Correlationism Redux – Instantiate this

I’ve been revisiting the argument against correlationism in chapter 1 of After Finitude. This has always struck me as perhaps the least interesting part of the book, and certainly the most misleading, insofar as it tends to draw the focus away from the more principled overcoming of correlationism (by pitching it against what Meillassoux now calls “subjectalism”) in chapter 2.

Nonetheless, the fact that I’m now back to working on Meillassoux draws me back into the fray. And it seems important to grasp what the proper strength of the arche-fossil argument is, to attain the clearest and strongest formulation of its challenge to correlationism. I guess part of what’s drawing me back is also the assessment of Meillassoux’s arguments adumbrated in comments here: Despite having what I think is a decent grasp of the nuances of Kant’s position, I find Meillassoux’s argument to be quite a piercing critique of the Kantian framework, and it’s worth trying to articulate why. In fact, this post will turn out to be a defense of the cogency of the correlationist position, but I’m far from sure whether the rejoinder works, and it is the first real response to Meillassoux’s argument I’ve managed to come up with, several years after first reading it.

As far as I can see, the very core of the argument turns on the transcendental, more precisely, the transcendental subject as something that must be ‘taking place’, in pp. 24-26 of After Finitude. Here, Meillassoux introduces the distinction between the transcendental subject as being “exemplified” and as being “instantiated.” This distinction corresponds, if I understand correctly, to the old distinction between universals ante rem, the Platonic Forms, and universals in rebus, the Aristotelian forms. Does the transcendental subject exist over and above, and prior to, its instances, i.e., ante rem, so that its instances are merely exemplifications? Meillassoux claims, and rightly so, that correlationists must answer no to this question, to avoid being dogmatists. So the transcendental subject exists only in its instances, i.e., in rebus, it exists only insofar as it has empirical instantiations. But this means that one can talk about (and investigate scientifically) the emergence of the transcendental subject, its passage from non-existence to existence (since one can talk about and investigate the emergence of its first instantiation), and importantly, one can talk about this passage as something that takes place in time (since one can talk about the passage from non-existence to existence of its first instantiation as something that takes place in time).

What is important here is that Meillassoux is not as it were imposing a foreign conception of time onto the Kantian framework, not as the argument has been presented up until now at any rate (I will return later to whether he eventually tries to do that). Kant has to agree that the first instantiation of transcendental subjecthood is something that took place at a certain point in time – at a certain point in time precisely as Kant understands time, that is. Transcendental subjecthood does need to be instantiated, and what instantiates it are empirical subjects with a certain temporal duration, and this instantiation did happen for the first time at some point (given Kant’s hypothesis concerning the origin of the solar system, it’s pretty clear that he thinks there was a time when the earth was around but there were no humans on it). But here comes the problem: Kant is also committed to claiming that time is nothing other than the form of inner sensibility of this transcendental subject. Thus, one might reasonably think that if the transcendental subject needs to be instantiated, then the form of inner sensibility of this transcendental subject also needs to be instantiated, and that these instantiations are co-extensive (abstracting for now from the fact that Kant thinks it is logically possible that a transcendental subject could have a different form of sensibility). So the first instantiation of the transcendental subject is also the first instantiation of the form of inner sensibility, i.e., time. But – paradox! – the first instantiation of time is now shown to be something that takes place in time. Time emerges in time. Kant cannot claim that time is ante rem, somehow existing over and above particular subjects with sensibilities; that would obviously reinstate the time-as-thing-in-itself conception. So he seems forced to give up the idea that there was a time prior to the first instantiation of transcendental subjecthood. A hefty price to pay.

The crucial question, I think, is this:

Can the in rebus instantiation of a universal be a condition of the possibility of the very thing in which it is first instantiated?

I think that the answer to this question is “yes,” because it seems that the instantiation can be what makes the thing in which it is first instantiated the thing that it is. So, presumably, the Aristotelian form (say, the form of a specific animal species, e.g., giraffehood) was thought to be a condition of the possibility of the individual things, i.e., the individual giraffes, in which it was instantiated, because they wouldn’t be giraffes if they didn’t instantiate giraffehood. This is the case whenever the universal in question is part of the essence of the thing in which it is instantiated. Thus, in many cases the instantiation of the universal is not the condition of the possibility of the thing, since the property instantiated is inessential to the thing being the thing it is. E.g., I instantiate “tiredness” now, but I will (presumably) still be me after drinking my cups of coffee tomorrow morning, despite the fact that I will no longer be instantiating tiredness.

