Forthcoming in The Philosophical Forum

My paper 'Propositions, Meaning and Names' is forthcoming in the Winter 2018 edition of The Philosophical Forum. It derives from a chapter of my PhD thesis and sketches an approach to the topics mentioned in the title. The approach to propositions and meaning it develops has other applications besides the question of the meaning of proper names, but that will have to wait (for the most part). This is my longest publication to date and is fairly ambitious. I've blogged here over the years about some of the ideas in it, and am glad to see them making their way to publication. It seems that philosophers who are especially interested in these topics often have to start from the beginning, and this is my start.

Granularity and Quine

In a former post I introduced the idea that meanings and the like can be carved up at different granularities. This was motivated using Kripke's famous puzzle about belief, and introduced as offering the key to a solution.

I plan to develop this doctrine of semantic granularity further, adding detail and removing certain possible misconceptions, in future posts. For the time being, however, I will defer that and outline a further application of the doctrine (the original one being to Kripke's puzzle). Several more applications have occurred to me since arriving at the doctrine, each time bringing great joy and encouragement, since they seem to suggest that it really is a good idea. Accordingly, this will in all probability be the first of a series of posts which as a whole may be called 'Applications of Granularity'.

The application I want to outline this time is to Quine's famous skepticism about meaning and propositions. Quine's position is not so much that there are no such things as meanings or propositions (where these latter are construed as sentence-meanings) - although he does sometimes seem committed to that too - but rather that semantic notions such as that of meaning are somehow second-rate, badly-behaved, and not worthy of serious thought.

(Quine's peculiar conception of serious thought, first-rate concepts, real scientificality and the like - which could be called a scientistic conception, but is, to be fair to science, really much narrower than that; what we really have is a bias in favour of notions which Quine for his own peculiar reasons thinks of as first-rate scientific ones - is a very interesting matter which I would like one day to scrutinize here at some length. But this will have to wait till another time.)

Now, the application of the idea of semantic granularity I want to outline here is not to the refutation of Quine's position, although it may go some way toward breaking its grip. Rather, my focus is the explanation of Quine's position; what was going on with him when he came to it, and secondly, what is going on when other thinkers feel his arguments to have force.

Quine's skepticism focuses on the, to him, confusing individuation-behaviour of intuitive notions of meaning. To give a sense of his position, I will first quote from a section of McGrath's Stanford Encyclopedia of Philosophy entry on propositions, a section called 'The Individuation of Propositions', and then give a couple of illustrative quotes from Quine himself.

Some Quotes Illustrating Quine's Position

This section can be skipped or skimmed depending on how much of a sense one wants to get of Quine's position, or how much reminding one needs. To skip it, just scroll down to 'The Diagnosis'.

Probably needless to say, these quotations by themselves, to a reader unfamiliar with Quine's writings on the subject, will not give the full picture of what he had to say; it was an issue he picked up again and again and said a lot about.

Here is McGrath in the SEP:

Some philosophers, notably W.V.O. Quine, recognize the existence of certain sorts of abstract entities but not others at least partly on the basis of concerns about identity conditions. Quine granted the existence of sets, in part because they obey the extensionality axiom: sets are identical iff they have the same members. When it came to properties, relations and propositions, however, he found no such clear criterion of identity. The property of being a creature with a heart, he noted, is distinct from the property of being a creature with a kidney, even if all the same things exemplify the two properties. 

It is a controversial matter whether Quine was right to demand such rigorous criteria of identity as a condition for acceptance of a class of entities. However, even if Quine asks too much, any good theory of propositions ought to have something to say about when propositions are identical and when they are distinct. Developing theories which give such accounts in a way that fits well with intuitive data concerning propositional attitude ascriptions would enhance our reasons to accept propositions.

Now a few illustrative Quine quotes.

From 'Two Dogmas of Empiricism' (1951 edition):

For the theory of meaning the most conspicuous question is as to the nature of its objects: what sort of things are meanings? They are evidently intended to be ideas, somehow -- mental ideas for some semanticists, Platonic ideas for others. Objects of either sort are so elusive, not to say debatable, that there seems little hope of erecting a fruitful science about them. It is not even clear, granted meanings, when we have two and when we have one; it is not clear when linguistic forms should be regarded as synonymous, or alike in meaning, and when they should not.

This paragraph from a section of Philosophy of Logic boldly entitled 'Propositions Dismissed':

The uncritical acceptance of propositions as meanings of sentences is one manifestation of a widespread myth of meaning. It is as if there were a gallery of ideas, and each idea were tagged with the expression that means it; each proposition, in particular, with an appropriate sentence. In criticism of this attitude I have been airing the problem of individuation of propositions.

