The Plane of Immanence

Over at The Naked Void, Nikola recently put up a post about Deleuze’s proximity to idealism (here). Very loosely, his argument ran that any philosophy of presence is essentially idealism, and that Deleuze’s notion of the plane of immanence commits him to such a philosophy of presence. As might be expected, I strongly objected to this characterisation of Deleuze, and I posted quite a long (albeit dense) comment, which tried to undermine the Badiouian assumptions latent in Nikola’s argument. Nikola has since posted a reply to my objections (here), and I feel like it would be more productive to re-present some of my original points and then show what appear to me as the inadequacies of Nikola’s response in light of them.

Insofar as this means that I have to discuss the plane of immanence, this also gives me an opportunity to better formulate some of the issues I have with Levi’s claims about ‘flat ontology’ and immanence (which are linked to here). I do like hitting two birds with one stone, and so I’ll address these after I discuss Nikola’s points.

1. Givenness and Totality

First, I’m going to try to rehearse (and slightly elaborate upon) the major points of my objection to Nikola’s initial post:-

1) Both Badiou and Heidegger think Being in terms of presentation or givenness (or presencing), and this is ultimately understood as a presentation to thought, such that Being is thought in terms of the structure of thought. For Heidegger, this means that Being is ultimately indexed to the complex existential structure of Dasein, and thus to the human. Badiou might thus appear to be quite different, but in truth he simply has a much more austere conception of thought – it has the bare structure of quantification. Thus, for both Heidegger and Badiou, to be is to be presented, even if the structure of presentation (indexed to the structure of thought) is different for them. Indeed, as one might suspect, this is precisely the point at which Heidegger and Badiou fall into correlationism and idealism, respectively.

2) When Badiou claims that ‘the One is not’, the claim is thus that the One, or the totality, is not presentable. This is intimately tied to his denial of the set of all sets, as for such a totality to be presented would be for it to be quantified over, and the count-as-one cannot cannot establish the totality as a quantificational domain insofar as that domain would have to be the set of all sets (insofar as for Badiou sets are what is presented, or beings).

3) The plane of immanence in Deleuze plays precisely this role of the One, or the whole, insofar as everything that is is situated at some point on the plane. As I have said elsewhere (here), the plane of immanence is Deleuze’s reworking of Spinoza’s notion of Substance.

4) However, Deleuze denies the equation of Being and presentation insofar as Being is not indexed to any form of thought, anything which ‘what is’ would be present to. This might sound strange, insofar as Deleuze describes his project as a transcendental empiricism, repeatedly deploys the term ‘givenness’ and characterises the virtual as the conditions of real experience. The point to make here is that for Deleuze this genesis of real experience is just the genesis of the thing itself. Beings are produced, change, and are dissipated on the plane of immanence, and it is in virtue of being situated on this same plane that they encounter one another. They are thus ‘given’ to one another, but only out of a more originary givenness which is not indexed to some structure which makes it ‘consistent’ or ‘unconcealed’.

5) One should not then be  able to interpret the plane of immanence as equivalent to Sartre’s consciousness, or even Fichte’s ‘pure absolute givenness’. For Deleuze, the plane of immanence is a real ontological structure, it is an aspect of Being as it is in itself, and every being has a certain relation to it insofar as they are situated upon it. However, this relation neither restricts the plane’s ‘pure immanent givenness’ to the related being (as if the plane was thereby internal to that being), nor is the relation like a relation between beings on the plane itself (i.e., we do not encounter the plane in the way that we encounter other beings).

6) The fact that we cannot encounter the plane in the way that we encounter entities upon it makes the plane unpresentable in a certain sense. We can thus agree with Badiou that the totality is not a presented or even presentable situation. However, this does not amount to Badiou’s pronouncement that ‘the One is not’. The plane is not given as things which are upon it are given, but is instead the field of givenness as such. We can still think the structure of totality and its role in the genesis of entities, without thereby having to conceive of this totality as something which is thereby itself thinkable. This links up with the claims I have been making in my other posts on Deleuze (e.g, here) that the Whole has no intelligible content, no idea or essence.