Let us look at how this question pertains to the matter at hand, by considering some particular instances:

1. The in rebus instantiation of transcendental subjecthood is the condition of the possibility of the empirical subject in which it is first instantiated.

First of all, note that this is definitely true within the Kantian framework. And moreover, it seems to follow the same pattern as with the Aristotelian form considered above: The empirical subject would not be the thing that it is, i.e., an empirical subject, if it were not an instantiation of transcendental subjecthood. Being an instantiation of transcendental subjecthood seems to be part of the essence of being an empirical subject.

2. The in rebus instantiation of transcendental subjecthood is a condition of the possibility of the time in which it is first instantiated.

This case is slightly different. Time is not a thing in which transcendental subjecthood can be instantiated. It is, if one follows Kant, a form of intuition. Nonetheless, one can still say that time is something “in which” or “within which” transcendental subjecthood is first instantiated. And again, the claim is definitely true within the Kantian framework. No transcendental subject, no time; but at the same time this transcendental subject must be instantiated in time: “it is all the same whether I say that this whole time is in Me, as an individual unity, or that I am to be found with numerical identity, in all of this time” (Critique of Pure Reason, A363). Why is this? Again, the justification for the claim seems to be that the entity in which the universal is instantiated would not be the entity it is if the universal was not instantiated in it: Time would not be what it is if transcendental subjecthood was not instantiated in it, in other words, transcendental subjecthood is part of the essence of time.


At some point along this line of argument, Meillassoux will have to protest. And I think the protest must come with respect to sentence 2. One way of protesting would be to ask what the argument for the claim “transcendental subjecthood is part of the essence of time” is; why on earth would one think such a thing? (Kant’s main arguments are in the Transcendental Aesthetic and the Transcendental Deduction). But this is not Meillassoux’s approach, since he wants to argue not that there are insufficient grounds for asserting the Kantian thesis, but that there are sufficient grounds for rejecting it, along what I think are the following lines:

“2 is false, because it can be shown (and is shown, by science) that transcendental subjecthood cannot be part of the essence of time. It simply cannot be the case that time would not be the thing it is, i.e., would not be time, if transcendental subjecthood was not instantiated in it. For science tells us about a time before the instantiation of transcendental subjecthood, from which we can conclude that time is capable of being what it is, i.e., time, without instantiating transcendental subjecthood, since time, as it was then, was the thing/entity it was without instantiating transcendental subjecthood.”

But here comes the main point I want to try out in this post, however inchoately: Does this challenge by Meillassoux not presuppose something concerning what time is? Consider the following answer:

“Time is not a thing which moves in time, thus one cannot speak of time “as it was then” or “time as it is now.” If transcendental subjecthood is instantiated in time, it is instantiated in time, period. It is true that other objects can begin instantiating, or stop instantiating, certain universals. E.g., I can instantiate the universal “youthfulness” now, but stop doing so in, say, a year or so… But time is not that kind of object, as can be seen by the following consideration: If one were to talk about “time as it was then” and “time as it is now,” one would have to say that time changes, but changes can only take place in time, thus there would have to be a second time, time2, in which these changes in the first time, time1, could occur. So one should talk about changes taking place in time, rather than talking about time itself as changing.”

