## Sunday, 6 January 2013

### The Guitar Language

Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. (Frege 1892, "On Sense and Reference")
I have an extremely liberal notion of what a language is---Lewis's abstract view. A language is any bunch of syntax, possibly along with meaning functions. The syntax can be pretty much anything; the symbols can be pretty much anything; the meaning functions can be pretty much anything; and the meaning values can be pretty much anything.

I want to define a language $\mathbf{L}_G$, which I'll also call the Guitar Language.

First let me stipulate (just for this context here)  that "$e$" be a name of my Epiphone guitar, and "$r$" be a name for my Rickenbacker guitar and "$y$" be a name for my Yamaha guitar. So, $e$, $r$ and $y$ are my guitars. (You do understand this! I have just temporally augmented your idiolect by a local baptism.)

Second let me define three propositions:
$p_1 =$ the proposition that Paul McCartney is a lizard.
$p_2 =$ the proposition that Yoko Ono was born in Wrexham.
$p_3 =$ the proposition that Ringo Starr plays drums.
Finally I define the Guitar Language $\mathbf{L}_G$:
(1) the alphabet of $\mathbf{L}_G$ is $\{e, r, y\}$. The only strings in $\mathbf{L}_G$ are these symbols.
(2) the meanings of these strings, relative to $\mathbf{L}_G$, are given by the following meaning function $\mu_{\mathbf{L}_G}$:
$\mu_{\mathbf{L}_G}(e) = p_1$.
$\mu_{\mathbf{L}_G}(r) = p_2$.
$\mu_{\mathbf{L}_G}(y) = p_3$.
(3) For any guitar $g \in \{e, r, y\}$, an action is a speech act of asserting $\mu_{\mathbf{L}_G}(g)$ in $\mathbf{L}_G$ iff it consists in tapping the machine head of the G-string of $g$ twice, with one's left thumb.
This language $\mathbf{L}_G$ is a very simple "signalling language". It has only three symbols and no significant (i.e., combinatorial) syntax. The contents of the signals are (eternal) propositions (usually, of course, the content of a signal is indexical in some way, such as "The house is on fire right now!"). Now what would it mean for an agent (or mind) to speak/cognize the language $\mathbf{L}_G$? What would it mean for the mind of an agent to assign these propositions to these symbols?

It seems that the right thing to say is that an agent cognizes $\mathbf{L}_G$ by being disposed to perform the relevant speech act of $\mathbf{L}_G$ when in the right mental state; i.e., when a symbol is "asserted", then the propositional content of the agent's mental state is identical to the propositional content of the symbol.

Unfortunately, speaking $\mathbf{L}_G$ requires being able to perform these speech acts, which means being able to tap the guitars, so even though you might speak/cognize $\mathbf{L}_G$, you might never get the chance to actually make an assertion in $\mathbf{L}_G$.

But just for good measure, here is a photo of the symbols, $e$, $r$ and $y$:

1. Hi Jeff,

I'm probably being dense, but I think clause (3) should read: "An action is a speech act of asserting $\mu_{L_G}(g)$ iff it consists in tapping the machine head of the G-string of $g$ twice, with one's left thumb."

Philosophical question: is it legitimate to stipulate the alphabet and the speech act separately? If it is, then there is an issue about radical underdetermination of alphabet!

2. Hi Tim,

I think you're right on both points.
On the first, I was originally thinking of writing "uttering $g$"; but I guess, properly speaking, what one asserts is the content ... I should change it!
The second point is right too - because "$g$" is unrestricted? I guess I just need the quantifiers written right (so the only things that can be asserted are elements of the alphabet). But hopefully, the context makes it clear.

Cheers,

Jeff

3. Hi Jeff,

I think maybe I was unclear on my philosophical question. What I had in mind was more related to what we were discussing a while back, about underdetermination of syntax. Here's the thought in more detail.

Suppose you're using the guitar language to make speech acts. I'm interpreting you, and I get to the stage of saying:

(a) Jeff asserts $p_1$ by tapping the machinehead of the G-string of $e$ twice, with his left thumb.
(b) Jeff asserts $p_2$ by tapping the machinehead of the G-string of $r$ twice, with his left thumb.
(c) Jeff asserts $p_3$ by tapping the machinehead of the G-string of $y$ twice, with his left thumb.

All good! But now why should I think that the alphabet of your language is $\{e, r, y\}$? A trivial alternative is that it is $\{e$'s machinehad, $r$'s machinehead, $y$'s machinehead$\}$. Less trivial alternatives involve permutation on $e$, $r$ and $y$.

4. Hi Tim,

Yes, right - apologies, I'm being slow ...

So, on my preferred (Lewisian) setup, we redefine a new guitar language, $L^{\ast}_G$, which has extensionally distinct syntax from the original $L_G$.

Then your argument shows that the U-facts (a), (b) and (c) (about Jeff's speech acts) underdetermine the C-facts -- so, it's underdetermined whether Jeff cognizes $L_G$ or $L^{\ast}_G$, even in the sense of underdetermining what the syntax is!

The only solution I can think of would be to require that when an agent cognizes the syntax of $L$, the distinguished syntactic items of $L$ would have to be "intentional objects" of the agent, so the agent intends to assign $p_1$ to $e$, etc. But, of course, even that might leave considerable indeterminacy! Particularly if one is sceptical about invoking heavy-duty intentional content.

Cheers,

Jeff