Henry, Chris

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Kent Academic RepositoryFull text document (pdf)Copyright & reuseContent in the Kent Academic Repository is made available for research purposes. Unless otherwise stated allcontent is protected by copyright and in the absence of an open licence (eg Creative Commons), permissions for further reuse of content should be sought from the publisher, author or other copyright holder. Versions of researchThe version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record.EnquiriesFor any further enquiries regarding the licence status of this document, please contact: researchsupport@kent.ac.ukIf you believe this document infringes copyright then please contact the KAR admin team with the take-down information provided at http://kar.kent.ac.uk/contact.htmlCitation for published versionHenry, Chris  (2016) Naturalising Badiou: Mathematical Ontology and Structural Realism.  Reviewof: Naturalising Badiou: Mathematical Ontology and Structural Realism  by Gironi, Fabio.   Pli:The Warwick Journal of Philosophy, 27 .   pp. 158-170.  ISSN 1367-3769.DOILink to record in KARhttp://kar.kent.ac.uk/56318/Document VersionAuthor's Accepted ManuscriptChris Henry University of  Kent - C.M.Henry@kent.ac.uk Fabio GironiÕs ÔNaturalising Badiou: Mathematical Ontology and Structural RealismÕ (pp. 158-170) Spinoza: The Proper Order of  Philosophy (2015) Pli: The Warwick Journal of  Philosophy, Volume 27. Gironi, F. (2014). Naturalising Badiou: Mathematical Ontology and Structural Realism. Basingstoke, Palgrave Macmillan. No doubt spurred on by ŽižekÕs repeated reference to him as a ÔmasterÕ Þgure, there is a penchant in BadiouÕs secondary literature to treat his Þgure as a target for assault. GironiÕs stated aim is Ôto offer a naturalist correction - something between a creative misreading and an unsolicited deliverance - of  Alain BadiouÕs philosophyÕ and can be seen as following in the footsteps of  LaruelleÕs brazenly polemic Anti-Badiou (2013), which also uses Badiou as a starting point for the authorÕs own work. Gironi uses BadiouÕs mathematical ontology to proffer his own naturalised version, yet what is left at the end is so far removed from BadiouÕs work that the two positions are nearly unrecognisable. Badiou is certainly not the only theorist to share the authorÕs position that mathematics holds a Ômetaontological weight [É] put upon twentieth-century metamathematical results and on their description of  a formally incomplete mathematical realityÕ; so why single him out? In fact, Gironi acknowledges himself  that Ôone of  the main vices of  continental philosophy is its penchant for endless, bromidic and intellectually incestuous exegesis of  Òmaster ÞguresÓÕ. So the question that faces the reader from the beginning of  this bookÐand a question that is never addressedÐis why does Gironi take aim at Badiou in the Þrst place. Naturalising Badiou is not a depth study of  BadiouÕs mathematical/ontological system at all: it is an exceptionally well supported tour (a full Þfth of  the page count is taken up by useful and interesting notes) through the history of  mathematics and its relationship with ontology that has been bookended by synopses of  BadiouÕs position on the issue. More importantly, it is a development of  GironiÕs own project towards an immanent mathematisation of  being, a project which tries to avoid both the idealist trappings of  BadiouÕs work and the issues plaguing a number of  other thinkers referenced. At tactical moments throughout the exegesis, Gironi takes time to spell out his own commitments to naturalist ontology and his formation of  its immanent relationship to mathematics, providing useful focal points to his synthetic exposition. Yet his attempt to target Badiou (or BadiouÕs simulacrum in the form of  the prophetic master) is never satisfactorily justiÞed. Is it a cynical attempt to cash in on BadiouÕs ever-increasing popularity and a burgeoning secondary literature? To claim so would be to undersell GironiÕs efforts, for Naturalising Badiou excels in demonstrating the easy command Gironi has over the detailed CHRIS HENRY $1material at hand and the important stance that he develops in his own right. However, the arrogant tone with which he sets about Ôeviscerating BadiouÕ and condescending Ôlesser postmodernistsÕ blots the clarity of  his work. Gironi develops his argument in Þve chapters. Chapter one proceeds by way of  a clear overview of  BadiouÕs ontological position with regard to mathematics, characterised by BrassierÕs term Ôscriptural materialityÕ (Brassier 2005). Mathematics, for GironiÕs Badiou, constitutes the language that does not represent