berke@ucla-cs.UUCP (11/01/87)
I just read this fabulous book over the weekend, called "The Vastness of Natural Languages," by D. Terence Langendoen and Paul M. Postal. If you have read this, I have some questions, and could use some help, especially on the more Linguistics aspects of the book. Are Langendoen or Postal on the net somewhere? They might be in England, the Publisher is Blackwell 1984. Their basic proof/conclusion holds that natural languages, as linguistics construes them (as products of grammars), are what they call mega-collections, Quine calls proper classes, and some people hold cannot exist. That is, they maintain that (1) Sentences cannot be excluded from being of any, even transfinite size, by the laws of a grammar, and (2) Collections of these sentences are bigger than even the continuum. They are the size of the collection of all sets: too big to be sets. It's wonderfully written. Clear wording, proofs, etc. Good reading. Help! Regards, Pete
rapaport@sunybcs.uucp (William J. Rapaport) (11/02/87)
In article <8941@shemp.UCLA.EDU> berke@CS.UCLA.EDU (Peter Berke) writes: >I just read this fabulous book over the weekend, called "The Vastness >of Natural Languages," by D. Terence Langendoen and Paul M. Postal. > >Are Langendoen or Postal on the net somewhere? Langendoen used to be on the net as: tergc%cunyvm@wiscvm.wisc.edu but he's moved to, I think, U of Arizona. Postal, I think, used to be at IBM Watson.
turpin@ut-sally.UUCP (Russell Turpin) (11/02/87)
In article <8941@shemp.UCLA.EDU>, berke@CS.UCLA.EDU writes: > I just read this fabulous book over the weekend, called "The Vastness > of Natural Languages," by D. Terence Langendoen and Paul M. Postal. > ... > > Their basic proof/conclusion holds that natural languages, as linguistics > construes them (as products of grammars), are what they call mega-collections, > Quine calls proper classes, and some people hold cannot exist. That is, > they maintain that (1) Sentences cannot be excluded from being of any, > even transfinite size, by the laws of a grammar, and (2) Collections of > these sentences are bigger than even the continuum. They are the size > of the collection of all sets: too big to be sets. Let me switch contexts. I have not read the above-mentioned book, but it seems to me that this claim is just plain wrong. I would think a minimum requirement for a sentence in a natural language is that some person who knows the language can read and understand the sentence in a finite amount of time. This would exclude any infinitely long sentences. Perhaps less obviously, it also excludes infinite languages. The reason is that there will never be more than a finite number of people (ET's included), and that each will fail to parse sentences beyond some maximum length, given a finite life for each. (I am not saying that natural languages include only those sentences that are in fact spoken and understood, but that only those sentences that could be understood are included.) In this view, infinite languages are solely a mathematical construct. Russell
lee@uhccux.UUCP (Greg Lee) (11/03/87)
In article <9445@ut-sally.UUCP> turpin@ut-sally.UUCP (Russell Turpin) writes: >In article <8941@shemp.UCLA.EDU>, berke@CS.UCLA.EDU writes: >> I just read this fabulous book over the weekend, called "The Vastness >> of Natural Languages," by D. Terence Langendoen and Paul M. Postal. >> ... > >Let me switch contexts. I have not read the above-mentioned book, >but it seems to me that this claim is just plain wrong. I would > ... >also excludes infinite languages. The reason is that there will >never be more than a finite number of people (ET's included), and > ... >Russell Although the number of sentences in a natural language might be finite, the most appropriate model for human language processing might reasonably assume the contrary. Suppose, for instance, that we wish to compare the complexities of various languages with regard to how easily they could be used by humans, and that we take the number of phrase structure rules in a phrase structure grammar as a measure of such complexity. A grammar to generate 100,000 sentences of the pattern "Oh boy, oh boy, ...!" would be much more complex than a grammar to generate an infinite number of such sentences. And the pattern seems easy enough to learn ... Concerning the length of sentences, I think Postal and Langendoen are not very persuasive. Most of their arguments are to the effect that previously given attempted demonstrations that sentences cannot be of infinite length are incorrect. I think they make that point very well. But obviously this is not enough To show that one should assume some sentences of infinite length. Greg Lee, lee@uhccux.uhcc.hawaii.edu
djh@beach.cis.ufl.edu (David J. Hutches) (11/03/87)
In article <9445@ut-sally.UUCP> turpin@ut-sally.UUCP (Russell Turpin) writes: >In article <8941@shemp.UCLA.EDU>, berke@CS.UCLA.EDU writes: >> ... That is, >> they maintain that (1) Sentences cannot be excluded from being of any, >> even transfinite size, by the laws of a grammar, and (2) Collections of >> these sentences are bigger than even the continuum. They are the size >> of the collection of all sets: too big to be sets. > >... I would >think a minimum requirement for a sentence in a natural language >is that some person who knows the language can read and >understand the sentence in a finite amount of time. This would >exclude any infinitely long sentences. > >Russell Because of the processing capabilities of human beings (actually, on a person-by-person basis), sentences of greater and greater length (and complexity) are more and more difficult to understand. Past a certain point, a human being will go into cognitive overload when asked to process a sentence which his or her capacities (short-term memory, stack space, whatever you want to call it) are not designed to handle. What the human being can, in practice, process and what is *possible* in a language are two different things. I think that it is the case that some theories of language/grammar explain the production of sentences which are grammatical by use of a generative model. In such a model, it is possible to generate sentences of potentially infinite length, even though it would not be possible for a human being to understand them. == David J. Hutches CIS Department == == University of Florida == == Internet: djh@beach.cis.ufl.edu Gainesville, FL 32611 == == UUCP: ...{ihnp4,rutgers}!codas!ufcsv!ufcsg!djh (904) 335-8049 ==