Reality Conditions

Wednesday, July 12, 2006

On Cats and Mats and Parts and Ontology

Brandon has a recent post presenting a philosophical puzzle. Suppose you have a cat, Tibbles, sitting on a mat. Define "Tibbs" to be the part of Tibbles including everything but its tail. It would seem that if Tibbles lost its tale, it would become Tibbs, and it would continue to be a cat; so Tibbs is a cat just as Tibbles is. Are they two different cats?

If you say yes, you are commited to saying that now there are really two cats on the mat, even though it seems there is only one. Moreover, by repeating the argument with other body parts instead of the tail (as small as you wish, even atoms) you can prove there are an enormous number of cats on the mat, where you can see only one; a bizarre conclusion. But if you say no, that Tibbs and Tibbles are the same cat, aren’t you contradicting yourself? After all, one has a tail and one hasn't; how can they be identical?

The technical name for this puzzle is The Problem of the Many, and it is discussed in this SEP entry. Brandon goves a summary of different solutions to it, none of them fully satisfactory. There are many similar ontological puzzles that philosophers delight on; for example:

The paradox of composition: Take a lump of clay and make a statue out of it. Are there now two different things, a lump of clay and a statue? Of course not, there is only one: the lump of clay is the statue now. But how can the lump be identical to the statue if they have different properties (e.g. one existed since long before the other one)? After all, must not identical things have all the same properties?

The problem of temporal parts: Think of a table at two different times, for example yesterday and today. Is the table of yesterday the same thing as the table of today? We would like to say yes (otherwise there exists a new and different table at any new instant of time) but how can they be if they have different properties (for example different things on it)? Perhaps we should say that the table-of-yesterday and the table-of-today are just two "temporal parts" of a unique four-dimensional objet which is the "word-tube" of the table. But then the two tables are not the same thing after all, just different parts of the same thing (and that same thing is a weird 4D object nobody would dream of speaking about outside physics or philosophy…)

I’m sure that with some ingenuity you can invent other puzzles of the same kind. The question I want to make is, are these questions deep? Does pondering them tell us anything about the Nature and Ultimate Structure of Reality, or whatever it is metaphysics is supposed to aim at discovering?

I’m sure many of my physicist readers (perhaps also my non-physicist ones) share my natural intuition about the answer: No! These are just trivial problems about finding the best way to talk about situations which are not really problematic at all. Philosophers that waste their time puzzling about them, are, well… wasting their time.

However, we must be careful not to be too dismissive (lest we should be accused of arrogance) without providing an explanation of why these are really non-problems. And babbling some positivistic or Popperian points about solutions to these problems not being testable will not do. There are many properly philosophical problems which do not seem, at least to me, as trivial and unreal as these ontological puzzles. Just to mention two among many: the mind-body problem, and the tangle of problems relating causation, determinism and free will. Can we give an account that distinguishes "real" philosophical problems from "unreal" ones?

A possibility that appeals to me is the broadly pragmatist stance that most philosophical problems consist in discussions about the best way to talk about some aspect of reality (the best conceptual scheme, if you please) where "best" means something like most prectically convenient, involving less tension with frames used in other areas, and so forth. The difference between "real" and "unreal" problems would then be that in the "real" ones the choice of way of talking/thinking about some things is intertwined with and affects many other areas of thought. For example, deciding whether determinism is compatible with free will is, by itself, just a "trivial" semantical question on how to define "free will"; but because our idea of freedom is connected with things of practical importance such as moral and legal responsibility, the problem of finding the best frame of concepts to talk about these things is a "deep" one. By contrast, the question of whether Tibbs is a different cat than Tibbles is one that has no practical significance whatsoever. And I don’t mean "practical" in a vulgar and utilitarian way, but in a broad way that refers to any consequences for our thoughts on other areas. The Problem of the Many, and similar ontological puzzles, seem to me to stand in "isolation" from scientific, legal, moral or other concerns. That it what makes them seem unreal. A rich philosophical problem, like the mind-body problem, is such because its core conceptual/pragmatical issue ("What is the best way of talking about persons, their thoughts and their brains?") is intertwined with and deeply affects our view of sciences like psychology, neurology, and artificial intelligence, and legal and moral questions about many practical issues (e.g. animal rights).