Is this a trick? Could one rephrase the point using, e.g., “parts of time” instead? If the instantiation of transcendental subjecthood is supposed to be the condition of the possibility of every part of time as well, then it might be claimed: “But a part of time, e.g., the part of time stretching from 16 to 15 million years before now, was what it was, e.g., a part of time, even though transcendental subjecthood was not instantiated in it. So transcendental subjecthood cannot be part of the essence of parts of time, and therefore cannot be part of the essence of time.” But I don’t think that this rephrased argument is sound. A universal can be part of the essence of an object, without being part of the essence of any part of that object. Let us stipulate that “philosopherhood” is part of my essence (doubtful though it is). Surely, that doesn’t commit me to claiming that any part of me has “philosopherhood” as part of its essence. So the fact that science can tell us about parts of time where transcendental subjecthood is not instantiated does not tell us that transcendental subjecthood is inessential to time considered as a whole. And since according to Kant, time as a whole is logically prior to its parts, one cannot claim that certain parts of time could happen independently of transcendental subjecthood being instantiated, even though they can certainly happen independently of transcendental subjecthood being instantiated in them.


I am still puzzling over whether this correlationist rejoinder can be adequate. And over whether the approach to the problem that I have considered here is on the mark: Is Meillassoux’s task really that of showing that “instantiating transcendental subjecthood” is not an essential property of time? Is the appeal to essential properties legitimate at all?

But if it works and is on the mark, I think that it dispels the worry of sliding from innocent-looking idealism to dinosaurs-are-God-testing-our-faith idealism faced with the ancestral realm: What it does, I think, is to position the ancestral back on the same footing as the rest of the empirical world. For it establishes that the instantiation of transcendental subjecthood can be a condition of the possibility of the time in which this instantiation arises, without it being necessary that transcendental subjecthod is instantiated in any particular part of time. So there is nothing particularly significant about the specific parts of time where transcendental subjecthood is, as a matter of fact, instantiated. What is significant is only that it is instantiated at some point of time or other. And this is how the transcendental subject can be correlated with all of time, but instantiated only in some of time.

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Meillassoux the neo-Cartesian

The invocation of a chasm between the archifossil-wielding, mathesis-brandishing, fideism-scorching scientistic Meillassoux of Après la finitude and the mourning-stricken, immortality-yearning, justice-hoping messianic Meillassoux of “Spectral Dilemma,” as well as the excerpts from L’Inexistence divine published in Harman’s book, is already somewhat of a trope amongst commentators on his work.

Problems of aligning these two branches of Meillassoux’ output might, I suspect, lead people to trim down or root out the parts that appeal the least to their particular inclinations, or even to commit the whole thing to the flames as overgrown and ludicrous, “speculative” in the worst sense. However, before doing so it is worthwhile to stop and consider whether one has been unable to see the tree for the rustling of the leaves: what if these two Meillassouxs are in fact complimentary and necessary aspects of a philosophy whose roots are neither scientistic nor messianic but rather neo-Cartesian?

The affinity of rationalist Meillassoux with Descartes is evident. But at first glance, the role of God in Descartes’ system – as perfect and necessary being, and a guarantor of the possibility of attaining knowledge – is vastly different from the role of the possible God-to-come in Meillassoux’ system. Meillassoux’ virtual God is neither perfect (it is neither omnipotent nor omniscient in the strict sense), nor is it necessary. And it has nothing to do with the possibility of attaining knowledge. Indeed, this is why it seems so incongruent with the argumentation of Après la finitude.

But I believe that underneath these superficial differences lies a more profound continuity. The role of God – for Descartes as well as for Meillassoux – is to serve as a guarantor for the possibility of realizing our essential human nature (and we can note that this human nature is as non-derivable from the mathematical nature of matter for Meillassoux as it is for Descartes). According to Descartes, our essentially thinking nature is realized in the attainment of knowledge, but the possibility of this realization requires the existence of a perfect and thus non-deceiving God. According to Meillassoux, on the other hand, our essential nature is that of hoping, as “desire crossed by thought” (excerpt from 2003 version of L’Inexistence divine, published in Graham Harman’s Quentin Meillassoux: Philosophy in the Making, p. 191), a hoping which is realized in the attainment of justice (a rather Kantian modulation of the conception of human nature, admittedly). But the possibility of this realization requires an entirely different God: not a necessary, perfect, and non-deceiving God, but an inexisting, powerful but imperfect, and innocent God. (Traditional conceptions of God succumb to the problem of evil, cf. “Spectral Dilemma.”) Thus “divine inexistence fulfills, for the first time, a condition of hope for the resurrection of the dead” (ibid., p. 192).


