Alice: I don't know what you mean by ‘glory’.

Humpty Dumpty: Of course you don't − till I tell you. I meant ‘there's a nice knock-down argument for you!’

A: But ‘glory’ doesn't mean ‘a nice knock-down argument’.

HD: When I use a word, it means just what I choose it to mean − neither more nor less.

A: But what you mean by ‘glory’ is different from what I mean by ‘glory’. Which one is what ‘glory’ really means?

HD: There is no such thing as what ‘glory’ means simpliciter.

A: And what does ‘simpliciter’ mean?

HD: Hmm. ‘Simpliciter’ means ‘absolutely’, ‘without qualification’.

A: So, ‘simpliciter’ does in fact have a meaning! And surely so does ‘glory’. And so on. Words must have a meaning. For, otherwise, the sounds we make are all meaningless!

HD: I didn't mean to say that ‘glory’ has no meaning simpliciter either! Rather what I think is that its meaning is both mind-dependent and language-dependent. Perhaps I should explain …

A: I hope it won't take long.

HD: First of all, a person can mean something; can use a word to mean something. For example, we might ask: what did you mean, or what were you referring to, when you said such-and-such?

But, second, also words can mean something. In the second case, what a word means depends on the language in question. Then, roughly, what a person usually means in using a word is what the word means in the language they speak. What I mean by ‘glory’ is what ‘glory’ means in the language I speak; what you mean by ‘glory’ is what ‘glory’ means in the language you speak.

A: The puzzling thing is how these words, or strings, and meanings get connected together.

HD: Indeed! How are strings ‘glued’ to their meanings or referents? How does ‘cat’ get glued to cats? And ‘star’ to stars? And ‘Aristotle’ to Aristotle?

I think there are two rather different kinds of ‘glue’. I think people keep mixing these up. The first involves the language alone, and I will call it the meaning-relation for a language: this connects strings to their meanings. On that, I am a conventionalist. But the second connection involves a speaker or agent, and I shall call it the cognizing relation: this relates minds to the language they speak.

A: For my language, it's my mind that does the connecting. So, I am puzzled …

HD: The distinction is needed because there are languages that others speak which may have the same strings, but different meanings; and there are languages that no one speaks. One may study languages independently of their speakers; or their minds, if you prefer.

A: I see: languages exist independently of speakers and minds. The speaker has left the building!

HD: I want to argue that a language is an abstract entity: a system of syntax and, in some cases, meaning functions. A language is not a concrete thing, with a mass, or a location, or a density, or a speed. A language may have intrinsic properties quite independently of the properties of a speaker who speaks the language.

A: But there are speakers who, as you say, ‘cognize’ languages?

HD: Of course!

A: I have never heard this word ‘cognizing’ before; but somehow I get what you mean …

HD: You had never heard the word ‘magnesium’ until you studied chemistry, but you picked it up. Just as then, your idiolect has just undergone a small shift to a new one.

A: The speakers have to re-enter the picture somewhere …

HD: The speaker, or their mind, is related to the language. One speaks a language by cognizing its syntax and its meaning functions. I speak a certain idiolect, Humptyese, by cognizing its syntax and meaning functions; whereas you speak your idiolect, Alicese, by cognizing its syntax and meaning functions.

A: On your view, the meaning relation is intrinsic to the language itself?

HD: The languages we are discussing are interpreted languages. But we might consider uninterpreted, or partially, or multiply interpreted, languages too, if we like.

A: That reminds me of Professor Tarski's work. Tarski defines the set of truths for certain kinds of ‘formalized’ languages. Tarski says that the object languages are required to be interpreted; and that one must have a translation from the object language to the metalanguage in order to formulate T-sentences, such as,

Tarski's object languages are simple in many respects, in order to have a precise syntactic description. But they are interpreted.

HD: And from this, one is led in a certain direction, which many authors see as counter-intuitive. In fact, some authors see it as a reductio ad absurdum of his work.

A: Why is defining the truths for a well-defined language problematic?

HD: Well, notice that the T-sentence for ‘Schnee ist weiß’ does not mention the language users, their usage patterns, their mental states, intentions, causal factors, and so on and so on. It states a property of an abstract system of syntax and meaning functions for an interpreted language, namely German.

A: Aha. I see! These authors see Tarskian semantics as missing something crucial.

HD: Yes; these authors insist that the semantic properties of a language, and in particular, the reference or meaning relation, have to be explained in terms of natural or intentional facts involving the speaker. Perhaps the use of the string; the mental states involved in speech-acts producing the string; its role in reasoning; its role in larger theories; its causal connections to its referent; and so on. Professor Putnam argued, in his 1985 article, ‘A Comparison of Something with Something Else’, that, because Tarski's approach omits facts about intentions and usage of strings, this work is not even semantics, and should be called a ‘non-semantic conception of truth’. Professor Field argued, in his 1972 article, ‘Tarski's Theory of Truth’, that Tarski merely reduced truth to primitive denotation, which should then be reduced to a physical relation.

