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[Xmca-l] Re: Objectivity of mathematics



My reading of Luis' "two cents" is that in order to empower students it is
necessary to foster an engagement with the objectivity described.  That, to
me, seems to be all about problem solving, i.e. discerning 'rationally'
important details of situations and determining what should be done in
relation to them.  I am surmising that such problem solving goes
hand-in-hand with a wider appreciation of that 'rationality'.

Best,
Huw



On 9 November 2014 18:05, Julian Williams <julian.williams@manchester.ac.uk>
wrote:

> 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!.?
> >>>
> >>
> >>
> >>
> >>
> >
>
>
>