which we can call biomers, are communicating systems that share information via biological messaging with other parts of their wholes, and in many cases communicate with other living and non-living parts of their environments. These communications function to maintain the biological integrity (or identity) of the organism and they control its growth. Artifacts have their teleonomy imposed by their creators.

Biocommunications are messages transferring information, for example inside the simplest single-cell organisms. For the first few billion years of life these were the only living things, and they still dominate our planet. Their messages are the direct ancestors of messages between cells in multicellular organisms. And they have evolved to become all human communications, including the puzzles and problems of metaphysics. A straight line of evolution goes from the first biological message to this Metaphysicist web page.

Like many metaphysical problems, composition arose in the quarrels between Stoics and Academic skeptics that generated several ancient puzzles still debated today. But it has roots in Aristotle's definition of the essence (ουσία), the unchanging "Being" of an object. We will show that Aristotle's essentialism has a biological basis that is best understood today as a biomereological essentialism. It goes beyond mereological sums of scattered objects because of the teleonomy shared between the parts, whether living or dead, of a biomeric whole.

First, back to Aristotle,

Is Aristotle here the source of the four Stoic genera or categories?
The term “substance” (οὐσία) is used, if not in more, at least in four principal cases; for both the essence (εἶναι), and the universal (καθόλου) and the genus (γένος) are held to be the substance of the particular (ἑκάστου), and fourthly the substrate (ὑποκείμενον). The substrate is that of which the rest are predicated, while it is not itself predicated of anything else. Hence we must first determine its nature, for the primary substrate (ὑποκείμενον) is considered to be in the truest sense substance.

Aristotle clearly sees a statue as both its form/shape and its matter/clay.
Both matter and form and their combination are said to be substance (οὐσία).
Now in one sense we call the matter (ὕλη ) the substrate; in another, the shape (μορφή); and in a third, the combination of the two. By matter I mean, for instance, bronze; by shape, the arrangement of the form (τὸ σχῆμα τῆς ἰδέας); and by the combination of the two, the concrete thing: the statue (ἀνδριάς). Thus if the form is prior to the matter and more truly existent, by the same argument it will also be prior to the combination.

The essence of an object, the "kind" or "sort" of object that it "is", its "constitution," its "identity," includes those "proper" parts of the object without which it would cease to be that sort or kind. Without a single essential part, it loses its absolute identity.

While this is strictly "true," for all practical purposes most objects retain the overwhelming fraction of the information that describes them from moment to moment, so that information philosophy offers a new and quantitative measure of "sameness" to traditional philosophy, a measure that is difficult or impossible to describe in ordinary language.

Nevertheless, since even the smallest change in time does make an entity at t + Δt different from what it was at t, this has given rise to the idea of "temporal parts."

Temporal Parts
Philosophers and theologians have for many years argued for distinct temporal parts, with the idea that each new part is a completely new creation ex nihilo. Even modern physicists (e.g., Hugh Everett III) talk as if parallel universes are brought into existence at an instant by quantum experiments that collapse the wave function.

David Lewis, who claims there are many possible worlds, is a proponent of many temporal parts. His theory of "perdurance" asserts that the persistence through time of an object is as a series of completely distinct entities, one for every instant of time. Lewis's work implies that the entire infinite number of his possible worlds (as "real" and actual as our world, he claims), must also be entirely created anew at every instant.

While this makes for great science fiction and popularizes metaphysics, at some point attempts to understand the fundamental nature of reality must employ Occam's Razor and recognize the fundamental conservation laws of physics. If a new temporal part is created ab initio, why should it bear any resemblance at all to its earlier version?

It is extravagant in the extreme to suggest that all matter disappears and reappears at every instant of time. It is astonishing enough that matter can spontaneously be converted into energy and back again at a later time.

Most simple things (the elementary particles, the atoms and molecules of ordinary matter, etc.) are in stable states that exist continuously for long periods of time, and these compose larger objects that persist through "endurance," as Lewis describes the alternative to his "perdurance." Large objects are not absolutely identical to themselves at earlier instants of time, but the differences are infinitesimal in information content.