A: So, this would be a reduction along the lines of,

HD: Yes, but it is difficult to carry this programme through; consequently, there appears to be a deep philosophical problem of making sense of semantic relations. Two kinds of approach have been offered in reply. First, naturalistic reductionism, reducing the ‘real’ semantic (reference or meaning) relation to relations involving causation, or language usage, or intentional states; and, second, deflationism, treating ‘refers’, ‘means’ and ‘true’ in a disquotational manner.

For an example of the former, several recent authors have argued for a kind of semantic reductionism now called ‘reference magnetism’. This requires a certain metaphysical doctrine: only certain classes and relations of things are natural. These are perhaps the extensions of physical properties and relations that figure in the physical laws; or perhaps extensions whose elements are naturally similar in some way. Second, it is proposed that these special classes and relations are thought of as being the only ones that are ‘eligible’ − that is, permitted − to be referents of predicates in languages. The reduction proposes that a necessary condition on an extension being a referent is its naturalness. If an extension is not natural, then it can't be a referent of a predicate. This approach is meant to rule out certain strange, crazy or weird extensions that philosophers have come up with.

On the second, deflationary, approach, the strings ‘true’ and ‘refers’ are governed by primitive disquotational axioms, taken as being analytic, constituting their meaning.

For example, the axioms one learns might be,

On this deflationary view, this is all one needs to say about reference and truth. Translational indeterminacies between languages of the sort discussed by Professor Quine and others are not only unproblematic, but represent important insights into any properly scientific approach to the topic of meaning and reference. But, at least for semantics, I disagree with both naturalistic reductionism and deflationism.

A: I am familiar with deflationism. But why do you disagree with the first approach?

HD: In a nutshell, I think it conflates semantics with cognition; semantic facts are metaphysically quite different from cognitive ones, and in particular, in their modal status. A semantic relation might be a meaning-relation or a referential string-thing relation, for an interpreted language. A cognitive relation might be the relation between an agent and the language they cognize; or the ‘assigning’ relation between an agent, strings and meanings.

A: So you take the distinction between semantics and cognition very seriously?

HD: I think the usual philosophical problems that have been identified do not really lie in semantic theory. Instead, I wish to argue that the semantic reference relation − for example, the relation that the string ‘Schnee’ bears to snow in German − cannot be a natural relation, in the sense of being a relation that contingently holds between items.

A: Cannot?

HD: A reference relation for a language is simply any string-thing relation one likes.

A: I am not sure why you think this …

HD: First, semantic relations are not binary relations. They are, at least, ternary, and involve language relativity. For example, consider the phrase

Of course, what a string means in a language, might depend on context too, thus,

Thinking of L as determining a function, μ_L, one could write,

$$\hskip -204pt\mu_L(\sigma \comma\; C)=M.$$

The crucial point is that semantics describes languages, not simply strings on their own; semantics studies systems of expressions and functions like μ_L. A string doesn't ‘naturally’ connect referentially to some meaning or referent. For semantic notions, language relativity is unavoidable. And I think the same is true for phonology, syntax and pragmatics. For example, how ‘ouch’ is to be pronounced, what its lexical role is, and what its governing pragmatic rule is: these are language-dependent.

A: Now I see: yes, this point is made by Tarski. The same string of symbols or phonemes might mean different things in different languages. In principle, anything could mean anything.

HD: We may call this Semantic Conventionalism. In his 1916 posthumous work General Course in Linguistics, Ferdinand de Saussure wrote that the sound signal is ‘arbitrary in relation to its signification, with which it has no natural connexion in reality’. And this is all there is to the conventionality of language.

A: So, a language L with its meaning function μ_L can be conventionally chosen. Much as a co-ordinate system for the sphere is, to a large degree, conventional. On this conventionalist view, no languages are ‘forbidden’?

HD: That sounds very 1968, but yes. Indeed, in ‘On Sense and Reference’, Gottlob Frege wrote, ‘Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something’. Some languages might be socially forbidden … and some languages might be weird, at least from the perspective of other speakers. But our limited experience causes us to underestimate how many languages there are.

There is a language in which ‘gloobydooby’ means Birmingham City FC, even though no one cognizes that language. The fact that there is no person who speaks a language in which ‘gloobydooby’ means Birmingham City FC is no reason to deny the existence of such a language.

A: In logic, we examine infinitary languages, like L _ω1,_ω, with infinitely long strings. And there are languages with uncountably many constants − for example, a constant c _r for every real r. The possibilities are endless.

HD: But no one cognizes such languages. Presumably, for biological and psychological reasons. It's hard to see how a human mind might cognize a language with infinitely long strings, or with uncountably many constants, without assuming an infinitary inflation of human cognitive capacities.

A: So, such languages are like Mr Wilde's fox hunters: unspeakable. I rather like this idea. For languages, existir es no ser hablado!

HD: I do not understand …

A: ‘To exist is not to be spoken’.

HD: Oh, like esse est percipi? I see. They do not require embodiment. We can study them, define them and prove facts about them, independently of whether anyone does or doesn't speak them.

A: An example involves Gödel's famous incompleteness result. This can be summarized by saying that the set of truths of the interpreted language L of arithmetic is not computably enumerable. No computer program can enumerate them all, without including some falsehoods or even inconsistencies. This property of L does not depend on speakers of L.

