Logics of Worlds

by Alain Badiou, Alberto Toscano (translator)

Logics of Worlds is the long-awaited sequel to Alain Badiou's much-heralded masterpiece, Being and Event. Tackling the questions that had been left open by Being and Event, and answering many of his critics in the process, Badiou supplements his pioneering treatment of multiple being with a daring and complex theory of the worlds in which truths and subjects make their mark - what he calls a materialist dialectic. The radical recasting of ontology in Being and Event is followed and complemented here by a thoroughgoing transformation in our very understanding of logic, conceived as a theory not of being but of appearing.

Unafraid to resurrect and reinvent the classical themes of philosophy, Badiou gives new meaning to concepts such as object, body and relation, mobilising them in arresting studies that range from the architectural planning of Brasilia to contemporary astronomy, and confronting himself with towering philosophical counterparts (Leibniz, Kant, Hegel, Kierkegaard, Lacan, Deleuze). The book culminates in an impassioned call to 'live for an Idea'.

Genres: Philosophy, Nonfiction, Contemporary, Logic, France

640 pages, Hardcover

First published April 24, 2006

About the author

Alain Badiou, Ph.D., born in Rabat, Morocco in 1937, holds the Rene Descartes Chair at the European Graduate School EGS. Alain Badiou was a student at the École Normale Supérieure in the 1950s. He taught at the University of Paris VIII (Vincennes-Saint Denis) from 1969 until 1999, when he returned to ENS as the Chair of the philosophy department. He continues to teach a popular seminar at the Collège International de Philosophie, on topics ranging from the great 'antiphilosophers' (Saint-Paul, Nietzsche, Wittgenstein, Lacan) to the major conceptual innovations of the twentieth century. Much of Badiou's life has been shaped by his dedication to the consequences of the May 1968 revolt in Paris. Long a leading member of Union des jeunesses communistes de France (marxistes-léninistes), he remains with Sylvain Lazarus and Natacha Michel at the center of L'Organisation Politique, a post-party organization concerned with direct popular intervention in a wide range of issues (including immigration, labor, and housing). He is the author of several successful novels and plays as well as more than a dozen philosophical works.

Trained as a mathematician, Alain Badiou is one of the most original French philosophers today. Influenced by Plato, Georg Wilhelm Friedrich Hegel, Jacques Lacan and Gilles Deleuze, he is an outspoken critic of both the analytic as well as the postmodern schools of thoughts. His philosophy seeks to expose and make sense of the potential of radical innovation (revolution, invention, transfiguration) in every situation.

Reviews

[Alex Lee · Rating 5 out of 5]

On the onset, Badiou's materialist dialectic seems fairly obscure. But while he doesn't speak much about it throughout his book, it becomes clear that his materialist dialectic is predicated on the same kind of formalization that has swept up modernist thought: the creation of formalism in order to express relations in thought.

While you can tell that Badiou doesn't want to dismiss his previous work, Being and Event in this one he seeks to engage with the non-philosophical more. To this end, while the previous was on ontology this book it seems far more about presentation, or existence. Having sublimated the formalisms of mathematics into philosophical thought, Badiou would introduce to us a more specific (and thus generalized) logic on which to understand the various collections and connections we witness in our everyday lives.

This formalism can be understood as the result of the Cartesian method of synthesis. One breaks down a situation into constituent atoms and then patches those atoms back together to come up with a composite world. The various different situations provide little input as to the method of the formalization, although the success of the formalization requires a method of atomization -- "chunking". How we decide to decompose a situation into chunks will in reverse allow us to assemble them back together.