This passage from the 'Meaning' entry in the playful Quiddities:

[...] what is it for two expressions to have the same meaning? They cannot have exactly the same use, for when we use one we are not using the other. One wants to say rather that they have the same meaning if use of the one in place of the other does not make any relevant difference. The question of sameness of meaning, then, comes down to the question what to count as relevant difference.

I see no prospect of a precise answer, nor any need of one. Everything real and objective having to do with our use of expressions, and hence with their meaning, can be said without positing any relation of full synonymy ofexpressions, or sameness of meaning. In describing ways in which an expression is used we may be said still to be explaining its meaning, but there is no lingering trace of a museum of labeled ideas nor of any clear and simple relation of paraphrase or translation.
[...]
I urged at the end of the entry on IDEAS that there is no place in science for ideas, and under KNOWLEDGE that there is no place in the theory of knowledge for knowledge. Now we find me urging that there is no place in the theory of meaning for meanings, commonly so called.

Finally, if a bit more detail is wanted, here are selections (kept in order) from a more nuanced discussion in section 42 of Word and Object, 'Propositions as Meanings':

A large part of learning 'apple' or 'river' was learning what counts as the same apple or river reexposed and what counts as another. Similarly for 'proposition': little sense has been made of the term until we have before us some standard of when to speak of propositions as identical and when as distinct.
[...]
If we are content to define identity of propositions by synonymy of sentences, there is no evident objection to calling propositions meanings of eternal sentences. Misgivings as to what sort of object such a meaning might be could be allayed, if one pleases, by identifying it with the very class of all those mutually synonymous sentences that are said to have it. The worry that remains is the worry over a suitable notion of synonymy of eternal sentences. If propositions are to serve as objects of the propositional attitudes, then the broad sort of sentence synonymy talked of in § 14 [Details of that don't matter here - TH] would be unsatisfactory as a standard of identity of propositions even if adequately formulated. It would be too broad. For it would reckon all analytic sentences as meaning an identical proposition; yet surely one would not want to regard all analytic sentences as interchangeable in contexts of belief or indirect quotation, especially if all mathematical truths are regarded an analytic. Hence Lewis and Carnap have resorted to narrowed derivative relations of synonymy, or intensional isomorphism in Carnap's phrase, as better suited to interchange in contexts of propositional attitude.
[...]
Mates, Church, and Scheffler have argued that Carnap's intensional isomorphism (and Lewis's earlier construction of similar character) is still too broad for interchange in contexts of propositional attitude. Putnam and Church have responded with proposals for further tightening the relation. Scheffler still finds loopholes, but part of his criticism can be annulled [...]
We do have our analyticity intuition, but it grades off. [...] Now there is no objection to a graded notion of synonymy or of analyticity, supposing it made reasonably clear; but it is unlikely to contribute directly or indirectly to a standard of identity of propositions. For propositions have to be the same or distinct absolutely; identity, properly so-called, knows no gradations.
These reflections count only against hoping to base identity of propositions on some sort of intensional isomorphism derived from the broad sort of sentence synonymy which is interdefinable with analyticity. We might still hope to construct some approximation to intensional isomorphism suitable for identity of propositions, in some other way than from the elusive broad notion of sentence synonymy.
[...]
This last point [No need to worry about what that was - TH] has the germs of an argument not only against our specific plan of a structural synonymy concept as a standard of propositional identity, but against the whole idea of positing propositions. For, insofar as we take such a posit seriously, we thereby concede meaning, however inscrutable, to a synonymy relation that can be defined in general for eternal sentences of distinct languages as follows: sentences are synonymous that mean the same proposition. We would then have to suppose that among all the alternative systems of analytical hypotheses of translation (§§ 15, 16) which are compatible with the totality of dispositions to verbal behavior on the part of the speakers of two languages, some are "really" right and others wrong on behaviorally inscrutable grounds of propositional identity. Thus the conclusions reached in § 16 may of themselves be said implicitly to scout the whole notion of proposition, granted a generally scientific outlook. The difficulties cited earlier in the present section are merely by the way. The very question of conditions for identity of propositions presents not so much an unsolved problem as a mistaken ideal.

The Diagnosis

As we can see, Quine's objection to meanings, propositions, etc. was based on the idea that there is no single, clear criterion of identity for them. Given the doctrine of semantic granularity, this is no surprise and no objection. The individuation of these things differs at different granularities. In the grip of preconceptions about how language must properly work, Quine mistook a feature for a bug.

(I say that 'the individuation of these things differs at different granularities', but that form of expressing the point could be misleading and sound like some kind of antirealism - I will address that at length in a future post. For now: the point could be more carefully put in terms of the truth-values of synonymy or non-synonymy sentences, or of identity or distinctness statements about meanings, propositions etc.