HD: Oh to be a logician, like you, Alice! I am just an egg.

A: But remarkably logical, for an egg.

In logic, we think of an intepreted language as a pair L = (S_L, I _L), where S_L is the syntax and I _L is the interpretation function, which specifies a domain and referents or denotations for the non-logical terms and meanings for the logical terms. For example, the interpreted language L of arithmetic is (S_L, N), where S_L is a first-order language with identity, with a constant ‘0’ and function symbols ‘S’, ‘ + ’ and ‘ × ’; and N is the interpretation of S_L whose domain is the set {0, 1, 2, …} of natural numbers, and which interprets ‘¬’ as ‘not’, ‘∧’ as ‘and’, ‘∀’ as ‘for all’, ‘ = ’ as identity, and where ‘0’ denotes 0, ‘S’ denotes the successor function, ‘ + ’ denotes addition and ‘ × ’ denotes multiplication. An L-sentence ϕ is true in L iff N satisfies ϕ, using Tarski's definition. Gödel's results imply that the truth set for L is not computably enumerable.

This conception of languages is in accord with yours too: ‘a system of syntax and meaning functions’. So I am curious: is your view of language as an abstract entity a widely held one?

HD: Arguably, three of the founders of semantic theory, Professors Carnap, Tarski and Montague held a view like this. But the view is stated quite clearly by Professor Lewis, in his 1970 article, ‘General Semantics’:

And he restates this view in his 1975 article, ‘Languages and Language’:

And a similar view was defended by Professor Soames in a 1984 article, ‘What is a Theory of Truth?’:

And Professor Soames adds,

A: But it is still very counter-intuitive to understand language not as a sociological or psychological phenomenon, involving language speakers, their usage patterns, and so on. Suppose we call this the social-pyschological view …

HD: Well, Professor Lewis also describes this more intuitive view too:

Lewis tries to do justice to both the abstract view and the social-psychological view by examining what it is for a population to use a language. Perhaps I can return to this later?

A: Professor Field's main objection to Tarski, if I remember right, is that the definiens for a semantic concept is simply a ‘list’. For example,

HD: My response is simply that this is precisely what one expects on the abstract view: definitions of semantic relations are listlike because semantic notions are language relative and languages are like functions. Notice that the name of the language disappears in the definiens. The resolution of the conundrum is that reference is not some peculiar physical or natural relation; rather, an interpreted language is – well, more exactly, determines – a function. So, for example, German is a language L such that ρ_L(‘Schnee’) = snow, and so on and so forth. Consequently, if one looks for something else that explains this referential ‘glue’, one will not find it. Referential glue is quite arbitrary and promiscuous.

A: Perhaps the following is an analogy. Consider a function F from alphabet {‘a’, ‘b’, ‘c’} to, say, the set {0, 1, 2}. Such a function is a set of ordered pairs. For example, suppose F is {(‘a’, 1), (‘b’, 2), (‘c’, 0)}. Then we may give the following definition of F:

Since F might be any function, there is nothing wrong with this. There is no special intrinsic connection between the arguments and values, no special glue, other than that they appear in the given ordered pairs. There is no such thing as the ‘natural’ function from the alphabet {‘a’, ‘b’, ‘c’} to the set {0, 1, 2} of referents.

Still, if I look at the Tarskian definition of truth or reference for a language, I see no semantic terms in the definiens. So, Tarski does seem to give a reduction of semantic terms …

HD: Tarski's definitions of semantic notions replace semantic notions with logical and mathematical ones along with notions from the object language. The definitions of semantic notions do not, however, explain ‘x refers in L to y’ in terms of some more basic natural, physicalistic or intentional binary relation that is language-independent or language-transcendent. Semantic relations just aren't what these authors think they are.

I think that, at bottom, these authors are making precisely the mistake that Professor Lewis alluded to, and ‘only confusion comes of mixing these two topics’: semantic relations, which connect linguistic strings to their meanings, are being mixed up with cognitive relations, involving agents' minds. The cognitive glue is quite different from the semantic glue.

A: Is the following an objection to your view? I surely could have spoken a different language, L say, whose meaning function maps the string ‘cat’ to dogs. And if I had spoken that language L, then I would not have been speaking the language that I do in fact speak. For ‘cat’ means cats in Alicese, but means dogs in L.

HD: Yes …

A: So, if ‘cat’ means dogs in L, then L cannot be Alicese. So, the semantic fact that ‘cat’ means cats in Alicese couldn't have been otherwise!

HD: Quite so! Indeed, as Professor Soames notes:

A: So, Alicese has an essential semantic property: the property of being a language in which ‘cat’ means cats.

HD: This point has appeared many times before, as the modal objection to the semantic conception of truth. For example, because semantic axioms,

behave as metaphysical necessities, Professors Field and Putnam took this as an objection.

A: I see … but, prima facie, that seems reasonable.