Further investigation would, I believe, deepen the affinity by showing how in both Descartes and Meillassoux their conception of God as well as of mathematized matter spring from the absolute starting point attained via thinking – the cogito for Descartes, the principle of absolute contingency for Meillassoux. Confirming this hypothesis would require showing how the absolute starting point in both cases clears a path from God to mathematized matter via mind-body dualism.

In Meillassoux’ case, this implies showing how the characteristics of the virtual God can be derived from the fact of the attainment of a concept of the principle of absolute contingency by a conscious material being. The briefest of sketches: Absolute contingency leads to the necessary mathematizability of matter, as gestured towards in Après la finitude. This demonstration of the quantitative essence of matter evinces the radically contingency of the qualitative essence of a human being capable of consciously grasping the principle of absolute contingency (i.e., mind-matter dualism). And from this qualitative essence we can finally derive our conception of the virtual God.

Similarly, the but from the opposite direction, the conception of God had in thinking leads Descartes to a trustworthy epistemology of clear and distinct perceptions, which is utilized to cognize the distinctness of extended matter and thinking self, thus leading to a conception of mathematical extension as the essence of matter.


That “further investigation” is something I hope to undertake, in further posts, and hopefully in an article to come at some point in the future. Then there’s also the question of assessing the neo-Cartesian approach…. For now, it’s good to be back!

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What is Time?

There’s a famous passage in the Critique of Pure Reason where Kant delineates the positions which one can take with respect to the status of space and time. It goes as follows:

Now what are space and time? Are they (1) actual entities? Are they (2) only determinations or relations of things, yet ones that would pertain to them even if they were not intuited, or are they (3) relations that only attach to the form of intuition alone, and thus to the subjective constitution of our mind, without which these predicates could not be ascribed to any thing at all? (Critique of Pure Reason, A23/B37-38, my enumeration).

It is common to view the first (actual entities) as representing Newton, the second (relations of things) as representing Leibniz, and the third (forms of intuition) as representing Kant’s own position. One can quibble about their accuracy, but in any case, I’m more interested in whether these positions are exhaustive. Of course, there are different views of time than those mentioned here, narrowly understood. But do we have any theories of time that are not permutations or combinations of these views, understood more broadly?

I can only think of two. To give some examples of philosophers that I see as staying within the boundaries delineated here by Kant: Badiou’s time is a variant of (3), a subjective time generated in the aftermath of an event. Heidegger’s time is also a (non-subjective) variant of (3), or perhaps (2) if you want to “object-orient” him (see here and here for some interesting discussion of his theory of time, or lack of it). Deleuze’s time…… well, it’s some strange combination of (2) and (3), or so it seems to me. As for the space-time of general relativity, it seems to be a (dynamic) variant of (1).

The first example would be the position that there is no such thing as time, that time is merely an illusion. Mach, McTaggart and more recently Julian Barbour defends this view, but it has been around since long before Kant’s time for sure. I find Barbour’s argument quite fascinating, though I’m not quite sure what to make of it. In any case, it is tempting to see this view as a radicalization of (2) and/or (3), adding only that time is a misunderstanding of the relations of things, or a non-veridical form of intuition, or something like that.

So I think that the most interesting example of someone who proposes a theory that is incompatible with all the three positions above is Quentin Meillassoux. How so? My reading of Meillassoux’ position is that

(4) Time is a modal principle.

That is to say, time is the principle of the exclusive necessity of contingency. Let me explain why this view seems to fall squarely outside of the three other positions. With respect to (1): It can sometimes sound as if the time Meillassoux describes is a supremely powerful entity of some sort. For instance: “Only the time that harbours the capacity to destroy every determinate reality, while obeying no determinate law – the time capable of destroying, without reason or law, both worlds and things – can be thought as an absolute.” (After Finitude, p. 62). However, according to Meillassoux, a necessary entity is impossible. And the time which he describes is necessary. So it clearly cannot be an entity. With respect to (2): It might seem as if Meillassoux’ time is precisely a determination of things, namely, their property of being necessarily contingent. However, the fact is that Meillassoux goes on to deduce, from the principle of time, that there must be something rather than nothing, that the thing-in-itself must exist. And moreover, the principle of time holds for the non-existent just as well as for the existent. And it holds not only for things, but also for determinations of things, relations, and laws. “Everything could actually collapse: from trees to stars, from stars to laws, from physical laws to logical laws” (After Finitude, p. 53). It seems clear, then, that time is “ontologically prior” to things, not a property of them. With respect to (3): It is quite obvious that there is nothing subjective about Meillassoux’ time, and that it is not correlational but absolute.