Part of Badiou's genius, especially with this previous book to this, the first Being and Event relied on his insight that mathematics at its root was conceptual, not formal (despite how we in post-industrial education are introduced to mathematics, as pure formalism). By grasping the concepts, we can then also understand that mathematics is philosophical in its nature, although it is of a different kind. Math follows the inductive "analytical" side of the method. The missing piece is the synthesis. This analysis-synthesis is central to the method of the ancient Greeks (such as with Euclid). Much of the surviving philosophy post-ancient Greece, only presents the synthesis side. As Irme Lakatos notes, Descartes realized their methods. Lakatos speculates that the "secrets" of the ancient Greeks had primarily to do with the method of analysis. The synthesis portion was given publicly and that's why the Euclidean method we have today is nothing but synthesis. We get the conclusions of their philosophy, but not their analysis. The end result of their analysis, however, is their axioms. Incidentally, analysis/synthesis is why mathematics and physics meld together so well. To dissolve a situation via a formalism and then to patch it back together allows one to continually create new models, new methods of dissolution and then synthesis (via application). The main hinge for synthesis and analysis is the cherished "occult hypothesis" by which one is able to grasp the missing "influx": how the atoms are cut and then how these atoms are stitched back together. For Newtonians, this occult hypothesis is gravity. The various other "conclusions" that theorists and scientists can come up with are varying but they consist of the "excluded middle". Slavoj Zizek for example, in Less than Nothing has the occult hypothesis of less than nothing, the theory of two vacuums.

What is perhaps wonderful about Badiou's approach, as well, is that he sidesteps the traditional jargon that Zizek has to deal with. Badiou can talk about past philosophers (but not necessarily). Comparatively Zizek, in order to make his point, MUST. This injection of mathematics is perhaps Badiou's greatest contribution. It is a great strength as well, for he is able to introduce new relations on their own, rather than having to continually modify language we are already familiar with.

What is weak about Badiou however, is that he adds little content to a situation. His formalism is a tool that can be used to recompose existing worlds and relate them to one another. While he dismisses Kant in this book, he misses Kant's greater understanding. As stated in his Critique of Pure Reason: mathematics is another synthesis. While math can be used analytically, and often is, its incompleteness in its axioms results from the fact that as a methodological field, math is stitched together through a variety of methods connected by sheer formalism. There is no one conception that rules mathematics in the same way that there is a singular conception that may rule Lacan or Descartes. So while formalism can be a method to note new connections, it cannot replace the intuition of thought itself. In fact, Badiou's method is not an explanation what so ever, even though he mistakes his method for Truth (which ought to be the explanation).

Two additional weaknesses to Badiou

1. He critiques Deleuze heavily in claiming that his fourfold thesis is a reversal of Deleuze's. This misses the point as both he and Deleuze understand that negation is not a rebuke of a logic but rather the emphasis of a missing totality. Badiou's own method of formalizing a transcendental envelope is predicated on the minimum gesture of negation of a missing piece. In fact, Badiou ends his book by noting that the presence of a body (or a grouping of conceptions as a topological family) is wholly subsisted on the missing of a minimum. His other critique -- that Deleuze reduces everything into a monotonous elan vital, similar to Spinoza's lack of a transcendental distinction of substances and subjectivity is well taken, however.

2. His main value in the conversation is his ability to provide surjection between the domains of math and philosophy. This theory of points (book IV) is a pretty good aesthetic, only missing Dedekind's cut of real numbers. While his analysis of what points provides to the conversation could have been (and should have been) interjected into his first book for the purpose of clarification, he misses out on providing an internal definition of knowledge even in this following book. One creates knowledge only when one can mark it, that is, surjectively translate it into a point. In fact, Weierstrass's genius at the end of the 19th century relied on solidifying what Descartes started: the overlay of points onto numbers in the form of analytic geometry. This move by 19th century mathematicians following Weierstrass's reluctant but compelling argument for what eventually comes modern day set theory is thus taken as being unequivocally true by Badiou and absorbed into his approach. Now, having explained the value of this formalistic surjection, Badiou misses the fact that the immanence of his theory is useless in itself (even though he was compelled to introduce it as a stand-alone 4th book).

