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[Xmca-l] Re: Objectivity of mathematics
- To: "eXtended Mind, Culture, Activity" <email@example.com>
- Subject: [Xmca-l] Re: Objectivity of mathematics
- From: Martin John Packer <firstname.lastname@example.org>
- Date: Sun, 9 Nov 2014 14:10:40 +0000
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- Thread-topic: [Xmca-l] Objectivity of mathematics
Agreed, Anna. Andy, I think, defines objective as what cannot be changed. I follow Julian in finding that confusing. Andy gave the example that human activity cannot change the fact that the world is round. Yet with enough atomic bombs humans could certainly change that fact! Less depressingly, human activity changes our material circumstances all the time, and we often employ mathematics in order to do this.
At the risk of repeating myself, I think we need to work hard to escape from false dichotomies such as objective/subjective, social/real, conventional/natural...
Brian Rotman has suggested that we need “to demolish the widely held metaphysical belief that mathematical signs point to, refer to, or invoke some world, some supposedly objective eternal domain, other than that of their own human, that is time bound, changeable, subjective and finite, making” (1987, p. 107).
On Nov 9, 2014, at 8:49 AM, anna sfard <firstname.lastname@example.org> wrote:
> I'm happy to agree with you, Andy. As I do with Martin. I think the two of
> you are on the same page, more or less, but get distracted by subtleties of
> word use. For instance, none of you said explicitly what is the category of
> things to which the adjective "objective" can be applied. Words or worlds?
> Being explicit on this point may help (as it helped me to understand that I
> have no use for this word, and this does not mean that I deny the existence
> of the/a "real world")
> -----Original Message-----
> From: email@example.com
> [mailto:firstname.lastname@example.org] On Behalf Of Andy Blunden
> Sent: Sunday, November 09, 2014 3:27 PM
> To: 'eXtended Mind, Culture, Activity'
> Subject: [Xmca-l] Re: Objectivity of mathematics
> A wonderful metaphor, Anna. But it isn't magic like it is in the fairy tale,
> is it? When the text gets out of control and unfolds according to "laws of
> its own," so to speak, that is *Nature*.
> That is all I am saying when I say mathematics is not *just* a social
> convention. And the same applies to other natural sciences.
> *Andy Blunden*
> anna sfard wrote:
>> There are two types of "validity" I think we can talk about here,
>> Andy, the external - one that manifests itself in the fact that
>> mathematics works for us in other things we do; and internal - the one
>> that stems from strict adherence to the rules of the game (discourse).
>> Re the latter, mathematical discourses are like the sorcerer's
>> apprentice's broom: once put in motion, they get life of their own and
> nothing can stop them.
>> Can somebody stop ME please? :-)
>> -----Original Message-----
>> From: Andy Blunden [mailto:email@example.com]
>> Sent: Sunday, November 09, 2014 3:02 PM
>> To: anna sfard
>> Cc: 'eXtended Mind, Culture, Activity'
>> Subject: Re: [Xmca-l] Re: Objectivity of mathematics
>> I think your quote expresses a truth, and an important truth.
>> It is more precise, but it is what I meant when I said earlier that
>> the unit of analysis "rotates.", with the mediator becoming the object.
>> The statement is still kind of agnostic on the question, isn't it
>> though, Anna? Mathematical relations are often only an approximation
>> to things happening in the material world, and the validity of the
>> mathematics is not thereby any the less for that.
>> *Andy Blunden*
>> anna sfard wrote:
>>> No, Andy, I don’t think this was, or should be, said. I apologize in
>>> advance for quoting myself, but it would be too much to try to say
>>> things anew in the middle of work on an all different text:
>>> "mathematical communication apparently reverses the developmental
>>> order known from colloquial discourses: whereas these latter
>>> discourses are created for the sake of communication about physical
>>> reality, in mathematical discourse objects are created for the sake
>>> True, also mathematical communication is supposed, eventually, to
>>> mediate practical activities, and thus to pertain, in one way or
>>> another to the world of primary objects that predate the discourse.
>>> However, this fact may easily escape one’s attention. The
>>> realization trees of mathematical signifiers [for the sake of the
>>> present conversation, you may replace the "realization trees" with
>>> "chains of signification"], although likely to have primary objects
>>> or processes on such objects at their basis, may be too rich and
>>> complex to be embraced at a glance. Leaving the concrete foundations
>>> of such trees temporarily out of sight may thus be the condition for
>>> the proficiency of
>> mathematical communication."
>>> Xmca-ing is addictive!
>>> -----Original Message-----
>>> From: firstname.lastname@example.org
>>> [mailto:email@example.com] On Behalf Of Andy Blunden
>>> Sent: Sunday, November 09, 2014 2:41 PM
>>> To: eXtended Mind, Culture, Activity
>>> Subject: [Xmca-l] Re: Objectivity of mathematics
>>> "Nothing outside the text" is a way of saying that "the text alone
>>> forms the object."
>>> Would you agree, in the context of mathematics, that the text alone
>>> forms the object?
>>> *Andy Blunden*
>>> Martin John Packer wrote:
>>>> Who has said that there is nothing outside the text, Andy? Not
>>> not Anna, not Huw, not me, not Ed, and not Luis so far as I can see.
>>> If this is the question that is at issue for you here, I think you're
>>> the only person for whom it is an issue.
>>>> On Nov 9, 2014, at 3:52 AM, Andy Blunden <firstname.lastname@example.org> wrote:
>>>>> Is there really *nothing* outside the text?