I remember Hägglund claiming something along the lines of “Meillassoux is trying to establish something that has power over time, rather than a conception of time”, and you could definitely argue from linguistic convention and say that he’s right. (I’ve written about Hägglund and Meillassoux on time before, here) But I’d rather say that Meillassoux has the first novel conception of time in quite some time.

At least as far as I am aware of. My general impression is that whereas we’ve seen a proliferation of philosophical theories of time in the last 100 years or so, Meillassoux’ proposal is qualitatively different.

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Inner Sense part I: On Asking Better Questions

I’ve spent years, and written close to hundred pages, on the problem of inner sense in Kant, and so it feels rather surprising that the major breakthrough of the past few weeks is framing the problem as the search for an answer to the following question:

Why do we need an inner sense?

Nonetheless, I think I’ve finally managed to come up with the right question. For it is far from obvious why we need an inner sense, even though it is quite obvious from the Critique of Pure Reason that Kant thinks we do; there is no agreement among commentators on what the answer to the question is, indeed, few commentators seem to have explicitly asked themselves the question at all (I am greatly indebted to Garth Green, reading his excellent book and interacting with him has definitely been the catalyst in my case); and the answers that have been put forward, either intently or by accident, are mostly underdeveloped and/or seriously flawed.

Inner sense has to do with time – yes. And it has to do with self-knowledge – yes. But the question of why we need it at all is primary. Only after understanding why it must be there in the first place can we go on to explicate time as its form, and why and how it can provide for self-knowledge. This is Kant’s philosophical methodology, of course: First and foremost an investigation into the conditions of possibility, in this case the possibility of theoretical experience. So what function, performed by inner sense, is a necessary condition of the possibility of theoretical experience? The question seems obvious, perhaps, but a look at the prevalent interpretations is instructive, and tells otherwise. The most common answers point precisely to time and/or self-knowledge: Inner sense is necessary because experience is only possible in time, or because it is a condition for self-knowledge. But both these answers encounter some immediate and in my view impassable obstacles. In short: Even if it is true that experience requires temporality, it is far from obvious that temporality must be given as the form of something properly described as an “inner sense” – why couldn’t the form of outer sense be space-time? And as to the second answer, self-knowledge is only a specific kind of experience, whereas the Critique is supposed to be concerned with the conditions of possibility of experience in general. (There is much to be said, of course, in defense of these positions. Indeed, that is what I’m working on at the moment, building up, all the better to tear down… The basic point, however, is that the answer to the question “why do we need inner sense?” cannot be temporality or self-knowledge as such, but in the best case a further explication of the necessary, inner, and sensible function “within” temporality or self-knowledge.)

It is wonderfully bizarre, how one can go on for years, poring over Kant’s texts, and his lectures, and his contemporaries, and his interpreters, and then the real progress comes not from some obscure Reflexion, nor from reading the Transcendental Deduction for the twelth consecutive time, but from being able to formulate a strikingly simple question about the subject matter one is studying. Is it normal, this huge gap between the time one starts researching a problem, and the time one actually manages to pose a question that gets to the heart of the issue?

I suspect it is (though maybe I’m just being defensive). For one thing, if I did not already have an answer of my own (to be elaborated in forthcoming posts), the question would have seemed much less clarifying and illuminating. I can see now why it is an important question, and how it frames the search for an adequate interpretation of inner sense in a most helpful way. But would I have been able to a year ago, or two? Without having swam about in the confusing details, the question would have been a mere empty reflection, a placeholder for something unknown.  There’s something Deleuzian to be said here, about learning, about questions and problems, and about stupidity. Moreover, there are many other possible, simple questions that are positively unhelpful, problems badly posed, a nice topical example here would be the question “which has priority, inner sense or outer sense?” This has been an influential question in the secondary literature, one which has rather overshadowed the one I have been proffering in this post, but it is also a question without a proper answer. There is no single and exclusive relation of priority between inner sense and outer sense. And since the question leaves open what inner sense is/does in the first place, the door is then open to ambiguities and misunderstandings based not only on different understandings of “inner sense”, but also on different understandings of “priority”.