The doctrine of temporal parts ignores the physical connections between all the "simples" at one instant and at the following moment. It is as if this is an enormous version of the Zeno paradox of the arrow. The arrow cannot possibly be moving when examined at an instant. The basic laws of physics describe the continuous motions of every particle. They generally show very slow changes in configuration – the organizational arrangement of the particles that constitutes abstract information about an object.

One might charitably interpret Lewis as admitting the endurance of the elementary particles (or whatever partless simples he might accept) and that perdurance is only describing the constant change in configuration, the arrangement of the simples that constitute or compose the whole.

Then Lewis's temporal parts would be a series of self-identical objects that are not absolutely identical to their predecessors and successors, just a temporal series of highly theoretical abstract ideas, perhaps at the same level of (absurd) abstraction as his possible worlds?.

Mereology
Mereology is the study of parts which compose a whole. What exactly is a part? And what constitutes a whole? For each concept, there is a strict philosophical sense, an ordinary sense, and a functional or teleonomic sense.

In the strict sense, a part is just some subset of the whole. The whole itself is sometimes called an "improper part."

In the ordinary sense, a part is distinguishable, in principle separable, from other neighboring parts of some whole. The smallest possible parts are those that have no smaller parts. In physics, these are the atoms, or today the elementary particles, of matter.

In the functional sense, we can say that a part serves some purpose in the whole. This means that it has may be considered a whole in its own right, subordinate to any purpose of the whole entity. Teleonomic examples are the pedals or wheel of a bicycle, the organs of an animal body, or the organelles in a cell.

The same three-part analysis applies to the question of what composes a "whole" object.

Some philosophers (e.g., Peter Unger and Peter van Inwagen) deny that composite objects exist. This is called "mereological nihiism," though a more accurate name would be "holistic nihilism," since it is composite wholes that they deny. They do not deny the parts, which they call "simples." Van Inwagen argues, for example, that tables are just "simples arranged tablewise," where the simples are partless objects.

Note that the arrangement of parts is not material, but immaterial information.

The strict philosophical definition of a composite whole, especially in analytic language philosophy, is just its being picked out by a philosopher for analysis. An example might be "there is a table," or in Quine's existential quantification form, "∃ x (x = 'a table')."

The ordinary sense of a whole is an object that is distinguishable from its neighboring objects. But such a whole may be just a part of some larger whole, up to the universe.

The teleonomic sense of an object is that it seems to have a purpose, the Greeks called it a telos, either intrinsic as in all living things, or extrinsic as in all artifacts, where the purpose was invented by the object's creator.

The most important example of a teleonomic process is of course biology. Every biological organism starts with a first cell that contains all the information needed to accomplish its "purpose," to grow into a fully developed individual, and, for some, to procreate others of its kind.

By contrast, when a philosopher picks out an arbitrary part of something, declaring it to be a whole something for philosophical purposes, perhaps naming it, the teleonomy is simply the philosopher's intention to analyze it further.

For example, something that has no natural or artifactual basis, that does not "carve nature at the joints," as Plato described it, that arbitrarily and violently divides the otherwise indivisible, is a perfectly valid "idea," an abstract entity. This notion that anything goes for the philosopher to select as a composite whole is known as "mereological universalism."

The combination of arbitrary objects is called a "mereological sum." A frequent example is a combination of the Statue of Liberty and the Eiffel Tower, although there is a strong teleonomic component to this mereological sum as they are part of the oeuvre of the great designer and engineer Alexandre-Gustave Eiffel. Remember, everything is identical to anything else "in some respect."

Mereological Essentialism

Aristotle knew that most living things can survive the loss of various parts (limbs, for example), but not others (the head). By analogy, he thought that other objects (and even concepts) could have parts (or properties) that are essential to its definition and other properties or qualities that are merely accidental.

Mereological essentialism is the study of those essential parts.

At his presidential address to the twenty-fourth annual meeting of the Metaphysical Society of America in 1973, Rod Chisholm defined "mereological essentialism," the idea that if some object has parts, then those parts are essential, metaphysically necessary, to the particular object..

I shall consider a philosophical puzzle pertaining to the concepts of whole and part. The proper solution, I believe, will throw light upon some of the most important questions of metaphysics.

The puzzle pertains to what I shall call the principle of mereological essentialism. The principle may be formulated by saying that, for any whole x, if x has y as one of its parts then y is part of x in every possible world in which x exists. The principle may also be put by saying that every whole has the parts that it has necessarily, or by saying that if y is part of x then the property of having y as one of its parts is essential to x. If the principle is true, then if y is ever part of x, y will be part of x as long as x exists.