Brandon does acknowledge by the end of his post that the problem would be unreal if it were not related to other concerns:

If a lot of this sounds like word-chopping, you're almost right. It certainly does seem like a lot of the mereological literature does get into word-chopping, and weird word-chopping at that. But it's not purely verbal, because it matters a great deal to the way we reason about identity, parts, and wholes…Which position you take can change the sort of objections you can make to other positions… it can change the way you think proper parts are related to wholes.

But I confess I don't see finding the best logically precise way of talking about parts and wholes something that "matters a great deal". Does it matter for practical, or for theoretical purposes? Not for practical ones; our ordinary language is good enough for describing things like parts of cats; I am not aware of practical concerns that require a more logically precise conceptualisation (as for example, a discussion about abortion may require a more precise conceptualisation of personhood than our unreflective one). But also not for theoretical purposes; because if one has the philosophical goal of finding a sort of "ultimate vocabulary", sharp and precise, which reflects in some sense the structure of the world, then one should not use in the discussion ordinary things like cats and tables One should make first an analysis of our deepest scientific theories, like Quantum Field Theory or perhaps String Theory, and design a conceptual frame that fits well with them. Of course, ordinary notions of "objects", "parts", "properties", "time" and so on would probably not map at all into the mathematical structure of these theories, and so the ontological puzzles I started with could perhaps not even be stated, let alone solved, by taking this route. They would be just riddles about how to make more precise an ordinary language we don't need to make more precise, either for theoretical or practical purposes. (I'm writing of course from a completely secular standpoint, so I pass over Brandon's mention of the structure of the Holy Trinity as an application of the ontology of parts and wholes).

Now I should say that not all philosophical problems seem to me to be pragmatical/conceptual. Some of them seem to me as straightforwardly factual as any scientific question. God exists or does not exist; there is a soul distinct from the body or there is not. (It is only when Cartesian dualism is ruled out and we shuffle around the merits of property dualism, nonreductive materialism, functionalism and eliminative materialism that the mind-body problem starts looking "conceptual" to me). And I still regard scientific questions, save perhaps for borderline cases like the interpretation of quantum mechanics, as factual and not pragmatical. But now the natural question would be, of course, how to distinguish "factual" questions from others. Quine made a convincing case that there was no deep distinction between what positivists like Carnap saw as factual questions and those they saw as philosophical/conceptual ones to be decided pragmatically. Many analytical philosophers who succeeded him interpreted that "ontological" questions were as factual and "real" as scientific ones and started to discuss them with complete earnestness, something I have criticized above. Can my position escape swinging to the other extreme and saying with Rorty that there is no such thing as "factual truth" and that all problems are just pragmatical ones about the best way of talking in a given situation? I hope so, because I have strong instinctive leanings towards scientific realism; but I have not yet figured out how. What I have said implies a rejection of "naive realism" in ontology, the idea that questions such as "do the parts of an object exist as objects?" is a "real" one that demands an answer. But in absence of a sharp criterion distinguishing science and philosophy, facts and conceptualisations, how can I treat the question "do electrons exist?" as a "real" one as I would like to?


  • I agree with your sentiment that the value in some of these philosophical problems comes only when you connect them up with other issues.

    I think mereology does connect up with causality, and may connect with philosophy of physics (if not physics itself) also. A couple of quick thoughts:

    Tibbles and Tibbs in most situations play the same causal role.

    If we think quantum systems interact with (observe/measure) each other in nature and not just in the context of a laboratory experiment, what does it take to compose an individual capable of such an interaction?

    Best regards - Steve Esser

    By Blogger Steve, at 8:34 PM, July 12, 2006  

  • Hi Steve,

    Perhaps my rejection of mereology and related areas was too glib, but I am not convinced by your examples. The question of which physical systems would "interact" with others and whether the parts o a larger system could be considered systems as well, seems to be an empirical one, or at least a "conceptual" one that pertains to the analysis of quantum mechanics, but quite far away from the abstract discussions typical of mereology (which work with ordinary-language conceptions of objects and parts, rather different from the quantum ones).