Of course, he realizes this implicitly, but he does not seem to understand, as Karl Marx and Immanuel Kant did, that navigating the interstice is what brings a formalism its value. Kant's genius lay in realizing the synthetic nature of phenomenon. His transcendental dialectic surpassed the different singular ("logically independent worlds" qua) faculties to give us a method of relating phenomenon together, stitching together a world through the continuance of their parts. Likewise, Marx explains exchange value through the various different use values of products: The connected use values of these products are what creates value for money, and those different kinds of money are in a way, different kinds of sublimated use values. In his approach here, Badiou continues to wrap different worlds as increasingly complex localizations that appear to one another, but in the process of doing so always presents it within an absolute envelope (m) that is routinely defined as the mode by which these different atoms can interrelate and be associated with one another. And while he states early on that there is no Being that covers all being, like there is no Body that can cover all, I do not think he realizes that by sublimating presentation as a formalization within these sets, he IS able to step outside of the pure multiples themselves and wrap all of being as only that which appears under immanence. At the end of this book, he laments the dismissal of concepts, quoting Descartes that mathematics is eternal. And yet, hasn't he contradicted himself? Badiou's rejection of Deleuzian immanence is contradictory to his attempt to accept a pure Transcendental qua Eternal Truth. He rejects this flip in Deleuze so he can then "discover" it again -- only doing so on his terms. Thus, Badiou defines early on that there is no Being -- that it there is no way one envelope can wrap all of the different worlds, and then he defines it through sheer nominalization (m) and then acts as though this nominalization surpasses the physical presentation of the logics of worlds, stating that there are worlds in which we cannot have access to because their presentation is too baroquely different from our own. So is this Truth Eternal (and thus, all-encompassing)? Or is he only talking about a truth that is contingent and only a type? He mistakes method for content and formalism for understanding.

This is the same entrapment that thinkers that the great Roger Penrose, or even Richard Dawkins falls into. Their sublime ability to create complex and yet fantastically concise occult hypothesis allows them the decompose and recompose with such sheer mastery that they have forgotten the reality of their own methods. They are hypnotized by their own defined immanence, forgetting that even in this present world there are points that lie outside of the rigor of their own presentations. Badiou follows this routine, coming to the conclusion to speak of the totality of Idea as an absolute shield. Nevermind the fact that such methodology did not exist for all time, and that the formalism of our own knowledge is a fragmentary creation of the conditions of what we accept to be knowledge. If our knowledge is fragmentary it is because we reject the interstices which give each world of knowledge value, a value which exists wholly outside of each field but is only understood as immanent to that field's own internal (non-)sense/consistency.

This tact understanding is also Deleuze's greatest insight which I think exceeds Badiou. Deleuze's own language: the conceptions of territoriality, plateaus and the like, consist of Deleuze and Guattari's genius at producing traces (rhizomes) by which different machinic assemblages influence one another. (Un)fortunately, Deleuzean language either leads people to reject it outright as being non-knowledge, as there is no "point" by which one can make heads or tails of it, books which review Deleuze and only write about a few of his concepts as though this is the great aspect that is to be gleamed or books which abandon Deleuze but are "about" Deleuze and seek to create their own immanence. Badiou's method does allow for some greater control in adjusting and decomposing with greater control, but I think that Badiou himself misses the larger aesthetic of Deleuze by pursuing too recklessly the desire for validation. On the one hand, Badiou understands that his philosophy only has value if he is able to connect it to real-life situations (thus his talking about life and death) but on the other hand, he wishes for the most obscure concepts in order to be recognized with his heroes, as a philosopher).

Having gone this far in the review, I do wish to pull back a little and return to the material dialectic. This insight is profound on its own, but Badiou misses stating it explicitly in his text because he is too enamored of his mathematical rigor: this point is simply that all creation of knowledge (analysis and the synthesis) is predicated on procedure. The truth of mathematics as a rigorous activity and the formation of knowledge as points wholly subsists on the exteriority of various groups that are able to formulate their knowledge as a logical consistency for their profession/activity. That is to say, the pure immanence of a specific approach requires the routine nullification of external connections in-itself. Worlds become whole when they eschew other worlds, and nullify the influence of exterior factors. This pure modeling becomes all the more valuable when it is connected to a process which then is able to modify one another. Professions like attorneys and architects are gatekeepers to officiated activity, activity which is inflated because of the formalism of capitalism... but that in itself, is to encroach on an entirely different subject.

I gave this book 5 stars because it's a tight work. It's flawed for the reasons I point out, but it's still well worth the read.