HD: Similarly, Professor David, in his 1994 book Correspondence and Disquotation, argues that, on a correspondence theory of truth, semantic facts − such as what state of affairs a sentence corresponds to in language L − should be contingent. But it seems to me perfectly compatible with a correspondence theory of truth that a semantic fact of the kind,

should be necessary. It may be contingent whether the state of affairs of snow's-being-white obtains or not; it may be contingent that anyone does or doesn't speak L. But it is not contingent that snow's-being-white is the state of affairs that L assigns to the string ‘Schnorbl este fnoffle’. In fact, one simply says that the value of the string ‘Schnorbl este fnoffle’ under L is snow's-being-white. With a distinct value, we just get a distinct language.

A: But, in the case of semantics, does not the extension of ‘cat’ in English change from world to world?

HD: Yes. But when we consider possible worlds semantics, such a language L specifies a reference or denotation function on the worlds, say ρ _L. Given a predicate P, and world w, each extension ρ _L(P, w) is a set or relation at that world w, the values of this function ρ _L. But values of a function should not be confused with the function itself. In different worlds, the extensions of the same word or string may be different. However, the reference function ρ _L doesn't itself change or vary in some further sense. The contingency lies in the cognizing relation; the necessity resides in the reference relation.

A: So, your position is this: an interpreted language L determines a semantic reference or meaning function, μ_L. Defining μ_L is separate from defining any other function, say μ_L* for some other L*. Every language is different from every other, much as every function is different from every other. If we compare a definition of the reference relation ρ_English for English with a definition of the reference relation ρ_French for French, there is nothing that ρ_English and ρ_French have ‘in common’. They're functions from strings to things. To suppose otherwise would violate Semantic Conventionalism.

HD: Yes.

A: It is initially counter-intuitive to recognize that semantic facts are necessities. But on reflection, I agree with you.

HD: And this yields the crucial conclusion: semantic facts cannot be reduced to use facts. For necessities cannot be reduced to contingencies.

A: In a sense, the semantic ‘gluing’ of strings to their meanings by languages is mathematical; and consequently not reducible to a physical relation at all. Whereas cognitive ‘gluing’, of a mind to the strings that the mind uses and therefore to some language, is not arbitrary in the same way.

HD: Yes, precisely.

A: Can nominalism make sense of your account of languages and language cognition? For languages are mathematical entities, and language cognition is now understood as a form of mathematical cognition!

HD: The languages that an agent cognizes are mixed or impure mathematical entities, to use the jargon from the philosophy of mathematics. An example would be a set of concrete things. The set is an impure set. Similarly, when an agent cognizes a language L, this capacity must, I think, involve a cognitive capacity to recognize and discriminate symbol tokens, such as letter or phoneme tokens: these are concrete things. Even so, the syntactical entities of any interesting language L are, normally, expression types: arbitrarily long finite sequences of symbols. Though all the individual symbols will have tokens, not all the sequences of these symbols will: there are some, of course, but infinitely many sequences are too long to be tokened.

Motivated by nominalistic concerns, one might try and make do with just the tokens instead. Professors Quine and Goodman tried, in a 1947 article ‘Steps Toward a Constructive Nominalism’, to formulate syntax without assuming types. But Quine, recognizing insurmountable difficulties, abandoned the proposed view rather quickly. For example, how many strings are there in the language of Professor Field's reformulation of Newtonian gravitational physics? There are ℵ₀ strings in this language! So one ends up denying that there are numbers, while asserting that there are strings, indeed ℵ₀-many; but these strings are finite sequences, which are themselves abstract.

A: I agree that this is odd, to say the least. Even so, isn't linguistics also an empirical science, concerned with the psychology of speakers? But on the view you defend, the semantic facts for a language are necessities; and these cannot be explained by facts about how strings are used, for such facts are contingent; while semantic facts are necessary. So, semantic facts cannot be explained by usage!

HD: I think the same goes for phonology, syntax and pragmatics too.

A: But this is where it becomes quite puzzling. For we want linguistics to be an empirical science. Do you think the semantic axiom that ‘Schnee’ refers in German to snow is empirically testable?

HD: I think a confusion arises here because German is a natural language, and is thought of in terms of a language community of speakers. So, to check facts about German I might, for example, travel to Munich as an amateur field linguist, and perform some bio-culinary experiments on Bavarians, observing their behaviour around cats and doughnuts, and so on; upon hearing utterances of ‘Das ist eine Katze!, ‘Zwei Krapfen, bitte!’, I accumulate evidence that, in German, ‘Katze’ means cat and ‘Krapfen’ means doughnut.

A: That seems correct! Why is there any confusion?

HD: Let us call the usage facts U-facts. Let us call the semantic facts S-facts. But let us also introduce a category of C-facts, of the form,

We might add certain parameters too, such as ‘cognizes at time t, at world w’. But let us simplify. To further simplify our analysis, suppose we accumulate U-facts for a single agent, A.

I believe that these U-facts may form evidence in favour of a more complicated claim, involving a C-fact and an S-fact, joined by a quantifier. Namely the contingent claim that,

Such a hypothesis helps to explain A's word usage. But I still maintain that the semantic subclause expresses some essential property of whatever L is asserted to exist.

If I accumulate U-facts for another agent, B, they might form evidence for a contingent claim that,

From these two, we can reasonably begin to conjecture that A and B cognize similar idiolects.