Chisholm draws three important conclusions.

(Al) If x is a part of y and y is a part of z, then x is a part of z (this is the transitivity of parthood).

(A2) If x is a part of y, then y is not a part of x (the whole is an improper part of itself).

(A3) If x is a part of y, then y is such that in every possible world in which y exists x is a part of y (can we explain this?).

For Aristotle, and in ordinary use, not every part of a whole is a necessary part (let alone in all possible worlds). How does Chisholm defend such an extreme view as his A3? We can speculate that he assumes that the essential nature of something must preserve its identity, so that A3 can be rewritten

(A3') If x is a part of y, then y is an essential, that is a necessary, part of y needed to maintain its identity.

Much of the verbal quibbling in metaphysical disputes is about objects that are defined by language conventions as opposed to objects that are "natural kinds".

Mereological universalism is the idea that an arbitrary collection of objects or parts of objects can be considered a conceptual whole – a "mereological sum" – for some purpose or other (mostly to provoke an empty debate with other metaphysicians).

Modern metaphysics examines the relations of parts to whole, whole to parts, and parts to parts within a whole using the abstract axioms of set theory, a vital part of analytic language philosophy today. Because a set can be made up of any list of things, whether they have any physical integrity or even any conceivable connections, other than their membership in the arbitrary set. Consider the "whole" made up of the Eiffel Tower and the Statue of Liberty!

Mereology is a venerable subject. The Greeks worried about part/whole questions, usually in the context of the persistence of an object when a part is removed and the question of an object's identity. Is the Ship of Theseus the same ship when some of the planks have been replaced? Does Dion survive the removal of his foot?

“When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to mean—neither more nor less."
The idea that an arbitrary collection of things, a "mereological sum," can be considered a whole, does violence to our common sense notion of a whole object. It is an extreme example of the arbitrary connection between words and objects that is the bane of analytic language philosophy.

Mereological universalism also leads to the idea that there are many ways to compose a complex material whole out of a vague collection of simple objects. This is what Peter Unger called the Problem of the Many.

It led Peter van Inwagen to his position of mereological nihilism, that there are no composite wholes. Van Inwagen says there are no tables, only simples arranged table-wise. The "arrangement" is the information in the table. When we can identify the origin of that information, we have the deep metaphysical reason for it essence. Aristotle called the arrangement "the scheme of the ideas."

By matter I mean, for instance, bronze; by shape, the arrangement of the form (τὸ σχῆμα τῆς ἰδέας); and by the combination of the two, the concrete thing: the statue (ἀνδριάς)
Van Inwagen makes an exception of living things, and Unger has abandoned his own form of nihilism in recent years. Both Unger and van Inwagen, now accept the idea that they exist.

Van Inwagen's says that his argument for living beings as composite objects is based on the Cartesian "cogito," I think, therefore I am. He proposes,

(y the xs compose y) if and only if
the activity of the xs constitutes a life.

If this answer is correct, then there are living organisms: They are the objects whose lives are constituted by the activities of simples, and, perhaps, by the activities of subordinate organisms such as cells; they are the objects that have proper parts. Therefore, if there are no organisms, then, since there are lives, the Proposed Answer is wrong. In Section 12 I gave reasons for supposing that there were living organisms. That is, I gave reasons that I intended to be available to the philosopher who, like me, thinks that there are no visible inanimate objects. (Most philosophers, unless they are Nihilists or general skeptics, will scarcely want reasons for believing in organisms.) I have argued that situations apparently involving tables and chairs and all the other inanimate furniture of the world are to be understood as involving only simples. There are no chairs, I maintain, but only simples arranged chairwise. My "reasons for believing in organisms," therefore, are reasons for stopping where I do and not going on to maintain that there are no organisms but are only simples arranged organically. My argument for the existence of organisms, it will be remembered, involved in an essential way the proposition that I exist.

Biomereological Essentialism

Information philosophy provides a much deeper reason for biological organisms as having "proper parts." These biomeric parts are created and maintained by anti-entropic processes that distribute matter and energy to all the vital parts using a biological messaging system to control the distribution of biological materials and free energy. There is a "telos" (or Aristotelian "entelechy," loosely translated as "having the final cause within") implemented by messaging between all the vital parts. We call this teleonomy.