[Alexander · Rating 4 out of 5]

Attributed to Plato by ancient astronomers, the question of how to ‘save the phenomena’ was, so it was said, among the most pressing of issues for the earliest star gazers. For, if according to the rationalist strictures of ancient cosmology, celestial motions were to be accounted for by the divine regularity of periodic movement, how was it that actual observation would reveal aberrant paths, retrogressions of planets and uneven solar passages? How could it be that the appearance of planetary motion not coincide with the being of their postulated reality? On the one hand, then, Being: simple, regular, and sanctified. On the other, Appearance: messy, bodily, and erratic.

In terms less cosmological but at least as Platonic, such is the project of Alain Badiou’s Logics of Worlds, which aims at just this reconciliation, appending, to his doctrine of Being - as laid out in his previous work, Being and Event - here, his logic of Appearing. It’s an undertaking just as ambitious and wide-ranging as it sounds, offering entirely new approaches to classic philosophical problems in their most universal breadth. From the most concrete to the most abstract: What is it to live? What is death? What is a body? How are we to understand change (from mere ‘modifications’ to - of course - the eruptions of events)? What about ‘objects’? Relations? Identity and differences? All these topics are broached here, with a distinctness entirely singular to this monster of contemporary metaphysics.

As for the nature and necessity of the ‘reconciliation’ (my term, not Badiou’s) involved, it has to do, largely, with the last (and thus most abstract) item on the list above: that of identities and differences. For where Being and Event leveraged the mathematics of set theory to ground ontology (and thus Being), it left Badiou with the problem of a rather restricted capacity to deal with differences. Among sets, identity and differences are defined by ‘belonging’ alone: if two sets have the same elements (a and b, say), they are identical; if they do not, if even one element is missing, then the sets are absolutely different. The stringency of this criteria left open the question of how to deal with relative differences: things which are similar or dissimilar to each other, the more and the less.

It’s here, in the effort to think though this almost maddeningly mundane issue, did Badiou run through the rigours of taking up set theory’s mathematical ‘rival’, category theory, in order to give it a ‘place’ among his grand system: that of dealing with the logics of appearance. Whence the full scope of Badiou’s effort here: to have bought together the two foundational frameworks of mathematics, all while extending the range and power of his philosophy to deal with questions that have riven the canon from Plato to Kant, Kiekregaard to Deleuze - all of whom make appearances in this book as so many foils through and against which Badiou carves out his own original place in the philosophical firmament.

—

What then, of its success? Impeccable in its execution, the Logics of Worlds resembles, in the finery of its construction, something of an art object no less than a philosophical treatise. I mean this as praise, but it’s also where I have the most trouble in taking on its prescriptions as my own. So tightly bound are the ideas here to one another - math bleeding into concepts bleeding into examples - that one gets the feeling that, for all its seeming capaciousness, the problems responded to are in many ways problems internal to Badiou’s own system itself. Did I need to run through 300 pages of the Grand Logic - the first half of the book - in order to give expression and formal grounding to the idea that sometimes, things are similar and dissimilar to one another by degrees?

Or is this, as it sometimes inescapably feels, Badiou dotting his i’s and crossing his t’s - a compulsion for completeness rather than an instrument of illumination? Similarly, the treatment of ‘relation’ here, itself responsive to critiques levelled at Being and Event’s quiescence on the issue, while delicate and original, still comes across as oddly isolated. What does one do with the theory of relations as derivative of multiplicity, other than note that it lends a neat coherence to Badiou’s preference for sets (which, in themselves, have no need for relations)? At my most ungenerous, the ‘saving of appearances’ here read not unlike the ever more complex addition of epicycles and deferents to early cosmological theories of geocentrism, meant to help square the theoretical circle of the sun revolving around the Earth.

Nonetheless, at his best, Badiou is a truly exhilarating author. His choice of enemies alone - what he calls ‘democratic materialism’, his peculiar but powerful characterisation of life lived without Events, roughly coeval with the reining ideology - make him worthy of reading. As the presentation of principles for an alternative way of living - one lives for the sake of an Idea or not at all says Badiou - in the Logics of Worlds, one gets a glimpse, too often obscured, of just what is possible when thought moves along axes orthogonal to world as we know it. Beyond knowledge, Events, the well of the void from which to draw the promise of the future. If we have the courage to seize it.