This is connected with Quine's point in the Word and Object selection above, 'For propositions have to be the same or distinct absolutely; identity, properly so-called, knows no gradations.' On my approach, it is not that identity needs to have gradations, rather that identity statements with meaning- or proposition-designating phrases come out with different truth-values when operating at different granularities.)

It is instructive here to see how I, with my doctrine of granularity, can and indeed must agree with a lot of the things Quine says on the way to his hostile position, and how with the doctrine of semantic granularity on board, we can see that the hostile position doesn't follow.

For example: 'The very question of conditions for identity of propositions presents not so much an unsolved problem as a mistaken ideal' from the Word and Object selection. Indeed, if the question is construed as asking for a single, all-purpose set of conditions, it does present a mistaken ideal. What the doctrine of granularity says is that the conditions are different at different granularities, and that is part and parcel of the power and flexibility of semantic notions as bundlers and separators of linguistic items and occurrences.

And from Quiddities, 'The question of sameness of meaning, then, comes down to the question what to count as relevant difference. I see no prospect of a precise answer, nor any need of one.' Note the 'one'; the whole point of the doctrine of granularity is that there is no one answer here.

I hope I have conveyed in outline how the doctrine of semantic granularity can explain and perhaps help break the grip of Quine's hostility towards meanings, propositions and the like. This application will, if I am right, only become clearer and seem stronger with the development of the doctrine I intend to pursue in future posts.

Note finally that despite the focus here (especially in the Quine quotes) mostly being on propositions construed as sentence-meanings, all this applies just as much to sub- and super-sentential meanings as well, for instance with names and the individuation of their "meanings", which I construe as name-uses or individual concepts, or with the meanings of larger things like arguments or speeches or books.

References

McGrath, Matthew (2008). Propositions. Stanford Encyclopedia of Philosophy.

Quine, W.V.O. (1986). Philosophy of Logic. Harvard University Press.

Quine, W.V.O. (1987). Quiddities: An Intermittently Philosophical Dictionary. Belknap Press of Harvard University Press.

Quine, W.V.O. (1951). Two Dogmas of Empiricism. Philosophical Review 60 (1):20–43.

Quine, W.V.O. (1960). Word and Object. The MIT Press.

Names and the Publicity of Meaning

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.

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.

Empty Names and Negative Existentials

Singular negative existential propositions such as 'Santa Claus does not exist' can be made to look puzzling without any explicit theoretical view on board, with Socrates-style questions such as: how can anything not exist? How can one ever truly say that something doesn't exist? For if one is right, there is no such thing as what one is talking about, and therefore one is talking about nothing.

Or: 'Santa Claus doesn't exist' – what is this thing which doesn't exist? How could there be such a thing?

For those who have a Millian conception of naming (and associated views of propositions), the problem of negative existentials assumes a particularly acute form. If all there is to the meaning of a name is its bearer, and if substituting co-referring names does not affect the 'proposition' (not my usage) expressed by the sentence, then how can a statement like 'Santa Claus does not exist' mean anything at all? Furthermore, how can it be true? And how can different true negative existentials have different meanings, as they seem to do?

All these questions push the Millian toward analysing existence statements – giving an account of what they really mean. (Witness for example Kripke's tortured discussion in Reference and Existence. Of course, he never officially and unequivocally endorses Millianism, but he's flirted outrageously with it in public and finds it intuitive.)
 
Having a non-Millian conception of naming such as the one I propose, on which names are recognized as being tied to individual concepts (or having uses - roles in the systems of language they occupy - which are semantically relevant), makes it a lot easier to answer these questions. But this does not mean that we are using individual concepts (or name-uses) as elements in an analysis of existence statements.

'N does not exist' does not, for instance, mean exactly the same thing as'“N” has no bearer' or 'The “N”-concept has empty extension' (that is, on a natural and sufficiently fine-grained conception of proposition-meanings): the existential proposition is not about a name or a concept.

We can say it is about N, if we understand 'about' as not having existential import, or we can say that it is not about any real thing, but it would muddy the waters intolerably to say that it is about a name or a concept.

And yet we can see what would make a person want to say that it is about a name or a concept. What we can truly and properly say is that, in 'N does not exist', the function of the name 'N' is not to pick out an object – rather, this name (rather than some other name) is used in order to bring a particular individual concept (or name-use) into the act (though I would not want to say 'under consideration', for it need not become an object of thought).

But then what do we say about the function of a name in a proposition like 'John is tall'? It is no less true to say that 'John' functions to bring a particular individual concept or name-use into the act, but here we can also say that it functions to pick out an object. But some have found it intuitive to say that a name functions purely to pick out an object. Given a certain very narrow concept of 'function', this is fine too, although it could be misleading – it could lead to the troubles of Millianism.