Ultimately, Deleuze escapes idealism from two different directions. On the one hand, he denies that the fact that each entity has some relation to the plane thereby internalises the plane or relativises it to that being (Husserl, Sartre, etc.). On the other, he denies that the plane, and thus Being as such, is indexed to any particular kind of being, way of being, or form of thought (Heidegger, Badiou).

One might want to claim that because Deleuze rejects the Badiouian/Heideggerian move, that he thereby automatically falls into the philosophy of presence. The idea behind this is that if one does not take Being to be the presencing of presence, then one thereby defaults to being a thinker of presence. This is just plain wrong, because the real impetus of Heidegger’s critique of the philosophy of presence is that  it involves a privileging of a certain mode of time – the present. Heidegger simply combines his attempt to give a broader account of the relation between Being and time with certain phenomenological prejudices, such that ‘coming to presence’ or ‘presencing’ is dependent upon that which it is present to – Dasein.

Deleuze carries out his own de-centring of the present, and rethinks the relation between Being and time independent of these phenomenological prejudices. Entities are ‘given’ on the plane of immanence insofar as they are generated, and this process of generation is thought not in terms of what is produced, as if the presence of a finished product is its telos, but is thought in its own right. To put it succinctly, for Deleuze, presencing is never presencing to (either to a being or to some form of thought), but is rather onto-genesis as such. The plane of immanence and the eternal return (the third synthesis of time) are intimately interwoven as the super-structure of Being as such – as the underlying structure of space and time, respectively.

2. One or Many Planes?

Nikola’s response to my objections is to appeal to Deleuze’s constructivism. He takes it that Deleuze’s constructivism undermines my claim that Deleuze denies that the plane of immanence is yoked to anything like a form of thought. As he says:-

“Throughout his career, Deleuze was adamant that the ‘plane of immanence’ should not be thought as a pre-given, nonintelligible totality. Quite the contrary, the ‘planomen’ is always a philosophical posit, a laying out of a plane as a “surface for the absolute movement of thought”.”

I’m afraid I’m entirely unimpressed by this point. The reason for this is that it effectively conflates two different senses in which Deleuze uses the term ‘plane of immanence’ in WIP. This is the difference between a plane of immanence (in the sense that there can be multiple planes of immanence) and the plane of immanence (in the sense that there is only one).

In the former sense, each philosopher lays out a plane of immanence upon which they lay out the concepts they create and the relations between them. The plane of immanence here corresponds to the ‘image of thought’ that the philosopher implicitly adopts as a condition of making any explicit claims or assumptions whatsoever. There are thus many different planes of immanence, corresponding to the different systematic thoughts of different philosophers, and although these are not themselves concepts for Deleuze, they are nonetheless created or posited by those thinkers. These planes of immanence are thoroughly relative to a particular conception of the structure of thought, and to a particular entity or set of entities.

However, Deleuze is quite explicit that the plane of immanence is not a plane of  immanence in the sense outlined above. It is not posited or constructed. Indeed, in WIP he takes it that Spinoza’s genius was in first revealing the plane of immanence. This is another point at which I believe Deleuze’s philosophical terminology is needlessly confusing, and I would rather he’d just used distinct terms here, but, this gripe aside, we should recognise that there is an exceptionally important distinction here: the idea of a plane of immanence is an epistemological notion, part of Deleuze’s constructivist conception of philosophical practice (which, as I stressed in my earlier discussions with Kvond, is rooted in his metaphysics, but distinct from it), whereas the idea of the plane of immanence is a thoroughly ontological notion, one that has its roots in the elaborate neo-Spinozan ontology that Deleuze develops before he works out any detailed conception of precisely what it is that philosophy (and thus ontology) consists in.

