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From: Herman Jurjus on 10 Aug 2010 02:54 Here are two questions about the following text: Frank Quinn, "The Nature of Contemporary Mathematics", (http://www.math.vt.edu/people/quinn/history_nature/nature0.pdf) Question 1: On pages 40-41, Quinn uses the terms 'object' and 'structure' in a remarkable way. Where I would say: R, C, Z[X] are structures, the elements of R, C, Z[X] are objects, Quinn says (if I read him correctly): R, C, Z[X] are objects, the elements of R, C, Z[X] are /not/ objects (see p 41), and as an example of a 'structure' he mentions 'addition' (p 40). This nomenclature seems non-standard to me. Are there any other books or authors that use the terms 'object' and 'structure' in this way? Question 2: On page 70, he mentions 'symmetric (or "new age") ring structures'. What on earth are these? Many thanks in advance, -- Cheers, Herman Jurjus
From: James Dolan on 10 Aug 2010 16:24 in article <i3qsvs$jl5$1(a)news.eternal-september.org>, herman jurjus <hjmotz(a)hetnet.nl> wrote: |Here are two questions about the following text: | |Frank Quinn, "The Nature of Contemporary Mathematics", |(http://www.math.vt.edu/people/quinn/history_nature/nature0.pdf) | |Question 1: |On pages 40-41, Quinn uses the terms 'object' and 'structure' in a |remarkable way. | |Where I would say: | R, C, Z[X] are structures, | the elements of R, C, Z[X] are objects, |Quinn says (if I read him correctly): | R, C, Z[X] are objects, | the elements of R, C, Z[X] are /not/ objects (see p 41), | and as an example of a 'structure' he mentions 'addition' (p 40). | |This nomenclature seems non-standard to me. Are there any other |books or authors that use the terms 'object' and 'structure' in this |way? it's not remarkable; it's pretty standard among a large subculture, perhaps the dominant subculture in contemporary mathematics. roughly speaking it's part of the language of category theory, but has currency even in fields that tend not to realize how much they've been influenced by category theory. -- jdolan(a)math.ucr.edu
From: david petry on 11 Aug 2010 09:14 On Aug 9, 11:54 pm, Herman Jurjus <hjm...(a)hetnet.nl> wrote: > Here are two questions about the following text: > > Frank Quinn, "The Nature of Contemporary Mathematics", > (http://www.math.vt.edu/people/quinn/history_nature/nature0.pdf) Check out section 10.7 of the article where he discusses constructivism. Mind boggling.
From: Jesse F. Hughes on 11 Aug 2010 10:09 david petry <david_lawrence_petry(a)yahoo.com> writes: > On Aug 9, 11:54 pm, Herman Jurjus <hjm...(a)hetnet.nl> wrote: >> Here are two questions about the following text: >> >> Frank Quinn, "The Nature of Contemporary Mathematics", >> (http://www.math.vt.edu/people/quinn/history_nature/nature0.pdf) > > > > Check out section 10.7 of the article where he discusses > constructivism. Mind boggling. > It sure doesn't sound like constructivism as I understand the term. -- "We want a single platform. We're trying to get there using the carrot, or blackmail, or rewards, or whatever you call it." -- Madison, WI, superintendent Rainwater grasps subtlety in the operating system wars.
From: Aatu Koskensilta on 11 Aug 2010 12:33
"Jesse F. Hughes" <jesse(a)phiwumbda.org> writes: > It sure doesn't sound like constructivism as I understand the term. Surely you've run into social constructivism (or constructionism) before? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechen kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |