Alan Cook asked me what was wrong with being a reductionist about inanimate objects such as chariots. His query was in regard to my draft, "Against Buddhist Reductionism." It is time to begin a response.
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Suppose I have a parcel of land P. I divide P into two subparcels of equal size, A and B. Thus P is a whole having exactly two proper parts, A and B. I put the two subparcels on the market for 100 K each. Mr. MoneyBags comes along and offers to buy my land. I agree, and he hands me 200 K from his bag.
"Not so fast, friend," say I. "You owe me twice that: 100 for A, 100 for B, and 200 for P, making a grand total of 400 K."
This sounds absurd because, since P is composed of A and B and nothing else, P is not a third entity 'in addition to' or 'over and above' or 'above and beyond' the sum A + B. Similarly, Milinda's chariot is not something 'in addition to' its parts. Furthermore, a smoking pipe is not something in addition to bowl and stem: when I clean my pipe, there aren't three things to clean: bowl, stem, and pipe. One more example. Suppose I buy a sixpack of beer. I have bought either one item or six items. If the express checkout line is for six items or fewer and I refuse to use that lane on the ground that I am purchasing seven items, then I am a very strange bird indeed.
So should we conclude that P = A + B? Should we embrace reductionism, the view that a whole is identical to its parts? If a whole is not something in addition to its parts, is it then identical to its parts?
But this seems equally mistaken. P is one; A and B are two. How can one thing be identical to two things? The puzzle can be put syntactically. In the open sentence, 'x is identical to y,' 'x' and 'y' must both be singular terms. How can one be singular and the other plural?
P is not something in addition to A + B. P is also not identical to A + B. We seem to be affirming both limbs of a contradiction. We seem to be affirming that P is not something in addition to A + B, but also that P is something in addition to A + B.
Unless one believes that some contradictions are true, then this contradiction needs to be removed. How?
I will stop here and pose the following questions to Alan Cook and to whomever else is interested. First, do you agree that a whole is not something in addition to its parts? Do you agree that a whole is not identical to its parts? Do you agree that these views are logical contradictories of each other? Do you agree that contradictions are never true of reality and must be removed? How do you remove the contradiction?
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P is one; A and B are two. How can one thing be identical to two things? The puzzle can be put syntactically. In the open sentence, 'x is identical to y,' 'x' and 'y' must both be singular terms. It is true that A and B are two things, but "A and B" and "A + B" are different. "A + B" is singular. The "+" function takes two individuals and outputs one. P is identical to the individual A + B, not to A and B. So the contradiction that you saw in the doctrine that a whole is identical to the sum of its parts turns out not to be a contradiction at all. To answer your other question, contradictions are never true of reality because, as is or ought to be well known, in any theory containing a contradiction, you can prove every other well-formed formula. If two contradictories are assertible, so are everything else. So, yes, I do think that wholes are identical to the sum of their parts, at least tentatively, because all of the alleged contradictions or theoretical warts that philosophers have discovered never turn out to be real (although they often teach something about the sensitivity required in the use of mereological language). Specifically, I am thinking of Hempel's "contradiction" (see this). My question is: What does the "+" function consist in? Is it simply a tool that we have to accept as primitive in any mereological theory, with no real-world counterpart? Or does the "+" function somehow imitate or model an actual cognitive operation that we perform when we see, say, the stem and the bowl together as constituting the pipe? I am not at all well-versed in the mereological literature, so if there are any good answers to this question out there, let me know where they are.
Posted by: Ian | Monday, 23 May 2005 at 13:25
"I do think that wholes are identical to the sum of their parts" It follows that my pipe = the sum, stem + bowl. But that can't be right. The sum can exist even if the pipe does not exist. More tomorrow, I hope.
Posted by: Bill Vallicella | Monday, 23 May 2005 at 22:40
Well, perhaps a stem can exist and a bowl can exist individually (unless when they are not part of the pipe they are not yet stems or bowls) but, at least within the identity as part-identity theory, the sum, the stem-plus-bowl, cannot exist while the pipe does not. I mean, something physically identical to the stem might be in New York and something physically identical to the bowl might be in California, in which case there is, I would say, no pipe. But as soon as they are conjoined, as soon as they become, in addition to whatever they were before, parts of the same thing, we have a sum - the pipe.
Posted by: Ian | Tuesday, 24 May 2005 at 17:50
Thh separation need not be that drastic. I pull stem from bowl. Stem is in right hand, bowl is in left. Now the pipe no longer exists. (A pipe is a smoking implement and I can't smoke anything with a disconnected bowl and stem.) But the mereological sum or fusion -- these are equivalent terms but technical terms -- exists. Its existence is automatic given the existence of pipe and of bowl. I get the impression that you do not understand the meaning of 'mereological sum.' I should write a separate post on this.