the emergence of  Being, so much as acting as an index of  the scriptural production of  difference. In other words, it is not the fact that, for Badiou, Being consists of  mathematical objectivities themselves but, rather, it is only through mathematics that we can articulate the productivity of  Being itself. Gironi is at pains to point out that Badiou is really interested in the second half  of  the term ontology, the language of  expressing Being, for any focus upon the ontic would risk entrapping thought within the realm of  presentation. What would be wrong with that? BadiouÕs oeuvre is rife with denigration of  the sensible over the truth of  thought and Gironi describes it through the concept of  God. In BrieÞngs on Existence (1998), Badiou highlights three Gods: the God of  metaphysics that runs from Aristotle to Descartes, which provides the philosopher a tool to make sense of  things; the God of  religion which facilitates a ÔvivifyingÕ engagement with life and which was replaced by the God of  metaphysics; and the God of  the Poets. For Badiou, the death of  God, which was announced by Nietzsche, was only Þnished by Heidegger for whom, through a ÔÒmeta-poetic metaphorizingÓ the post-metaphysical philosopher hopes for a re-injection of  meaning into the world and orients his own Þnite being towards an attentive but passive receptivity to the historical self-presencing of  BeingÕ (Badiou 1992: 43). Accordingly, the individual can only have faith in a meaning-to-come, anchored in a poetic description of  the realm of  presentation which takes its place as the third God. Gironi shows that ZFC set theory is BadiouÕs answer to HeideggerÕs self-presencing: an immanent expression of  Being that does not itself  constitute an object. Set theory thus avoids any metaphysics of  representation itself, whilst still being able to truthfully express Being. Furthermore, as Gironi shows, the Cartesian-inspired axiomatic decision that is BadiouÕs replacement for God (following the ÔCantorian revolutionÕ that revokes the Þnitude of  the ontic in favour of  the inÞnite set) avoids the trappings of  various other versions of  the One, such as a recourse to description, a repressed inÞnity (Heidegger/Wittgenstein) or an inÞnite One (Nietzsche/Bergson/Deleuze). Instead of  remaining within the representative boundaries of  the One, Badiou offers a Ômathematically articulated possibility of  thinking real differences between inÞnitiesÕ (Gironi 2014: 32). Despite agreement with BadiouÕs support of  immanence and the revocation of  all types of  One however, Gironi Þnishes the chapter by pointing out three elements of  BadiouÕs work that he cannot accept, the Þrst of  which provides the problematic for the rest of  the book. Firstly, Gironi takes issue with BadiouÕs split between the empirical and the ontological. How can changes in the ontological be assumed to correspond to the empirical world? Secondly, how are non-ontological situations (i.e. situations in the every-day and non-mathematical sense) to be understood? Thirdly, what, he asks, is the relationship between the four types of  situation that are characterised by BadiouÕs four truth procedures (politics, science, love and CHRIS HENRY $2art)? Are these situations merely analogous to each other, or are there any underlying similarities? This important initial chapter is balances an exposition of  BadiouÕs position, making a good case for BadiouÕs contextualisation within an Althusserian and post-Platonic milieu, and a portrayal of  issues in the relationship between the ontological and empirical. However, having Þnished the chapter, I was still unsure of  GironiÕs intended project and why Badiou in particular was being used to foreground the discussion. His project does becomes clearer in the next chapter, however this is a book that rewards a patient reading through to the end. GironiÕs second chapter opens up discussion to various perspectives in mathematical ontology, engaging with what Badiou denigrates as the Ôlittle styleÕ, or the ÔphilosophyÕ of  mathematics. Beginning with a fuller development of  BadiouÕs inability to offer Ôan intelligible account of  the relationship between the ontological and the empiricalÕ (2014: 2), Gironi aptly uses another of  BrassierÕs terms, ÔnoocentrismÕ, to point the Þnger at BadiouÕs dogmatic and reductive rationalism. The main issue for Gironi is not that Badiou distinguishes between matter and thought (Gironi himself  holds to a representational/computational theory of  mind which runs counter to some versions of  naturalism), but that BadiouÕs rationalism removes the legitimacy of  the natural sciences to inform thought. Gironi makes a strong