But teleonomy, which depends on the communication of abstract messages between the biomers, is not possible in a materialist metaphysics that denies the existence of immaterial ideas.

We should distinguish ordinary biomeric parts that can fail and be replaced from those that cannot be replaced. These vital biomers are essential in a stronger sense. Without them, the teleonomy of the whole is destroyed. The organism decays to smaller living things and possibly all the way to dead material ("dust to dust").

Basics of Mereology
Why is mereological thinking so important in metaphysics today? With the emphasis on materialism, the material elements appear to be the fundamental parts of reality. A number of thinkers have produced a rich set of papers and books (see Varzi). We can use examples from Achille Varzi's excellent article on mereology in the Stanford Encyclopedia of Philosophy that show how we talk about what are parts and wholes. The ways in which parts interact and indeed communicate with one another is not yet a part of today's mereology.
A preliminary caveat is in order. It concerns the very notion of ‘part’ that mereology is about, which does not have an exact counterpart in ordinary language. Broadly speaking, in English we can use ‘part’ to indicate any portion of a given entity. The portion may itself be attached to the remainder, as in (1), or detached, as in (2); it may be cognitively or functionally salient, as in (1)–(2), or arbitrarily demarcated, as in (3); self-connected, as in (1)–(3), or disconnected, as in (4); homogeneous or otherwise well-matched, as in (1)–(4), or gerrymandered, as in (5); material, as in (1)–(5), or immaterial, as in (6); extended, as in (1)–(6), or unextended, as in (7); spatial, as in (1)–(7), or temporal, as in (8); and so on.
(1) The handle is part of the mug.
(2) The remote control is part of the stereo system.
(3) The left half is your part of the cake.
(4) The cutlery is part of the tableware.
(5) The contents of this bag is only part of what I bought.
(6) That area is part of the living room.
(7) The outermost points are part of the perimeter.
(8) The first act was the best part of the play.

All of these uses illustrate the general notion of ‘part’ that forms the focus of mereology, regardless of any internal distinctions. On the other hand, the English word ‘part’ is sometimes used in a broader sense, too, for instance to designate the relation of material constitution, as in (9), or the relation of mixture composition, as in (10), or the relation of group membership, as in (11):

(9) The clay is part of the statue.
(10) Gin is part of martini.
(11) The goalie is part of the team.

The mereological status of these relations, however, is controversial. For instance, although the constitution relation exemplified in (9) was included by Aristotle in his threefold taxonomy of parthood (Metaphysics, Δ, 1023b), many contemporary authors would rather construe it as a sui generis, non-mereological relation...or else as the relation of identity ...., possibly contingent or occasional identity.... Similarly, the ingredient-mixture relationship exemplified in (10) is of dubious mereological status, as the ingredients may undergo significant chemical transformations that alter the structural characteristics they have in isolation... As for cases such as (11), there is disagreement concerning whether teams and other groups should be regarded as genuine mereological wholes, and while there are philosophers who do think so ..., many are inclined to regard groups as entities of a different sort and to construe the relation of group membership as distinct from parthood... For all these reasons, here we shall take mereology to be concerned mainly with the principles governing the relation exemplified in (1)–(8), leaving it open whether one or more such broader uses of ‘part’ may themselves be subjected to mereological treatments of some sort.

Finally, it is worth stressing that mereology assumes no ontological restriction on the field of ‘part’. In principle, the relata can be as different as material bodies, events, geometric entities, or spatio-temporal regions, as in (1)–(8), as well as abstract entities such as properties, propositions, types, or kinds, as in the following examples:

(12) Rationality is part of personhood.
(13) The antecedent is the ‘if’ part of the conditional.
(14) The letter ‘m’ is part of the word ‘mereology’.
(15) Carbon is part of methane.

