One sort of consideration which may seem to augur for Millianism, and against both descriptivism and my view of names, comes from the idea that meanings must be public items, shared by communicators. If the subject matter of semantics is supposed to be the public meanings of linguistic expressions - where this might be conceived as the stuff we must have implicit knowledge of in order to be competent speakers - then it is hard to see what, in any given case, could be essential to using a name correctly, except for using it to denote the right bearer. On the other hand, there does seem to be a technique of using certain empty names like 'Santa Claus' which is more specific than: using it such that it has no bearer. But perhaps we want a minimal conception of semantics on which such specific techniques are regarded as extra-semantic.
Given such a minimal conception of semantics, it will be hard to avoid the conclusion that belief-contents, proposition-meanings and propositions and have more to their identity than their structures and the semantics of their components. (That is, unless we are prepared to bite bullets like: '”Hesperus is Hesperus” means the same as “Hesperus is Phosphorus”'.) And if we accept this, then we must deny that the identity of a proposition can always be reckoned as being determined by its structure plus the meanings of its parts, in the relevant minimal sense of 'meaning'.
We can reinstate compositionality either by moving to a very coarse-grained notion of belief-contents or propositions (and so biting the bullet on 'Hesperus is Hesperus' and 'Hesperus is Phosphorus'), or by moving to a finer-grained conception of the meanings of parts such as names, a conception which will include things beyond public meanings and minimal competence conditions. This latter is, in effect, what I advocate in my view of names as having uses, or being tied to individual concepts, which can differ even though the names do not differ as regards extension.
'Hesperus and Phosphorus' seems to be a different proposition – seems to mean something different from – 'Hesperus is Hesperus'. And, quite apart from any general thesis about meaning-determination, this difference seems like it has to be laid at the door of the names 'Hesperus' and 'Phosphorus'. And that is what my view of names enables us to do, while remaining invulnerable to Kripkean anti-descriptivist arguments.
Why can't we all go home, then? Well, this kind of solution seems to worry people. It seems like they can see what its virtues would be, but don't feel they can help themselves to it. I suspect that one of the major causes of this reluctance is some kind of conceptual intuition to the effect that meanings – anything worth calling 'a meaning' – have, by definition, to be public and shared by competent communicators. I suspect that another major cause, perhaps even more active, is that people have sensed that on this way of going, there won't be any general story to tell about how to count meanings – i.e. about how to determine whether to say that two expressions, or instances thereof, are synonymous or not.
We can appease the first worry to some degree, I think, by allowing that there is a natural conception, which it is not improper to use the word 'meaning' in connection with, according to which meanings, in order to be meanings, must be public and shared. But we can also have a richer, more idiolectic conception, and maintain that this is what we're talking about in connection with names, and the semantic difference between 'Hesperus and Hesperus' and 'Hesperus is Phosphorus'.
Furthermore, these two sorts of conceptions need not be seen as two utterly different things, but as continuous. Both deal with systematic use-patterns of signs, or roles of signs in systems. Taking the 'public and shared' conception as our starting point, we may yet ask: how public and how shared must these use-patterns or system-roles be to count as meanings? We could have a conception on which the patterns or roles must be shared by all who competently speak the language. But how do we individuate languages? Peter Ludlow's recent work on 'the dynamic lexicon' can help prepare the ground for what I am saying here, being consonant with it in important ways.
This appearance of continuity and fluidity is not some nasty imprecision in our philosophy, but a faithful capturing of the facts. People differ from each other – and from themselves over time – in their use of symbols and the way their understandings work, and in most cases, the question whether two symbol-instances align in meaning can be given different answers for different purposes. When we're talking about something we're both familiar with, and our ideas of that thing are similar enough, our talk can be said to align in meaning. But notice that, in speaking just then of ideas being similar enough, I have already hinted that there might be a finer granularity at which our ideas are not type-identical – a finer granularity at which it may be said that we don't mean exactly the same thing. This seems realistic.
Regarding the second worry, my answer is already implicit in the above; I think the most fruitful response is not to try to explain it away, but to embrace it. There is no single way of counting meanings, since we can individuate them and count them differently at different granularities. We are already pushed toward this by considering Kripke's puzzle, and its character as a solution there is only strengthened when we see it has further applications, such as here to this worry about the very idea that names have internal meanings, to questions about the individuation of facts, and elsewhere.