argument against BadiouÕs revelatory theory of  science: because of  BadiouÕs unwillingness to do away with the split between the ontological and the ontic (favouring the former), novelty according to Badiou can only be a radical break from that which is already known. Yet, as Gironi explains, the progression from Galilean mathematisation (starting with observation and measurement of  phenomena) towards DiracÕs Ômethodological revolutionÕ (where mathematics itself  became an inductive tool for new phenomenic aspects) could only come about via NewtonÕs initial success at conceptualising general mathematical laws (such as the law of  universal gravitation). As he concludes, Ôit is simply not true that the mathematised concepts employed by contemporary physics retain Òa relation to the world which means that they cannot be deduced from any mathematical corpus whatsoeverÓÕ (2014: 40). As a solution to BadiouÕs prioritisation of  the rational over the empirical, Gironi takes a surprising turn to neurophysiology in order to naturalise thought. Because, for Gironi, naturalism is the removal of  any supernatural causes of  Being, and that Ôall there is is what the natural sciences describeÕ (2014: 6), neurophysiology is interesting for Gironi therefore because it places the sense of  mathematics and the physical world together in empirical perception. Arguing that the cognitive neurosciences hold the potential to explain the Ôbrain-dependent conditions of  possibility of  our mathematical cognitionÕ, GironiÕs aim is to keep mathematics as Ôthe highest form of  thoughtÕ but, through Ôa naturalist demystiÞcation of  its originÕ (i.e. debunking Þctionalised accounts of  the creation of  rationality), Ôplacing it on an immanent continuum with the rest of  realityÕ (2014: 59). Mathematics remains the highest form of  thought not because of  BadiouÕs subtractive distrust of  the sensible, but because it simply works with science as the way of  knowing about the world. GironiÕs commitment to naturalist ontology is set out in chapters three and four, and it is here where he starts developing his own project. Chapter three presents an overview of  CHRIS HENRY $3GironiÕs commitments with regard to both metaphysics and the historicity of  conceptual systems (bearing in mind that neurophysiologyÐas the immanent form of  human investigationÐis also now a key part of  the system he advocates). In what is perhaps an attempt to ward off  any criticism that he idealises naturalismÐas Badiou idealises mathematicsÐGironi reassures the reader that he holds, rather than a dogmatic ÔpositionÕ, a ÔstanceÕ that Ômay involve or presuppose some beliefsÕ, but that cannot simply be equated with these beliefs. By admitting that Ôthe logical priority goes to a mind-independent reality which must be (transcendentally) taken as condition of  possibility for our access to itÕ, Gironi removes the supernatural from his stance and immunises himself  against claims to reductionism (2014: 72). It is through his cautious positioning and a clear engagement with Collingwood and Bachelard, that Gironi can show how scienceÕs Ôendlessly self-critical stanceÕ ensures that none of  the claims that science makes act as mind-independent entities that lie outside the boundaries of  critique. This is what Gironi calls Ôtransgressive naturalismÕ (ibid.). Following a path that Gironi draws from Kierkegaard and Heidegger to Levinas, transgressive naturalism argues that, Ôreality cannot be fully grasped by the raw power of  reason since it exceeds conceptual captureÕ (ibid.), yet science still remains the best way of  developing an understanding of  it. In connection with an introductory paragraph on the responsibility of  science in Kant, Gironi allies himself  with Bachelard in claiming that the Ômark of  the scientiÞc intellect [É] is the endless dialectical struggle against the laziness of  thoughtÕ (2014: 79). Given that there ÔisÕ a world to be known (realism) and that this ÔisÕ is Ôall there isÕ (naturalism), GironiÕs realist metaphysics can be both naturalist and historicist; an immanent part of  the world itself, the conceptual apparatus of  mathematics is thought by the human but remains, as Deleuze would put it, problematic (and therefore ever questioning) in its lack of  totality. Having established the immanent role that mathematics takes in understanding the mind-independent world, Gironi takes up the task in chapter four of  explaining how (and precisely what) mathematics articulates. Comparing epistemic structural realism (ESR) to ontic structural realism (OSR), Gironi argues that it is only the latter to which a realist can turn to in the hope of  understanding the world. As