This is not uncontentious. For instance, to some philosophers the thought that such abstract entities may be structured mereologically cannot be reconciled with their being universals. To adapt an example from Lewis (1986a), if the letter-type ‘m’ is part of the word-type ‘mereology’, then so is the letter-type ‘e’. But there are two occurrences of ‘e’ in ‘mereology’. Shall we say that the letter is part of the word twice over? Likewise, if carbon is part of methane, then so is hydrogen. But each methane molecule consists of one carbon atom and four hydrogen atoms. Shall we say that hydrogen is part of methane four times over? What could that possibly mean? How can one thing be part of another more than once? These are pressing questions, and the friend of structured universals may want to respond by conceding that the relevant building relation is not parthood but, rather, a non-mereological mode of composition... However, other options are open, including some that take the difficulty at face value from a mereological standpoint ... Whether such options are viable may be controversial. Yet their availability bears witness to the full generality of the notion of parthood that mereology seeks to characterize. In this sense, the point to be stressed is metaphilosophical. For while Leśniewski's and Leonard and Goodman's original formulations betray a nominalistic stand, reflecting a conception of mereology as an ontologically parsimonious alternative to set theory, there is no necessary link between the analysis of parthood relations and the philosophical position of nominalism.[5] As a formal theory (in Husserl's sense of ‘formal’, i.e., as opposed to ‘material’) mereology is simply an attempt to lay down the general principles underlying the relationships between an entity and its constituent parts, whatever the nature of the entity, just as set theory is an attempt to lay down the principles underlying the relationships between a set and its members. Unlike set theory, mereology is not committed to the existence of abstracta: the whole can be as concrete as the parts. But mereology carries no nominalistic commitment to concreta either: the parts can be as abstract as the whole...

With these provisos, and barring for the moment the complications arising from the consideration of intensional factors (such as time and modalities), we may proceed to review some core mereological notions and principles. Ideally, we may distinguish here between (a) those principles that are simply meant to fix the intended meaning of the relational predicate ‘part’, and (b) a variety of additional, more substantive principles that go beyond the obvious and aim at greater sophistication and descriptive power. Exactly where the boundary between (a) and (b) should be drawn, however, or even whether a boundary of this sort can be drawn at all, is by itself a matter of controversy...

The usual starting point is this: regardless of how one feels about matters of ontology, if ‘part’ stands for the general relation exemplified by (1)–(8) above, and perhaps also (12)–(15), then it stands for a partial ordering—a reflexive, transitive, antisymmetric relation:

(16) Everything is part of itself.
(17) Any part of any part of a thing is itself part of that thing.
(18) Two distinct things cannot be part of each other.

Note that all of Varzi's examples are conventional (and thus arbitrary ) definitions. So information philosophy could add a few more examples, which might be "natural kinds." Broadly speaking, these are wholes whose parts are demarcated by identifiable natural processes rather than human conventions.

  1. Biological organisms, whose parts are created and maintained by anti-entropic processes that distribute matter and energy to all the vital parts. There is a purpose or "telos" (Aristotle called it a built-in telos or "entelechy") implemented by messaging between all the vital parts or "proper parts." A biomereological essentialism notes that every biomer (a biological part) is normally in direct or indirect communication with vast numbers of other biomers in the living organism. Communication is information that is neither matter nor energy. It is the ideal content of the message that implements the organism's "telos."

  2. Human artifacts. Here the "telos" comes from the creator. The leg of a table is an essential part of the original design. Such proper parts often have recognizable functions, so when they are missing the whole is no longer functional.

  3. Physical combinations of elementary particles into nuclei and chemically emergent combinations of atoms – water from hydrogen and oxygen and salt from sodium and chlorine.

  4. Cosmological and other material objects formed with an anti-entropic process that created their information. Astronomical bodies were pulled together by gravity into information structures. Crystals grow information rich structures (e.g., snowflakes).

To be sure, many of these "wholes" can survive the loss of some parts. But we are back quibbling. When their efficient/material causes and their formal and final causes are "teleonomic" and not simply arbitrary human conventions, we can say these are "natural kinds."

The problem of composition becomes more severe when some metaphysicians consider matter to be infinitely divisible, just as the real number line contains an infinite number of numbers between any two numbers (and a higher order of infinity of irrational numbers!).

By contrast, the metaphysicist's view is that matter is discrete, not infinitely divisible like the continuous spatial and temporal dimensions. The Greek materialists argued for simple atoms separated by a void. Ludwig Boltzmann and Albert Einstein showed that the atoms of 19th-century chemistry really exist. In modern physics the simplest elementary particles are quarks, leptons, and bosons. So let's suppose that we have a region of space with two oxygen atoms in it. It seems reasonable to say that it contains two simple things (the atoms).

