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.

Wild Thoughts on Modality, Propositions and Concepts

Here. (Readers who like Sprachlogik for its clear-headedness are duly warned that this title is no joke.)

Individual concepts and modality at Philosophy etc.

I've got a guest post at Philosophy etc., 'An advertisement for individual concepts'. The comments are more substantial than the original post.

The proposal made there is closely connected with the ideas featured in my Sketch of a Way of Thinking about Modaliy, part 2 of which will be posted in the next few days.

Sketch of a Way of Thinking about Modality - Part 1

[This is old and my thinking on the subject has changed quite a bit (for the better I'm pretty sure). It may be of historical interest, or interesting if you're interested in how my ideas have developed. See my more recent 'Necessity as an Attribute of Propositions' - 22/10/15]

[UPDATE: This sketch, except for parts of part 2, will soon be made mostly redundant by a paper I am working on. I expect to make a draft of this paper available in early November. A link will appear here. - TH 13/10/2011]

[UPDATE 2: The paper mentioned above is here.]

[UPDATE 3, March 2013: What appears below has been left so far behind that I'm almost embarrassed about it. For my latest on these topics, see An Account of Subjunctive Necessity.]

This is the first installment of a two-part series of posts where I aim to sketch some ideas about modality which will feature in a book I am working on, Necessity and Conceptual Systems. The material is still very much under development, and I apologize for the obscurities which the reader will inevitably find in it. Comments and criticisms are very welcome.

In this first part, I will introduce the approach, and indicate how it handles the necessary a posteriori, using 'Hesperus is Phosphorus' as a case-study. In part 2 I will discuss the notion of de re modality, of essence, and natural-kind examples such as 'Water is H20', as well as some more general issues which arise on my approach (especially to do with epistemic modality and ascriptions of intentional content).

In the Golden Age of analytic philosophy, necessarily true propositions were widely taken to be those which are satisfied by (or 'come out true' on) all configurations of some conceptual or linguistic system. Possibility was understood in terms of satisfaction by at least one configuration. Our conceptual system, our means of understanding the world, is here thought of as something like a model, or a machine, which has moving parts, and which can be put into various positions or configurations. Each configuration can be thought of as corresponding to, or satisfying, or even being, a set of propositions. (I have taken many liberties in the formulation of this description.)

Conceptual or linguistic systems of the kind in question were thought to be describable with "semantical rules" for a language, and necessary propositions were thus commonly taken to be a priori and true "in virtue of the meaning" of the terms involved (cf. Carnap's Meaning and Necessity, Ayer's Language, Truth and Logic). This yields a notion of necessity reminiscent of the notion of truth-functional tautologousness. (Earlier, in the Tractatus - which was a major inspiration to both Ayer and Carnap - this relationship is much closer than mere reminiscence.)

This sort of view was attacked by Quine in at least two ways (cf. his 'Truth by Convention', 'Two Dogmas of Empiricism'). Quine's undifferentiated picture of language had a sobering or worrying effect, but it did not stop people carrying on with some version of the view in question. This is connected with the fact that it amounted to a kind of quietism or abstinence with respect to the relevant sorts of notions (semantic, modal), rather than a sustained attempt to attain positive insight about them.

The really decisive blow to the Golden Age view of modality came from Kripke. His fundamental contribution was to persuasively argue that the a priori does not coincide with the (metaphysically) necessary, and relatedly, that epistemic modality ("what could be the case") is to be distinguished from metaphysical modality ("what could have been the case" in a certain unrestricted sense). This contribution was closely bound up with Kripke's ideas concerning naming and reference, more on which in a moment. The recognition of the necessary a posteriori in particular, and the associated idea that conceivability doesn't entail possibility, has led to a reaction against views of modality of the Golden Age sort.

(About 'metaphysical modality': one sometimes hears it said of a philosopher that they countenance metaphysical modality, as though this indicates that the person holds some sort of doctrine, which may be quite esoteric. But 'metaphysical modality' is just a label for me - synonymous with 'subjunctive modality' - for a notion "detected" in the logic of language. That said, someone who felt this notion was, e.g., a trivial artifact of the way we happen to talk, rather than a deep artifact of the way we think, would probably not want to use this label.)