Posted by: Bill Vallicella | Tuesday, 24 May 2005 at 18:37
In what I say, I’m going to be “painting in broad strokes”, doing a lot of “handwaving” – the usual philosopher’s euphemisms for presenting the basic outline of of a position while falling far short of the standards of clarity and rigor. With that said, here goes. Out of the examples of partite entities on the table (pipes, chariots, tracts of land), let’s consider the pipe, since it has fewest parts. With regard to a single pipe, I propose the following: When counting pipes, it counts as one. When counting nonassembled physical objects, the stem and the bowl each count as one, constituting a collection of two. To offer some handwaving definitions of key terms here: A practice of counting is a practice in which we establish a one-to-one correspondence between the contents of experience and the integers. A physical object is pretty much what physicists call a rigid body; i.e., something to which the law of inertia applies. As for nonassembled: Let’s say that to assemble is “to perform a process which transforms a single physical object into multiple physical objects, through ordinary mechanical means”; Likewise, to disassemble is “to perform a process which transforms a single physical object into multiple physical objects, through ordinary mechanical means.” I’m going to have to be even vaguer and more intuitive about ordinary mechanical means; I have in mind pretty much what we mean when we distinguish between breaking or smashing something and taking it apart. I suspect that “ordinary mechanical means” could, I think, be given a reasonably precise definition: perhaps appealing to some combination of the following criteria: -- The process makes use of the five simple machines (screw, wedge, etc) or some similarly specified class of mechanical devices; -- The amount of force required to accomplish the process; -- The predictability, repeatability and reversibility of the process by human beings (when we disassemble the pipe we get pieces that look the same each time, unlike when we smash the pipe.) -- The history of the object (We can disassemble objects that were originally assembled, “along the lines” – both literally and figuratively – that they were originally assembled.) To repeat, then: When counting pipes, the pipe counts as one. When counting nonassembled physical objects, the stem and the bowl each count as one, constituting a collection of two. Properly understood, there is no contradiction here. The appearance of contradiction arises when we mix up our practices. II. I’m going to try to anticipate a possible response/objection here (and it’s likely not to be the exact form in which the objection occurs to anybody who actually reads this.) From this viewpoint, I have evaded the original question, which could now be asked again, more forcefully, as follows: Which practice, with its associated practices of counting and differentiating of objects, “carves nature at its joints” – “shows us how things really are?” I’ve never been sure that I understand the force of the “really” and the italics in that question. Moreover, I question whether all the philosophers who claim that there’s a clear sense to the question agree on what that sense is. To try to explain: It seems to me that some philosophers believe that there must some one account that answers both of the following questions: (1)How are things really?” (2)“What’s the most general and inclusive overall account of things? This seems to me to confuse two different conceptions of what ontology is: what we might call the Universal Theory conception on the one hand, and the Appearance vs. Reality conception on the other. On the Universal Theory view, the goal of ontology devise a single, logically coherent theory or language that explains everything – how we count pipe parts, how we count pipes, and how we talk about the world such that paradoxes, or the appearance thereof, arises when we talk about certain subjects in certain ways. I think, although it would take a long time to defend the claim, that it’s only on the Universal Theory view that we have to posit features of reality like “the whole subsisting in and through its parts.” (I don’t mean to parody Bill’s or anybody else’s language here; it’s just that I remember reading things that sound vaguely similar to that, and I’m too lazy to go look them up.) I see no reason to believe that the most complete general account of everything will, in the strict sense, be a theory, that sense that it has all the logical characteristics we expect of a well-formed theory: avoidance of contradiction, etc. On the other hand, on the Appearance vs. Reality conception of ontology, the ontologist should be willing to toss stuff out: if a particular practice, theory, language or “discourse” is not logically tractable, that shows that it’s not part of reality. (This move is known as eliminativism; although that term is frequently mildly pejorative, I think most philosophers, as well as most rational people, are eliminativists about some things.) There are divisions within this camp as well; the principle one concerning whether the criteria appealed to in our ontological theory (logical tractability, explanatory coherence, permanence, or whatever) are criteria or sign of reality, or are what we mean by reality. I don’t want to get into that question now. – I do want to insist, though, that that question doesn’t make sense on the Universal Theory vision of ontology. In other words: if the question be raised, “Is their some one true theory that correctly represents the way things are? And does that theory include reference to some category of entities – the things that, in the ultimate sense, exist?” I have intuitions that go both ways. If however, the following set of claims be made: (1)There is a single consistent theory T that explains everything that has ever happened, and everything that’s ever been thought and said; (2) Theory T makes essential reference to some class C of basic entities; (3) It follows from (1)1 and ()2 that all and only those entities in C are real. I’d say this is clearly wrong. I’m also aware that I’m waving my hands much too frantically now, and I’d better quit while I still have a scrap of credibility left. III. Bill, a while ago you put up a post that you introduced as being a sort of preface to your book – in it, you started off talking about the reality of a rock in the desert and the heat of the sun. I liked that post, because it defined a common starting point and clarified where our paths diverge (i.e., where I think you go astray.) I started a response that I never finished; I’ll try to dig it out and get it up on my new blog.
Posted by: Alan Cook | Saturday, 28 May 2005 at 22:32
Alan, Thanks for the very interesting and rich response. My puzzle was this. (1) The pipe is not identical to its parts. It is one; they are two. (2) The pipe is identical to its parts. It is not something in addition to its parts. To avoid the contradiction, you distinguish between two practices of counting. (Reminds me of Baxter -- I'll have to re-read his articles.) If we are talking about the pipe, it is one; if we are talking about its parts, they are two. Are you saying that in reality neither (1) nor (2) are true? That in reality the pipe is neither identical to its parts nor not identical to them? So a person is neither a bundle of skandhas nor not a bundle of skandhas? But let's avoid Buddhist exegesis or else we will never get anywhere. I would say that that metaphysics attempts to get at ultimate reality. So it operates with an appearance/reality contrast. And yes, it "throws some stuff out" except that I would not call this eliminativism. For example, Berkeley does not eliminate stones (to use the Big Ho's favorite example), which is precisely why the good bishop cannot be refuted by kicking a stone. What Berkeley is doing is giving an account of stores and physical objects generally that identifies them with collections of (the accusatives) of ideas. His theory is not eliminativist but identitarian. He does not deny the existence of phyiscal objects; he gives an account of what they are. I'm glad you got something out of the post on the rock in the desert sun. It was a bit obscure -- even to me. Let us see where our paths diverge.
Posted by: Bill Vallicella | Sunday, 29 May 2005 at 16:42