    By Anonymous Anonymous, at 8:52 PM, July 12, 2006  

  • If you followed my comment on Brandon's post, and the robust interchange that followed, you will see I am quite baffled as to what the problem is supposed to be. It seems to be motivated by a concern about substitutivity. If 'x is F' is true, and if 'y is not F' is true, then x cannot be identical with y (meaning identity in the logical sense, not: x = y, not any other sense, if there is one). Thus if x has a tail, and y does not have a tail, x /= y.

    But this ignores the effect of tense. If it was the case that x had a tail (past tense), and it is not the case that y has a tail, this does not rule out x=y. How can it? If I say 'I had more hair when I was 18', obviously the 'I' refers to me.

    This is not an exception to substitutivity. 'had a tail' and 'has a tail' are not the same predicate. Indeed, different instances of 'had a tail' may not represent the same logical predicate. It may be Tibbles had a tail (on Monday) but not that Tibbles had a tail (on Tuesday).

    By Blogger Edward Ockham, at 10:18 AM, July 14, 2006  

  • >>>>>
    After all, one has a tail and one hasn't; how can they be identical?

    There you go: obviously they can't. That's because both statements are present tense. But clearly, 'one cat had a tail' and 'the same cat now has no tail' are perfectly consistent.

    By Blogger Edward Ockham, at 10:21 AM, July 14, 2006  

  • Ocham, I don't see the relevance of tense for the problem of the cats. We are not comparing the cat before and after losing its tail. We are comparing, at the same time, the whole cat and the cat minus its tail ("abstracting" the tail).

    You seem to be just assuming that the latter, Tibbs, is not a cat. But there are many prima facie arguments that it is a cat. For example, if the tail is chopped then nobody would deny Tibbs is a cat, yet Tibbs has undergone no intrinsic change. Tibbs had from the beginning all the cat organs, DNA, etc, which are plausably necessary and sufficent conditions for cathood. And so on.

    My "deflationist" position agrees that Tibbs (with the tail attatched) is not a cat, but not because of logic, but because our ordinary laguage (OL) does not consider it a cat. Which is only saying that senteces like "There is only one cat in the house" are perfectly true in OL, and that I see no pressing need for building up a technical mereological language that complements it. I don't see this as a "deep" fact about ontology, however. And I answer the prima facie arguments I presented above saying that OL does not include general principles about intrinsicness, necessary conditions for applications of concepts, and so on, but only pragmatical conditions of assertability. This is not rejecting that sentences in OL can be true, if they are uttered when those conditions are met, but it is rejecting that they must have a truth-value when our ordinary practices make no distinctions (such as between Tibbs and Tibbles) that create assertability conditions for senteces identifying or distinguishing them.

    By Blogger Alejandro, at 7:40 PM, July 14, 2006  

  • "...if the tail is chopped then nobody would deny Tibbs is a cat, yet Tibbs has undergone no intrinsic change. Tibbs had from the beginning all the cat organs, DNA, etc, which are plausably necessary and sufficent conditions for cathood. And so on."

    If the tail is chopped, you are considering that the "whole cat minus tail" is the cat. Why? Why don't you call the tail "the cat"? After all, that part still has cat DNA. As regards to the organs, what if you took the stomach out of the cat? Wouldn't you still called it a cat?
    What if you chopped its legs? I think you would still consider it a cat (and would not call the legs "the cat"). So where's the limit? What's intrinsic to the cat? What if you chopped him in symetrical halves? Would you have two cats? What if you took off his head? Which part would you call a cat?

    It all reminds me of what Roman Polanski said in "The tenant": "If you cut off my head, what would I say... Me and my head, or me and my body? What right has my head to call itself me?"

    By Anonymous Anonymous, at 12:57 AM, July 15, 2006  

  • So many questions... but what is your point?

    By Anonymous Anonymous, at 1:00 AM, July 15, 2006  

  • My eyes glaze over when I encounter discussions like these. Here is a metaphysics paper that you may find interesting. Yes, I wrote it.

    By Anonymous Anonymous, at 6:10 AM, July 15, 2006  

  • >>>
    Ocham, I don't see the relevance of tense for the problem of the cats. We are not comparing the cat before and after losing its tail. We are comparing, at the same time, the whole cat and the cat minus its tail ("abstracting" the tail).