My approach to modality retains the view that necessity - metaphysical necessity - can be fruitfully understood in terms of invariance through all configurations of a conceptual system. But it also takes Kripke's separation of the a priori and the metaphysically necessary fully to heart. This latter point is one respect in which my approach differs from that of the two-dimensional semanticists. Another key contrast is that the possible worlds framework is not fundamental to my view.

Broadly speaking, I handle the necessary a posteriori by doing two things. Firstly, I work with a much more fine-grained notion of 'conceptual system' than did the logical empiricists. (The sense of 'fine-grained' here should become clearer in a moment.) Secondly, I embrace a certain kind of semantic externalism - roughly, the view that sense doesn't determine reference (other ways to put this which for me are roughly equivalent: intension doesn't determine extension, concept doesn't determine object).

I will illustrate how this works with respect to a classic example of the necessary a posteriori: 'Hesperus is Phosphorus'.¹

I follow Kripke in holding that proper names do not have reference-determining senses (which hangs together with semantic externalism via Putnam's idea of Twin Earth), and also that proper names do not have a semantics which can be given in the form of general conceptual content such as definite descriptions, or clusters thereof (irrespective of whether this content can be said to determine reference).

I do not, however, accept the (to my mind very strange and confused) idea that proper names are 'mere tags' (Ruth Barcan Marcus's phrase), that all there is to the meaning of a name is its referent, etc. This idea is sometimes associated with Mill's claim that names have no 'connotation', only 'denotation', and also with the phrase 'direct reference'.²

We have individual concepts - concepts of individuals, of particular objects - and we often associate these with proper names. This sheds light on Kripke's rigid designation thesis (the thesis that a referring proper name designates the same object in all possible worlds at which that object exists). 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 associated individual concept. We may thus distinguish rigid designators such as ordinary proper names, which designate rigidly because they are directly associated with individual concepts, from other rigid designators such as definite descriptions in mathematics.

Once we recognize individual concepts in this way, we can say that when someone accepts that Hesperus is Phosphorus (having previously taken them to be distinct), there is a change in their conceptual system - in the relevant fine-grained sense. Of course, in a more coarse-grained (and more ordinary) sense, we can say that they have before and after the same conceptual system. The fine-grained change consists in the unification of two individual concepts. The original concepts, we might say, are not blended irrevocably but remain as aspect-concepts united under a common master. From now on, it should be kept in mind that conceptual systems will usually be individuated here in this fine-grained sense.

In the former conceptual system (call this 'the Babylonian system'), where the Hesperus-concept is separated from the Phosphorus-concept, the distinctness of Hesperus and Phosphorus is invariant through all configurations of the system; if one positively believes that Hesperus and Phosphorus are distinct, one will say that, although it might conceivably turn out that Hesperus is Phosphorus after all, given that it isn't, Hesperus could not have been Phosphorus. (And one will of course be wrong.) In the latter conceptual system (call this 'our system'), where the Hesperus- and Phosphorus-concepts are unified, the identity of Hesperus and Phosphorus is invariant through all configurations of the system; when one knows that Hesperus is Phosphorus, one will say that, although it might conceivably turn out that Hesperus is distinct from Phosphorus after all, given that it isn't, Hesperus could not have been other than Phosphorus.

Now, with our fine-grained understanding of conceptual systems in place, I maintain that we can still say that all (metaphysically) necessarily true propositions are satisfied by all configurations of their host conceptual systems. We can even say that a truth is metaphysically necessary iff it is satisfied by all configurations of its host system. We just can't say that all propositions which are satisfied by all configuration of their host systems are necessary truths. So far, then, we can say what distinguishes necessary from contingent truths, but we can't say what distinguishes necessary truths from other proposition which are satisfied by all configurations of their host systems - we might call these 'false propositions of necessary character'. What can we say that will do this?

I think we can say something like: a proposition P is necessarily true iff it is satisfied by all configurations of its host system and the concepts involved in P are jointly adequate to their objects with respect to P.

