FOM: Stanley Rosen responds to : Lakatos, Objectivity. . .
Robert S Tragesser
RTragesser at compuserve.com
Fri Dec 19 18:04:20 EST 1997
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Date: Fri, 19 Dec 1997 16:37:17 -0500
To: Robert S Tragesser <RTragesser at compuserve.com>
From: stanley rosen <srosen at bu.edu>
Subject: Re: Lakatos, Objectivity, Gen Intellectual Interest,
Political Agendas
Dear Bob,
the debate about Lakatos, objectivity, and social construction is
very resonant. I knew Lakatos briefly, and in fact was invited by him to
spend a semester at the LSE, but despite an initial enthusiasm on his part,
he very soon turned nasty, and I stayed away from him. It is perhaps not
relevant to your philosophical discussions, but I believe that he was quite
mad, although obviously extremely intelligent.
I don't pretend to understand the distinction between aristocratic
and humanitarian mathematics. It sounds like a category mistake to me. As
to Lakatos, he may have been a humanitarian in the abstract, but this was
never visible in any particulars that I observed. He despised almost
everyone and was unusually frank in his denunciations of colleagues, in
particular of their intellectual and political shortcomings. I would call
him a typical aristocrat
of the intellect, but one whose intelligence was clouded over by the usual
bourgeois neuroses of the spirit.
I would not presume to comment on any mathematical point from
within
mathematics. But I cannot help asking myelf what it means to say that
mathematics is a social construction. Is it possible that this view is
itself the result of two antecedent sources: first, the general
dissemination of 19th century historicism into our own century, as is
especially evident in the extraordinary popularity and influence of
Nietzsche, and the offshoots of Heidegger's hermeneutical interpretation of
human existence; and second, the incredible technical complexity of
mathematics itself.
I know nothing of Professor Feferman's philosophical views, but I
presume he does not regard operations on natural numbers or the properties
of simple geometrical shapes as social constructions. But as soon as
mathematics becomes axiomatized and is turned into a formal game, then
human
invention enters into the picture, and there can be no doubt that
mathematical artifacts are produced, the significance of which is open to
influence by political fashion, social ideology, etc. Furthermore, there
are fashions in mathematics that don't seem to be explicable in purely
mathematical terms. But the fashions don't produce the mathematics. I
think it is more accurate to say that the modern world (the dominant
world-view that we call "the Enlightenment") and so modern society is itelf
a MATHEMATICAL construction, that is, the product of the unleashing of
mathematical creativity and the astonishing fact that mathematics actually
applies to and allows us to reconstitute the spatio-temporal world.
Peraps one could say that the unleashing of mathematics was itself
motivated
by a philosophico-political decision, namely, to become masters and
possessors of nature (Descartes). But I don't see how that makes
mathematics itself a social construction.
Well, those are my quick reactions to the debate that i saw a bit
of
in the FOM E-mails, and which you recount. If you think that they are of
the slightest interest to anyone, don't hesitate to forward them. If not,
send them into oblivion.
Stanley
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