The general problematic I am exploring on this blog is the contemporary trend towards the construction of what could be called an “immanent Platonism”, which strictly speaking is an oxymoron. This problematic is that of a pluralist, diachronic, democratic, apophatic ontology. It is exemplified to varying degrees by the work of Badiou, Latour, Stiegler, Laruelle.
I consider that any concept these thinkers propose is to be evaluated in terms of that problematic. Another problematic, expressing a trend that I find quite worrisome, as I am encountering it with increasing frequency, is mathematical reductionism.This reductionist problematic gives primacy to mathematics as descrition of the real, and evaluates other philosophies primarily in terms of their mathematical dimension.
Among all these thinkers, Badiou’s position is particularly fragile, as he proclaims that “mathematics is ontology” and founds this ontology on ZFC set theory. He thus seems to invite the mathematical reductionist critique that his vision of mathematics is anachronic and incomplete.
However, Badiou is occasionally quite explicit that he is not employing philosophical concepts mathematically, but rather making a metaphorical use of mathematical concepts, applying them to many other domains. The work of a pure mathematician, for example Jean-Yves Girard, does not encompass that range of application.
One would never read Badiou for his philosophy of mathematics, which is the most synchronic part of his system. His most recent work, presented in his seminars, represents a “diachronic turn”, but his account of the historical dimension of mathematics and of science, and more generally his account of change, is still insufficient.
Similarly, one would never read Laruelle for his philosophy of science. He seems to be aware of the difficulties with Badiou’s solution, but Laruelle does not help us to see how both he and Badiou are involved in the same enterprise. Laruelle makes frequent use of the term “science”, but this use is itself purely allegorical.
Laruelle explicitly rejects Badiou’s “strong” use of the mathematics of set theory, but does not see that it is relativised by his turn to category theory, nor that is accompanied by an allegorical use. Laruelle’s own solution is to make a “weak”, allegorical, use of quantum physics as a style of thinking, but his explanations are scientifically vague, incomplete, and one-sided as well as philosophically obscure, due to his use of his typically inadequately defined but quite abstract vocabulary.