First I want to say that I am not concerned to provide a reductive analysis of modal concepts. Relatedly, I am happy for the relevant modal notions and my ternary relation of 'adequacy' to be explanatory of each other; I do not suppose it is a one-way street, where my notion does all the explaining, nor do I take my notion to be more "fundamental" in any metaphysical sense. I am interested in showing (and making) connections.

I will make a start at explicating the above proposal by indicating how it applies to the 'Hesperus is Phosphorus' case. In the Babylonian system, the Hesperus-concept and the Phosphorus-concept are not unified (are taken to represent distinct objects), but they both have the same object, the same extension, and so together (jointly) they are inadequate to their objects with respect to 'Hesperus is not Phosphorus'. So their proposition 'Hesperus is not Phosphorus' fulfills the first condition given above, before the 'and' - it is satisfied by all configurations of their system - but it does not fulfill the second. Our Hesperus- and Phosphorus-concepts, which also have the same extension, are in contrast united, as aspect-concepts, under a common master concept (the concept of Venus). Hence they are adequate to their objects - or object - with respect to our proposition 'Hesperus is Phosphorus'.

Why do I not simply say that a proposition is necessarily true iff it is satisfied by all configurations of its host system and its concepts are jointly adequate to their objects? Why do I add 'with respect to that proposition'? I will explain this with an example. Assume for the sake of argument that Hesperus (Venus) is necessarily not intelligent - i.e. that Hesperus could not have been intelligent. Now, suppose someone believes that Hesperus is intelligent, and necessarily so - loosely speaking, that it is part of their concept of Hesperus that it is intelligent. In that case, their concept of Hesperus would not be adequate to its object with respect to 'Hesperus is intelligent'. But they may know, for all that, that Hesperus is Phosphorus, and so their concepts of Hesperus and Phosphorus might be jointly adequate to their object with respect to 'Hesperus is Phosphorus'.

Conversely, someone may know that Hesperus is necessarily not intelligent, while mistakenly believing that Hesperus is not Phosphorus, thus having an adequate conceptual situation with respect to propositions about the intelligence of Hesperus, but not with respect to propositions about the identity of Hesperus and Phosphorus.

Speaking broadly, necessity is, on this understanding, not simply a matter of a proposition having a certain status in a conceptual system. It is, as well as that, a matter of the system being adequate to its objects with respect to that proposition. The adequacy of some set of concepts to their objects obviously depends on the identity (and nature) of those objects - and this is not in general determined by the system. (This is how semantic externalism fits in.) Hence you cannot, in general, tell simply by looking at a proposition in a system whether or not it is necessarily true - there are a posteriori necessities.


The compatibility of externalism with rigid designation
(Postscript added 14 August, 2011.)

It may look as though there is a tension between my externalist claim that the extension of an individual concept is not in general determined by the concept itself, and the claim that names rigidly designate: if names are tied to individual concepts, and individual concepts do not in general determine their extension, it looks like a given individual concept can have different extensions in different environments. This is so (at least, when we individuate concepts internally) but there is no real tension here: the rigidity applies to names in use - names tied to token individual concepts embedded in an environment. Individual concepts are not like general concepts: the whole point of them is to apply to one particular object. And so the contrast between names and definite descriptions remains: when we consider counterfactual scenarios and hold the meaning of our terms fixed, our names which are tied to individual concepts always refer to 'the same object'.

This is all perfectly compatible with the fact that the same concept, in a different environment, might be connected up to a different object. The extension of our individual concepts may in some cases even change over time: if an object we know is replaced with a substitute, and we don't notice, after a while it will become true to say that our individual concept has changed its extension. But we don't let the extension change "across possible worlds" when representing counterfactual scenarios using a particular individual concept in a particular environment.

Part 2.

Individual concepts are under-discussed in contemporary philosophy. For further online reading on what they can do, see:

- My post at Philosophy, et cetera, 'An advertisement for individual concepts'

- A recent article by linguist Barbara Abbott, 'Support for Individual Concepts'.

- John McCarthy's article, 'First Order Theories of Individual Concepts and Propositions'. (Warning: arguably contains some use-mention confusion.)

Interestingly, neither of these authors are (primarily) philosophers.