If one elides the distinction between the epistemological notion and the ontological notion, then it is indeed very easy to read Deleuze as an idealist or correlationist of some stripe. However, what I find most perplexing about Nikola’s retreat to this kind of  reading is that it actually bypasses his initial concerns with the philosophy of presence. This is because one effectively claims that one of the major structural features of Deleuze’s ontology is relative to an ‘image of thought’ or to some thinker who posits it. If this is true, then of course the distinction between Being and thought collapses. There is then no need to discuss the traces of the philosophy of presence in Deleuze’s ontology at all. If one conflates Deleuze’s ontological Spinozism and his epistemological constructivism, then the fact of Deleuze’s idealism follows automatically.

I think this kind of mistaken reading of Deleuze’s constructivism is endemic of a wider misunderstanding of the place of WIP in relation to the rest of his work. This conflation of the two distinct notions of ‘plane of immanence’, goes hand in hand with the conflation of the distinction between concept and Idea that I have mentioned elsewhere (here).

In short, if I were to sum up the significance of Deleuze’s epitemological constructivism, I would say this: for Deleuze, it is not reality that is constructed, but rather the machinery through which we get a grasp upon it. The conceptual is not a part of the world just waiting for us to grow into it, it is something constituted and developed within the world itself.

3. Immanence and Causality

What is the plane of immanence then? As I have already noted, the plane of immanence is Deleuze’s attempt to rework Spinoza’s notion of Substance in a manner compatible with Heidegger’s insights into the ontological difference, and his own commitment to a strongly univocal ontology. What does this amount to though? I don’t believe I can give a completely adequate account of the plane of immanence here, but I can elaborate on a few of the things I have already said, and point in the direction of a few ideas which need further development. Importantly, I will not say much about the virtual here, and the status of the plane as the totality of the virtual. Suffice it to say that I do not see there being a separate plane which is the totality of the actual. The plane of immanence is just the totality of what exists as such.

Firstly, we all know that the plane of immanence is meant to exlude any and all ontological transcendence. The real point of this, in Kantian terms, is to eliminate any unconditioned condition. So, everything that is situated on the plane of immanence is conditioned. The question is: what is this conditioning, and what are we to make of it? I think the answer is fundamentally that conditioning is causal. Everything is conditioned just in the sense that everything is produced out of and situated within networks of causal interaction.

This ties in to what I have been saying about the importance of sufficient reason in Deleuze”s philosophy (here and here) everything has reason insofar as it is the product of an inexhaustible set of causal conditions, but at no point do we run out of such conditions, reaching either a necessary entity that provides its own reason (onto-theology, as in Spinoza and Leibniz) or a pure rupture of transcendence in immanence (negative theology, as in Badiou and Meillassoux).

Now, this doesn’t mean that causality must be understood in the standard law-governed way it is understood in Kant and Hume. It depends upon a far more interesting account of causality, which is present in Deleuze, but I have not entirely gotten to the bottom of yet. There are nonetheless a few points that can be made about it.

Firstly, for Deleuze, entities are constitued out of other entities. However, the important point is that they are constituted out of the interactions of these entities. These interactions are properly causal interactions. A new entity is born out of such interactions just in case the parts generate new capacities for interaction as an assemblage that they did not previously possess. This is just the idea of emergence (now espoused by everyone and his dog).

The important implication of all this is that, although new and very different kinds of causal interaction emerge out of the kinds of causal interactions that take place in the populations of entities that form their substratum, these emergent kinds of causality are nonetheless still kinds of causality. At no point do we leap from some set of causal interactions to some set of non-causal interactions, whatever a non-causal interaction might be.

(It must be pointed out that Deleuze’s notion of quasi-causality is not some kind of non-causal interaction between entities, but is part of his account of the actualisation of the virtual, which I won’t go into here.)

