Some people (ahem) want to discuss the notion of a many-one identity relation. I'm a bit puzzled by such talk, since I think it's constitutive of our concept of identity that it's one-one. We don't balk at cases like "Benjamin Franklin is the inventor of bifocals", "Hesperus is Phosphorous", and "Cat Stevens is Yusuf Islam". We might even have many-many cases of identity, like "The candidates who raise the most money are the candidates who get the most votes", though there might be a good way to analyze this in first-order predicate logic with the usual representation of identity. I'm not exactly sure what to make of many-many claims, but set them aside for now.
One has plenty of examples of identity in language from which we try to build our notion, and or familiar identity sign is doing a pretty good job of this. If many-one identity were part of our ordinary concept of identity, we should expect to see all sorts of ordinary uses of it. So, what are the cases that force us to consider a many-one notion? If many-one identity is supposed to be so intuitive, how come we don't see examples of it? How come all uses of it seem ungrammatical and weird?
The only (ordinary) examples I can think of are examples that involve the Trinity. The Father, Son, and Holy Ghost are (is?) one thing, which is God. Is your claim that many-one identity makes exactly as much sense as the Catholic Trinity?
[Note, by the way, that I don't think that claims about intuitions and linguistics are deeply informative about the nature of reality. I'm also not claiming that there's no room for some kind of generalized notion of identity to explain what we mean by "nothing over and above" kinds of claims. I just think it's a mistake to identify this notion with our ordinary uses of identity.]
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6 comments:
Barak,
I assume you're referring to me in this entry. (Why did you post your own entry instead of commenting on my last one?) Anyway, I of course have some comments.
First of all, nothing I say will ever be incompatible with one-one and many-many identities. The one-one cases are well enough understood, and the many-many cases are best understood in terms of plural logic: if xx=yy, then for each z, z is one of xx iff z is one of yy. (I'm not sure what you mean by your comments about many-many identities.)
I don't think it is constitutive of our concept of identity that it is one-one. I think that is a prejudice of philosophers that think too much in terms of first-order singular predicate logic with singular identity. I have asked a lot of non-philosophers about many-one identities and they all think it makes perfect sense and don't see why I bother to argue for this. They tell me it seems obvious. And I have asked a lot of them. But on the other hand, I don't think this should count for much at all. If you think it is constitutive of your concept of identity that it is one-one, then I am simply proposing a revision of your concept of identity since I think it suffers from Post-Quinean logical prejudices.
You say on the one hand that you think we build our notion of identity from examples in language, but then on the other hand that you don't think claims about linguistics are deeply informative about the nature of reality. I find this puzzling. But in any case, from the latter of your claims you should be able to seriously consider many-one identities even if there are no good examples of it in language. But I also think there are some good examples of many-one identities in ordinary languages that make perfect sense. For example, one kilometer is thousand meters (it is them!). Also, those cups of water are that mug of water (they are it!). Further, some languages, Norwegian included, makes no distinction between 'am', 'is', and 'are' as we do in English. In Norwegian we use 'er' when flanked by 'I', 'you', 'he/she/it', as well as 'we', 'you' (plural), and 'they'. Thus, we should not think that it is so obvious that our concept of identity, unless it is language-relative (which is absurd) is such that it makes no sense to say things like 'it is them' and 'they are it'. Some languages simply don't distinguish between the two copulas. I thus take it our concept of identity is inter-languageish rather than intra-languageish.
But again, I don't think the purely linguistic evidence counts for much at all ontologically speaking.
About the catholic trinity case: many-one identities are supposed to make much more sense than this case. Come on... But note again that you should not be fooled by the surface structure of English by becoming puzzled as to whether there should be an 'are' or an 'is' representing the identity relations.
Finally, at times you seem to misunderstand the whole project. You say:
"I'm also not claiming that there's no room for some kind of generalized notion of identity to explain what we mean by "nothing over and above" kinds of claims. I just think it's a mistake to identify this notion with our ordinary uses of identity."
But that is the whole point! What we're looking for is a generalized notion of identity that can, among many other things, explain the phrase "nothing over and above" (as well as my own favorite "nothing under and below"). Further, no one should identify this generalized notion with our ordinary one-one notion, if not only on syntactical grounds alone! We're looking for a notion that can capture EVERYTHING we mean by 'identity' not just the one-one claims.
Thus, your last paragraph seems to say that you actually agree, or at least not disagree, with the project...
Break free from surface grammar! We're doing ontology.
Wow, this comment became a bit long.
-Einar
Hey Einar,
A couple of comments, though this might not address quite everything you've brought up...