[Owlseyes]

"Je suis aussi connu comme un militant politique qui cherche la voie d'un nouveau communisme"
Alain Badiou

[Shulamith Farhi · Rating 4 out of 5]

While not all of the book succeeds, the parts that do make it an essential appendix (it is fruitful to think of the entire thing as a long footnote) to Being and Event.

The introduction and first book make an exciting promise the rest of the book only partially lives up to. The materialist dialectic is an important orientation in thinking, extending many of his earlier claims in Theory of the Subject and resituating them in his modern system. The formal theory of the subject begins to fill in the most important gap in Being and Event, namely how subjects subsist once they are formed. The theories of points and bodies, in the same vein, flesh out the skeleton present in his earlier works.

Books 2, 3 and 4 fare less well. The "Greater Logic" subsumes "formal logic" in an interesting way, but the whole thing is founded on the possibility of an "objective phenomenology" which is not adequately defended in the book. Central concepts such as world, transcendental, atom etc assume the possibility of formal semiotics (meaning-making) without meaning-makers. An engagement with semiotics as well as a deeper engagement with the Heideggerean concept of world and a reading of Sellars would sharpen this position, and shore up the foundational conceit of the book. Another avenue of elaboration, would put Badiou in dialogue with the analytic philosophy literature sparked by Nagel on phenomenology from a scientific point of view.

In the same way that Being and Event can be said to provide a minimal metaphysics for the claim that there are evental subjects, this book provides a minimal metaphysics for the claim that the subsistence of these subjects can be thought within a generalized theory of strategy/war (in this regard it is interesting to note that Spartacus, Alexander and Mao are all central examples). The book discloses Badiou's world at the time of writing, and the structure of the book as well as the copious and fascinating footnotes highlight the difference from Being and Event. Just as the almost deductive structure of Being and Event paralleled the argumentation, here when Badiou compares the book to a world, we know he is not exaggerating.

This book opens a number of fruitful avenues for further thinking. The relation between category theory and ontology is still being contested, and Badiou's reading of the 3 kinds of logic is probably not the final world on the logical structure of different worlds. A proper analysis of this would have to present an analysis that takes as its central focus the construction of logics in philosophy and in worlds and would link this idea to his earlier concept of the space of compossibility. Another fruitful approach would be to read the concept of world in the history of philosophy and social theory, along with the evolution in the world of social relations (linking it to a Marxist problematic). Badiou's presentation of non-classical logic could be deepened by further engagement with the literature on paraconsistency and intuitionistic logic as well as the literature on polyvalence and dialogical logic, to name a few.

A fascinating book, well worth reading for understanding the trajectory of perhaps the most exciting thinker working today.

[J. Moufawad-Paul · Rating 3 out of 5]

Sometimes you have to wonder about someone's philosophy when the majority of their rabid fans outside of philosophy, but in other academic departments (or not), hold them up as brilliant but can only explain what they mean in other obscurantisms. And sometimes I tend to sympathize with my colleagues who focus on analytic philosophy and their complaint (though it's not always fair) that most continental philosophy is just psychobabble designed to seem profound and trick people into lauding it as the new philosophy. Still…

After finishing Being and Event years back, and then detouring through the excellent (but needlessly obscurantist at points) *Theory of the Subject*, I picked up Logics of Worlds. My problem with B&E was that, as a historical materialist, I have a problem with the return to grand metaphysical projects (even those that claim they aren't that, but really are), the kind of speculative ontology that was declared theological and anti-materialist by Feuerbach––and even he was mired in idealism.

Thus, Logics of Worlds ends up becoming, despite some great parts, precisely the kind of removed-from-reality project this kind of speculative ontology can and will become so that, by the standards of Badiou's own political tradition, it falls flat. The fact that it has to deform history in order to get its point across demonstrates the problem with this kind of ontological project approach––it's the kind of "totalizing" the post-structuralists falsely ascribed to historical materialism, that is the *wrong* kind of totalizing. Take, for example, what Badiou says about Quebec, Quebec Nationalism, and Kanehsatake: anyone who knows anything about the anti-revisionist marxist trajectory in Quebec would know that Badiou's assessment is quite wrong and behind the times, demonstrating no knowledge of the event in question and drawing out a phenomenological meaning based on a pretty piss-poor grasp of what happened and the meaning that was forced there by militants. Other strange statements about important moments and movements in history abound (i.e. like the completely erroneous parallel he draws between the Khmer Rouge and the Shining Path, claiming they are both variants of maoism when the former never saw itself as thus in any way shape or form), which kind of renders his "materialist dialectic" somewhat useless since it cannot really tell us anything meaningful about history.