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Contingency and the Limits of Science

So, after browsing through the Speculative Turn (pdf here), and the comments on it by Hypertiling here, I thought that I might post the following article. Actually, it’s a few years old now, but it’s still fairly representative concerning my views on the relation of Meillassoux to science and scientific research (stylistically, it leaves something to be desired, I’m afraid). Most of it is about a view on the limits of science advocated by Nicholas Rescher, and I argue that his epistemological theory can only be admitted by complementing it with Meillassoux’ speculative theory. But more broadly, I think it relevant to the issues brought up by Brassier, as well as to the critiques of Meillassoux’ engagement with science, in The Speculative Turn. If, as Brassier claims: “the problem is one of granting maximal (but not, please note, incorrigible) authority to the scientific representation of the world while acknowledging that science changes its mind about what it says there is.” (The Speculative Turn, p. 64), then my article basically claims that if we follow this problem through to its ultimate consequences, Meillassoux’ theory all of a sudden seems like a pretty convincing solution.


Contingency and the Limits of Science

Is it plausible to imagine science pacing on into the future, forever posing new problems and answering new questions, never coming to a halt? There are two main threats to such a scenario. The first, obvious one is the threat of perplexity, of unanswerable questions. Perhaps there are some questions that we can raise, but also see that we are in principle powerless to answer. The other one is the threat of completion, the possibility of a completed science. In this case, it would come to a halt not because of its inability but precisely because of its actualized ability to answer all possible questions. Among those defending an open-ended view of science against these threats is Nicholas Rescher, in his book The Limits of Science. I will argue, however, that this view is the philosophical commonplace of the twentieth century: The claims of late 18th-century physicists with regards to the nearly completed state of their field (just before the revolutionary breakthroughs of relativity theory and quantum mechanics) have been amply ridiculed. Equally, positing scientifically unsolvable questions has a bad track record; thus even the problem of subjective experience and qualia is generally considered, among philosophers, as a hard problem of consciousness rather than as an impossible problem.

Rescher’s book is interesting to us because it poses this question on a theoretical level; it deals with what science could possibly do, and thus abstracts away from the contingent limitations of time, money, energy, public support, etc. This allows me to bring out the properly science-fictional scope of the claim of science’s limitlessness. In fact, it will also allow me to play the pied piper to the children of open-ended science. According to the argument of this article, the epistemic considerations of Rescher come up short when faced with some of the more interesting science-fictional scenarios – in this case, time travel. In attempting to defend the limitless conception of science, it will therefore be necessary to introduce a metaphysical supplement, an absolute principle, which I will obtain from Quentin Meillassoux. The logic of Rescher’s argument exemplifies a broad philosophical tendency Meillassoux calls «correlationist», while at the same time pointing towards its self-overcoming. In one sense, I will be arguing that Meillassoux’ views nicely complement those of Rescher. In another sense, I will try to lead you, as well as Rescher, from common-sense assumptions about science, through considerations of time travel, before throwing you into a world of absolute contingency.

