Hi John: Your points about the instability of words and logical terms are well taken, and, I believe, well-recognized by those inquirers who are culturally competent in the history of language development.
And, yes, similar principles hold for mathematics, although the “wavelength" is a tad longer and the “amplitudes" are shallower. :-) So, yes, the meanings of symbols change in time. Nevertheless, it is important to recognize that human communication can be successful without using the exactness of the real number system. 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! Secondly, I would note that the terminology for the metallic elements has been remarkably stable across cultures and millennia and has severed to ground and stable the languages of the hard science while permitting the emergence of new terms of greater and lesser scale. The crucial issue is when are titrations of meanings to the finest possible scale necessary? And, for teachers, how do you select the appropriate titrations of meanings for your student? If the scale is to crude, the students learn little. If the scale is to fine, the students learn little (and become frustrated.) Finally, I recall a visit to Krakow and a visit to Copernicus’s (1473-1543) equipment. I was amazed by the very fine details of the engraved markings on copper plates, indicating that they were aware of the needs for accurate measurements. Cheers Jerry > On Jan 16, 2017, at 3:56 PM, John F Sowa <s...@bestweb.net> wrote: > > On 1/16/2017 3:32 PM, Clark Goble wrote: >> I think one can still manage how symbols grow. That is consider them >> bundles of process. The question ends up being what the limits of the >> symbol are. Of course that becomes a complex topic too. > > I don't believe that it's possible or desirable to put any limits on > the way symbols grow. Any attempt would "block the way of inquiry." > Basic issues: > > 1. The vocabulary of every natural language is limited by the need > for every generation of infants with no prior experience and > a limited attention span to learn the structure and a basic > vocabulary. > > 2. But continuity implies that no finite vocabulary can adequately > name and describe everything anyone might encounter during a > lifetime (or even a day). > > 3. Therefore, the basic vocabulary a child learns must be extensible > in an unlimited number of ways. > > 4. For any theory in mathematics or science, it's important to have > precise definitions. But those definitions are limited to the > theory for which they have been defined. > > 5. No theory of science remains fixed for very long. And scientists > usually keep the old vocabulary, but redefine the words as new > phenomena and ways of explaining them are discovered. > > 6. For examples, just think of the way Newton's vocabulary has been > redefined in the 20th century. > > For more examples, see the following slides: > http://www.jfsowa.com/talks/natlog.pdf > > Slide 17 of natlog.pdf summarizes the issues about "microsenses", > which are the minute changes that occur from one occurrence of a > word to another. > > Slide 18 quotes the lexicographer, Sue Atkins, who devoted her > career to defining word senses. But after all that work, she > admitted "I don't believe in word senses." See below for a > copy of that slide. > > John > _________________________________________________________________ > > Slide 18 of http://www.jfsowa.com/talks/natlog.pdf > > “I don’t believe in word senses.” > > The title is a quotation by the lexicographer Sue Atkins, who > devoted her career to writing and analyzing word definitions. > > In an article with that title,* Adam Kilgarriff observed that > > ● “A task-independent set of word senses for a language is not > a coherent concept.” > > ● The basic units of meaning are not the word senses, but the actual > “occurrences of a word in context.” > > ● “There is no reason to expect the same set of word senses to be > relevant for different tasks.” > > ● “The set of senses defined by a dictionary may or may not match > the set that is relevant for an NLP application.” > > ● Professional lexicographers are well aware of these issues. > > ● The senses they select for a dictionary entry are based on editorial > policy and assumptions about the readers’ expectations. > > * See http://www.kilgarriff.co.uk/Publications/1997-K-CHum-believe.pdf > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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