opposed to WorrallÕs ESR and its curtailment of  knowledge to epistemic structures which then have an empirical relationship to the world, OSR ontologises structures and argues that in fact there is nothing to know but structures. Building on Ladyman, French and Ross, Gironi argues that OSR provides a groundwork for natural realism through rejecting an a priori world of  being to that which is structured in favour of  a world that consists through structure alone. In lieu of  atomist or epistemic structuralist accounts, Gironi helpfully shows how Ladyman and Ross both argue that one can still think naturalistically of  a world really composed of, for example, protons, but where Ôtheories in which protons are elements characterize real structureÕ (Ladyman, Ross et al. 2013: 127). As a compromise between full-scale structuralism and non-structuralist Platonism then, mathematics, for Gironi, takes the role of  an explanatory structure that Ôat an elementary scaleÕ blurs with concrete reality without one being reducible to the other. CHRIS HENRY $In the Þnal chapter, Gironi sums up his position to offer, what he describes as, Ôa much needed naturalist supplementation to BadiouÕs philosophyÕ. Given that much of  the secondary literature on Badiou makes the claim that his biunivocal positioning of  thought and sensibility is too strong a divide, GironiÕs argument is interesting. For him, Badiou does not go far enough and, rather than mathematics being premised on Being itself, Gironi argues that it does not present anything and stands entirely on its own weight. Summing up his stance, Gironi claims that, Ôthere is nothing more to the matter/form distinction than there is to the abstract/concrete one, but rational thought is ontogenetically possible thanks to the pre-noetic existence of  object and extra-mental structure: the real is the causal antecedent of  the conceptualÕ (2014: 120). Gironi brießy turns to BadiouÕs conception of  the subject as the driver for change arguing that, because his own position removes the ontological support for the mathematical veridiction of  BeingÕs novelty, BadiouÕs militant-subject cannot, in truth, be the key to political (or scientiÞc, etc.) revelation. Given the strength of  his argument throughout the book, this argument feels like (excuse the pun) a natural conclusion and a suitable critique of  Badiou. However, GironiÕs attempt to outline his position by juxtaposing it to BadiouÕs means that the Þve pages he devotes to BadiouÕs truthful subject leaves a lot to be desired and his critique is not developed as fully as it could be. As even a cursory glance at a bibliography of  BadiouÕs works will show, BadiouÕs project is primarily a political one, motivated by the desire to explain the emergence of  the new from historical situations. By setting Badiou up as the straw master to be demolished, Gironi seems to miss the role that axiomatics takes in BadiouÕs project: set theory is a secondary priority to his Maoist-derived philosophy, even if  it is more prominent in his later work. Thus, if  Gironi is to supplement BadiouÕs philosophy, then what is GironiÕs theory of  the militant subject? How is the individual to resist the trappings of  capito-parliamentary sophistry? Given that Gironi has repudiated the status of  truth in BadiouÕs militant, is it now even possible to ask this question? GironiÕs focus on the relationship between mathematics and ontology is very well developed, providing an excellent overview and allowing him to put forward a novel and important thesis. It should be read by anyone interested in the topic. However the lack of  further engagement with BadiouÕs political project will prevent this text from being of  signiÞcant use to most Badiou scholars.  CHRIS HENRY $5Bibliography Badiou, A. (1992). Manifesto for Philosophy. New York, State University of  New York Press. Badiou, A. (1998). BrieÞngs on Existence: a Short Treatise on Transitory Ontology. Albany, State University of  New York Press. Brassier, R. (2005). "Badiou's Materialist Epistemology of  Mathematics." Angelaki 10(2): 135-150. Gironi, F. (2014). Naturalising Badiou: Mathematical Ontology and Structural Realism. Basingstoke, Palgrave Macmillan. Ladyman, J., D. Ross and H. Kincaid, Eds. (2013). ScientiÞc Metaphysics. Oxford, Oxford University Press. Laruelle, F. (2013). Anti-Badiou: The Introduction of  Maoism Into Philosophy. London and New York, Bloomsbury. CHRIS HENRY $6

Naturalising Badiou: Mathematical Ontology and Structural Realism

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Naturalising Badiou: Mathematical Ontology and Structural Realism

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