Showing posts with label Millianism. Show all posts
Showing posts with label Millianism. Show all posts
Wednesday, 2 July 2014
Tuesday, 17 June 2014
Names, Meaning and the Articulation Assumption
Here I want to suggest one reason why people have had trouble seeing a middle way between descriptivism and Millianism about names - that is, why my sort of view of names has not already prevailed or at least become a prominent option. (It is far from the only reason, and I will consider others in future posts.) This may also afford us some insight into why both descriptivists and Millians endorse their respective views.
The articulation assumption is that, if you say that names have meanings beyond their referents, you have to be able, at least in principle, to specify what they are, and in some way which articulates or unpacks these meanings. The assumption is at work in B's role in this short dialogue:
A: Names have meanings over and above their bearers.
B: What's the meaning of 'John Nash', then?
I am envisaging B's reply here as a Millian-leaning attempt to embarrass A out of their assertion.
And what I want to say here is that A need not have anything to reply here, in order to have respectably made their assertion.
To see this, it helps to reflect that, in saying 'what the meaning of' an expression is, what we are doing is giving, or at least referring to, an expression which has the same meaning as the one whose meaning is in question. And there is no reason why a name like 'John Nash' needs to be synonymous with any other expression, let alone one with more structure (so that it could be said to articulate or unpack the meaning of 'John Nash').
One of the functions of semantic notions is to bundle and separate instances of expressions. We bundle by ascribing the same meaning, we separate by ascribing different meanings.
Frege, who notoriously says precious little about his senses, at one point says that the sense of 'Aristotle' might be: the teacher of Alexander. (I reproduce his style of formulation, using a colon and no quote marks, but I don't mean to say this is clear and unambiguous.) But we don't need to do any such thing.
Making the articulation assumption could be one of the forces pushing thinkers who are impressed by anti-descriptivist arguments, such as Kripke's, toward Millianism. Likewise, it could be one of the forces pushing thinkers who are impressed by anti-Millian considerations, such as the apparent difference in meaning between 'Hesperus is Hesperus' and 'Hesperus is Phosphorus' and the apparent meaningfulness true singular negative existentials like 'Santa doesn't exist', toward (perhaps sophisticated) forms of descriptivism.
Once you reflect that the articulation assumption is false, it becomes clear that there is a middle way, quite immune to both sets of problems.
The articulation assumption is that, if you say that names have meanings beyond their referents, you have to be able, at least in principle, to specify what they are, and in some way which articulates or unpacks these meanings. The assumption is at work in B's role in this short dialogue:
A: Names have meanings over and above their bearers.
B: What's the meaning of 'John Nash', then?
I am envisaging B's reply here as a Millian-leaning attempt to embarrass A out of their assertion.
And what I want to say here is that A need not have anything to reply here, in order to have respectably made their assertion.
To see this, it helps to reflect that, in saying 'what the meaning of' an expression is, what we are doing is giving, or at least referring to, an expression which has the same meaning as the one whose meaning is in question. And there is no reason why a name like 'John Nash' needs to be synonymous with any other expression, let alone one with more structure (so that it could be said to articulate or unpack the meaning of 'John Nash').
One of the functions of semantic notions is to bundle and separate instances of expressions. We bundle by ascribing the same meaning, we separate by ascribing different meanings.
Frege, who notoriously says precious little about his senses, at one point says that the sense of 'Aristotle' might be: the teacher of Alexander. (I reproduce his style of formulation, using a colon and no quote marks, but I don't mean to say this is clear and unambiguous.) But we don't need to do any such thing.
Making the articulation assumption could be one of the forces pushing thinkers who are impressed by anti-descriptivist arguments, such as Kripke's, toward Millianism. Likewise, it could be one of the forces pushing thinkers who are impressed by anti-Millian considerations, such as the apparent difference in meaning between 'Hesperus is Hesperus' and 'Hesperus is Phosphorus' and the apparent meaningfulness true singular negative existentials like 'Santa doesn't exist', toward (perhaps sophisticated) forms of descriptivism.
Once you reflect that the articulation assumption is false, it becomes clear that there is a middle way, quite immune to both sets of problems.
Wednesday, 2 January 2013
Notes on Identity (and the idea of a 'law of metaphysics' concerning it)
(I) Everything is identical with itself and with no other thing.