So, economic entities such as various kinds of businesses and financial institutions have their own complex kinds of causal interactions, and these emerge out of the kinds of complex interactions of the social entities they are made up of, and so on, down to molecular interactions, atomic and sub-atomic interactions and beyond. This means that any given interaction between entities at some higher level is always instantiated in entities at a lower level. The last withdrawal in a bank run which brings down the bank might be carried out by an employee of a business, but this act is itself involves a series of social interactions between his boss and himself, himself and the teller, and the teller and whoever else is needed to make the withdrawal, and these interactions are themselves transmissions of sound, light and pheromones which are subject to processing by the individual’s brains, subject to various factors, and so on down the line.

The important point is that athough the individual interactions between higher-level entities are always manifest in particular interactions of their parts, the general form of such interactions is not easily (or even possibly) modelled in terms of those kinds of interactions. This is what emergence consists in: the genesis of new general forms of systematic interaction which are irreducible to the general forms of systematic interaction that they are manifest in.

The plane of immanence is thus stratified (as we all know from ‘the geology of morals’ in ATP), and the apparent laws governing the entities found at any given strata are immanent to that strata. They are themselves produced. (This is where Deleuze shares a certain affinity with Meillassoux, but to explore it more, and to properly locate the contrast between their differing conceptions of the continency of laws is a greater task than I can hope to fulfill here.)

Moving on, what we can now see is that the plane of immanence is brimming with causal interaction and nothing but. When in ATP Deleuze & Guattari talk about words and molecules interacting, or semiotic fragments and chemical interactions rubbing shoulders, we can see that this does not indicate some special form of interaction which is thereby non-causal. It is in virtue of them being situated in their different places in the causal-mereological networks which run through the plane of immanence that they can indirectly affect one another. Everything can affect everything else insofar as they are all woven together into a complex tapestry of causal relations, some of which form the mereological threads which bind the tapestry together. There is no entity which is located outside this theatre of causal interactions, which might condition without being conditioned.

4. Onticology and ‘Flat Ontology’

Here then is my problem with Levi’s claim that his flat ontology is immanent in a manner comparable to Deleuze’s ontology: he seems to take it that only some interactions are causal. Moreover, although he claims that everything can affect everything else, he does not ground this claim in the kind of stratified mereological superstructure that Deleuze posits. There is no potential chain of indirect causation linking every entity insofar as they are all situated within the same causal-mereological network. This isn’t to say that Levi says nothing about mereology, or that he says nothing about the stratification of spatio-temporal scales and the concept of emergence. The problem is that these things do not occupy the central role that they occupy in Deleuze, and thus aren’t quite integrated with some of his other theoretical commitments.

Take for example his concern with whether numbers exist. Of course, he has himself said that he is not sure whether numbers exist, whereas Harman explicitly affirms the existence of numbers. However, for Deleuze, this would not even be a legitimate question. For anything to exist it must be theoretically possible to situate it within the causal-mereological nework that criss-crosses the plane. For numbers to be a candidate entities one would not only have to be able to posit the parts out of whose interactions are constituted, but one would have to show how it is that there could possibly be indirect causal interactions between numbers and other entities, and importantly, this means being able to show in principle that these interactions can be manifest in the interactions of their parts with other things (all the way down, as in our bank teller example). What this means, is that if I am to interact with a number, there must be some point at which we can locate the possibility of my parts (or parts of parts, etc.) interacting with the parts of that number.

I won’t go into the other examples of entities that Levi endorses the existence of (such as fictional entities and symbolic entities), as there has already been much confusion here. I suspect that when Levi talks about these as being non-material and non-causal, he is making some form of artificial distinction whereby the interactions of certain kinds of entities (say physical entities) are causal, but that some entities are manifest in a physical substratum without thereby being physical and thus without their interactions being causal. I still think this is problematic, but it is harder to work out Levi’s exact position here. The crucial issue is whether Levi would accept that the interactions between non-physical entities are manifest in the interactions between their physical parts. If this were the case then his restricted notion of causality would be compatible with Deleuze’s position, but if not, it would be incompatible.