Peter van Inwagen denies the mereological sum. David Lewis defends it.
Recent mereological debates in metaphysics have taken this form:
Mereological nihilist: There are two things in this region.
Mereological universalist: There are three things in this region (the two simples and the mereological sum).

Now a metaphysicist can still argue cleverly and cogently about the proper number of parts and the choice of the proper whole. The oxygen atoms each contain eight protons, eight neutrons, and eight electrons. So one possible count is the 48 sub-atomic particles that are visible. We can go deeper by noting that the nuclear particles are each made up of three quarks, which are not observable. We then can count 112 parts to the whole?

And the metaphysicist has a strong argument for the two simple atoms to be considered a whole. If the two atoms are very close, they can form an oxygen molecule. Even when disassociated, quantum mechanics that treats them as a quasi-molecule is more accurate than a description as two independent atoms.

To summarize, the Eiffel Tower and the Statue of Liberty in our arbitrary set do not "compose" a "natural" object just because we group them together in a set.

Van Inwagen and Unger Verbal Dispute
Let's take Peter van Inwagen's version of Peter Unger's 1980 argument for nihilism, which van Inwagen cleverly shows is actually an argument for universalism!
Unger's argument may be compactly formulated as a reductio. Assume I exist. Then certain simples compose_me. Call them 'M'. Now, a single simple is a negligible item indeed. Let y be one of these negligible parts of me—one that is somewhere in my right arm, say. Now, consider the simples that compose me other than y ('M — y'). Since y is so very negligible, M — y could compose a human being just as well as M could. We may say that M and M — y are "equally well suited" to compose human beings. And, of course, for any simple y, "M — y" will be as well suited to compose a human being as M are. Moreover, it would be surprising indeed if there were not a simple z such that "M + z" were as well suited to compose a human being as M are. It would, in fact (if I may once more use this phrase), be intolerably arbitrary to say that M composed a human being although M — y didn't and M — y didn't and M + z didn't. Suppose, therefore, that M — y et al. do compose human beings. Then there are present, in pretty much the same place, the "M — y man," the "M — y man," and the "M + z man." And, of course, simples being so numerous, in any situation in which we should ordinarily say that I was alone in a room, there will be present in that room an enormous, albeit finite, number of men. Some of these will be practically indistinguishable from me and some will be noticeably smaller. There will, for example, be legions of men who are composed entirely of simples that are among the simples we have already mentioned but who lack a right arm. It is, however, perfectly ridiculous to suppose that there are that many men about. But the only alternative is to say that neither M nor any other simples compose a man, and, therefore, to say that I do not exist. Suppose, however, that someone replies by saying that it's even more ridiculous to say that there are no men at all, and that we must therefore suppose that there are many more men than we thought.
Information philosophy provides the exact "selection principle." One selects "M,", the actual, the "concrete" van Inwagen. All others are fictions or mere possibles.
We respond as follows: anyone who does bite the bullet and who concedes that there are "all these men" and who also wishes to say that he exists will need a "selection principle," a principle that selects one man out of an enormous class of overlapping men to be himself. But because there is no significant difference between, say, the M man and the M — y man, any principle that identifies me with one of them must be intolerably arbitrary.

This completes my reconstruction of Unger's argument. The argument seems to presuppose the following four propositions.

These sets are just abstract possibilities.
(1) In every situation of which we should ordinarily say that it contained just one man there are many sets of simples whose members are as suitably arranged to compose men as any simples could be.