Consider what results when we try to express (I) in first-order logic:
Consider what results when we try to express (I) in first-order logic:
(FOL I) (x) x = x ~ (y)(y = x ~ y = x)
For a closer articulation, let us introduce a function SelfOf() - the identity function – and a distinctness relation D, yielding
(FOL I 2) (x){ x = SelfOf(x) ~ (y)(y = x y D x)}
This shows what we are doing in the case where we use something like (I) to introduce 'identity' and cognates, e.g. making sure it's not taken qualitatively. We are presupposing, using, the notions of self and distinctness/otherness, and showing how identity connects with them; if we had fixed interpretations for 'D' and 'SelfOf', we could use (FOL I 2) to define '='. And we could of course reverse this, presupposing '='. (In the first use, we would naturally emphasise 'self' and 'no other thing', or just 'other', in pronunciation. In the second, we would emphasise the word 'identical'.) We can also presuppose nothing, and take these propositions as just specifying how these notions are to relate to each other.
All these construals can be called grammatical in Wittgenstein's sense. But now, is there some other way of taking (I)? It can certainly look that way in philosophy. ('Law of Metaphysics'.)
It can look as though (I) is ruling out worlds where the identity relation looks like this:
or like this:
and ruling in this sort of picture:
But no one wants to say that these worlds are real, or even possible. So then can't we – mustn't we - take this ruling in and out as grammatical too?
Somehow, instead of seeing it that way, philosophical thinkers try to give it another, impossible sort of application – or so I want to say. But what is this other application, and how am I to describe it without falling prey to the sort of confused thinking I am trying to correct?
What makes these mistakes, or confusions, hard to correct is their slippery, elusive character. (This no doubt has to do with the way so many of our key terms slip and slide so naturally between slightly different uses.)
It is not as if my opponent thinks their Law of Metaphysics is empirical, or anything like that. Rather, they have a spurious category for it, I want to say – or, at the very least, they spuriously categorize it.
They fail to make a category at the right level, so to speak – fail to regard identity statements as being sufficiently special in their fundamental workings. Instead, they are assimilated to other relational statements, giving rise to the conception of a special sort of fact (which we have some kind of special access to, perhaps).
A purported picturing of the world as being one way rather than another. A purported division in some space of representations. Also, perhaps some vague conception of an analogue of empirical verification – as it were, rational perception (cf. Plato, Goedel, the notion of an “eye of Reason”). The sort of thing no one would ever feel like positing for 'Bachelors are unmarried' (except perhaps in a heroic effort to be consistent).
How is it that this comes about here, and not, say, with 'Bachelors are unmarried'? I believe it arises from the mixture of two modes of representation. This should become clear in a moment.
* * *
It is odd the way (I) can inspire phrases like 'Law of Metaphysics' while 'Everything exists' is much less likely to. Of course, for the latter to be false, there would have to be things which do not exist, which is obviously contradictory. OK, but isn't that also true of the following natural description of “what it would take for (I) to be false”?: there would have to be things which do not bear the identity relation to themselves, or distinct objects between which it holds.
It is as though the two conflicting things here are less similar, a bit further apart in language, than in the existence case.
What if I had said 'there would have to be things which aren't themselves, or things which are other things'? That sounds more flatly contradictory; no one, unless doubly perverse, would formulate a “Law of Metaphysics” running 'Things are themselves'. (Butler's Dictum is not generally presented as a Law of Metaphysics.) The flavour changes markedly when we bring in 'identical', talk of 'bearing the identity relation' etc. That is where we begin to get the mixture of modes of representation.
A natural picture to illustrate, or put by, 'Everything is what it is' would be:
Somehow, instead of seeing it that way, philosophical thinkers try to give it another, impossible sort of application – or so I want to say. But what is this other application, and how am I to describe it without falling prey to the sort of confused thinking I am trying to correct?
What makes these mistakes, or confusions, hard to correct is their slippery, elusive character. (This no doubt has to do with the way so many of our key terms slip and slide so naturally between slightly different uses.)
It is not as if my opponent thinks their Law of Metaphysics is empirical, or anything like that. Rather, they have a spurious category for it, I want to say – or, at the very least, they spuriously categorize it.
They fail to make a category at the right level, so to speak – fail to regard identity statements as being sufficiently special in their fundamental workings. Instead, they are assimilated to other relational statements, giving rise to the conception of a special sort of fact (which we have some kind of special access to, perhaps).
A purported picturing of the world as being one way rather than another. A purported division in some space of representations. Also, perhaps some vague conception of an analogue of empirical verification – as it were, rational perception (cf. Plato, Goedel, the notion of an “eye of Reason”). The sort of thing no one would ever feel like positing for 'Bachelors are unmarried' (except perhaps in a heroic effort to be consistent).
