‘Badiou and Plato: An Education by Truths’ reviewed by Bill Bowring

There is a certain vulgar “Marxism” which treats Plato (428-348 BC) with suspicion, and for didactic purposes divides philosophy into two schools, “idealist” (Plato) and “materialist” (Aristotle, Plato’s pupil, 384-322 BC). Neither Marx nor Engels had such a pejorative assessment of Plato.

Marx, for example, cited Plato many times, especially in Chapter 14 of Volume 1 of Capital, as an example of the writers of classical antiquity, who were “exclusively concerned with quality and use-value”. He continued: “This standpoint, the standpoint of use-value, is adopted by Plato, who treats the division of labour as the foundation on which the division of society into estates is based” and his footnote had the citation in Ancient Greek, in which he read Plato (Marx 1976, 487-8).

And in 1877 Engels, in Anti-Dühring, wrote concerning the same passage: “Herr Dühring has nothing but sneers for Plato’s presentation – one which, for his time, was full of genius – of the division of labour as the natural basis of the city (which for the Greeks was identical with the state)”. For Marx and Engels, Plato was a worthy predecessor.

In our own time Alain Badiou, who made his way through a Maoism on which he continues to reflect critically and self-critically (as a good Maoist), is the most prominent materialist philosopher. He has described himself as a Marxist, although his philosophy in no way concerns the critique of political economy, and asserts consistently that he is a Communist. I agree with him, in the sense given by Marx in 1845 in The German Ideology: “Communism is for us not a state of affairs which is to be established, an ideal to which reality [will] have to adjust itself. We call communism the real movement which abolishes the present state of things. The conditions of this movement result from the premises now in existence.”

In his 2010 Second Manifesto for Philosophy, Badiou clarified the reason he turned to Plato:

the philosophical position I combated twenty years ago was principally the Heideggerian position in its French variants (Derrida, Lacoue-Labarthe, Nancy, but also Lyotard) … My `Platonic gesture’ was to reaffirm the possibility of philosophy in its original sense – namely the articulation … of a crucial categorical triplet: that of being, the subject and truth … by the construction of a new concept of truth or truths. I set myself up, in sum, against the critical ideal of deconstruction. (117-8).

Adam Bartlett, who teaches at Monash University, is a distinguished Badiou scholar. This is his latest monograph; another is on its way. He positions Badiou as follows:

Badiou duly identified his own project as a ‘contemporary Platonism’ … at once faithful to the mathematical conditioning of thought, whereby the most rigorous thinking of being passes through the most contemporary discoveries in mathematics, and to the ‘Platonic gesture’ that declares ‘there are truths’ (2)

There is more than a gesture. As Bartlett points out, Badiou’s four conditions for the existence of philosophy – the thinking of being, art, love and politics – are also the subject matter of Plato’s Dialogues, with which Bartlett is also impressively familiar. It is only a shame that Bartlett wrote and published before the publication in 2012 in French and in English of Badiou’s Plato’s Republic. Simon Critchley has described this text – 372 pages of it – as “something really remarkable: a complete reimagining of the founding text of philosophy … an utterly contemporary transposition”.

Plato’s Dialogues are united by the figure of Socrates, an educator who insists that he knows nothing, is not paid a penny for his labours, and whose unceasing struggle is against sophistry. For Plato, as explained by Bartlett,

what usually passes for education, in any state, the teaching of skills for commercial prowess, technical skills which serve the whims of interest and power, or a training in debate which might ensure the subject a reputable place within the polis, does not ‘deserve the name’ of education.

For Bartlett, `Plato’s fundamental claim, a claim that links the entirety of the dialogues, is that “non-sophistry is possible”’.

This book is divided into six chapters: State, Site, Event/Intervention, Fidelity, Subject, Generic. The reader of Badiou will see at once that these are Badiou’s central categories. Thus, this is primarily and engagement with Badiou, explaining his concepts and arguments by continual reference to Plato’s own engagement. It is possible to recommend this text, with some reservations explored below, to an attentive reader who is a specialist in neither Plato nor Badiou, but for whom the idea of “an education by truths” is attractive – and in the present climate of the privatisation and commodification of education, entirely necessary.

Thus the “State” explored in Chapter 1 is the Athenian state, which in the end found Socrates’s presence and continued existence to be intolerable, so that he had to be executed. Bartlett concludes the chapter by asserting that he has tried to “demonstrate that under the condition of Badiou’s distinction between the situation and its state the possible place for the arrival of something other than the rule of interest and the conceit of knowledge might be found.” (61).