Let us now take a representative selection of the questions raised at the beginning of this section, showing how they can be answered with the conceptions of propositions and naming I favour. This is done without giving an analysis of existence statements (in the classical sense of giving something else which they are then said to mean). As with identity statements, the trick is to treat existence statements on their own terms, and to recognize that they occupy a special role for us, and work in a quite particular way.

How can anything not exist?

Just as we sometimes use names in a way which carries existential import, as in 'John is tall', and sometimes use them in a way which does not, as in 'Santa Claus does not exist', 'Some children believe in Santa Claus', we use terms like 'there is', 'something' and 'anything' in two different ways: with or without existential import. A clear example of the latter sort of use would be a kid saying 'I don't believe in Santa Claus, the Easter Bunny, or anything like that'.

The difficulty and puzzlingness of the above question derives from this ambiguity. The thorough answer is: in the sense of 'anything' etc. in which they carry existential import, nothing can fail to exist – i.e. it is not the case that it is possible for anything to not exist, but in the sense of 'anything' etc. in which they do not carry existential import, there are indeed things which do not exist.

At this point, individual concepts (notions of things), or name-uses can be brought into consideration, to help us make sense of the fact that we talk like this. What gives rise to it is that we sometimes have individual concepts without objects, name uses where the name lacks a bearer. We then formulate propositions which, if we treat them by analogy with propositions like 'John is tall' and 'Someone is in this room', look as though they would have to involve (existing) things in order to be true, in the way that these propositions would have to involve John and a person in the room – but in fact they face no such requirement. We use them in connection with objectless concepts, bearerless names etc. (and this connection is quite different from that which holds between 'John is tall' and John himself).

How can one ever truly say that something doesn't exist? For if one is right, there is no such thing as what one is talking about, and therefore one is talking about nothing.

In light of the above, this question can be disposed of quickly. We can truly say that something doesn't exist by using 'something' in the sense in which it doesn't carry existential import, and in virtue of the fact that we have objectless individual concepts and involve them in our talk. In the sentence after the question ('For if one ...'), 'there is no such thing as' and 'nothing' are used in their existential-import-having senses, and so there is no real conflict in what is being said here. It is just being said in a potentially misleading way.

How can a statement like 'Santa Claus does not exist' mean anything at all?

The proposition works by means of the fact that the name 'Santa Claus' brings an individual concept (or a way of using a name) into the act – not by referring to it, but because that is the concept tied to that name (or that is the way that name is used). The proposition is true iff the concept (or name-use) of 'Santa Claus' has an object.

This is not to say that the proposition means the same as any proposition about concepts or name-uses, or that the proposition holds of just the same possible situations as those of which what is said on the right hand side of the 'iff' holds. We are using the biconditional here not to give an analysis but to give a necessary and sufficient condition for the proposition in question, which we have before us, actually being true.

How can different true negative existentials have different meanings, as they seem to do? 
 
By bringing different individual concepts (or name-uses) into the act. 

Reference

Kripke, Saul A. (2013). Reference and Existence. The John Locke Lectures. Oxford University Press. 

Propositions: A Neo-Wittgensteinian Approach

(Added October 2016: my most up-to-date treatment of propositions can be found in Chapter 6 of my PhD thesis. This is an early, undeveloped attempt.)

As I use the term 'proposition', propositions are propositional signs (e.g. declarative sentences) together with their internal uses or meanings, plus any external projective relations borne to reality by the component signs.

This is partly inspired by the conception of propositions espoused in the Tractatus, but also the conception of meaning espoused in Part I of Philosophical Grammar, 'The Proposition and its Sense' and various contemporaneous documents of Wittgenstein's thought– that is, the middle Wittgenstein. Roughly speaking, the 'projective relations' component comes from the Tractarian conception, and the internal meaning component comes from the later conception of meaning.

Before explaining, in my own terms, these conceptions as I have them, I will briefly quote these sources. Here is entry 3.12 of the Tractatus:

I call the sign with which we express a thought a propositional sign.—And a proposition is a propositional sign in its projective relation to the world.

And here is an excerpt from remark 27 of Philosophical Grammar:

[…]

A name has meaning, a proposition has sense in the calculus to which it belongs. The calculus is as it were autonomous. - Language must speak for itself.

I might say: the only thing that is of interest to me is the content of a proposition and the content of a proposition is something internal to it. A proposition has its content as part of a calculus.

The meaning is the role of the word in the calculus.

The meaning of a name is not the thing we point to when we give an ostensive definition of the name; that is, it is not the bearer of the name.

