John, (01)
If you are correct in the following, and I tend to agree with it, and it
could be made better known, then much wasted text could be eliminated. (02)
JFS> ...all of mathematics, including formal logic, is based on a subset
of the same semantics
> we use in using ordinary language... (03)
There are too many discussions of formal semantics in which someone
objects, "but you're leaving X out!", where X refers to some aspect of
natural language semantics. In fact, I've been that someone too many
times! Doh! But I've also been on the other side, and felt that
"Whereof one cannot speak, thereof one must be silent." in support of
some elegant but limited formalism. (04)
I came across something today that possibly adds an interesting twist to
this idea that formal is a subset of natural semantics or, at least,
that formal semantics uses a subset of the *mechanisms* people use in
speech semantics. Researchers have found that Jazz musicians, while
improvising, use the same part of their brains, which includes Broca’s
area, they use when generating speech:
http://seedmagazine.com/content/article/creation_on_command/ , "The
scientists argue that expert musicians create new melodies by relying on
the same mental muscles used to create a sentence; every note is another
word." So perhaps not only mathematics and formal logic are based on a
subset of the mechanisms of NL semantics, but music may be too. (05)
John Black
www.kashori.com (06)
John F. Sowa wrote:
> Phil,
>
> I sympathize with your criticisms, because I believe that the work on
> formal semantics for natural language, although interesting, is not
> psychologically or linguistically realistic.
>
> Instead of assuming that NL semantics is based on formal logic,
> I believe that all of mathematics, including formal logic, is based
> on a subset of the same semantics we use in using ordinary language.
> To use Wittgenstein's terminology, mathematical notations and rules
> of inference are specialized "language games". They use a *subset*
> of the mechanisms that people use when they talk and listen.
>
> Following is a paper I wrote that discusses those issues:
>
> http://www.jfsowa.com/pubs/lgsema.pdf
>
> Abstract and opening paragraph below.
>
> John
> _____________________________________________________________________
>
> Language Games, A Foundation for Semantics and Ontology
>
> John F. Sowa
>
> The issues raised by Wittgenstein’s language games are fundamental to
> any theory of semantics, formal or informal. Montague’s view of natural
> language as a version of formal logic is at best an approximation to a
> single language game or a family of closely related games. But it is not
> unusual for a short phrase or sentence to introduce, comment on, or
> combine aspects of multiple language games. The option of dynamically
> switching from one game to another enables natural languages to adapt
> to any possible subject from any perspective for any humanly conceivable
> purpose. But the option of staying within one precisely defined game
> enables natural languages to attain the kind of precision that is
> achieved in a mathematical formalism. To support the flexibility of
> natural languages and the precision of formal languages within a common
> framework, this article drops the assumption of a fixed logic. Instead,
> it proposes a dynamic framework of logics and ontologies that can
> accommodate the shifting points of view and methods of argumentation and
> negotiation that are common during discourse. Such a system is necessary
> to characterize the open-ended variety of language use in different
> applications at different stages of life -- everything from an infant
> learning a first language to the most sophisticated adult language in
> science and engineering.
>
> This is a preprint of an article that appeared as Chapter 2 in
> _Game Theory and Linguistic Meaning_, edited by Ahti-Veikko Pietarinen,
> Elsevier, 2007, pp. 17-37.
>
> 1. The Infinite Flexibility of Natural Languages
>
> Natural languages are easy to learn by infants, they can express any
> thought that any adult might ever conceive, and they are adapted to
> the limitations of human breathing rates and short-term memory.
> The first property implies a finite vocabulary, the second implies
> infinite extensibility, and the third implies a small upper bound on
> the length of phrases. Together, they imply that most words in a
> natural language will have an open-ended number of senses -- ambiguity
> is inevitable. Charles Sanders Peirce and Ludwig Wittgenstein are two
> philosophers who understood that vagueness and ambiguity are not defects
> in language, but essential properties that enable it to express anything
> and everything that people need to say. This article takes these
> insights as inspiration for a system of metalevel reasoning, which
> relates the variable meanings of a finite set of words to a potentially
> infinite set of concept and relation types, which are used and reused
> in dynamically evolving lattices of theories, which may be expressed
> in an open-ended variety of logics.
>
>
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
>
>
>
> (07)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (08)
|