Regardless, the example of numbers presents us with things that if they were to exist would be unequivocally non-causal. This shows us that whatever Levi means exactly by ‘flat ontology’ it is somewhat distinct from both Deleuze and DeLanda (although these two should be kept distinct). For both of these, the flat plane has its own (stratified) structure. To situate entities on the plane is to be able to fit them into this structure. For DeLanda, universals are suspect insofar as they cannot be located at any point, and his attempt to construct a neo-nominalist position out of Deleuze is motivated by this. Although I think his position ultimately misses the mark, this gesture of excluding certain kinds of entities insofar as they cannot be situated is totally Deleuzian. Deleuze is a self-proclaimed materialist, and with this comes the implication that all there is are reciprocally interacting and adapting flows of matter (where matter is not equivalent to unformed Aristotelian ‘stuff’, but this another post entirely). For something to be immaterial, and thus to be worthy of denying existence to, is for it to be in principle unlocatable in the causal-mereological structure of the plane of immanence.

We might thus summarise the worry in this way. There are two possible gestures involved in invoking a flat ontology: a levelling gesture which supposedly refuses to give any kind of ontological privilege to any entity, and a limiting gesture which excludes those entities that cannot be situated on the resultant ‘flat’ plane of existence. Levi’s onticology seems to want to perform the first gesture without the second, and not only does this distance him from Deleuze and DeLanda, but it actually threatens his enactment of the first gesture. This is because it is the very framework which enables (and requires) Deleuze and DeLanda to exclude certain kinds of entities which also enables them to guarantee the fact that all entities are subject to affection, and thus that there are no entities which affect without being affected (and thus constitute unconditioned conditions). It is unclear how entities like numbers, if they were to be allowed, could be put in such a position.

In short, I would suggest that Deleuze’s notion of radical immanence does not lend itself to the kind of ontological promiscuity that Levi is espousing.

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Appropriate descriptors: (neo)rationalist, left-accelerationist, socratic wanderer, heretical Platonist, computational Kantian, minimalist-Hegelian, heterodox Foucauldian, dialectical insurgent, conceptual mercenary, philosopher of fortune.

17 thoughts on “The Plane of Immanence”

  1. De: “For numbers to be a candidate entities one would not only have to be able to posit the parts out of whose interactions are constituted, but one would have to show how it is that there could possibly be indirect causal interactions between numbers and other entities, and importantly, this means being able to show in principle that these interactions can be manifest in the interactions of their parts with other things (all the way down, as in our bank teller example). What this means, is that if I am to interact with a number, there must be some point at which we can locate the possibility of my parts (or parts of parts, etc.) interacting with the parts of that number.”

    Kvond: I am curious, what are the “parts” of my thought of my friend Peter? Can you show that the parts of my friend Peter correspond to all the restrictions you place on “entities”? What are the “parts” of my thought “Ahha!”? What are the parts of my thought “thank you”?

  2. For anyone who is interested I posted a comment on Nikola’s post, as I am somewhat clear as to the content of his response. Hopefully we’ll get to the bottom of it though.

    Kvond: In my opinion ‘thoughts’, along with ‘propositions’ are pseudo-beings, rather than real beings. They are not themselves part of the causal-mereological network I talked about above, even if we can talk about them in systematic ways. This is just to say that the notion of a ‘thought’ as a discrete entity, although often essential in a practical sense is useless for describing what really is. What you are doing when you are ‘thinking about Peter’ is of course something that is manifest in the causal network, it is just not correctly described by postulating some kind of entity called a ‘thought’ or something like a representational relation.

  3. I have a quick question:

    Where does the interpretation you have outlined here place Deleuze’s writings on mathematics?

    As I am sure you are aware, in “Difference and Repetition,” for instance, he repeatedly refers to the kind of “stratification” you identifiy in this post. The stratification, however, is described like this: “for example: mathematical, mathematico-physical, chemical, biological, psychical, sociological and linguistic Ideas” (D&R, 187). Similarly on p. 183-184, about “Ideas which correspond to mathematical relations and realities,” for example. I don’t think these kinds of remarks are at all restricted to “Difference and Repetition,” either.

