[Xmca-l] Re: Objectivity of mathematics

[Andy Blunden]

Nice to meet you xmca, Luis.
The claim: "the question of objectivity can only be asked and 
investigated within what Foucault used to call a regime of truth" is 
what is at issue here. This is not actually something which can be 
decided by questions of cultural psychology. Of course, Uzbekh peasants 
and Papuan tribespeople find syllogistic logic and mathematical 
abstractions senseless. Of course, mathematical concepts develop along 
with industry. All this is known to xmca-ers. It is not a question of 
whether mathematics is a cultural construct (or social convention) but 
whether it is *only* such a convention. Of course it is an historical 
accident that the decimal system of number is used in arithmetic and 
Roman letters in algebra, and that so much of mathematics is elaborated 
through equations, but this is not the point, is it? Is there really 
*nothing* outside the text?
My claim is that it is both a "social convention" (since we have adopted 
this term here) *and* a natural science. And *in that sense* it is like 
any other natural science. Mathematics differs from the other natural 
sciences in many respects, but in the fundamentals it is the same. If 
natural science is *nothing but* a set of social conventions, then so is 
mathematics.
Do you want to make that claim, Luis?
You note that: "Mikhailov is not saying that we invented ex nihilo the 
idea of the sun as something round." Not *ex nihilo*. So I guess we 
agree, yes?

Andy
------------------------------------------------------------------------
*Andy Blunden*
http://home.pacific.net.au/~andy/


Luis Radford wrote:
> Here are my two cents to this interesting discussion.
>
> The question of objectivity has been a central question in understanding
> what is meant by mathematics. Sociologists of knowledge, even those
> inclined to think about the world as culturally formed (e.g., Berger,
> Luckmann, and even Karl Mannheim), have usually preferred to stay away
> from a sociological understanding of mathematics.
> The crux of the problem seems to me to be this: If we do not have a clear
> sense of what we mean by mathematics, we won’t be able to tackle the
> question of its objectivity. Mathematics objectivity, I think, cannot be
> established on the basis that 4x7 = 28, regardless of the culture. What is
> often missed in examples of this kind is that the examples are already
> embedded in a particular rationality (numbers are treated as
> decontextualized quantities and the multiplication operator bears an
> abstract, specific meaning). It is “objective” only within a culturally
> institutionalized way of thinking and doing about quantities.
> My argument does not amount to saying that in another culture 4x7 may be
> equal to 20 or something else. What I am trying to say is that the
> question of objectivity can only be asked and investigated within what
> Foucault used to call a regime of truth (the Western contemporary regimes
> of truth include a strong interest in abstraction and in expressing
> abstractions in a written manner). When the Jesuits brought Euclid to
> China in the 17th century, they did not simply brought Euclidean theorems;
> they also brought new ways of thinking about figures where proving things
> in a syllogistic manner makes sense. They brought an Euclidean regime of
> truth.
>
> In the attached chapter, I refer to a psychological expedition that
> Wassmann and Dasen carried out several years ago with Yupno subjects (from
> the Madang Province of Papua New Guinea). The example illustrates, from
> another angle, the previous idea. Wassmann and Dasen used the following
> “Bride price story”: “You want to marry P’s daughter. The bride price was
> set at 19 pigs. You have already paid 8 pigs. How many will you have to
> pay later?” The answer was: “Friend, I am not rich enough to buy a new
> wife. Where would I find 8 pigs? Besides, I am an old man and have no more
> strength.” As the interviewers remark, “After this he could not be moved
> to tackle the problem again, it having been rejected as preposterous” (W &
> D). Although the question seems to make sense because of its “contextual
> cultural nature” (pigs, bride price, etc.) the way the question is asked
> is already asked within a certain rationality that provides us (no the
> Yupno) with a range of expected responses. The rationality has its own
> normativity (which is partially explicit, partially implicit) from where a
> kind of objectivity can be spoken about.
> The Euclidean and the Yupno examples do not explain, however, what can be
> understood by “mathematics.” They do not provide any hint about from where
> the various forms of mathematics we see in the world may come.
> Following Ilyenkov, I see mathematics as idealities. Of course, not
> platonic idealities. I see mathematics rather as idealities or generals,
> in Hegel’s sense.  I have suggested that Mathematics is crystalized human
> labour. More precisely, Mathematics (taken as an ethno-plural noun here)
> are (like knowledge in general) an evolving culturally codified synthesis
> of doing, thinking, and relating to others and the world.
> Mathematics, in this sense, cannot be equated to social practices. They
> are syntheses of social practices. Mathematics, as Hegelian generals, are
> put into motion, actualized and transformed through social practices.
> Within this context, the Yupno mathematics are syntheses of reflection and
> action in the form of the Yupno activities.
>
> To come back to the question of objectivity and to Martin’s and Andy’s
> reply to Julian’s post, I am reminded of a beautiful passage from
> Mikhailov’s “The  Riddle of the Self.” Mikhailov asserts that “People
> could see the sun as round only because they rounded clay with their
> hands. With their hands they shaped stone, sharpened its borders, gave it
> facets” (Mikhailov, 1980, p. 199).
> Mikhailov is not saying that we invented ex nihilo the idea of the sun as
> something round. Nor that the sun was already round having all the
> Euclidean properties of geometric spheres (symmetries, etc.) before we
> noticed it for the first time. We qualify the sun as round because we have
> experienced and objectify roundness through embodied activity and
> recognize (as far as our culturally evolving perceptual systems allow us
> to do) a similarity with artifacts we and others before us have shaped to
> satisfy some needs.
>
>
> Luis
>
> On 8/11/2014, 7:18 PM, "Andy Blunden" <ablunden@mira.net> wrote:
>
>   
>> Oh dear! some times I despair of the possibility of communication.
>> That the Earth is round is a social convention, but it is not *only* a
>> social convention; it has a sound basis in material reality. That is to
>> say, Julian, no amount of discoursing and activity can alter the fact
>> that the world is round. The roundness of the Earth is also outside
>> discourse and activity, even though it is made meaningful and known for
>> us only thanks to discourse/activity.
>> Driving on the right is subject to discourse/activity. In about 1968
>> Sweden changed from left to right. RIght-hand driving is *only* a social
>> convention.
>> Simple, eh? I would have thought so.
>> Andy
>> ------------------------------------------------------------------------
>> *Andy Blunden*
>> http://home.pacific.net.au/~andy/
>>
>>
>> Martin John Packer wrote:
>>     
>>> And also that the earth is round is a convention! Go figure!
>>>
>>> Martin
>>>
>>> On Nov 8, 2014, at 5:55 PM, Julian Williams
>>> <julian.williams@manchester.ac.uk> wrote:
>>>
>>>   
>>>       
>>>> I'm struggling to keep up here... Surely I didn't hear Andy Blunden
>>>> say that 'objectivity' implies stuff that can't be transformed? I'm
>>>> sure I must have misremembered that!.?
>>>>     
>>>>         
>>>
>>>   
>>>       
>
>