http://math.bu.edu/people/nk/rr/
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Debunking the Conventional Wisdom about the Science Wars, Especially
the Sokal Affair and its Aftermath
== Gabriel Stolzenberg
In essays posted at this site, I use close readings of the science
wars literature to debunk the conventional wisdom about them,
especially about the Sokal affair and its aftermath. In doing this, I
try to adhere to standards of rigor comparable to those of my
profession, mathematics. I look forward to all criticism that is made
in the same spirit.
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“It Makes Me Laugh” Is Not an Argument
[The Social Text] article is structured around the silliest
quotations I could find about mathematics and physics (and the
philosophy of mathematics and physics) from some of the most
prominent French and American intellectuals. (Sokal, A House Built on
Sand: 11)
But is it the quotations that are silly or Sokal’s readings of them?
How can we tell? Many reasonable statements admit ludicrous
misreadings. We need arguments. But Sokal doesn’t offer any. Indeed,
he seems oblivious to the need for them.3 He continues:
Now, what precisely do I mean by “silliness”? …First of all, one has
meaningless or absurd statements, name-dropping, and the display of
false erudition. (11)
This is a good definition or at least the beginning of one. But
having given it, Sokal promptly launches into his own display of name-
dropping, false erudition and absurd statements! This runs from the
top of page 12 through “OK, enough for examples of nonsense” on page
13. I quote some fragments of it below. The name-dropping is evident.
4 That there is also false erudition and absurd statements will be
demonstrated below.5 Sokal writes (12):
Here, for instance, are Gilles Deleuze and Félix Guattari holding
forth on chaos theory….6
And there’s much more—Jacques Lacan and Luce Irigaray on differential
topology…7
—but don’t let me not spoil the fun.8
…[Latour] claims that relativity cannot deal with the transformation
laws between two frames of reference but needs at least three.9
I will spoil the fun. Sokal commits at least four significant mistakes.
Deleuze and Guattari: Chaos theory? As Sokal now knows, contrary to
his jeering, “Here, for instance, are Gilles Deleuze and Felix
Guattari holding forth on chaos theory,” the authors are not talking
about chaos theory. Talk about false erudition.10 So far as I know,
Sokal has not publicly acknowledged this blunder. However, in 1997,
in a lecture following one by Sokal, Arkady Plotnitsky pointed out
that, not only is the passage in question not about chaos theory, it
doesn’t even look as if it is. Moreover, in 1998, in Fashionable
Nonsense (156), Sokal and Jean Bricmont themselves take pains to make
clear that it is not about chaos theory.11 But they did not tell
their readers that this contradicts Sokal’s jeering remark in A House
Built on Sand.
Lacan: Differential topology? Differential topology is sophisticated
mathematics. There is nothing in the passage that Sokal describes as
“Lacan on differential topology” that requires any knowledge of it.
Nor does Lacan pretend otherwise. But by describing the passage as
“Lacan on differential topology,” he encourages his readers to
suppose falsely that, in it, Lacan pretends to know sophisticated
mathematics. Here is the passage in question.
This diagram [the Möbius strip] can be considered the basis of a sort
of essential inscription at the origin, in the knot which constitutes
the subject. This goes much further than you may think at first,
because you can search for the sort of surface able to receive such
inscriptions. You can perhaps see that the sphere, that old symbol
for totality, is unsuitable. A torus, a Klein bottle, a cross-cut
surface, are able to receive such a cut. And this diversity is very
important as it explains many things about the structure of mental
disease. If one can symbolize the subject by this fundamental cut, in
the same way one can show that a cut on a torus corresponds to the
neurotic subject, and on a cross-cut surface to another sort of
mental disease.
Although this can be formulated in terms of differential topology, it
requires nothing nearly so sophisticated. It is mathematics for an
eager amateur, the sort of thing one can find in a popular book.
Furthermore, on Sokal’s view of Lacan, if he was pretending to use
something as fancy as differential topology, he would have been sure
to let us know. As for the quote itself, unlike Sokal, I realize that
I do not understand it nearly well enough to judge it. However, I can
say this. Besides the Möbius strip, the three surfaces that interest
Lacan arise from the three different ways of ‘gluing’ the opposite
edges of a rectangle, depending on whether orientations are preserved
or reversed. His evident familiarity with this and the distinction he
notes between such surfaces and a sphere (one cannot draw a knot on a
sphere) suggests a better command of the mathematics than I expected
him to possess.
Irigaray: Borders of fuzzy sets. Here is the remark of Irigaray to
which Sokal is referring when says, “And there’s much more—Jacques
Lacan and Luce Irigaray on differential topology—but don’t let me not
spoil the fun.”
The mathematical sciences, in the theory of sets, concern themselves
with closed and open spaces… They concern themselves very little with
the question of the partially open, with sets that are not clearly
delineated [ensembles flous], with any analysis of the problem of
borders [bords]… 12 (Irigaray)
There is nothing here about differential topology. Indeed, on my
reading, Irigaray is not talking about any kind of topology except to
note correctly that little if any of it promises to be of much use in
studying the problem of borders for sets that are not clearly
delineated, i.e., for fuzzy sets or vague predicates. If Sokal finds
this a hoot, he probably missed the obvious connection between “the
problem of borders” and “sets that are not clearly delineated.” The
following statement in Fashionable Nonsense (120-121) strongly
suggests that he did.
For what it’s worth, the “problem” of boundaries [bords], far from
being neglected, has been at the center of algebraic topology since
its inception a century ago, and “manifolds with boundary” [variétés
a bord] have been actively studied in differential geometry for at
least fifty years. 13 (Sokal and Bricmont)
As a reply to Irigaray, this is risible. What do the boundaries
[bords] of algebraic topology have to do with the problem of borders
[bords] for vague predicates, e.g., for color names? In a novel I
just read, Milan Kundera says about one of the characters:
He knew there existed a border beyond which murder is no longer
murder but heroism, and that he would never be able to recognize just
where that border lay. (Immortality, 105)14
Is Sokal suggesting that with the aid of algebraic topology, with its
great theorems about cycles and boundaries, Kundera’s character might
after all be able to recognize just where that border lay?15 I am
sure he is not and that the reason it seems otherwise is that he has
failed to consider the relevance of Irigaray’s mention of fuzzy sets
for understanding what kind of borders she is talking about.16
Indeed, it is precisely the fuzziness of a fuzzy set—the vagueness of
a vague predicate—that makes its border problematic.
Latour: Frames are not enough. Finally, contrary to what Sokal would
have us believe, in the quote below, Latour does not say that
relativity “cannot deal with” the transformation laws between two
frames of reference but “needs at least three.”
If there are only one, or even two, frames of reference, no solution
can be found…. Einstein’s solution is to consider three actors: one
in the train, one on the embankment and a third one, the author
[enunciator] or one of its representants, who tries to superimpose
the coded observations sent back by the two others.17
The first sentence mentions two frames but says nothing about
transformation laws or a need for a third frame. The second sentence
has nothing about relativity theory not being able to deal with the
transformation laws between two frames or needing a third frame. How
then did Sokal ‘find’ these two assertions in Latour’s remark? For
the one about the transformation laws, see “Reading Latour reading
Einstein” just below. As for the claim that Latour says we need a
third frame, he does say that we need a third actor. Determined to
make it be a frame, Sokal assumes that Latour doesn’t understand the
difference between an actor and a frame of reference! Isn’t this
convenient? For a more thorough discussion, see “Reading Latour
reading Einstein” below and “I am not a reference frame” in “Reading
and relativism”
<...>
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--ravi
