Sunday, 6 January 2013

The Abstract View: Two Analogies

What I've called the Abstract View of languages is the view set out by Lewis (1970, "General Semantics" and 1975, "Languages and Language") and Soames (1984, "What is a Theory of Truth?"). The view may be partially explicit, or implicit, in the writings of others (e.g., Tarski, Carnap, Montague). Languages are systems of syntax, along with (but not necessarily along with) semantics and pragmatics. Syntax is understood very liberally (anything can count as a symbol or a sign), and the assignments of meanings and pragmatic contents are arbitrary.

So, this is consistent with a kind of Semantic Conventionalism ("anything can mean anything"), which has the further consequence that meaning relations needn't be reduced to physicalistic/naturalistic relations. They are simply stipulated or defined mathematical functions, assigning meanings to strings. And, crucially, the syntactic, semantic and pragmatic properties of a language $\mathbf{L}$ are not dependent in any way on whether there are even any agents/minds that speak, or "cognize", the language. For example, there is no further ground level naturalistic or intentional fact in virtue of which the string "Schnee" means snow in German. It is a property (an essential property) of German that the referent in German of "Schnee" is snow. Because there is nothing physical/naturalistic "connecting" strings and their meanings, except the particular meaning function intrinsic to the language, then we expect list-like definitions of semantic notions, such as,
$x$ refers to $y$ in German if and only if either ($x$ = "Schnee" and $y$ = snow) or ($x$ = "Wasser" and $y$ = water) or ...
I think this resolves Hartry Field's request for a further reduction of "primitive denotation" (in his classic 1972 paper, "Tarski's Theory of Truth").

This concept of languages permits a certain division of labour in linguistic theory (and in philosophy of logic and language): syntax/semantics has been separated from the problem of language cognition. The syntax theorist is now free to dream up any system of syntax she likes; the semantic theorist is now free to dream up any system of syntax and semantic features she likes. These areas have been moved more-or-less entirely into applied mathematics. On the other hand, what is involved in cognizing, or speaking, or implementing, or realising, a language in some physical system (like a brain or computer) is now conceptually separate. Which patterns of neural activation occur during language acquisition or during particular speech acts, how linguistic stimulus inputs are processed, how token sounds and inscriptions are physically produced, etc, are problems of cognitive science, and not syntax or semantics per se.

I think there are two useful analogies for this view.

1. Computer Programs

A computer program is a sequence of instructions for performing a computation. But the computer program is itself not a concrete entity. In some sense, the physical system "implements" or "realizes" the program. As in the language case, one can study the properties of a computer program $P$ independently of its implementation. For example, one might show (mathematically) that the program $P$ will never halt on a certain input $n$. Or one might show that for any given input of size $n$, there is an upper bound $f(n)$ on how long, or how many steps, the program takes to compute an output.

So, on this analogy, languages are like computer programs. One can investigate their properties independently of their "implementation". And, if one has determined that a program has a certain properties, this will allow one to make inferences & predictions about how a physical system behaves if it "implements" that program. Analogously, one can study languages independently of whether they are "cognized"; and, if one has determined that a language has certain properties, this will allow one to make inferences & predictions about how an agent behaves if they "cognize" that language.

2. Abstract Structures in Applied Mathematics

Probably the earliest abstract structures that human minds found out about were the system $(\mathbb{N}, +, \times, \le)$ of natural numbers, and the system $(\mathbb{R}, +, \times, \le)$ of real numbers. Somehow, our ancestors got the basic ideas, and this developed until significant clarity was achieved in the 19th century. And similarly with the abstract structure of Euclidean space, $\mathbb{E}^3$: it was implicitly believed that physical space must have this structure, until it was realized that physical space needs to be distinguished from various mathematical spaces.

There is some reasonable sense in which, although our knowledge of these three abstract structures arose from our sensory experience, the study of the abstract structures could then be detached from questions about whether physical things "instantiate" these structures. So, the pure mathematician is left alone to study these structures, and countless others, including all sorts of generalizations (metric spaces, topological spaces, manifolds, rings, fields, groups, etc). And the applied mathematician/theoretical physicist focuses on those which have found instantiations (or approximate instantiations).

How exactly a mathematical structure is "instantiated" physically is an interesting and quite difficult philosophical problem, connected to debates about the applicability of mathematics and various indispensability arguments.

On the abstract view, languages are thought of in pretty much the same way as the theoretical physicist or applied mathematician might think of the abstract structures (manifolds, Lie groups, etc.) invoked in physics.

4 comments:

  1. While it may be arbitrary, some system of a predicate calculus may be expanded upon mathematically to produce a language capable of being interpreted into values of number equatable with physical objects. A reverse reduction can be performed, but it must be non-explosive logically yet inductive and also contain computations if we are to unite the theoretical with the physical.

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  2. *equatable to physical objects (correction)

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  3. The illusion of consciousness, what fools us is that we believe we're watching and think language is separate. It's true our brain has a binding problem but that isn't the Hard Problem of consciousness. The point is we create a false duality when in fact we face a non-dual system. There are two, one, and three. Us and the Other. Ourselves, and the physical, spiritual and God. That is my belief.

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  4. as far as whether cognition is an result/effect of the brain, solely, I believe that it is evolutionary based. You must remember we come from the singularity; we, everything, existence it was all once one. I believe we come from nature and are nature, but too often that is forgotten. I believe computation, mathematics, mathematical logic, and formal logical theorems represent very powerful linguistic tokens of types, implicit to the types and intuited by the one seeing the token in their mind. Over time at first we were one with nature, but we have forgotten. We need anamnesis for our amnesia.

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