1 I pass over one well-known issue here, to do with the fact that Hesperus/Phosphorus might not have existed. There is a discussion of this on Greg Frost-Arnold's blog. If one is really worried about this, consider instead the example 'If Hesperus exists, then Hesperus is Phosphorus'.

2 It should be noted, however, that Mill's claim is appropriate if 'connotation' is interpreted to mean 'reference-determining sense' or 'general conceptual content', and likewise that the phrase 'direct reference' is appropriate if 'direct' is interpreted to mean 'not via general conceptual content' or 'not via reference-determining sense'.

Three True Semantic Externalisms

Putnam's catchphrase 'Meanings ain't in the head', and the associated label 'semantic externalism', are not without ambiguity, as many authors have pointed out. My aim here is not to separate and discuss everything which 'semantic externalism' could reasonably mean, or even everything it has meant to philosophers, but rather to identify three different true and insightful things it can mean. I believe that having all three insights, and having them separate, can pay big dividends in the philosophies of language and modality, but I won't try to make a case for that here.

We can look at language and thought on three levels:

1. Local marks and noises, local neural and sensory events.
2. Sense; game and moves; conceptual system and configuration; intension; internal content.
3. Reference; extension; external content in abstraction from internal.

We can individuate thoughts and propositions according to 2 alone, 3 alone, or 2 and 3 together. For example, on 2 alone, 'I am here' is the same proposition when you an I utter it, or when I utter it in different locations - we are making the same sort of move in the same sort of language-game. On 3 alone, 'I am here' expresses the same proposition as 'John is at location X' when the former is uttered by John at location X - extension (reference) is the same. On 2 and 3 together, 'I am here' is distinct when uttered by different people and at different locations, due to difference in extension, and also distinct from 'John is at location X' when both are uttered by John at X, due to conceptual difference (difference in sense, intension, language-game).

To take another kind of example, on 2 alone, 'Hesperus is Phosphorus' is distinct from 'Hesperus is Phosphorus', but identical to the Twin Earthian thought or proposition 'Hesperus is Phosphorus' - call this thought or proposition 'Twin-"Hesperus is Phosphorus"'. On 3 alone, 'Hesperus is Phosphorus' expresses the same proposition as 'Hesperus is Hesperus', but not the same proposition as any thought about Twin Venus. On 2 and 3 together, 'Hesperus is Phosphorus' is distinct from 'Hesperus is Hesperus' (due to difference with respect to 2), as well as from Twin-'Hesperus is Phosphorus' (due to difference with respect to 3) and from Twin-'Hesperus is Hesperus' (due to difference with respect to both 2 and 3).

The three semantic externalisms which I want to identify and separate can all be seen as underdetermination theses. They are:

Wittgenstein externalism: 1 doesn't determine 2 (i.e. local happenings don't determine intension).
Intension-based Putnam externalism: 2 doesn't determine 3 (i.e. intension doesn't determine extension).
Happenings-based Putnam externalism: 1 doesn't determine 3 (i.e. local happenings don't determine extension).

Note that the first two externalisms don't imply the third - while the relation of determining is arguably transitive, the relation of not determining isn't. Note also that 'determine' here means 'always determine' or 'generally determine' - determination in some cases is not being ruled out. I should also say that I attach no great importance to the labels used here for the three externalisms.




Finally, note that the expression 'internal content' above is not supposed to express the problematic notion of narrow content. Narrow content is often thought of as a kind of minimal intension, sense or internal content which is determined by happenings inside an agent's brain or body. That problematic notion isn't being discussed here.

I am currently working on a book on modality, in which this separation plays a key role.

Tristan Haze

Suggested reading

For Wittgenstein externalism: Wittgenstein's Philosophical Investigations. Also his Zettel, and other later work.

For the Putnam externalisms: Putnam's classic 1975 paper 'The meaning of 'meaning', published in Minnesota Studies in the Philosophy of Science 7:131-193, reprinted in The Twin Earth Chronicles: Twenty Years of Reflection on Hilary Putnam's ``the Meaning of `Meaning' '' edited by Andrew Pessin & Sanford Goldberg, 1996, published by M. E. Sharpe.