I do not, however, want to give the impression that I agree with everything in Part I of Philosophical Grammar. Indeed, immediately after the passage quoted above, Wittgenstein asserts that the name 'N' is synonymous with the definite description 'The bearer of “N”'. I think this is a sheer mistake, for Kripkean reasons which were not highly visible when Wittgenstein was writing – these expressions exhibit, for example, different behaviour across counterfactual scenarios. But this doesn't mean I don't agree with Wittgenstein's general way of thinking about (internal) meanings as roles in language-systems – I just don't agree about this case, i.e. don't agree that 'N' and 'The bearer of “N”' play the same role.

And remark 36:

If we look at the actual use of a word, what we see is something constantly fluctuating. In our investigations we set over against this fluctuation something more fixed, just as one paints a stationary picture of the constantly altering face of the landscape.

When we study language we envisage it as a game with fixed rules. We compare it with, and measure it against, a game of that kind.

And from the earlier work in Philosophical Remarks:

3. […] The words 'Colour', 'Sound', 'Number' etc. could appear in the chapter headings of our grammar.

7. Grammar is a 'theory of logical types'.

15. What does it mean, to understand a proposition as a member of a system of propositions? (It's as if I were to say: the use of a word isn't over in an instant, any more than that of a lever.)

I will now briefly explain what I mean by 'projective relations' (or 'external meaning') and 'internal meaning'. As a preliminary, I should say that I make no presumption that I mean what Wittgenstein meant in the Tractatus by 'projective relations'. The ideas are certainly related, but I think not likely to be the same, especially since I have two components side by side here – internal and external meaning – the first of which is inspired by later work of Wittgenstein's. The second component I have been inspired by the Tractatus to gloss as 'projective relations', but since in the Tractatus it was the only component besides the sign, it seems reasonable to suppose that the Tractarian notion may have covered more, so to speak, than mine. Furthermore, this way I adopt of distinguishing between internal and external aspects of meaning – although it owes a lot to Frege's distinction between sense and reference and similar earlier distinctions, and does some of the same work, is not quite there even in the later Wittgenstein, although his work no doubt helped us along the way to it. Rather, it begins in a clearly recognizable form with Putnam's Twin Earth thought experiment and subsequent discussions of semantic externalism.

I will try to explain what I mean by 'projective relations' by explaining how, and why, this notion differs from that of 'referential relations': we can distinguish between my name 'O' for some object in my environment, and a name 'O' used in exactly the same way (internally speaking), but for another object, e.g. by a Twin Earth counterpart of me. For this, the notion of referential relations does the job. But there is an analogous distinction we can make for terms which fail of reference. For example, 'John' when I falsely believe that a man called John came to my friend's house, when my friend has in fact fabricated the whole thing, and 'John' used in the same way on Twin Earth. Both terms fail to hit a mark, so to speak, but their trajectories are in different places. Or: both fail to catch anything in their net, but the nets (which are the same) are cast in different places. So we can say that 'John' and Twin Earth 'John', as well as 'O' and Twin Earth 'O', bear different projective relations to the environment. As for referential relations on the other hand, both 'John' and Twin Earth 'John' bear none, and so cannot be differentiated on that score.

To be clearer about what I mean by '(internal) uses or meanings': by 'internal use' I do not mean to include all the historical facts about how the symbol gets used – rather, I use it similarly to 'internal meaning', namely to mean something like: an expression's role in the language-system it belongs to. Uses or meanings can be individuated in different ways – at different granularities, and factoring in different sorts of features..

So, we may say that propositions are propositional signs together with their internal meanings and their external meanings. And internal meanings can be carved up at different granularities – what you may at one granularity call two instances of the same proposition may at another granularity count as (instances of) different propositions.

As with my account of names, this account of propositions can only be properly understood once the distinction I make between internal and external meaning, and my doctrine of semantic granularity, are properly understood. I will try to explain these things in forthcoming posts.

There seems to me to be an important methodological difference between, on the one side, this conception of propositions which I advocate, and on the other side, certain conceptions prominent in contemporary analytic philosophy. The conceptions I have in mind could be called more technical – we may roughly characterize them by saying that they perform theoretical identifications; they conceive objects, often using formal methods such as basic set theory, and then identify propositions with these. Two basic examples are:

(1) Sets of possible worlds conceptions, on which, for example, the proposition that snow is white is identified with the set of possible worlds in which snow is white.

(2) Russellian conceptions, on which, for example, the proposition that Socrates is mortal is identified with the n-tuple whose first member is Socrates, and whose second member is mortality.

And things get more sophisticated from there – to take three examples: Russellian annotated matrices, two-dimensional semantic values, and objects comprising, among other things, sentences of formal languages.

It is important to realize that there is a methodological difference here, lest it appear that my account is so to speak on the same level, playing the same game, only less precise and less technically developed than, e.g., those mentioned above.

