Tuesday, January 31, 2012

Proof-theoretic semantics

After my previous post about the "meaning is use" credo, I got an email pointing out papers by Nissim Francez and Roy Dyckhoff which develop a Proof-Theoretic Semantics for natural language, and logic also. A good paper to start with is "Proof-theoretic semantics for a natural language fragment," Linguistics & Philosophy 33:447-477 (2010). Other papers appeared in Studia Logica (2010) and Review of Symbolic Logic (2011).

Proof-theoretic semantics is, as the name implies, offered as an alternative to the usual model-theoretic semantics. While I studied formal semantics (which was always model-theoretic) like every other linguist interested in formal approaches, I have to admit I never liked it very much. So I find these new developments extremely encouraging. Here is a quote from the paper in L&P:

For sentences, replace the received approach of taking their meanings as
truth conditions (in arbitrary models) by an approach taking meanings to
consist of canonical derivability conditions (from suitable assumptions).

Arguments against model-theoretic semantics for natural language are certainly out there (e.g. Michael Dummett), but no one has done much about it for an alternative approach. I am certainly in favor of this new set of ideas; these authors develop a direct proof system for natural language in which the "rules of use" for linguistic elements are used precisely as their definitions. And they also highlight some interesting arguments in favor of these sorts of meanings in a cognitive system.

Thursday, January 5, 2012

Meaning is use?

My heart sank a little when I learned of Michael Dummett's death this week. I also learned, however, that he was a follower of the latter-day Wittgenstein credo that "meaning is use." In other words, to understand a word's meaning is precisely to be able to use it correctly, to comprehend its uses. I, too, favor this account of things, and indeed it is pretty commonly assumed in many computational applications. Word senses are often identified with usage patterns in one way or another.

When discussing the idea that "meaning is use" with a colleague a little while ago, however, he was taken aback. "How could any cognitive scientist," he asked, "seriously hold such a view?" His objection seems to be that, cognitively speaking, a word's meaning should be equated with some kind of conceptual space that can be cognized. The problem, I'm told, is that a "usage" is not a cognitively real object.

On the other hand, I think that a cognitive notion of "concept" is actually pretty weak. I'm not acquainted with much empirical literature on this, but it would be worth reading up on how "concepts" have been shown to be cognitively real. And what is the concept behind a word such as and? I'm told that cognitive scientists allow a distinction between function words and content words, wherein function words such as and are tacitly allowed to have "use-based" meanings but content words are supposed to have conceptual meanings. Hmm, so perhaps meaning is use sometimes, even in cognitive science?

Lastly, let's consider a more modern approach like embodied cognition. This, very briefly, is the stance that studying human cognition must be undertaken by recognizing the complete context of the human. Humans seeking to understand words actually learn them by doing, by using them. So even if there is a cognitive "concept" behind a word, this is attained mostly by learning the conventional usage of the word, which is not purely linguistic but interacts with the world as well. It seems that the usage of a word could actually be used to bootstrap the concept behind it.