On Cats and Mats and Parts and Ontology
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?