To my way of thinking, those objects which are sometimes identified with propositions are models of, so to speak, real propositions. It may in some cases of other views be indeterminate, or in determinate cases may vary from case to case, whether there is substantive disagreement here or only terminological difference. I am not trying to police other people's use of words, and if they want to call technical constructions like those mentioned above 'propositions', I am not going to object (although I prefer to talk differently). But when these things are said to be – without the words I am about to use being given special technical meanings – objects of belief, or meanings of sentences, or the things we convey in communication, or work with in deductive arguments, I become uneasy at the very least, and in many cases (e.g. set-of-worlds conceptions) disagree confidently. Such ideas seem like category-mistakes to me, or perhaps more true to the case, so impossibly revisionary that they constitute methodologically misguided philosophy (I am thinking of David Lewis here).

My method, then, is to work with semantic concepts more as they are, treating them as more sui generis. I think this is what Wittgenstein did, and what Moore did (I have not gotten a lot out of Moore directly), and I think it is also the way Kripke works in Naming and Necessity and auxilliary works like 'A Puzzle about Belief' (but this is not to deny that much of that work was informed and inspired by Kripke's formal work). I am trying to refine special versions of these notions for philosophical purposes – I am not doing ordinary language philosophy, for example, or concerning myself directly with how “the folk” think about meaning. Rather, I am using my natural lights as one of those folk, together with what I've learned from philosophers, and trying to do philosophy of language in a way which stays close to the phenomena and works with intuitively compelling considerations.

One reason this sort of methodology has fallen out of favour in some circles, I think, is Quinean skepticism about semantic concepts, and hangovers therefrom. Few still go as far as Quine, but the confusing individuation-behaviour he cited as his main reason for abandoning serious use of semantic concepts - the phenomenon I explain in terms of semantic granularity-shifts – seems now to militate, not toward self-conscious abandonment of semantic concepts, but supposed “reconstructions” or cleaned-up versions of them which are so far from the real thing, that they are better thought of as models – models which involve serious idealizations and often great limitations.

So far, I have said in broad outline what propositions are on my account: propositional signs together with their internal meanings (i.e. systematic roles) and their external meanings. I have said a little bit about internal/external meaning, deferring further explanation to other posts. And I have made some methodological remarks about what sort of account this is.

A word on my concept of 'propositional sign': this is no purely syntactic category (whatever that means exactly). Its objects – the things which are propositional signs – are indeed to be regarded as syntactic items, not intrinsically carrying meaning, but the concept which picks them out should probably be thought of as doing so via the broadly semantic notion of a proposition. That is, propositional signs do not count as such in virtue of their intrinsic syntactic features, but because they get used propositionally. This of course means that we haven't got any kind of reductive analysis here of 'proposition', or a 'propositional sign', or 'used propositionally' for that matter, but that was never the intention. (I am sympathetic to Wittgensteinian views on this matter. For example, I think it can be said that 'proposition' is not a sharply bounded concept. Perhaps it can be said to be a family resemblance concept. Perhaps it can be said to function by means of paradigms.)

A word on type-token ambiguity: I have deliberately left my account type-token ambiguous. Just as with sentences, I think we should have a type-token ambiguity which can be resolved when need be, when talking about propositions on my conception. So that we can say (in “token” mode) things like 'Regarding that proposition written on that piece of paper ...' and 'Regarding the proposition that just came out of your mouth ...' without any inaccuracy (e.g. without having to maintain that, strictly speaking, we were talking about instances of propositions, so that to make what we said both explicit and literally correct we should have to add 'instance of a' before 'proposition' in the exampled phrases), but also, for example, 'He uttered the same proposition as I did'.

A word on usage: 'proposition' is often used in such a way that no particular signs – whether tokens or types – are part of the entity in question. For example, when it is said that 'Snow is white' and 'Schnee ist weiss' 'express the same proposition'. I have no special problem with talking like that, and am open to doing it myself in informal contexts or the context of someone else's philosophy, but on my account, and the way I like to use words in conjunction with it, what we are talking about in such cases is not a proposition, but a proposition-meaning. (We may think of proposition-meanings as comprising both internal and external aspects, as propositions minus the sign, so to speak. And of course we may also pick out just one component.)

I will conclude by mentioning some applications to, or connections with, other topics. One application of the account is in solving Frege's Puzzle, in the way indicated in the post on names. Another, where granularity comes into its own, is with Kripke's Puzzle (about belief), which I will discuss in a future post. Among other applications which will be dealt with in future posts are accounts of three major notions in propositional typology: the a priori/empirical distinction, the analytic/synthetic distinction, and the distinction between necessity and contingency in the metaphysical or subjunctive sense.

