Jerry and Clark, In mathematics, logic, computer science, physics, engineering..., precision in measurement, reasoning, and communication is essential. I am not denying that.
But I also believe that Peirce's point that "symbols grow", Wittgenstein's language games, and Sue Atkins' remark that "I don't believe in word senses" are fundamental to language -- and every other semiotic system. Atkins and Kilgarriff are lexicographers -- and so was Peirce. It's no accident that his most profound writings came *after* his work on the Century Dictionary. He was also a logician, mathematician, physicist, and engineer. I believe that his later work is the most profound writing about balancing and relating *all* the issues of language, logic, science... JLRC
yes, similar principles hold for mathematics, although the “wavelength" is a tad longer and the “amplitudes" are shallower.
Yes, but mathematicians never assume that any terms have universally accepted definitions. They never say "set theory" by itself. Even the qualifications ZF or VNBG in front of "set theory" are not sufficient. In any publication, mathematicians have to be very specific about the slightest details of notation and punctuation. JLRC
I am reminded of workers in public health, where the joke is: Measure with a micrometer, mark with a pencil and cut with an axe!
That's good. It reminds me of the one about economics: Department chairman: I've heard that you give exactly the same exam every year. Aren't you concerned that your students might get a copy from someone who took the course last year? Professor of economics: That's OK. I use the same questions, but I change the answers every year. CG
while we may figuratively characterize a series of tone as ‘blue’ it seems that conceptually we can still make a distinction between sound and color that is a limit on the symbol. I think we can make such distinctions without cutting off inquiry. Indeed we make such symbolic distinctions all the time.
I completely agree -- and so would Peirce, Wittgenstein, Atkins, and Kilgarriff. In any specific document, we can be as precise as necessary for that application. But we can never assume that the words in one document have precisely the same "meaning" as the same words in another document. Differences in the instruments used, the human procedures, the methods of gathering data, and even the time of day can affect the "microsenses". CG
My own position is that of course connotations can go wild and symbols grow in these unwanted ways. That doesn’t mean we can’t talk of more limited symbolic generals from a logical perspective.
I agree. But it's a matter of degree. As we can see, science and engineering do succeed -- eventually. But there have been many, many communication failures along the way -- and dead bodies as testimony. John
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