    What I am wondering, then is: do you take these kinds of passages by Deleuze to be unfortunate (because by his own philosophy “mathematical” should not have a place on that list)? Or do you have a different way of reconciling it with your causal, mereological account of Deleuze?

  4. This is a really excellent question, and I really believe that the real open problem in Deleuze’s philosophy is how one situates mathematics in relation to it. I think I have a different edition of D&R to you, which means I can’t quickly comment on the sections you’re quoting, but they do pose problems for the interpretation I’m advocating. I can’t present an entirely adequate counterpoint, but I can gesture in what I believe to be the right direction.

    Deleuze talks about Ideas as being actualised in spatio-temporal dynamisms. Given this, it is hard to see how there could be anything like an idea of Space or Time, as these are universal conditions under which there are ideas as such. I’m tempted to say something similar about the mathematical. What kind of spatio-temporal dynamisms are mathematical (and mathematico-physical) ideas actualised in? It seems as if in this case we are not really talking about virtual structures which are actualised in specific processes within the world, but rather talking about totally abstract structures that may be part of the conditions of actualisation as such. This is not very precise though.

    Think of it in these terms: all other kinds of ideas are localised to some stratum, and they correspond to particular kinds of processes that can take place on this stratum, but mathematical ideas are entirely stratum independent. However, this is to say that every idea necessarily instantiates some mathematical forms which can be abstracted from the particular stratum within which it is to be found. Chaos theorists use the term ‘universality’ to talk about this. So, for example, the fegenbaum number is found in all kinds of period doubling cascades, and those cascades take place in all different kinds of fluid mediums, as well as turning up in socio-economic processes and probably all kinds of others. Here we seem to have identified a kind of singular universal which is totally unbound by its instantiation in any kind of material substratum. On the other hand, the idea corresponding to the process of central urban decay (a process so well described by Jane Jacobs), is one that is tied to a greater or lesser extent to a certain substratum (namely, the urban level of the social realm).

    Working this out in detail involves working out Deleuze’s account of difference in more detail. Specifically, it involves working out precisely what Deleuze intended to put in place of the Aristotelian, Leibnizian and Hegelian accounts of difference and generality. I don’t think anyone has actually done this properly. DeLanda had a go, but his account doesn’t connect the two extremes. All we have are kinds reduced to higher level process on the one hand (e.g., animal populations in place of species), and abstract universal singularities on the other (e.g., the same singularity actualised in both the soap bubble and the crystal), but we don’t have a good account of what there is in between. For example, where does prostitution fit? Prostitutes are not like lions, they do not form a larger population which continually replenishes itself (as well as going through adaptive evolution), but neither is prostitution substratum independent, it is very much grounded in the specifics of human civilisations, it just happens to be the case that wherever you get a human society you get prostitution (and its various recognisable features). There are a whole set of intermediary cases in which we talk about relative levels of substratum independence, but the mathematical case is most definitely entirely independent.

    The other two things I would point to in talking about mathematics in Deleuze are the following:-

    1) When we get the more detailed working out of the idea of the plane of immanence and the stratification of levels in ATP, we do not get a corresponding talk of anything like a mathematical level, or mathematical objects. D&G are happy to talk about molecules and words interacting, but they aren’t happy to talk about molecules and numbers or equations (not in the sense of symbol strings) interacting.

    2) D&G never know where to place pure mathematics in WIP. Applied mathematics is there to a certain extent, insofar as it seems that it is the use of applied mathematics that distinguishes the sciences. However, there is no clue as to where pure mathematics is: is it science, or philosophy, or something else entirely?