References

Wittgenstein:

Wittgenstein, Ludwig (1974). Philosophical Grammar. Blackwell.

Wittgenstein, Ludwig (1975). Philosophical Remarks. University of Chicago Press.

Wittgenstein, Ludwig (1922). Tractatus Logico-Philosophicus. Dover Publications.

Other:

Saul A. Kripke (1980). Naming and Necessity. Harvard University Press.

Saul A. Kripke (1979). A puzzle about belief. In A. Margalit (ed.), Meaning and Use. Reidel.

Names: Between Mill and Frege

Followup posts: 

Empty Names and Negative Existentials

Names and the Articulation Assumption

Names and the Publicity of Meaning

(Added October 2016: my most up-to-date treatment of names can be found in Chapter 6 of my PhD thesis. This is an early, undeveloped attempt.)

Kripke at the beginning of 'Vacuous Names and Fictional Entities':

One of the main concerns of my previous work (Kripke 1980) [Naming and Necessity] is the semantics of proper names and natural kind terms. A classical view which Putnam mentioned, advocated by Mill, states that proper names have as their function simply to refer; they have denotation but not connotation. The alternative view, which until fairly recently has dominated the field, has been that of Frege and Russell. They hold that ordinary names have connotation in a very strong sense: a proper name such as ‘Napoleon’ simply means the man having most of the properties we commonly attribute to Napoleon, such as being Emperor of the French, losing at Waterloo, and the like. Of course, intermediate views might be suggested, and perhaps have been suggested.

My aim here is to propose just such an intermediate view. In future posts I will flesh out the proposal and offer some speculations about why it has not been generally adopted already.

As is well known, the cardinal problem with Millianism about names is Frege's Puzzle, given in his famous article 'On Sense and Reference': Millianism leaves us unable to semantically distinguish, in a systematic compositional way, 'Hesperus is Phosphorus' from 'Hesperus is Hesperus'; since Hesperus is Phosphorus, both names involved in those propositions have the same referent, and thus, on the Millian view, the same meaning. But the two propositions do not seem to have the same meaning - the first is an empirical scientific discovery, and the second is not. Further problems arise with singular negative existentials like 'Santa does not exist' - here, in addition to Frege's-Puzzle-type problems of differentiation ('Santa doesn't exist' and 'Noddy doesn't exist' mean different things, even though both names are the same as regards their referents; neither has one), we have the problem of seeing how any of them could be true, or even mean anything.

As is also well known, the cardinal problems for descriptivism - what Kripke above calls the view of Frege and Russell - are given by Kripke in Naming and Necessity. I will not try to summarize Kripke's whole case properly, but it is often divided into three prongs: the semantic objection, the epistemological objection, and the modal objection. Very roughly, the semantic objection is 'Which description or descriptions constitute the meaning of some given name? Isn't any answer bound to be arbitrary? And since different people might associate different descriptions with the same name and the same object, how aren't they just talking past each other when they use the name?'. The epistemological objection is 'Take any plausible meaning-giving description or cluster thereof. I can surely use the name in question correctly without knowing all this - I don't have to know much of anything about someone in order to pick them out with a name'. And the modal objection is 'Suppose "Aristotle" means "the teacher of Alexander". How does it come about, then, that "Had things gone differently, Aristotle might not have been the teacher of Alexander" seems true, while "Had things gone differently, Aristotle might not have been Aristotle" seems false?'.

I am not concerned here to argue that no versions of Millianism or descriptivism have legs. I will not, for example, argue against Millianisms which try to fill the apparent semantic gap in their accounts by means of linguistic pragmatics, nor will I argue against "wide-scope" or "actualizing" versions of descriptivism. I want to propose what I think is an elegant and natural view in between Millianism and descriptivism which avoids the problems of both.

I have two ways of expressing what I take to be essentially the same view, but others may prefer to think of me as offering a disjunction of two structurally similar views. The first is in terms of the use of a name, or the role it plays in the system of language to which it belongs. The second is in terms of individual concepts - the ideas of particular objects which we (sometimes) tie names to. I more-or-less identify these things in my own thinking, but since the concepts 'use' and 'role' on the one hand, and 'concept' and 'idea' on the other are quite different (as are the uses or roles of these terms!), it is worth giving both formulations, in case someone prefers one over the other. The use-conception is inspired, at least in part, by Wittgenstein (particularly the middle period, for example Philosophical Grammar). The concept/idea-conception is more traditional.

The view, then, is that names have uses, or are tied to individual concepts, and that these are partly constitutive of their semantics. (We may say that uses, or individual conepts, constitute the internal meanings of names.)