    Brandon also made the same point about tense not being relevant. I think it is, because this pseudo problem doesn't get off the ground without the argument that if x has a tail and y doesn't then x is not identical with y.

    This argument is valid. Similarly the argument you have just given, that if we compare a whole cat, and a cat minus a tail, then there must (by implication, but of course you haven't spelled this out) be two cats.

    But there are not two cats. There is Tibbs, who is a cat minus a tail. And there is Tibbles, who used to be a whole cat. But Tibbs = Tibbles, they are one and the same cat. So there is only one cat. But, you object, Tibbs is not a whole cat, and Tibbles is. No, I respond, Tibbles is not a whole cat. He used to be. Tibbles is a cat minus a tail. And Tibbs used to be a whole cat.

    Neither you nor Brandon have given a coherent argument to support your idea that there is some kind of problem here. I repeat: what is the problem?

    My "deflationist" position agrees that Tibbs (with the tail attatched) is not a cat, but not because of logic, but because our ordinary laguage (OL) does not consider it a cat.

    I still don't understand this at all.

    By Blogger Edward Ockham, at 8:32 AM, July 15, 2006  

  • Here are the assumptions I am using, all of which are basic ideas that are embedded in ordinary language.

    1. Identity is essentially a linguistic concept. I.e. 'a = b' is true only if 'a' and 'b' refer to a single thing, and reference is a linguistic concept.

    2. Things with different properties cannot be identical. I.e. Fa and ~Fb entails a is not identical with b.

    3. But the same thing can have different properties through time. Thus its not having been the case that Fa, its being the case that Fb, is perfectly consistent with a=b

    4. Things can be composed of parts. From the assumptions above, it then follows that if x is composed of certain parts, and y is composed of certain parts, and the parts are different, then the things are different. It also follows that a thing may have been composed of different parts than what the same thing is now.

    5. A thing is not identical with its parts. That is because the parts are many things, but the thing composed of them is one thing, and one thing cannot be many things. (i.e, the 'being composed of' relation is not the identity relation). This is of course perfectly consistent with the idea that that things can change through time in respect of their properties and their composition.

    6. There is only one cat in the house down the road. There was only one cat in the house yesterday. There has been only one cat in that house all week.

    These principles are perfectly consistent and lead to no paradox or puzzle of the sort you are suggesting.

    What is interesting is why people get so puzzled about them.

    By Blogger Edward Ockham, at 9:29 AM, July 15, 2006  

  • Ocham, joining your assumptions 5 and 6, it follows that (if Tibbles is a cat) neither Tibbs nor any other part of Tibbles is a cat, not even Tibbles-minus-one-atom (where the dashes mean we are considering that part of Tibbles while the single atom is still attached to it, not the cat resulting from really taking away that atom). Now perhaps for a solid object as a cat you can find a boundary delimiting "the whole cat" and defend your claim that anything smaller than this is not really a cat, and perhaps even claim ordinary language to be on your side. But what would you do for a cloud, which has vague boundaries? (See the SEP entry linked in the post for a discussion).

    By Anonymous Anonymous, at 12:47 AM, July 16, 2006  

  • If Tibbles is a cat, and if there is one cat next door (as indeed there is) then it follows logically that no proper part of the cat next door is a cat. If even one of them was a cat, there would be more than one cat next door, and there isn't.

    When I say 'follows logically', I mean, using the principle that if Fa but not Fb, then a is not identical to b. Most logicians accept this.

    Your point about clouds is interesting. Perhaps we can accept that a cloud can be made up of many clouds. But we do not count cats in this way.

    >>> Now perhaps for a solid object as a cat you can find a boundary delimiting "the whole cat" and defend your claim that anything smaller than this is not really a cat>>>

    You are sliding towards a different problem here. My point is a logical one only. Given that X is a cat, and given that there is only one cat, it logically follows that anything smaller than X is not a cat.

    0. X is cat
    1. Y is smaller than X
    2. Y /= X (because it is not true that X is smaller than X)
    3. Assume Y is a cat.
    4. Then X is a cat, Y is a cat, and Y /= X.
    5. From the definition of the number '2' it follows that there are two cats.
    6. But there is only one cat.

    By Blogger Edward Ockham, at 4:46 PM, July 16, 2006  

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