They only compose something in a verbal debate.
(2) The members of each of these sets compose something.
They are only logical man-descriptions used in a sophistical argument.
(3) Each of these "somethings" is a man provided there are any men at all.
He does exist, embodied as the author of this important book. The others only subsist as ideas, logical man-candidates, as he calls them.
(4) If I exist, there is a man. It would be possible to view the problem of the many (as it touches one's own existence) in a slightly different way: One might reject (3) and contend that, in a situation of which we should ordinarily say that it contained just one man, there is just one man, provided there are any men in that situation at all; the other "somethings," one might say, are not men but "man-candidates," things in many respects suitable for being men but which aren't men because some other thing of their type has bested them in a competition whose prize is the privilege of being the only man in that situation. I call this a "slightly" different view of the problem of the many (conceived as primarily a problem about one's own existence because, like Unger's view, it demands a solution in the form of a selection principle. Unger's view of the problem demands that I discover a way of selecting one man among many to be myself; the alternative view demands that I discover a way of selecting one man-candidate among many to be a man. (Once this selection has been made, of course, there is no problem about which man is myself, there being only one man "there." One might, of course, raise the question why I should suppose that I am the man, and not merely one of the also-rans.) Now, both of these views of the problem seem to me to rest upon Universalism. It is difficult to see what other basis one could have for accepting proposition (2) of the preceding paragraph. But I reject Universalism. I therefore deny that in a situation of which we should ordinarily say that I was the only man present in it, there are an enormous number of things—sums, collections, clouds, or aggregates of atoms, "cohesions of particles of matter anyhow united," men, man-candidates, categorize them as you will—which are pretty much alike and which are all candidates for the office of being myself.
Does van Inwagen contradict his premise that the various minutely smaller or larger M ± x are indistinguishable from himself, much more than just "remotely like me?" Or is this just Unger?
In my view, I am present in that situation, and none of the other things present—simples, cells, the cat in my lap—is even remotely like me. In particular, there are no things that are almost as large as or minutely larger than I. Suppose, for example, that Celia is one of my cells. The cells that compose me, of course, compose me. But "the cells that compose me other than Celia" do not compose anything whatever, and the same goes for "the simples that compose me other than Simon."

"Your rejection of 'Universalism' is a red herring. You still face a problem of the many. You haven't dealt with the fact that M and M — x and M — y and M + z are equally well suited to compose a man, and, in fact, equally well suited to compose you. You may protest that if M compose something, then M — x don't and M — y don't, and so on. You may say that there are simples that compose you, and that any simples that compose you are exactly those simples. But what's so special about those simples? If the xs compose you, after all, there are ys which are not (quite) those xs but which are equally well suited to compose you. Why don't they? To state this problem in its full generality, I shall have to make use of some sort of abstract object such that, for any xs, the xs define or pick out a unique object of that type. Sets would seem to be admirably adapted to this purpose. We pose the problem thus. Suppose for the moment that you exist. Consider the set of simples S whose members compose you. Now consider all the sets of simples that have nearly the same members' as S (it will make no difference to the force of our argument how we spell out this rather vague requirement) and whose members and the members of S are equally well suited to compose a man. Having got these sets before your mind's eye, forget our momentary supposition that you exist. (There obviously exist sets having the properties of the sets we are considering, whether or not you exist.) Now, which of these sets is such that its members compose something? What principle of selection will you apply to them to determine which of them is the set the members of which compose something?"

Simply wrong? "M,", the actual van Inwagen, is the set that consists of all his simples and only his simples. His simples change rapidly with time, of course. See persistence
N o n e. There is no such set. No set is the set that contains just the simples that compose me or the set that contains just the simples that compose anything having proper parts. This is because parthood and composition are vague notions.
References
Burke, M. B. (1994). "Dion and Theon: An essentialist solution to an ancient puzzle." The Journal of Philosophy, 91(3), 129-139.
Chisholm, R. M. (1973). "Parts as essential to their wholes." Review of Metaphysics 26: 581-603.
Leonard, H. S., & Goodman, N. (1940). "The calculus of individuals and its uses." The Journal of Symbolic Logic, 5(2), 45-55.
Lowe, E. J. (1995). "Coinciding objects: in defence of the 'standard account'." Analysis, 55(3), 171-178.
Unger, Peter, "The Problem of the Many", Midwest Studies in Philosophy 5.1 (1980): 411-468.
Unger, Peter, "The Mental Problems of the Many", Oxford Studies in Metaphysics, Vol.1 (2004): 195.
Van Inwagen, Peter, 1990, Material Beings, Cornell
Van Inwagen, P. (1981). "The Doctrine of Arbitrary Undetached Parts," Pacific Philosophical Quarterly, 62, 123-137.
Van Inwagen, Peter. 1987. "When Are Objects Parts?" In Philosophical Perspectives. Vol. 1 Varzi, Achille, Mereology,Stanford Encyclopedia of Philosophy
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