The reason I brought up the challenge in the way I did was because I found our differences of intuition so striking that I thought it important to try to locate our difference. I thought that if we could talk about ordinary examples of the many-one identity relation, you would either convince me that the many-one identity is unproblematic and that I've had it all along, or that your notion is simply different from mine, albeit one that's in the same neighborhood and one that is applicable to all the cases I'd put it to, and then some additional ones -- that's what I meant by generalization. And I'm still not sure where we stand on this score -- I agree that your account must be a generalization on the ordinary one-one identity, but is it a generalization on our very concept of identity?
I'm not sure what to make of the intuitions of your friends, or of the syntactic features of the copula in Norwegian. Certainly, it would be unfortunate if it turned out that different languages fostered different notions of identity... In any case, I still feel confident saying that these examples are ungrammatical in English, and that this should count as evidence that they are unnatural. If they are grammatical to some speakers, that might only mean that the syntactic test that I'm suggesting simply won't apply in Norwegian, since the copula doesn't distinguish between singular and plural terms. You still owe us an explanation of why they're ungrammatical in English, given that these claims should be natural.
And grammaticality aside, I wasn't trying to be unfair with the Trinity case -- that was really the only half-way plausible example I could think of. I hadn't considered your measurement examples, but they also aren't entirely straightforward. The object in question is the thing that is being measured -- either the distance between two points that can be measured in kilometers or meters, or the liquid that can either be measured in cups or taken as the whole mug. Either way, it's not surprising that we can make measurements in different units, and that we can make a measurement come out "1" in some system and "1000" in some other system. But that's not to say that we are looking at one thing that's also one thousand things! We are, after all, merely looking at some water, or some region of space.
Actually, here might be a better example: "The 52 cards is (are?) the deck." Again, the grammar is wrong in English, but we can talk about that later. Does this prove that there is a many-one identity between the cards and the deck? Not so much. We can, following Frege, think of this more of a problem about counting and sortals than about identity. Of course, there is a "nothing over and above" intuition to be spelled out somewhere, but this doesn't immediately get us to many-one identity.
Barak,
I don't know, nor do I care, how to individuate concepts. I provide a concept that I think deserve to be called a concept of identity. If you don't want to call it identity, call it something else, say, schmidentity. All that matters is that it does what i want it to do, namely explain why unrestricted composition is not only true, but necessarily true, why we don't need to believe in tables as something over and above their parts (ontological parsimony), why we don't need to believe in junk and hunk, why ontological dependence between parts and wholes is nonsense, why there are no coinciding objects, avoid the embarrasment of not knowing what a composite object is, and many more things. In short, call it what you want, but enjoy its fruit. As our good old friend Bill once said: 'what's in a name?' (Though I do think that it is a form of identity because when properly articulated we see that there is no ontic difference whatsoever between its relata.)
You say that because some examples of many-one identity are ungrammatical in english that is evidence that the concept is unnatural. I don't get this. I take it that because they are grammatical in many languages (e.g. norwegian and hungarian) that is evidence that the concept is natural. Why should the grammatical structure of english be priviliged? As long as at least one language makes them grammatical, there is no reason to deny its naturalness. I guess I just don't understand this obsession with grammar. I take concepts to be independent of surface grammar of any language, and I take these concepts to be what we use in understanding the structure of the world (in carving up reality).
You say:
"Either way, it's not surprising that we can make measurements in different units, and that we can make a measurement come out "1" in some system and "1000" in some other system. But that's not to say that we are looking at one thing that's also one thousand things!"
I take the fact that we can consider the very same distance, say a road, and say both that it is one kilometer and a thousand meters to be evidence that we can consider the same world, or the same part of the world, in many difference ways. The same thing is BOTH one kilometer and a thousand meters. It all depends on how we consider it. Of course that is not to say that we can according to the rules or conventions of language consider it in two incompatible ways at once. But we can consider it as one kilometer and we can consider it as a thousand meters, and in both cases we are considering the very same things. There is no ontic difference between the one kilometer and the thousand meters, merely different ways of considering or carving up the world. In the same way, we can consider the table as one table or as four legs and a table top. There is no ontic difference between the table and the four legs and table top, merely different ways of conceiving or carving up the world. That is the main intuition behind saying that the table is identical to the four legs and table top. This is what seems so obvious to me (as well as to my non-philosopher "friends") that I don't understand how you can deny it.
I don't understand why I owe you an explanation of why some many-one identity claims are ungrammatical in english. (You should ask Amy instead...) Nor do I understand why they should be natural in english, or even what you mean by a concept being natural.
Finally, I find the Frege solution unsatisfactory in these cases because it seems to preclude irreducibly plural predication. I want to be able to say for example 'those things are five in number' and be talking about and predicating something directly of those things (not about some concept).
Of what I have said, what do you think is false?