Individual concepts or name-uses do some of the work Frege wanted to do with his senses, but there are important differences. One important difference is that Frege held, of his senses, that they determine reference, whereas individual concepts or name-uses avowedly do not do this in general; someone on Twin Earth can use a name in the same pattern (i.e. with the same concept or use), but with a different referent - in a word, semantic externalism is true of individual concepts or name-uses. (We can of course have a notion which adds an extensional component to the individuation of these things, so that two concepts or uses are distinct if they have different objects, or different projective relations to reality, but we can also isolate the internal component.)

Another important difference is that, while Frege indicates that the sense of a name is that of, or can be given by means of, a definite description, I hold no such thing with respect to individual concepts or name-uses. Names are in an important sense indefinable, as Wittgenstein held in the Tractatus. But that does not mean their referents are all there is to (what you might, though possibly misleadingly, call) their meanings, i.e. Millianism doesn't follow. (Wittgenstein expresses Millianism too in the Tractatus, when speaking of 'names', although there is an exegetical question whether this term is meant to cover ordinary proper names, which is what I am talking about, or names in some philosophically idealized sense, e.g. names in an "ideal logical language".)

Individual concepts or name-uses combine, in a very simple way, the difference-making power of Frege's senses with invulnerability to Kripke's arguments against descriptivism. 

Frege's Puzzle is solved, much in the same way as Frege did with his senses: 'Hesperus is Phosphorus' and 'Hesperus is Hesperus' are different propositions with different meanings, since 'Hesperus' and 'Phosphorus' are tied to different individual concepts and have different uses. (Likewise with 'Clark Kent' and 'Superman'.)

But unlike with Frege's senses, this conception of names is not only compatible with Kripke's rigid designation thesis, but predicts it, at least when formulated in terms of individual concepts: if names are associated with individual concepts - concepts of particular objects - then it is immediate that they will designate the same object in all possible worlds where that object exists; designating another object is out of the question, since we are holding fixed the meaning of the proper name - the associated individual concept.

Individual concepts or name-uses also allow for an important kind of flexibility, which we must recognize in order to solve Kripke's puzzle about belief. We can individuate name-uses and individual concepts - as well as the uses or meanings of other terms, and other concepts, and larger units such as propositions - at different granularities, so that what at one granularity might count as instances of different uses/concepts may count on another (coarser) granularity as instances of the same. This is an important ingredient of my view, and will be discussed in a future post.

I have now at least mentioned all the main ingredients of the view of names I want to propose. Further posts - on semantic granularity, on internal and external meaning, and on why the view I propose hasn't already been generally adopted - will fill out the picture. I will conclude this post by trying to avert a couple of possible misunderstandings:

(1) The term 'individual concept' is sometimes used in philosophical logic and technical philosophy of language to refer to functions from possible worlds or state-descriptions to individuals (or similar constructions). I am not using it that way. For one thing, that way of going would make the problem of empty names harder - i.e., it would reduce the utility of my approach with respect to the problem of empty names - since one needs individuals for the functions to map to. For me the notion of an individual concept is more basic - it is just a refined version of the ordinary idea of an idea of an object.

(2) I am not saying that any sort of theory which associates names not with name-uses or individual concepts (in my sense), but with something else, and calls the associates 'the semantic values' of the names, is wrong. My attitude here is that expressed by Chalmers in this passage from 'The Foundations of Two-Dimensional Semantics':

A methodological note: in this paper I will adopt the approach of semantic pluralism, according to which expressions can be associated with semantic values in many different ways. Expression types and expression tokens can be associated (via different semantic relations) with extensions, various different sorts of intensions, and with many other entities (structured propositions, conventionally implied contents, and so on). On this approach, there is no claim that any given semantic value exhausts the meaning of an expression, and I will not claim that the semantic values that I focus on are exhaustive. (I think that such claims are almost always implausible.)

References

Chalmers, David J. (2006). The foundations of two-dimensional semantics. In Manuel Garcia-Carpintero & Josep Macia (eds.), Two-Dimensional Semantics: Foundations and Applications. Oxford University Press.

Frege, Gottlob. (1952). first pub. 1893. ‘On Sense and Reference’, in P. Geach and M. Black (eds.) Translations from the Philosophical Writings of Gottlob Frege, Oxford: Blackwell.

Kripke, Saul A. (1980). Naming and Necessity. Harvard University Press.

Kripke, Saul A. (2011). Vacuous Names and Fictional Entities. In Saul A. Kripke (ed.), Philosophical Troubles. Collected Papers Vol I. Oxford University Press.

Wittgenstein, Ludwig. (1922). Tractatus Logico-Philosophicus. Dover Publications.

Wittgenstein, Ludwig. (1974). Philosophical Grammar. Blackwell.