[Hainamoration · Rating 5 out of 5]

a Work of monstrous import. those of the school of intellectual dilettantism, first Quit yourself! but mostly don't tread on him. luckily and to be charitable, those analphabets and priests of death and old-guard haven't the inclination. To the Book: without his Being and Event, logics of worlds is pure cypher--
so, assuming fluency: theory of point, bodies, formalism of the subject, distributivity, antonic worlds, real change etc.
indefinitely extend (extensity) and vitalize his programme: Materialist Dialectic
in sum-- "there are only bodies and languages, except that there are truths!"
freely dis-coursing on His Axiomatic-set theory, 'artifactual philosophy', historical situationalism etc. he sets about lobotomizing the obscure and reactive among us. he simultaneously remains faithful and outlying his previous elaboration. stylistically he combines poetics and patient enumeration with incredulous force. closest to T.O.E. (theory of pas-tout: the 'except that' or everything).

treat this book with proper Fear.
End.

[J. · Rating 4 out of 5]

the handicap at the outset: the typical problem with philosophers' later works... that they correct the problems that moderate and reasonable reflection finds with the brilliant and unjust works of boldness that, preceding them, violently illuminated some irregular fragment of the real... but without digging deeply enough, perhaps without sacrificing enough?, so that relevance is lost. thus X's later works solve problems that are problems with X's early work, but which perhaps are not so much our problems...

[Mariam Rawwas · Rating 4 out of 5]

Badiou begins with a fundamental maxim: "There are only bodies and languages, except that there are truths," which he deems the "axiom" of the "materialist dialectic." Large passages of the opening recapitulate familiar themes for Badiou: tired polemics against postmodernism, an anthropocentric (Aristotelian) reading of ethics against the "human animal," an attempt to circumscribe politics within a given set of transcendental categories (here, the faithful, the obscure, and the reactive), a lazy attempt at mathemic construction (regarding the subject's relation to the evental present), and the four epistemological domains of truth-production (which always stumbles on the stubborn heterosexuality of Badiou's gloss on the amorous, despite his protestations—for the record, I agree that, in a certain sense, all amorous relations are "hetero"-sexual in that homosexuality simply installs sexual difference amidst a gender instead of between them (à la Mitchell), but Badiou simply does not go there). What's so stunning about all this is Badiou can be rigorously exact when he wants to be, especially with his engagements with "mathematics as ontology," but this is re-doubled with a seeming need to bloat his tomes to 600+ pages via endlessly unnecessary pontifications. In the transition from being to appearing (a seeming response to phenomenology), Badiou moves to a conception of "worlds," which mostly retains the recourse to set theory (though helpful to clarify, against the analytics, that of course our worlds are not classical, for they do not and have never conformed to classical logic). The true transition from ZFC to category theory (or rather, its supplementation with) comes via the introduction of the morphism, as a class of objects alongside objects themselves, allowing Badiou to think relation alongside elements of a set. This clarifies what is at stake in an event: from one situation of "universal exposure" to another. Through this recourse to algebraic topology, Badiou can also cipher bodies as sites of potential fidelity to an event, points as sites of intensity, though this also brings out his maximalism in full force: I simply do not believe that one can formally deduce that the rupture which is maximalist in its intensity is necessarily the politically desirable one, which goes to perhaps the fundamental issue at the heart of Badiou's project, which is the valorization of rupture in itself as a break with the existing order. Badiou's reconciliation of ZFC and category theory with thinking through political situations and the phenomenological in general is genuinely alluring, but is perhaps not as impressive when one considers that formal logic is a human enterprise, and moving back from formalism to human perception is possible quite simply because the former emerged through a movement in the opposite direction from the latter. Also, the recourse to the same set of philosophical, literary/poetic, artistic, musical, etc. examples gets a bit tiring once you've already encountered Badiou's glosses on those figures. Nevertheless, there remains something so neat and tidy about the way that Badiou proceeds and the results he manages to produce that it is difficult not to get sucked into the charm and the beauty of it all.

