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.



  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.