Responding to James Elander's (JE's) post of Mar 7, 2013 10:47 PM (Much of JE's original post pasted below my signature for ready reference): What an excellent contribution, JE, thanks! > "It is not how much you cover but how much you > uncover," (Harold Fawcett) > Terrific! There is much to ponder for all of us in this wise perception. I googled for Harold Fawcett, but now have some doubts. Was Harold Fawcett the Professor at Ohio State University from 1932, who later became a member of NCTM? Google gives us: http://www.ohioctm.org/fawcett.htm , which states: I had a couple of doubts originally, which I had written up below - they've happily been removed so I've removed my observations below!! Google also gives us: http://education.stateuniversity.com/pages/1984/Fawcett-Harold-P-1894-1976.html He seems to have been a remarkable person. I had not known anything about him earlier. Thanks, JE! > It was B Peirce. who defined Math as:
> "The science of drawing necessary conclusions." ...
> Which brings up the question, What are > conclusions based on? (All conclusions are based on > undefined terms, > defined terms, basic assumptions, and previous > conclusions or laws and in Math theorems.) > Indeed. There is a great to understand and more deeply explore in Peirce's famous observation, which I may do in due course (probably elsewhere; see below). [However, what you've quoted was a saying from "Charles Sanders Peirce", NOT "B. Peirce"].
Charles Sanders Peirce was one of the most original and profound mathematicians/scientists /thinkers/ philosophers the USA (and, indeed, the world!!!) has been privileged to have EVER had, I believe. See, for instance:
(Google has fetched me over 70,000 links - of which I shall mention one more, perhaps the most important one, below).
Charles Sanders Peirce was remarkably also, I believe, a very deep and profound 'linguist' - long, LONG before Noam Chomsky's work brought linguistics to the fore as a scientific discipline!!!
Peirce was one of the late John Warfield's "landmark thinkers" - and Warfield owed much to Peirce's profound thinking on a whole variety of disciplines. Because of Warfield's huge respect for Peirce's thinking, I've tried to read up as much as I could get about and by him.
There is a special website devoted to Peirce and his writings:
This is what the website says about Peirce, which is FAR more than what I had stated above:
"Who is the most original and the most versatile intellect that the Americas have so far produced? The answer "Charles S. Peirce" is uncontested, because any second would be so far behind as not to be worth nominating. [He was] mathematician, astronomer, chemist, geodesist, surveyor, cartographer, metrologist, spectroscopist, engineer, inventor; psychologist, philologist, lexicographer, historian of science, mathematical economist, lifelong student of medicine; book reviewer, dramatist, actor, short story writer; phenomenologist, semiotician, logician, rhetorician and metaphysician."
DESPITE all of the above, Charles Sanders Peirce and his works are unfortunately not at all adequately known today and are, I believe, scarcely understood in the community of scientists!
When I get OPMS properly going (to be able to do some of the things I intend for it), I should like to put some work into the 'Mission':
"To make the works of Charles Sanders Peirce as widely known as they deserve to be".
I have to stop now as there is also a workshop to prepare for. I may revert to the rest of JE's post later.
GSC James Elander (JE) posted Mar 7, 2013 10:47 PM > Teaching Math > It was Harold Fawcett, one day when we were walking > around the Mormon > Square in Salt Lake City, who made a statement I have > never forgot. He > said, "It is not how much you cover but how much you > uncover." > It was B Peirce. who defined Math as: "The science of > drawing > necessary conclusions." Which brings up the question, > What are > conclusions based on? (All conclusions are based on > undefined terms, > defined terms, basic assumptions, and previous > conclusions or laws and > in Math theorems.) > The check list, put out by the NCTM in1947, with a > few additions is > appropriate today as then. (Most people do not > understand the forms of > implications and valid or invalidity > A teacher needs to feel that their subject is the > most valuable and > sells the subject to the students as needed for > success. Yes, a > teacher is a salesman. > I could go on! > <SNIP>