A: So, the logical role of U-facts − word usage, associated intentions, inferential practices and so on − in linguistic theory is to constrain the C-facts, what language an agent cognizes?

HD: That is the idea. If an agent uses the word ‘Katze’ in a certain way, then they might cognize a language L such that ‘Katze’ refers in L to dogs.

A: So, it seems that, properly speaking, the various agents in a speech community do not, usually, cognize exactly the same language.

HD: Precisely.

A: But meaning in the sense of what an individual speaker means is related to their use of strings and their mental representational states?

HD: Yes. Though it needn't be public or conscious. On the contrary, the mental state of cognizing a language is largely private and unconscious. I think this is the norm. I have even heard people disparage this view as Humpty Dumptyism, but I am not upset by that!

A: I suppose that Professor Wittgenstein is the nemesis of any Humpty Dumptyist?

HD: Opposition to private languages is found in Professor Dewey's writings before it was adopted by Wittgenstein many years later. For both, the arguments were behaviouristic or naturalistic, as Quine was to emphasize, for example, in his 1968 John Dewey Lectures, ‘Ontological Relativity’. There, Quine himself repudiates as ‘uncritical semantics’, the ‘myth of a museum in which the exhibits are meanings and the words are labels’.

A: I find it hard to adjudicate … where would modern linguistics stand on this?

HD: Well, this is a thorny topic. What I think − and I think it is the correct view within scientific descriptive linguistics − is that agents speak an idiolect, which may be changing all the time. Maybe it can change in a nanosecond. Maybe you shift into different idiolects as the context changes. Why not? Perhaps one speaks more than one, perhaps many, idiolects. Perhaps micro-idiolect might be the right notion. Also, I cannot see why one must insist that such idiolects be ‘public’ or ‘manifestable’. I have no objection to innate ideas, to private grasping of concepts, to intentional realism, to there being very peculiar psychological states shared by no one, and so on. Linguists are bound to take a variety of views on such matters, though.

A: But there do seem to be public languages. All the natural languages which have names are usually thought of as public languages. They involve speech communities. For example, what is English?

HD: The abstract view naturally fits with the notion that idiolects are basic, because there is fluctuation and variation across communities and over time. Since these idiolects are different, they must be individually cognized by speakers. Consequently, public languages, allegedly common to a speech community, are not theoretically basic for linguistic theory, except perhaps for branches like sociolinguistics.

For example, in his 1975 article, ‘Knowledge of Language’, Professor Chomsky writes,

A: So linguistics should be methodologically individualistic?

HD: Yes. The language(s) cognized are idiolects or micro-idiolects. One may cognize many at a time. Bilingual speakers cognize distinct idiolects − for example, varieties of English and Punjabi − that are not easily mutually interpretable. And individuals can modify the idiolect they cognize in various ways: for example, phonetically. If they cognize two languages, they can perform interesting operations on them, such as mixing/fusing them. For I can say, ‘Would you like a Krapfen?’ or ‘Ich bin very very glücklich!’. The point is that cognizing an idiolect, or several, is the mental state of an individual cognitive system. There is no role for a mental state of cognizing, or partially cognizing, a ‘common shared language’. More recently, Chomsky talks of ‘I-languages’, for internal languages, as being the proper subject of scientific linguistics. As I understand the terminology, the I-languages are idiolects. And he talks also of ‘E-languages’, for external languages, each of which corresponds roughly to a single public, shared, language spoken by a speech community. There is an important difference, however, in metaphysics between myself and Chomsky, who claims that I-languages are mental objects, whereas I claim that they are abstract objects, carrying their intrinsic syntactic, semantic, etc., properties essentially, for the reasons we discussed earlier.

A: So, English is an E-language? And Alicese is an I-language?

HD: You cognize Alicese. I cognize Humptyese. This conversation is witness to the great overlap of these idiolects, which are, to a large degree, mutually intelligible. The problem is that we must recognize that there is a large, heterogeneous speech community; there is no single language that all speakers cognize. The idiolects spoken overlap a good deal, but they inevitably vary somewhat. Not everyone in a speech community has the same lexicon, the same meanings for words, the same pronunciations, the same pragmatic rules, and so on. If they vary, even a tiny bit, they are different.

A: The tiniest change produces a new idiolect or language?

HD: To use Professor Quine's terminology, languages are individuated very finely: by exact sameness of phonology, syntax, semantics and pragmatics.

A: So, … English isn't really a language at all in your sense ….?

HD: Although we were using English in our examples earlier, that is, in fact, somewhat misleading, yes. I am not sure what to say English is. Often, we can easily switch to talking of the idiolect we call ‘A-English’, where A is the speaker in question. Or, we may talk of the variety of English spoken by A.

A: Perhaps we should take these ‘varieties’ seriously, and think of each ‘natural’ language not as a particular language but as a set of languages? So, when we say that I speak English, really what we mean is that I speak a variety of English − some idiolect that is an element of English?

HD: Alternatively, we might try and define a unique language, English, which functions as an external normative standard for the language community, but which no individual speaker cognizes, of course. This would require smoothing out the discrepancies between idiolects, and invoking a powerful version of collective normativity: for example, counting those who assign the concept UNINTERESTED to the string ‘disinterested’ as being mistaken as to what they ought to mean, which is the concept NOT HAVING A PARTICULAR INTEREST.

A: On this view, there is a common shared E-language, which is an external standard, and from which idiolectic deviations are mistakes. Whereas on the I-language view, the idiolectic variations are not mistakes.

HD: This is very controversial: prescriptivism. I am more sympathetic to what linguists call ‘descriptivism’, but prescriptivism seems to be very popular with philosophers.

A: Maybe the following is a case to illustrate. I used to pronounce ‘schedule’ as ‘shedule’, but increasingly I say ‘skedule’.

HD: Well, if you make a performance error relative to the idiolect you speak, then this is a violation of the intrinsic rules of your idiolect, the language you cognize. You will normally recognize this yourself. There is a kind of normativity that arises from the properties of your own idiolect; let's call it idiolectic normativity.

A: So this would include things like stammerings, ums and errs, mispronunciations …

HD: A performance error occurs when your speech performance violates, or is out of kilter with, the properties of your own idiolect. But, in your ‘schedule’ case, it does not seem to be a performance error. It seems that your idiolect has a string pronounced as ‘shedule’ at time t ₁ and a string pronounced as ‘skedule’ at later time t ₂. So, your idiolect is shifting. Or perhaps you are, in an important sense, cognizing several idiolects, and one is ‘fading out’, as it were.

A: Yes, idiolects can shift, for various reasons …

HD: Of course! In fact, very quickly. I can ‘baptise’ something, introducing a new name in my idiolect, tagging the object. As in the case of the examples discussed by Professors Barcan and Kripke. My idiolect has been modified: extended. Also, I can borrow meanings, somehow. I do not quite know the details of the cognitive mechanism; but clearly we can copy or borrow meanings from others. With language acquisition, when children acquire a language, they do not just acquire any old language from syntactico-semantic heaven. They gradually acquire an idiolect which resembles the idiolects of those around them. Their idiolect − more exactly, the sequence of idiolects − slowly converges towards an approximate standard in their speech community.

A: To apply it to my case, I can see a kind of reason why it's better for me say ‘skedule’ instead of ‘shedule’: namely, social co-ordination. The speakers around me tend to say ‘skedule’ instead of ‘shedule’: my idiolect shifts and it becomes easier for me to process incoming messages from others and for them to process messages from me. Mutual ‘decoding’ becomes easier. It isn't conscious, though. But I think that social co-ordination has normative value. And I may defer to expertise too in order to improve social co-ordination.

HD: It is rational for humans to improve co-ordination and to share expertise!

A: Any rational creature, talking eggs included.

HD: Of course.

A: So, let's assume that this is so. Then while you are entitled to your meaning for ‘glory’, meaning what it does in your idiolect, and likewise I am entitled to my meaning for ‘glory’, meaning what it does in my idiolect, nonetheless there is a broader language community relative to which your meaning is non-standard, whereas my meaning is standard. By the social co-ordination princple, I'm therefore entitled to request that you improve social co-ordination by using a shared meaning. And there's a nice knock-down argument for you!

--------------

At this, Humpty Dumpty sat and thought for a while.

--------------

HD: Do you recall Professor Quine's famous puzzle? A human rushes past The Mad Hatter, who utters ‘gavagai’. The Mad Hatter always tends to behave like this. Let us define Madhatterese to be the idiolect that The Mad Hatter cognizes. Then, given his speech behaviour, what does the Madhatterese word ‘gavagai’ mean?

A: Yes, Quine's argument for indeterminacy of translation …

HD: Quine suggests that it is not semantically determinate whether ‘gavagai’ should be translated as ‘Lo, a human!’, or ‘Lo, humanhood instantiated!’, or ‘Lo, an undetached human part!’, and so on.

A: I heard something like this from my set theory teacher once. The example she discussed involved Skolem's Paradox. Let me now see how to reformulate the ‘gavagai’ example on your conception of languages. First, we define two languages L and L*, with reference functions ρ _L and ρ _L* such that,

Then there is no question as to what the strings mean! It is a matter of definition that ‘gavagai’ refers to humans in L and refers to undetached human parts in L*. So, it really isn't a puzzle about semantics.

HD: Precisely.

A: But, on the other hand, we still have not settled what The Mad Hatter himself means in using these strings, given only the U-fact that The Mad Hatter utters ‘gavagai’ when there are humans nearby. If there are humans nearby, then there are undetached human parts nearby, and vice versa. We do not know if The Mad Hatter cognizes L or cognizes L*. Or perhaps neither. If we cannot pin this down, then the U-facts do not uniquely determine the C-facts.

HD: It seems to me that all of these puzzles allegedly about semantics, for which Wittgenstein, Quine, Putnam and Kripke are rightly famous, can be reformulated in the same manner. Suppose the language L assigns electrons to ‘electron’, while L* assigns protons to ‘electron’. Do scientists cognize L or L*? Or, suppose that the symbol ‘plus’ means addition in L, and means quaddition in L*. Do we cognize L or L*? These are not problems in semantics at all! They are problems in cognitive science.

