[Xmca-l] Re: Objectivity of mathematics

[Julian Williams]

Andy (if you haven't forgotten this prehistoric post by now, nearly a day
later!)

I don¹t disagree that in some sense the 'social convention' (of
mathematics) may be not, per se, 'objective' (in the sense that it can
'easily' be re-written)  and also that maths can be conventional as well
as 'objective'. But I still think its objectivity 'exists' to be
transformed and developed, just as other natural sciences do.

I guess the way I use 'subject' and 'object' (and
subjectivity/objectivity) implies that the concept of 'object' and
'objectivity' only makes sense in terms of a dialectic of activity. So
let's begin with the monist hypothesis that 'nature' (or as some say
'god') includes everything, humanity, matter, discourse, experience,
perezhivaniya one and all.

But 'we' (OK hang in here I know this we is a problem.. What is
'objective' is then dialectically related to who the 'we' is that is
collectively considered to be acting - e.g. Are 'we' humanity as a whole,
the clique of professional mathematicians, or ... ) find ourselves to be a
part of this whole mess: we 'subjects' , our subjectivity and agency are a
part of it, but we experience 'the other' stuff (not 'us') as 'objects' to
act on .. Of course here the dialectic of subject-object means the
'object' may be represented in terms of our needs (e.g. 'That rabbit looks
yummyŠ' ).

I think Pierce's 'firstness' includes this 'other'- objectivity is
constituted by the other's firstness to begin with. When you say the earth
is 'round', you allude to the firstness of the world that we come to
manage as 'roundness'.

Then, it seems some of us are concerned with the 'shift' that takes place
when the collective 'we' start to communicate and discourse tends to lose
its direct connection with action on the 'other' objects (including
firstness). The 'object(s)' now begins to include our concepts developed
in communicative discourse including 'round' and 'circle', i.e.
mathematics.

My argument (last post - here we are at last) argued that the
objectivity/validity of this mathematics/discourse rests on (and only on)
the degree to which it is in some sense satisfactory 'in practice'.

Here Mike Cole's post (if I got it right) picks me up and I think he is
right - I have confused 'objectivity' with 'validity'. This is because the
'object' we call mathematics is always hypothesised to be  'valid': that
is, when we work on the 'object' mathematics, mathematicians are
critiquing and transforming what is taken to be the state of the art in
mathematical 'validity' or 'truth'.

Julian

Ps Skimming forward: Luis cites Foucault's 'regime of truth' for
mathematics. Im not sure if you - Luis -  will agree with this Luis, but
my reading of Foucault is that he uses this term (i.e. Regime of T) as a
tool to critique the power structures within the discipline. Observing
that validity of mathematics is upheld by such a regime should - if we
agree with Foucault - provoke us to smash it to piecesŠ no?

:-)



On 09/11/2014 00:18, "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!.?
>>>     
>>
>>
>>
>>   
>