Questions about Quinn
in [Math]
|
Prev: snow
Next: sum(floor(k/a)*floor(k/b),k=1..a*b-1)
From: FredJeffries on 11 Aug 2010 13:53 On Aug 11, 7:09 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > david petry <david_lawrence_pe...(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. He's using the term in the sociological as opposed to the mathematical sense. See Peter Berger's "The Social Construction of Reality" http://en.wikipedia.org/wiki/The_Social_Construction_of_Reality
From: david petry on 11 Aug 2010 16:18 On Aug 11, 10:53 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > On Aug 11, 7:09 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > > > > > > > david petry <david_lawrence_pe...(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. > > He's using the term in the sociological as opposed to the mathematical > sense. See Peter Berger's "The Social Construction of Reality"http://en.wikipedia.org/wiki/The_Social_Construction_of_Reality- Yes, of course, but do mathematicians ever use the term in that sense? It already has a mathematical meaning.
From: Jesse F. Hughes on 11 Aug 2010 19:49 Aatu Koskensilta <aatu.koskensilta(a)uta.fi> writes: > "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? Not in philosophy of mathematics circles, where constructivism has a rather different meaning. I understand why this viewpoint is called "constructive", but it surely isn't my default meaning of constructivism in mathematics. -- Jesse F. Hughes "You may not realize it but THOUSANDS of people read my posts. You are putting your stupidity on wide display." -- James S. Harris knows about wide displays of stupidity.
From: FredJeffries on 11 Aug 2010 22:11 On Aug 11, 1:18 pm, david petry <david_lawrence_pe...(a)yahoo.com> wrote: > On Aug 11, 10:53 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > > > > > On Aug 11, 7:09 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > > > > david petry <david_lawrence_pe...(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. > > > He's using the term in the sociological as opposed to the mathematical > > sense. See Peter Berger's "The Social Construction of Reality"http://en..wikipedia.org/wiki/The_Social_Construction_of_Reality- > > Yes, of course, but do mathematicians ever use the term in that > sense? It already has a mathematical meaning. When I was a student my aunt once picked up my "Group Theory" book, started paging through it and then put it down exclaiming "I thought it was a sociology book." Quinn says, "Comments are welcome."
From: Herman Jurjus on 12 Aug 2010 06:12
On 8/10/2010 10:24 PM, James Dolan wrote: > 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. Ok, thanks. But can you mention a few example texts? I'm quite familiar with category-language, but I've never seen a category theory text that talked in Quinns way. For the sake of clarity: calling something like R or C an object is not strange to me. The things I find strange are: - calling the -elements- of R -not- mathematical objects - referring to something like 'addition' as '-a- structure' (I would call, for example, (R, +) 'a structure', and addition could then be called 'some form of structure defined on R'. But Quinn seems to take this one step further. It could also be that I'm reading too much in his words, of course.) -- Cheers, Herman Jurjus |