A: As I said a moment ago, Professor Skolem has a similar argument, in connection with non-standard models. In your formulation, it is like this. Suppose L maps the string ‘number’ to the standard numbers 0, 1, 2, …, while L* maps ‘number’ to elements of a non-standard model of Peano arithmetic. Then do number theorists cognize L or L*?

HD: Problems previously thought of as semantic indeterminacies have now become indeterminacies of language cognition: a certain mental cognizing state of the speaker is undetermined or perhaps even indeterminate.

A: So, if I understand the overall argument correctly, there are three main steps.

First, through a thought-experiment concerning a certain hypothetical scenario and a certain body of U-facts, we obtain a dilemma: either there is no fact of the matter as to which language L is cognized, or some underlying U-facts have been omitted.

Second, we insist that all the U-facts have been specified.

This yields Quine's conclusion.

HD: Consequently, to dispute Quine's conclusion, we need to clarify Quine's conception of what a full specification of the U-facts amounts to. For Quine, this involves physicalism about facts and empiricism about meaning assignment.

A: Which rules out certain certain kinds of ‘mysterious’ assignment of meaning? For example, a primitive grasping of universals, or forms, or concepts or propositions?

HD: Yes, a certain kind of physicalistic empiricism implies that it is indeterminate what language is cognized. Regarding the relation of indeterminacy and the empiricist theory of meaning, Quine comments in his 1969 article ‘Epistemology Naturalized’,

A: Well, I suppose the question is: do we have no choice?

HD: In ‘Languages and Language’, Professor Lewis introduces an indirect proposal for analysing ‘A cognizes L’, but this is based on the notion of a population speaking a common, or shared, language L.

Professor Lewis then goes on to embed this account of a population ‘using’ a common language within his more general account of convention. It is here that my view diverges. His account assumes that languages are E-languages. As I said earlier, I think this is the wrong place to begin, because cognizing a specific language, an idiolect, is an individual mental state.

A: So, in each case, we are looking for some extra U-facts about the agents themselves which tell in favour of their cognizing L and not L*.

HD: Yes, this is the central problem identified by Quine. What are the kinds of meanings that a mind can grasp and can assign to strings? How are we to understand notions such as:

For example, it seems to me that the debates within the ‘theory of reference’ for proper names are crucially about the assignment notion ‘A uses the name n to refer to x’. We might call these semantico-cognitive assignment relations.

If we simply assume some such notions, we can define ‘A cognizes the semantics of L’ by saying simply that A assigns meanings to strings just as the language L does. The agent and the language are in harmony. So, suppose we write ‘μ_L(σ, C)’ for the meaning of σ in context C in L. Then the definition, more formally, is:

1. (COG1) A cognizes the semantics of L iff, for any lexical L-string σ, context C, A assigns μ_L(σ, C) to σ in C.

In one of the ‘Objections’ in ‘Languages and Language’, Lewis cites a definition like (COG1) and replies,

But my reply to this is that an agent's cognizing a language is not really a convention to perform such an action, because I do not think the speakers all follow the same conventions. The conventionality of language is encapsulated by Semantic Conventionalism, that we discussed before: the meaning relation is conventional, much as a co-ordinate system is.

Furthermore, the language user does assign meanings to strings, does bestow meanings, does assign referents, does baptise new referents, does borrow meanings, and so on. It seems to me that these are actions performed by language users, frequently unconsciously. So, here my view diverges from Lewis's.

A: Is the real problem one of cognitive ‘access’ or ‘contact’? We must look for some meaning entity that minds are in contact with. For example, it is difficult to see how the mind might ‘assign’ the appropriate referents to strings like ‘the electromagnetic field’, which requires a physical field as referent, or ‘the Church-Kleene ordinal’, which requires an abstract referent. And, on the other hand, we do seem to be in immediate contact with sense data or stimuli. So, it's easy to agree with Quine that, given our broadly scientific picture of how the mind relates to the world, ‘one has no choice but to be an empiricist’ for linguistic meaning.

HD: The age-old epistemological conflict between Empiricism and Rationalism resurfaces as a conflict concerning language cognition, concerning what kinds of entities can be assigned as meanings of strings and how this might work.

For Quine there are determinate meanings of a sort: stimulus meanings. But such stimulus meanings are nothing like propositional content. Let M be the stimulus meaning of ‘gavagai’ for The Mad Hatter. This is a set of retinal and auditory stimuli types. By language inculcation, i.e., conditioning, The Mad Hatter's cognitive system has assigned M to the string ‘gavagai’. Behaviourists called this ‘association’. And, the consequence is that the Mad Hatter has a disposition to assert the string ‘gavagai’ whenever the environment causes a token of any stimulus type in M. Such a token might be caused by a cleverly disguised dummy, an experimental setup in a neuro-psychology laboratory, or by a Cartesian demon.