Chapter 2, on the “Site”, introduces Badiou’s fascination with contemporary mathematics, and the ontology he develops in relation to it. Those who find Badiou’s close attention to mathematics eccentric should reflect on the fact that Karl Marx wrote extensively on mathematics. His Mathematical Manuscripts, edited by S. A. Yanovskaya, were published in English by New Park in 1983, and the full text, nearly 300 pages, is available in PDF on the www.marxists.org website. In his review published on the same web-site, Andy Blunden wrote:

The actual historical development of mathematics over the last century and a half has moved on from the particular problems with which Marx was concerned in relation to calculus, but has confirmed the essence of Marx’s ideas on the subject.

These problems, however, continually re-emerge at a deeper level and are linked to methodological problems in all branches of science, and close study of Marx’s method is essential – his synthesis of the logical and historical; his insistence on the highest standards of precision in science and contempt for all ‘sleight of hand’ etc.; his insistence on the sublation of the old into the new, established more concretely with every further development of the new. Only by his struggle to develop his algebraic method of differentiation could Marx bring out what was new in the calculus.

And here I come to my one serious criticism of Bartlett, who otherwise succeeds in writing about difficult and complex matters with admirable clarity.

On page 73 Bartlett refers to “the rigorous and systematic thinking of pure multiplicity established in ZFC set theory.” There is no footnote or other explanation here, and far too much is expected of the reader, who almost certainly will never have heard of ZFC.

ZFC is in fact the abbreviation for “Zermelo–Fraenkel set theory with the axiom of choice”. This is named after the mathematicians Ernst Zermelo (1871-1953) and Abraham Fraenkel (1891-1965). It is the most influential of several axiomatic systems that were proposed in the twentieth century to formulate a theory of sets – that is, a theory of everything there is – which could be free of paradoxes such as Russell’s paradox. Russell’s paradox (also known as Russell’s antinomy) was discovered by Bertrand Russell in 1901. Russell showed that the naive set theory created by Georg Cantor leads to a contradiction.

On page 211, in Chapter 6, “Generic”, Bartlett not only refers once more to “ZF axioms of set theory” without any explanation, but also mentions Cohen (first mentioned on page 205) in connection with AC (the axiom of choice) and CH (the continuum hypothesis). This, Bartlett should have explained, is a reference to the great mathematician Paul Cohen (1934-2007). Cohen developed the mathematical technique called “forcing”, which he used to prove that neither the continuum hypothesis (CH), nor the axiom of choice, can be proved from the standard Zermelo-Fraenkel axioms of set theory. In conjunction with the earlier work of Gödel, his proof showed that both of these statements are logically independent of the ZF axioms: these statements can be neither proved nor disproved from these axioms. In this sense, the continuum hypothesis is undecidable, and it is the most widely known example of a natural statement that is independent from the standard ZF axioms of set theory.

This may all, of course, be Ancient Greek to most readers of this review, and much of Badiou’s work and the conclusions he draws, must be taken on trust. Competent mathematicians say that Badiou is pretty good.

And I can say without fear of contradiction that Karl Marx would have found this work and Badiou’s reflections on it, in relation to politics in particular, utterly fascinating and vitally important.

Chapter 3 is “Event/Intervention”, and Bartlett says: “We are certainly not saying that Plato had a theory of the event, but we are saying that in Plato there is an event – Socrates’ encounter with the sophists and therefore the state.” (103)

Chapter 4, “Fidelity” focuses in particular on the militant, who functions according to Badiou “by conviction,” or a “knowing belief” or confidence. “A militant is simply one who enquires into what he does not know, predicated on the confidence that, to quote Mao, ‘we will come to know all that we do not know’.” (132).

Chapter 5, “Subject”, contains the following stirring passage: “As we have stressed, the Socratic lesson of the Phaedo does not concern death but the very possibility of a life lived by truths. The Platonic ethic is that of Badiou: continue! Continue, in the face of the triumph of sophistry to be the immortal that you also are.” (185)

I hope that in this short review I have conveyed the importance of Badiou and Plato to contemporary Marxists; and especially those struggling against sophism in the academy. Those who want to understand Badiou (and Plato) better will find much to enjoy, and perhaps even a source of inspiration. Bartlett concludes: “Education understood as only by truths over and over again has had to force its way back into and through the knowledge of the city for which it was nothing.” (231)

4 August 2014