Rescher’s contradiction

Are there legitimately scientific questions that science is powerless to answer? To this question one could, of course, answer with a no by definition. It could be claimed that any question which is in principle impossible for science to answer, is not a legitimate scientific question. But Rescher wants to make a substantive claim in saying that there are no such questions, or rather that there are, and can be, no such questions which can be identified. He distinguishes between three different theses as to the unsolvability of questions, three insolubilia theses: 1) The permanence of unsolved questions. This is just what Rescher himself defends, against claims about the possibility of «complete» science, and thus completely acceptable for him. The reason for this is, of course, that it does not entail insolubilia as such, because it does not say that any question is unanswerable, but merely that there will always be unanswered questions, this thesis «is perfectly compatible with the circumstance that every question that arises at a given stage will eventually be answered» (Rescher 1999: 112). 2) The existence of insolubilia. This means that there are «immortal questions» (Rescher 1999: 112), questions science can never answer. Rescher will not argue directly against this proposition, but rather against the strengthened thesis: 3) The existence of identifiable insolubilia. And indeed, it is reasonable to claim that thought of insolubilia only becomes interesting once you are in a position to actually put forward a candidate. The crux of Rescher’s defense against the possible existence of identifiable insolubilia, the one which his entire discussion revolves around, is his claim that «Present science cannot speak for future science» (Rescher 1999, 103). Thus, a question that looks completely irresolvable at a given time cannot because of this be identified as an insolubilium, as the history of science clearly shows. Rescher points to many past mistakes, where problems supposedly beyond the reach of human science have received solutions based on later science, science which those judging the problems as irresolvable clearly did not and could not expect. When it comes to making secure inferences from the answers, theories and methods of present science to that of future science, Rescher claims that this «is in principle impossible» (Rescher 1999: 103). And this is where it gets interesting: this claim about in principle impossibility seems to me remarkably strong. I will proceed by attacking it directly, thus bringing out his supporting arguments and claims along the way. The question which arises immediately, for me at least, is whether one could derive an insolubilium directly from it, by inferring that the question «What are the answers, theories and methods of future science?» is in principle unanswerable. If this is not a legitimate scientific question, one wonders what makes it different in kind from other questions about future states of objects and systems. In other words, it seems that the future accomplishments of science constitute a limit of science: «Given that it is effectively impossible to predict the details of what future science will accomplish, it is no less impossible to predict what future science will not accomplish» (Rescher 1999: 103). This puts a limit to prediction, one of the aims of science (according to Rescher). It also clearly puts a limit to description, explanation and control of future science, those being the three other aims of science listed by Rescher. Thus, he seems to contradict himself. Compare with:

The one and only thing that is determinate about science is its mission of description, explanation, prediction and control over natural phenomena, and the commitment to proceed in these matters by empirically based rational controls for the testing and substantiation of our assertions that have become known as ‘the scientific method.’ Everything else – methods, mechanisms, theories, and so on – is potentially changeable. (…) An enterprise that, on the cognitive/theoretical side, did not aim at either the description or explanation of nature, and that, on the applied/pragmatic side, did not aim at either prediction or control, simply could not count as natural science (Rescher 1999: 104).

Saying that future science does not count as a «natural phenomenon» is not a plausible claim either. Bringing this out even more clearly, Rescher says a bit further on: «Nobody can say what science will and will not be able to do» (Rescher 1999: 108). But can science? If it can’t (if that is impossible), then there is something science cannot and will not be able to do. If Rescher has an answer to this, it seems to be the following claim:

To be sure, if predictability is seen as the hallmark of the scientific, then there cannot be a science that encompasses all human phenomena (and, in particular, not a science of science). But of course, there is no reason why, in human affairs any more than in quantum theory, the boundaries of science should be so drawn as to exclude the unpredictable. Even before the rise of stochastic phenomena in quantum physics, one might have asked: must scientifically tractable phenomena be predictable? Can science not tread where predictability is absent? When we encounter strange ‘intractable’ or ‘inexplicable’ phenomena, it is folly to wring our hands and say that science has come to the end of its tether. For it is exactly here that science must roll up its sleeves and get to work (Rescher 1999: 109).

Here, it seems, Rescher tries to avoid contradiction by claiming that prediction is not necessary for science. The question then becomes, which of the other aims of science are compatible with Rescher’s views, when it comes to future science? Is it describable? Controllable? Explainable? As I’ve already been suggesting, if we could describe or explain future science, it seems we first would have to be able to predict it in some detail. The comparison with quantum theory might suggest something else, namely that questions about predicting future science are scientifically illegitimate, in the same way that questions about the time of decay of a specific radioactive particle is illegitimate. But we do not have a scientific theory that rules out predicting future science, in the same way that quantum theory rules out predicting the precise time of decay. What we have is a philosophical theory that rules it out, and this seems to put Rescher back with the philosophers he wants to distance himself from. So, even if you concede to Rescher that questions about the prediction of future science might possibly be illegitimate, and in that case they would not count as limits, this does not resolve his problem. The problem is rather that there is no reason analogous to the uncertainty principle applicable to predictions of future science. As a matter of fact there is no clear-cut scientific reason at all to suppose that a predictive science of science is impossible. If we have reasons for supposing that, they are Rescher’s philosophical ones – even though Rescher himself argues that philosophical preconceptions should never try to delimit science and its capabilities.

