Phil, (01)
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. (02)
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. (03)
Following is a paper I wrote that discusses those issues: (04)
http://www.jfsowa.com/pubs/lgsema.pdf (05)
Abstract and opening paragraph below. (06)
John
_____________________________________________________________________ (07)
Language Games, A Foundation for Semantics and Ontology (08)
John F. Sowa (09)
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 openended 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. (010)
This is a preprint of an article that appeared as Chapter 2 in
_Game Theory and Linguistic Meaning_, edited by AhtiVeikko Pietarinen,
Elsevier, 2007, pp. 1737. (011)
1. The Infinite Flexibility of Natural Languages (012)
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 shortterm 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 openended 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 openended variety of logics. (013)
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