"Mathematics is a language." At this moment in time, the cited page contains three quotations on why mathematics should be regarded as a language. My knee-jerk reaction, and it's just that I'm afraid, is that mathematics is not a language in say the way that English is a language. Why? Well, if English and mathematics were languages, you could translate texts between them. You can use English (or any other natural language) to write mathematics and about mathematics, but I don't see you translating, except in some cranky manner, a book — any book — written in a natural language into mathematics. Another thought: is mathematics langue or parole? If the former, are there any examples of the latter? Why do mathematicians bother with natural language at all? No, the mapping between language and mathematics is more complicated than that which can be expressed by the copula. An interesting site nonetheless.
[via the Cut the Knot site, via a thread on L S Vygotsky, via a Language Hat entry on language and cognition]
Posted by jim at July 14, 2003 04:31 PM | TrackBackcharles wells's
_handbook_of_mathematical_discourse_
http://www.cwru.edu/artsci/math/wells/pub/abouthbk.html
is well worth a look; he takes the
"mathematics 'is' a language" metaphor
a little too literally in certain sentences
but is well aware overall that it *is*
a metaphor. he usually speaks instead
of "the mathematical register" as a
collection of habits of speech (and writing)
useful in discussing mathematics (whatever
*that* is . . .); the _handbook_ catalogues
some of these in the hope of making it easier
for those (teachers) able to "speak mathematics"
more or less unconsciously to communicate
somewhat more effectively with those (students)
still unfamiliar with the conventions.
that this whole process is entirely different
from learning a language rightly-so-called
should of course go without saying.
whaddaya gonna do.
Interesting. Take a look at M. Ali Khan's essay, The irony of/In Economic Theory (in an issue of MLN I edited a some time ago);
http://muse.jhu.edu/demo/mln/108.4khan.html
and his discussion of Mathematics is a Language/Mathematics is Language, etc.
Vlorbik-- Thanks for the pointer. The PDF is over 200 pages, so it'll take a while to read and digest.
Miladus-- Thanks for the URL to the article. I've started looking over it.
Posted by: jim on July 15, 2003 09:04 AMNote this page at the same site.
Posted by: Justin on September 25, 2003 09:28 AMJustin: Thanks for the link which somehow got mangled by MT. Here it is again. Will take a look at it.
Posted by: jim on September 25, 2003 10:20 AMDrat, I should have known it would get mangled. In fact, I did suspect it would, and meant to check after posting, but somehow forgot.
Posted by: Justin on September 25, 2003 11:56 AM