RE: [xmca] a minus times a plus

["Eugene Matusov" <ematusov@UDel.Edu>]

Dear Mike--

You wrote,
> And for sure, Eugene, it is a cardinal error to believe that the enemy
> of
> your enemy is your friend. Maybe, maybe
> not. Like all laws of social science, it all depends.

Actually, it worked rather well during the WWII for the Allies (US-UK) and
the USSR. Their cooperation in opposition to the Nazi Germany was governed
by the Arabic wisdom "an enemy of your enemy is your friend." It can be
powerful indeed but as you said it is not universal.

As to the natural language and the formal logic (math), in natural language
(+1)*(+1)=-1, according to famous anecdote, "The most celebrated [Sidney]
Morgenbesser anecdote involved visiting Oxford philosopher J. L. Austin, who
noted that it was peculiar that although there are many languages in which a
double negative makes a positive, no example existed where two positives
expressed a negative. In a dismissive voice, Morgenbesser replied from the
audience, 'Yeah, yeah.'"

Take care,

Eugene

> -----Original Message-----
> From: xmca-bounces@weber.ucsd.edu [mailto:xmca-bounces@weber.ucsd.edu]
> On Behalf Of Mike Cole
> Sent: Wednesday, April 29, 2009 8:38 PM
> To: eXtended Mind, Culture, Activity
> Cc: backontrack@wwscholars.org; Zoi Philippakos; PIG
> Subject: Re: [xmca] a minus times a plus
> 
> Eugene, the mixture of plus and minus was the focus of my inquiry.
> Natural
> language understanding
> of double negatives solves that problem for 2 numbers, beyond which I
> assume
> natural language needs
> a notation system to keep track.
> 
> So far Jerry Balzano's mirror explanation seems like it has the best
> chance
> with my grand daughter (in
> part because i can actually imagine creating the demonstration that
> lines up
> intuition and notation). I
> have not had time to read all of the notes in this thread owing to
> heavy
> teaching and extra lecture schedule
> and a rash of recommendation letters out of season (which I will accept
> as a
> sub for swine flu). But
> simply in scanning could I make a plea for socio-CULTURAL
> constructivism? If
> we do not keep what is
> essential to human forms of human sociality in the discussion, we might
> as
> well be talking about bonobos
> who, at least, know enough to make love not war.
> 
> And for sure, Eugene, it is a cardinal error to believe that the enemy
> of
> your enemy is your friend. Maybe, maybe
> not. Like all laws of social science, it all depends.
> 
> mike
> 
> 
> On Wed, Apr 29, 2009 at 1:44 PM, Eugene Matusov <ematusov@udel.edu>
> wrote:
> 
> > Dear everybody--
> >
> > In response to Mike's profound inquiry of why a minus times a minus
> is a
> > plus, I was thinking that it is a mathematical model of the Arabic
> wisdom
> > that "an enemy of my enemy is my friend." Of course, the latter is
> not
> > always true -- we have plenty of examples when enemy of our enemy is
> still
> > our enemy (or just indifferent) and, thus, for these types of social
> > relations, the mathematical model of (-1) x (-1) =1 does not work.
> Just
> > consider, for an example, the relations among the US, Al-Qaida, and
> Saddam
> > Hussein.
> >
> > The issue for me is why the Western civilization prioritizes (and
> then
> > mathematizes) social relations described in the Arabic wisdom. One
> answer
> > is
> > because "the real world" works according to these social relations
> (i.e.,
> > the social relations is just an example of the truth out there). An
> > alternative explanation is that the Western civilization can afford
> and
> > might be even benefit from imposing these social relations on "the
> real
> > world" that by itself is indifferent to any social relations (and
> thus
> > mathematical models). Any other explanations?
> >
> > What do you think?
> >
> > Eugene
> >
> > > -----Original Message-----
> > > From: xmca-bounces@weber.ucsd.edu [mailto:xmca-
> bounces@weber.ucsd.edu]
> > > On Behalf Of Ng Foo Keong
> > > Sent: Wednesday, April 29, 2009 12:23 PM
> > > To: ablunden@mira.net; eXtended Mind, Culture, Activity
> > > Subject: Re: [xmca] a minus times a plus
> > >
> > > Is Mathematics _merely_ socially constructed, or is there something
> > > deeper and inevitable?
> > >
> > > I think this deserves a new thread, but I couldn't manage to start
> one.
> > > Let me try to draw out and assemble the line of discussion that
> spun
> > > off from the "a minus times a plus" thread.
> > >
> > > In her inaugural post to xcma, Anna Sfard about talked "rules
> > > of the mathematical game" among other things.
> > >
> > > Then Jay Lemke said:-
> > > > ...
> > > > I think it's important, however, to see, as Anna emphasizes,
> > > > that there is a certain "arbitrariness" involved in this, or
> > > > if you like it better: a freedom of choice. Yes, it's
> > > > structure-and-agency all over again! Structure determines that
> > > > some things fit into bigger pictures and some don't, but
> > > > agency is always at work deciding which pictures, which kind
> > > > of fit, which structures, etc. And behind that values, and
> > > > culture, and how we feel about things.
> > >
> > > -----
> > > Then I (Ng Foo Keong) said:-
> > >
> > > > regarding structure and agency, arbitrariness:-
> > > > i think now it's time for me to pop this question that has been
> > > > bugging me for some time.  i am convinced that mathematics is
> > > > socially constructured, but i am not so convinced that
> mathematics
> > > > is _merely_ socially constructured.  if we vary across cultures
> > > > and different human activities, we might find different ways
> > > > in which patterns and structure can be expressed and yet we might
> > > > find commonalities / analogies.  the question i am asking is:
> > > > is maths just a ball game determined by some group of nerds who
> > > > happen to be in power and dominate the discourse, or is there
> some
> > > > invariant, something deeper in maths that can transcend and unite
> > > > language, culture, activity .... ?
> > >
> > > Foo Keong,
> > > NIE, Singapore
> > >
> > > -----
> > > Then Ed Wall said:-
> > >
> > > > Ng Foo Keong
> > > > As regards your question about mathematics being socially
> > > > constructed, I'm not entirely sure what you mean by
> > > > mathematics or what kind of evidence would convince you it
> wasn't.
> > > > Suppose I said that there was evidence for innate subtizing.
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