A: Perhaps Quine's own approach, with its behaviourist overtones, is a bit too limited? Must all empiricists work within such limited framework? For example, can the empiricist not appeal to inference? Associating sentences, or mental representations, with each other, by finitary rules? Can the empiricist also not appeal to theories as implicitly determining meanings? You mentioned earlier that perhaps one might appeal to natural properties and kinds?

HD: Empiricists vary quite a bit on how much metaphysics they can stomach. But an extended empiricist theory of meaning assignment might involve sensory meanings, inferential connections, conceptual role in accepted theory, causal connections, and natural kinds/natural similarity relations. And although many authors have contributed in various ways, probably the main architect of this is Professor Lewis himself. We might call it the Lewisian Standard Model for Metasemantics.

A: And does it succeed?

HD: I am unsure. But, as Professor Lewis mentions, in one case where it doesn't fix a unique language cognized, one might conclude that, here at least, this is what one expects. This is for vagueness; for terms like ‘bald’ and ‘tall’, it is indeterminate what precise language one cognizes. Perhaps the physicist can define these precise languages. Vagueness turns out to be neither semantic, nor epistemic, nor ontic; it is cognitive.

A: I am still bothered by the examples we discussed above. Consider our earlier puzzle about whether Professor Gowers cognizes a language L in which ‘number’ denotes the standard numbers or a language L* in which ‘number’ denotes the non-standard numbers. Although, for any sentence in both languages, the truth values are the same, it seems reasonable to say that the propositions expressed usually differ.

For example,

while,

And presumably, when asserting the string ‘every natural number has a unique prime factorization’, Professor Gowers thereby expresses a belief in the former proposition, and not the latter. So, it is determinate that Professor Gowers cognizes L and not L*. This C-fact is determined by a certain kind of U-fact involving appeal to intentional states, with propositional content. That is, the Quinian claim to have specified all the U-facts is not correct.

HD: This suggests that we take the cognitive assignment of a proposition to a string as basic.

A: Suppose that, for the languages in question, we have a function π_L which maps any sentential string σ of L, any context C, to a proposition π_L(σ, C). For example,

1. (COG2) A cognizes L only if, for all L-sentences σ, contexts C, A assigns π_L(σ, C) to σ in C.

HD: This is plausible, though it may violate the limits of empiricism. How might it be connected to verbal behaviour? How is it connected to U-facts?

A: Perhaps assigning a proposition to a string correlates with being disposed to assert it when one believes it:

HD: But people sometimes lie. A person might assign p to σ, and be disposed to assert σ in context C, even though believing ¬p in context C. Speech acts cannot be tied so closely to propositional content. Rather they are tied to a network of interconnected beliefs and desires.

A: Yes, that is too quick. Instead, try:

One might allow then for contexts where lying is justified, and then what one asserts may differ from, and even contradict, what one accepts. And instead we can adopt a somewhat hedged claim about speech acts:

1. (SA) Other things being equal: A is disposed to assert σ in context C only if A believes in context C the proposition that A assigns to σ.

HD: Is the claim about speech acts meant to be an analysis, or a contingent claim?

A: I am unsure; but, in any case, I think it is roughly right. If so, then I can see roughly how this theory logically relates C-facts to U-facts. Suppose that our evidence includes,

1. (U) Other things being equal, Naomi is disposed to assert ‘Das ist eine Katze’ in context C only when she believes that the ostended entity in C is a cat.

We can present a proposed explanation of that U-fact based on the theoretical assumptions:

1. (COG2) A cognizes L only if, for all L-sentences σ, contexts C, A assigns π_L(σ, C) to σ in C.

2. (SEM) π_German(‘Das ist eine Katze’, C) = the proposition that the ostended entity in C is a cat.

3. (SA) Other things being equal: A is disposed to assert σ in context C only if A believes (in C) the proposition that A assigns to σ (in C).

along with the empirical claim,

1. (E) Naomi cognizes German.

For suppose (E): Naomi cognizes German. So, by (COG2), Naomi assigns π_German(‘Das ist eine Katze’, C) to ‘Das ist eine Katze’ in context C. So, by (SEM), Naomi assigns the proposition that the ostended entity in C is a cat to ‘Das ist eine Katze’ in context C. So, by (SA), other things being equal: Naomi is disposed to assert ‘Das ist eine Katze’ in context C only if Naomi believes in context C the proposition that Naomi assigns to ‘Das ist eine Katze’ in context C. So, other things being equal: Naomi is disposed to assert ‘Das ist eine Katze’ in context C only if Naomi believes that the ostended entity in C is a cat. QED!

HD: Very good! Dispositions to verbal behaviour of an agent can be explained by what language the agent cognizes. So, as we concluded earlier, the U-facts do not determine the S-facts. Rather, the S-facts and C-facts together explain the U-facts.

A: I have a rather strong intuition that, unless one simply accepts the indeterminacies, the indeterminacy puzzles can't be resolved without requiring that speakers assign genuine propositional content to sentential strings; and perhaps one should explore meaning assignment to subsentential strings too, using the more basic ‘semantico-cognitive notions’, as you call them, such as,

And we need not insist that these cognitive assignment notions be reducible or definable in more basic physicalistic terms.

HD: So, when one uses a word, it means just what one assigns it to mean − neither more nor less.