One point that Sokal and Bricmont miss making because of their fragmented
approach to out-of-context quotes is the suspicious resemblance of Latour's
"third observer" in his account of special relativity theory to Bergson's
account (possibly via Deleuze's book on Bergson). Latour rarely gives
reference to the sources of his ideas, preferring to appear to have created
them out of whole cloth. He claims that in Einstein's special relativity
theory there is a third observer who is describing the two observers
mentioned in the exposition. Bergson makes a similar move in claiming that
there is a unitary time subsuming the relative times of the two observers in
Einstein. Sometimes, as in Latour's account, this is the time of the third
observer subsuming the other two. Latour and his critics, as well as his
physicist defender David Mermin confuse the issue of the number of physical
"observers" needed in special relativity with the philosophical question of
whether in thinking about some topic we are also thinking about ourselves
thinking about it. (This latter issue leads to the old paradoxical claim
that one cannot imagine oneself dead or unconscious, because one is
imagining oneself consciously imagining oneself dead or unconscious. ) The
third observer is not one of the observers in the physical system, but is
this self-conscious theorist or reader thinking about the other two physical
observers. Both Latour, Sokal and Bricmont, and Mermin treat this
transcendental conscious observer as if it were an actual, physical observer
located somewhere in the physical space-time being described.

Ironically, David Bohm, whose deterministic quantum theory is admired by
many of the physicist science warriors, has speculated in manners strangely
similar to Bergson concerning notions that there might be other ways to
think about or make models of physical processes other than the classical
ones. This has been elaborated on by Capek, and the suggestions resemble in
many respects Bohm's suggestions about trying new imaginary models and
rejecting Bohr and Heisenberg's claim that we are trapped conceptually in
classical models -- that supposedly prevents us from thinking directly about
quantum reality.

One philosopher who makes use of Bergson's ideas concerning time and process
is Gilles Deleuze. Sokal and Bricmont seem to be particularly annoyed at
Deleuze because he was excessively praised by Michel Foucault. (Deleuze and
Guattari shared many interests such as anti-psychiatry and rejection of
unitary systems, were both gay, interested in sadomasochism, and evidently
took drugs together).. Much of the rancor in the science warriors' attack on
the postmodernists seems to be jealousy at their undeserved fame. In
Bricmont's case, the perhaps undeserved Nobel Prize and excessive fame of
the popular writings of Ilya Prigogine, a fellow Belgian physicist who
occasionally mentions Bergson and postmodernism, seem to stoke the fires of
his resentment. Sokal and Bricmont should feel less of this now that they,
through the Sokal hoax and this book, themselves have achieved worldwide
fame.

Sokal and Bricmont, like many of the uncritical epigones of Deleuze
interested primarily in gay liberation, anti-psychiatry movements, focus on
Deleuze's work with the psychiatrist and political activist Felix Guattari.
Deleuze collaborated in his later life on a number of wild and unbuttoned
books with his buddy. Sokal and Bricmont treat the two together in their
critique, but have the harshest words for a passage by Guattari alone, with
which they conclude as the ultimate in nonsense. Certainly Guattari, a
lifelong rebel (whose early support of the Algerian independence and of
reform of authoritarian mental institutions was admirable) rebelled even
against the revolutionary sects he joined. His raging against the Oedipus
complex seems to betray a major one of his own. Guattari was much wilder and
sloppier in his writing than Deleuze, and the latter permitted much looser
and free-associative formulations in joint productions written with his
companion. However, Deleuze also wrote some seven academic books on various
philosophers, such as Leibniz, Spinoza, Kant and Nietzsche, that Sokal and
Bricmont do not discuss. For instance, Deleuze's book on Leibniz, The Fold,
contains references to topology (the mathematics of continuity), the use of
which by postmodernists Sokal and Bricmont descry. Since Leibniz was an
inventor of both the calculus and analysis situs (precursor of topology) and
made the principle of continuity central to his philosophy, these references
are not guilty of the irrelevance of which Sokal and Bricmont accuse
Deleuze's other references to mathematics.

One claim that Sokal and Bricmont make throughout their work is that if the
authors they criticize and expose are using scientific metaphors to
illustrate their philosophical, psychological or literary ideas, these would
not be illuminating to an audience ignorant of science. They suggest these
scientific or mathematical examples are simply added to impress the
scientifically illiterate literateurs. This may be the case with some of the
phrases of Kristeva and Lacan. However, another use of scientific and
mathematical concepts in philosophy is as models for metaphysical
speculation. Since much of our thinking is based on images and spatial
diagrams (following Kant but pace Hegel, Wittgenstein, and others), the
precise, worked-out structures of mathematics and physics can suggest
metaphysical models. Here the mathematical models are not window-dressing to
impress the ignorant, but sources of admittedly vaguer metaphysical
extrapolations. Deleuze, in a manner similar to (though nowhere as ably done
as) Whitehead, mathematical structures are used as models for metaphysical
ideas. Sokal and Bricmont do not totally reject philosophical thinking or
even metaphysics, as they present some philosophy of science in order to set
aside skepticism and to argue against relativism and subjectivism.

Sokal and Bricmont do comment on two of Deleuze's serious works. Bricmont
also mentions, in an open letter concerning the dropping of Bergson from the
English edition of the book that Bergson's influence on Deleuze shows the
relevance of the former. Evidently Anglo-American analytic philosophers
convinced Sokal and Bricmont to ignore Bergson in the English edition,
though several English books on Bergson have recently appeared. Ironically,
two of the passages in Deleuze that they ridicule assert that relativity
theory, measurement in quantum theory, and information in statistical
mechanics should not be interpreted subjectively.(pp. 14-150). This agrees
with Sokal and Bricmont's own position, but they do not note this. It would
spoil the fun.