[David · Rating 5 out of 5]

Short first thoughts: Look, I really enjoy reading Badiou. For me, that's a key aspect to start with. I read a bunch of his stuff, and, though I am also quite politically sympathetic to where he's coming from, and I have learned much from him that way, I don't think I would keep reading if it weren't for the fact that, damn it, I find him fun to read. (Mostly. The math gets a little dry at times, even for me, a mathematician.)

And this is mostly quite enjoyable Badiou. He's hunting big game here, but he's also engaging with a lot of different thinkers and writers. And history too. That's another thing that I'm not sure he always gets enough credit for: he's an avid and sharp reader of others. He can engage with Kierkegaard fruitfully. And Sartre's plays, and Pessoa's poetry, and Julien Gracq's novel _The Opposing Shore_ (which I only read because it popped up here -- and it is very good).

He's quite inspiring, too. He challenges you to live, and to live for an Idea. Contrast that to the various sad excuses for life we're told to accept in this dreary and pointless and exploitative and polluted structure we inhabit? I'll take it. So read, and my it help you, too, find ways to live for an Idea, and to identify a Truth to which you can maintain your fidelity.

Note: You can probably read this without reading _Being and Event_. And it has more engagement with works of art and literature, if that's the kind of thing you enjoy. B&E definitely adds to the experience of reading this, but much of this stands on its own.

Note 2: If you *do* know some mathematics, I recommend that you sometimes jump forward to the mathematical details and then circle back to these engagements with poetry and history and battles and books. Badiou does use language that can sometimes be pretty dense. (I reject that he is being deliberately obscure, and find that criticism from others lazy and unconvincing.) But if you know some math and have looked over his derivations, I found it snapped some of the earlier discussions into place for me.

[Yasha · Rating 5 out of 5]

While the first book in this series focuses on the dialectics of Being and Change (Event), this one is more concerned with Being and Appearance. The mathematics at play in this book to explore this relationship is Category Theory, or the abstract study of objects and their relations. Lessons from this subject show how sufficiently large/complete/internally coherent systems of relationships (importantly things become contextual and relative in themselves) can completely support fully coherent logical structures of meaning and appearance.

This one really blew my mind with its use of mathematics the most.

[Benjamin · Rating 5 out of 5]

Possibly my biggest problem with reading Badiou is the fact that once he hits the formal proofs of his concepts and principles I always get lost in a mire of set theory and logic that my tiny mind can't handle. In which case, it was with great trepidation that I set about reading "Logics of Worlds", the follow-up to his intriguing/baffling "Being and Event". I changed my approach and didn't resign to my lack of understanding and painstakingly pursued each proof in laborious detail to make sure that every sentence was understood. In honesty this worked well until Book 6 when I put the book down and didn't come back to it for a fortnight. I was pretty much lost and had to rely upon my understanding of the phenomenological analyses and applications to thinkers to get me through.

That's just my personal experience of the book. My feelings on it are different. Far from being an impenetrable trawl, it was an enlightening, engaging and exciting work that makes you feel like you're really having a whole world opened up to you. It's exciting to read books that you may not agree with, but you feel pushing against you and challenging you to rethink everything. As usual, the writing sways from dense formalism to sheer lyricism with ease, both captivating and taxing at once.

Not recommended if you haven't read "Being and Event". If it's been a while since reading it, it's also worth revisiting "Theoretical Writings" or "Infinite Thought" as a refresher, then get stuck in. It's going to be a long journey, but worth it.

[Charles · Rating 2 out of 5]

Long, tedious, unnecessarily complex, and not particularly convincing.

[Chris · Rating 5 out of 5]

Review coming soon.

[Andrew Glynn · Rating 4 out of 5]

Less cohesive than part 1 but in many ways more interesting.