Friday, 17 August 2012

Language Relativity (or: Does a Cow Eat Without a Knife?)

I wonder if you know what
(1) Estas constipado?
means (in Spanish; no, sorry, I'm not doing the upside down question-mark thing). When I first heard this, with my pigeon Spanish, I took it to mean, "Are you constipated?", but it simply means, "Do you have a cold?"

Surely no one thinks that a string of phonemes (or letters, if you prefer orthography) has a meaning all of its own. A string can only mean something relative to some language. That is, if $\sigma$ is a string, then the meta-string
(2) $\sigma$ means $m$
does not, strictly speaking, express a complete thought. It should be,
(3) $\sigma$ means-in-$L$ $m$
where $L$ is an interpreted language.

Logicians and others have developed a very detailed theory over the last hundred years or so of uninterpreted languages. We sometimes use the notation "$\mathcal{L}$" to refer to uninterpreted languages. And, obviously, it doesn't make sense to ask of an string in $\mathcal{L}$ what it means. For it means nothing. Only when one has an interpreted language $L$ does the question, "what does $\sigma$ mean in $L$?" make sense. This is language relativity. Meaning/reference, and so on, has to be language relative (or intepretation relative). So, we sometimes represent an interpreted language as a pair $(\mathcal{L}, I)$.

Another example is:
(4) "sensible" is true of $x$ iff $x$ is sensible.
seems ok to a deflationist. But it is, strictly speaking, missing a parameter. And the parameter does make a difference, for:
(5) "sensible" is true in English of $x$ iff $x$ is sensible.
(6) "sensible" is true in Spanish of $x$ iff $x$ is sensitive.
The same orthographic string---i.e., finite string of Latin letters---has different meanings in English and Spanish (the somewhat different pronunciations, however, break the symmetry here).

Linda Wetzel gives the following example in her SEP article Types and Tokens.
Even being similar in appearance (say by sound or spelling) to a canonical exemplar token of the type is not enough to make a physical object/event a token of that type. The phonetic sequence
[Ah ‘key ess ‘oon ah ‘may sah]
is the same phonetic (type) spoken in Spanish or Yiddish. Yet if a Spanish speaker uses it to say a table goes here, she has not, in addition, said a cow eats without a knife in Yiddish. She has not said anything in Yiddish, however phonetically similar what she said might be to a sentence token of Yiddish. So her token is a token in Spanish, not Yiddish. Meaningful tokens are tokens in a language.
Wetzel makes two points here. The first concerns tokens: meaningful tokens are only meaningful in virtue of being tokens of some type in a language. The second point is to provide a neat example of language relativity, namely,
(7) [Ah ‘key ess ‘oon ah ‘may sah] means-in-Spanish that a table goes here.
(8) [Ah ‘key ess ‘oon ah ‘may sah] means-in-Yiddish that a cow eats without a knife.
(Unfortunately this example is only 99% neat, as my wife tells me that "acquí es una mesa" is not properly formed Spanish. Ho hum.)

As soon as one appreciates the importance of language relativity for linguistic notions (grammaticality, phonology, semantics, pragmatics), then one notices something that at first sight seems odd. Consider again,
(6) "sensible" is true in Spanish of $x$ iff $x$ is sensitive.
One might, naively, think this semantic fact is a contingent fact. After all, to find out this fact, one might jump onto an EasyJet flight, head off to Madrid, and check the speech behaviour of Madrileños.
But do a thought experiment. Suppose that $L$ is an interpreted language such that,
(9) "sensible" is true in $L$ of $x$ iff $x$ is from Belgium.
My intuition here is that $L$ is not Spanish. (This isn't a proof that $L$ isn't Spanish.) If that is right, then interpreted languages carry their interpretations essentially, and consequently semantic facts, such as (6), are necessities.

This conclusion (whether one accepts it or not) relates to the modal (and temporal) individuation of languages. I am inclined to say that even fluent competent English speakers in fact speak (or cognize) slightly different languages: idiolects. If the language I speak is $L_1$ and the language Robbie speaks is $L_2$, then there are certain differences---pronunciation, lexical, some semantic and pragmatic variation---between $L_1$ and $L_2$. One might say that $L_1$ and $L_2$ are "variants" of English but all this means is that $L_1$ and $L_2$ are both similar to English, a language that no one, strictly speaking, speaks!

As soon as one goes down this road, then all sorts of interesting phenomena happen. Semantic facts are facts about specific languages, and are necessities. There is no philosophical problem of reference. In principle, given an uninterpreted syntax $\mathcal{L}$, an interpretation can pair of any string with any meaning, generating countlessly many different languages. The famous questions about semantic indeterminacy become questions about what language one speaks/cognizes. Interesting questions about "reference magnetism" become questions about cognizable languages (or, at least, become closely connected with cognitive questions, rather than purely semantic ones).

For example, consider a non-standard model $M \models PA$. The Skolemite sceptic asks, or wonders, how it becomes determinate (or how we might know) that the interpretation of the language $L$ spoken by a number theorist when they do number theory is $\mathbb{N}$ or $M$. Well, if $\mathcal{L}$ is the underlying syntax, then perhaps the language $(\mathcal{L}, M)$ is, in some sense, not cognizable. One can (as I am doing) refer to this language, using singular terms or variables. But, perhaps, one can't speak this language.

So, to be as clear as possible, the rough idea is:
(i) The language $(\mathcal{L}, \mathbb{N})$ is cognizable.
(ii) The language $(\mathcal{L}, M)$ is not cognizable.
But even if (ii) is true, I'm still not sure why. Non-standard models are indeed strange (the most interesting instance of this for countable models of $PA$ is Tennenbaum's Theorem). On my view, cognizing a language $L$ consists in the matching up of the meanings of $L$ with the meanings one's mind assigns to strings. But why the human mind assigns the concept NUMBER to the string "number" in English (or variants) rather than the concept $M$-ELEMENT is not clear to me. Perhaps the concept $M$-ELEMENT is a concept one cannot "get" or "grasp" without first getting the concept NUMBER.

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