Come on, it's obviously true! Do you really believe with a straight face that the table is ontologically something over and above its parts? What is it supposed to be that is not just projecting features of language on to the world itself?
-Einar
PS: In 1923 Russell warned against what he called 'the fallacy of verbalism':
"In dealing with highly abstract matters it is much easier to grasp the symbols (usually words) than it is to grasp what they stand for. The result of this is that almost all thinking that purports to be philosophical or logical consists in attributing to the world the properties of language."
"Ever since Kant there has been a tendency in philosophy to confuse knowledge with what is known. It is thought that there must be some kind of identity between the knower and the known, and hence the knower infers that the known is also muddle-headed"
And already in 1878, C.S.Peirce complained:
"[a] deception is to mistake a mere difference in the grammatical construction of two words for a distinction between the ideas they express. In this pedantic age, when the general mob of writers attend so much more to words than to things, this error is common enough."
Come on, join the team!
Hey, I'm not linguistic-turn style philosopher. I don't think that we can only analyze concepts through language or something like that. My claim is much weaker. I understand your claim to be that many-one identity claims are natural and part of our ordinary concept of identity; I think that, if they were natural in the way that you suggest, then all languages would let us make these claims. I could spell out my argument Fred-style if you'd like, but I'll refrain.
Now, it's not that I'm privileging one language over another; all that I'm saying is that if some language rules a construction to be ungrammatical, that is prima facia reason to believe that the kind of proposition expressed is unnatural or unintuitive. Languages are the kinds of things that evolved to enable us to express the kinds of things that we naturally want to express -- wouldn't it be weird if a language ruled something ungrammatical (or even infelicitous) something that is part of our ordinary stock of concepts? If we couldn't say something like "Bachelors are unmarried"? Just because the construction is permitted in some languages (such as Norweigian) doesn't mean that English is any less of a counter-example.
So, put simply, my argument (if it works) doesn't conclude that your view is false. It concludes that many-one identity is unnatural or counter-intuitive. Even if you accept my argument, you're still open to hold that many-one identity is some kind of surprising philosophical result, or that many-one identity exists as an interesting generalization (which would need to be spelled out) of our ordinary concept that explains "nothing over and above" type intuitions.
That said, I agree that we can divide up the world in different ways, nothing over and above, blah blah blah. But this doesn't suffice to give us composition as identity.
Barak,
I see. This is better. But I'm still a bit puzzled. Do ALL languages need to make a certain distinction in order for that distinction to be natural? That seems too much. Some languages (I have been told by linguists) don't have the subject-predicate distinction we are so used to. Does that mean that it is not natural, or even worse, that there are no objects? Some languages don't have number words higher than three. Does that mean that all numbers above three are unnatural? I don't think so.
So as I understand it, I don't think that your argument shows that a concept of many-one identity is unnatural just because some examples of it are ungrammatical in english. But in any case, I am in this particular case happy with providing metaphysical discoveries (if I am able to coherently articulate the view in more logical terms).
Finally, I think the fact that we can carve the world up in various ways does, when properly articulated, suffice for many-one identity. We can carve the table up into one table and we can carve the table up into four legs and a table top. However we carve the world up, it stays the same. Hence, table = its parts.
-Einar
PS: I still wonder what you think composite objects are if not all their parts and without committing the fallacy of verbalism.
Hey Einar,
I'm not sure what I want to say exactly, so I'll give you two answers.
First, my fall-back position: I merely said that evolutionary pressures on language are such that languages should develop, over time, to allow us to express what we want to express. If you give me a language that, for whatever reason, these pressures weren't exerted in the same way, we should expect very different languages, but not necessarily ones that respect our ordinary concepts. Thus, if a language is relatively new, and/or spoken by a relatively small community in isolation, there is less pressure on the language to develop in some ideally useful way.
Now, what I'd rather say is that *all* languages do, in fact, turn out to be useful in the respect I have in mind. And I do feel pretty comfortable saying that languages are useful in this way. I'm not sure which langauges you had in mind as not subject-predicate, but at least one linguist assures me that we have good reason to think that all languages are subject-predicate. Some langauges, such as Arabic and Irish, may not appear subject-predicate on the surface, since the verb comes first (or word order is just strange). Nonetheless, these languages still show good evidence of having verb phrases as meaningful semantic units, separate from the determiner phrase. And as for numbers, I assume you're talking about Piraha? That's the only language I'm aware of like that, and I don't think enough data is in on Piraha to say much about it yet...
Anyway, what I have in mind by "carving things up differently" does not entail that the parts are identical to the wholes. I do think that each carving is, in some sense, equally good, though pragmatic pressures will often select one (or a small number) of carvings as seeming more natural. But I still don't see where this buys us identity of parts and wholes. All it buys us is different schemes, but not the identity of the schemes.
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