How is it that this comes about here, and not, say, with 'Bachelors are unmarried'? I believe it arises from the mixture of two modes of representation. This should become clear in a moment.
* * *
It is odd the way (I) can inspire phrases like 'Law of Metaphysics' while 'Everything exists' is much less likely to. Of course, for the latter to be false, there would have to be things which do not exist, which is obviously contradictory. OK, but isn't that also true of the following natural description of “what it would take for (I) to be false”?: there would have to be things which do not bear the identity relation to themselves, or distinct objects between which it holds.
It is as though the two conflicting things here are less similar, a bit further apart in language, than in the existence case.
What if I had said 'there would have to be things which aren't themselves, or things which are other things'? That sounds more flatly contradictory; no one, unless doubly perverse, would formulate a “Law of Metaphysics” running 'Things are themselves'. (Butler's Dictum is not generally presented as a Law of Metaphysics.) The flavour changes markedly when we bring in 'identical', talk of 'bearing the identity relation' etc. That is where we begin to get the mixture of modes of representation.
A natural picture to illustrate, or put by, 'Everything is what it is' would be:
Things are represented as dots and are shown “just being themselves”. Whereas the natural picture to put by (I) is:
And here we get the feeling of a contrast, of substance, of something being ruled out. Namely stuff like:
The mixture of two modes of representation here consists in the fact that each dot in the picture is taken to represent a different object, and yet lines are drawn indicating the identity relation – lines which could only be of use if two dots sometimes represented one object.
* * *
With identity statements, merely specifying the relation in question (identity) and the pair of objects involved in the ascription (assuming the names involved refer) fails to specify 'what is said' in any natural sense, however minimal. This problem cannot be avoided either by expelling repetitive identities from language – there can be multiple different non-repetitive identities concerning one and the same object.
If you find this strange or unacceptable, I suggest you have in the back of your mind a conception of relations which identity does not really fall under. Perhaps you are picturing something like the dots above, and imagining relations as encoding further information on top of that structure. This may be a good conception, in which case you should stop classifying identity as a relation, stop classifying identity statements along with propositions like 'John loves Mary'. This, rather than, e.g., moving to an unnatural conception of 'what is said' – which is, I think, what hard-line Millians such as Scott Soames do.
This move in semantics to an unnatural conception of what is said, then, may have an origin related to that of the conception of a Law of Metaphysics discussed critically above. Also, they can be made to support each other: if it's a 'substantial metaphysical fact' that everything is identical to itself, then a repetitive identity is an instance of this, and so perhaps it inherits some metaphysical substantiality for itself, in which case perhaps there is an informative, substantive extensional core to extensionally equivalent identity statements – something which they all say. Conversely, if we take this last thing for granted: what sort of thing does a repetitive identity say which an empirically informative counterpart also says? It had better not be something trivial, since the latter doesn't seem to say anything trivial, in any sense of 'say'. And so what sort of thing is this non-trivial thing which repetitive identities say? Perhaps we could call it 'an instance of a Law of Metaphysics'!
* * *
With identity statements, merely specifying the relation in question (identity) and the pair of objects involved in the ascription (assuming the names involved refer) fails to specify 'what is said' in any natural sense, however minimal. This problem cannot be avoided either by expelling repetitive identities from language – there can be multiple different non-repetitive identities concerning one and the same object.
If you find this strange or unacceptable, I suggest you have in the back of your mind a conception of relations which identity does not really fall under. Perhaps you are picturing something like the dots above, and imagining relations as encoding further information on top of that structure. This may be a good conception, in which case you should stop classifying identity as a relation, stop classifying identity statements along with propositions like 'John loves Mary'. This, rather than, e.g., moving to an unnatural conception of 'what is said' – which is, I think, what hard-line Millians such as Scott Soames do.
This move in semantics to an unnatural conception of what is said, then, may have an origin related to that of the conception of a Law of Metaphysics discussed critically above. Also, they can be made to support each other: if it's a 'substantial metaphysical fact' that everything is identical to itself, then a repetitive identity is an instance of this, and so perhaps it inherits some metaphysical substantiality for itself, in which case perhaps there is an informative, substantive extensional core to extensionally equivalent identity statements – something which they all say. Conversely, if we take this last thing for granted: what sort of thing does a repetitive identity say which an empirically informative counterpart also says? It had better not be something trivial, since the latter doesn't seem to say anything trivial, in any sense of 'say'. And so what sort of thing is this non-trivial thing which repetitive identities say? Perhaps we could call it 'an instance of a Law of Metaphysics'!
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