Sokal and Bricmont hold up for ridicule selective passages in Deleuze's
Difference and Repetition concerning the differential calculus. They quote
long passages, followed by the remark that the passage is meaningless or
nonsense (pp. 151-155). They claim that the problems of the calculus were
solved by Cauchy in the early nineteenth century. (They even claim that the
problems "were solved by the work of d'Alembert around 1760," (p. 151)
though d'Alembert did not clarify in terms of inequalities or explicitly
apply the limit concept that he advocates in the Encyclopedia.) They claim
the status of the infinitesimals in the derivative is no longer worth
bothering about, as it has been replaced by the limit.

Sokal and Bricmont's comments on Deleuze on the calculus resemble Bertrand
Russell's comments on Zeno's paradoxes of motion. Russell claimed that the
nineteenth century theory of real numbers and Weierstrass's "static theory
of the variable" solves Zeno's paradoxes (and makes irrelevant the
reflections on them of process philosophers like Bergson). But some later
analytic philosophers noted that showing that mathematics is internally
consistent hardly solves the physical version of Zeno's paradoxes. Unless
one is willing to say that the mathematical structure (of all the real
numbers) is physically existent, or one says that the mathematical formalism
is all we need and that questions of physical reality should be rejected (a
position that a scientific realist would have to reject) then there is still
a physical problem of motion and infinitesimal processes, and the question
of whether an infinite number of acts can be performed in a finite time.
Similarly, Sokal and Bricmont, claim that the question of the status of the
infinitesimal is eliminated by the limit notion. Sokal and Bricmont claim
that Cauchy solved the problems of the status of infinitesimals with the
concept of the limit and criticize Deleuze for puzzling over the status of
differentials. If, indeed, the only consistent way to present derivatives
were by reducing them to limits, this would be true. That is, if the
infinitesimal has been reduced to a meaningless notational component of a
ratio that is really a limit, then puzzling over the status of the
infinitesimal in isolation is made obsolete. However Abraham Robinson's
non-standard analysis (and Lawvere's less well known category theory
approach) has shown how one can make direct mathematical sense of
infinitesimal quantities without resorting to the replacement of their
ratios by limits, and eliminating the individual differentials.

Deleuze seems to borrow some of his discussion from Hegel. Similar criticism
to that of Sokal and Bricmont has been made of Hegel., claiming that
Cauchy's formalization of the concept of limit has made all such discussion
otiose. However some are beginning to reexamine Hegel's writing on the
calculus with less dismissive attitudes than had Whitehead and Russell.

Marx also wrote philosophical discussions of the calculus. Edmund Wilson,,
consulted a mathematician, who told him that Marx's comments on the calculus
were worthless, and Wilson duly reported this. Some Marxist mathematicians,
on the other hand, have defended the value of Marx's remarks on the
calculus, even claiming he arrived at results similar to Cauchy. Marx's
side-kick Friedrich Engels wrote far worse stuff concerning elementary
algebraic operations and the dialectic. Would leftist Sokal move from a
similar discussion of Marx and Engels on mathematics to discrediting Marx's
insights about capitalism as Intellectual Impostures moves from Lacan's,
Irigaray's or Kristeva's mathematical errors to question their honesty?

Sokal and Bricmont skip a number of linking passages in Deleuze's
discussion, that treat in great detail writings of various mathematicians
and philosophers. These include early nineteenth century figures such as the
mathematician Wronski (a mathematician with whose Wronskian matrix they are
undoubtedly familiar, but whose mysticism probably embarrasses them) and the
philosopher Salomon Maimon. In one of the passages that they do quote, they
omit by means of ellipsis the reference to Maimon and Wronski's
philosophical approaches to the calculus, that would help make sense of some
of the "nonsense" of the passage. Deleuze does not simply discuss the early
nineteenth century debates on the "metaphysics of the calculus," but also
uses twentieth century philosophers of mathematics, such as Albert Lautman
who wrote in the 1930s and Jules Vuillemin, a contemporary analytic
philosopher. Lautman, whose conception of mathematical problems Deleuze
uses, had a correspondence with great logician Jacques Herbrand and the
philosopher of mathematics Jean Cavaillès, and was praised in a
commemorative volume by the mathematician Jean Dieudonné, suggesting that
his understanding of logic and mathematics was taken seriously by his peers.
Several French philosophers of mathematics were inspired to attempt to build
on Lautman's approach to a logic of mathematical problems and
interpretations because of Deleuze's lectures.

Obviously Deleuze is no mathematical virtuoso, but his treatment of the
issues of the calculus is far more detailed, informed and serious than Sokal
and Bricmont let on. For instance Sokal and Bricmont note in footnotes that
some of Deleuze's errors are shared by Hegel, such as a dated treatment of
functions in terms of Taylor series, but they neglect to note that Deleuze
himself, in discussing Hegel mentions that he is well aware that the series
approach to the calculus has been replaced in modern writers.

According to the standard account of the Sokal hoax, scientifically
illiterate literary critics and sociologists have been bamboozled by the
pretentious claims of French postmodernists concerning science. Ironically
those same benighted scientific illiterates now have to take on faith the
words of physicists Sokal and Bricmont concerning the errors of the French
theorists. In some cases the great unwashed masses of humanists and social
scientists may be misled again.





Val Dusek
Department of Philosophy
University of New Hampshire
Durham, NH 03824
USA