    Personally, I think Deleuze never worked out a really adequate account of the nature of mathematics. He certainly used mathematical concepts, and commented on certain specific issues (differential calculus being the obvious one), but I don’t think he ever worked out the relation between mathematics and ontology proper. This is one place in which Badiou certainly surpasses Deleuze. This is not to say that we should thereby be Badiouian (I think we should not), or that there are no resources in Deleuze to develop an account of mathematics (I have some rudimentary ideas), but I do think this is a point where we must aim to think beyond Deleuze himself, even if it is in his spirit.

    To point in the right direction: the key is to think the relation between Being and the Universal.

  5. Thank you, that was a thoughtful response. I agree that this is perhaps THE open problem of Deleuzian philosophy, which is of course why I wondered how you see it.

    About ATP – I don’t know, not that I have looked carefully at this but there is at least the different models of the “The Smooth and the Striated” plateau….. where the mathematical model appears alongside the physical model, the technological model and the aesthetic model. But this is more an exegetical question, really. The main point, on which I agree completely with you, is that he never seems to have fully worked out the relation of mathematics to ontology.

    Myself, I have mostly been tempted to go in the other direction to the one you opt for here – that is, to affirm that mathematics is on par with the other levels or strata. I have two main reasons for this:

    1) There is no evidence I am aware of that points to Deleuze ever thinking of any special role to mathematics. On the other hand, there is a lot of – admittedly circumstantial – evidence that he did NOT consider mathematics “special” in any deep sense, any more special than physics, biology, or other levels.

    2) I do not know how to give a Deleuzian account of mathematics which would be more “normal”, i.e. that could distinguish clearly between mathematics and reality while giving mathematics some role with respect to reality – while also maintaining the univocity of being. I don’t think Delanda really manages this, for example.

    On the other hand, I do not know how to give an account of this “flat ontology”-reading of mathematics either…..but, by the way – I find the interview with Matthew Watkins in Collapse I, “Prime Evolution,” a tantalizing glimpse of what might perhaps be an answer to your question about: “What kind of spatio-temporal dynamisms are mathematical (and mathematico-physical) ideas actualised in?”

  6. I’ve never read the Matthew Watkins interview, but I will have to give it a go.

    I think the crucial point to make in relation to your reading is that we must be careful not to confuse physics with the physical, biology with the biological, and mathematics with the mathematical. That Deleuze did not consider mathematics special in some senses (i.e., as Badiou does in his equation of mathematics and ontology) does not mean that it is not significantly different in other respects. There might be no mathematical domain of analogous to the physical and biological domains, even if the actual practice of mathematics is not ontologically distinct from that of physics and biology.

    The point I would make about univocity is that the best way to maintain univocity is to deny that there are any mathematical entities at all. To put it in a simple way, there may be triangular things, but that doesn’t mean that there are triangles. The class of triangles is a set of abstract pseudo-objects, and to say that there is a triangle that has three angles of equal size is not to say anything about anything that actually exists. My triangular key chain isn’t part of the set of triangles, even if it instantiates a triangle which is found in it.

    You might want to say that making mathematical ideas (if there are such ideas) radically different from other kinds of idea would constitute a break with univocity, but I think this is wrong, insofar as what matters is processes of actualisation, and there would be no specifically mathematical processes of actualisation, it would rather be a matter of some mathematical ideas being involved in every actualisation. This would maintain univocity, insofar as there would be no privileged kind of actualisation which corresponded to the special kind of idea.

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  8. Hi Peter, sorry to necro, but this is a great post. If you get the time, can you say more about Deleuze’s idea of Aeon? In Deleuze’s idiom is this another term for the plane of immanence, just inflected through the problem of time? Is it safe to identify Aeon with the space time manifold as such? Where do you think deleuze would fit in in terms of some of the contemporary contemporary positions on time?: moving spotlight, perurantism /block eternalism, presentism, and so forth.

  9. Nothing smart to say other than I really like this, and find it useful – not in the sense of ‘how to understand Deleuze?’, but rather a useful engagement with the plane of immanence. So thanks for taking the time. I will be ordering your book on OOP & Harmen consequently.

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