This isn’t the end of the troubles for this particular argument. Even if it could be scientifically established by the best science of our day that making predictions about future science is outside the range of science, it does not automatically follow that this should be the case in the future. Rescher himself makes this exact argument concerning the case he is comparing with, namely quantum theory, some pages earlier! There he discusses von Neumann’s attempt to establish that all possible future theories must be «uncertain» in the way present theories, incorporating Heisenberg’s uncertainty principle, are. Rescher says: «But the ‘demonstration’ proposed by von Neumann in 1932 places a substantial burden on potentially changeable details of presently accepted theory. The fact remains that we cannot preclude fundamental innovation in science: present theory cannot delimit the potential of future discovery» (Rescher 1999: 103). It might seem as if Rescher wavers on this particular point, as he only a few pages earlier seems to suggest the opposite: «The most that science can reasonably be asked to do is to predict what it itself sees as in principle predictable – to answer every predictive question that it itself countenances as proper. Thus if quantum theory is right, the position and velocity of certain particles cannot be pinpointed conjointly. This renders the question ‘What will the exact position and velocity of particle X be at time t?’ not insoluble but illegitimate. Question-illegitimacy represents a limit that grows out of science itself – a limit on appropriate questions rather than on available solutions» (Rescher 1999: 99). It seems as if Rescher wants to have it both ways with respect to quantum theory; certain questions in quantum theory are not insoluble, but illegitimate, even then they are really just contingently illegitimate because some new scientific revolution might make those questions legitimate by making them solvable. This means that we cannot be sure that the question «How does light behave when it is travelling at a speed of 2c (c being the speed of light)?» will not become a legitimate question either. Some future advance might turn out to show that this is indeed possible and proceed to describe how it would behave, and, even without that, the laws of nature might themselves be susceptible to change. Rescher says: «He [Collingwood] held, in particular, that the uniformity of nature must be presupposed if the scientific enterprise is to succeed. But who is to say that cosmology may not decide tomorrow that the universe is partitioned into distinct compartments (and/or eras) within which different ground rules apply – that is, that the ‘laws of nature’ in the universe are not uniform? What seems an absolute presupposition of science at one point may be explicitly denied at another» (Rescher 1999: 106). One must conclude from this, that whether a question is legitimate or illegitimate does not matter when it comes to deciding whether it is ultimately insoluble. Questions about the ether? Sure, they are illegitimate now, but perhaps the universe will enter into a new era tomorrow, one where the ether is part of its structure? It cannot be ruled out. In fact, from this the open-endedness of the scientific endeavor follows automatically, at least in the weak sense that even if science were to become «complete», it could still be rendered obsolete at any moment by a change in the laws of nature. Would this also entail that there can be no insolubilia, because any question might become solvable in the future? To find that out, I will take a closer look at what «future possibility» means, or rather: what it could mean and what Rescher could allow it to be. The question is: What if you could know the future?

Back to the future

Though I find it to be his most solid defense, Rescher does not really make his claim based on the possibility of changes in the laws of nature, but mostly on what he calls a «fundamental epistemological law: the cognitive resources of an inferior (lower) state of the art cannot afford the means for foreseeing the operations of a superior (higher) one» (Rescher 1999: 97). The concepts with which such superior cognizers solve their problems are in many cases simply not available to the inferior cognizers. Like Rescher says, «Newton could not have predicted findings in quantum theory» (Rescher 1999: 97). The superior cognizers would, in the case we have considered, be future science and scientists, and the inferior ones would be present science. Intuitively, this seems like a perfectly correct statement, which could be generalized into a law. Presumably, this law is what makes Rescher think that we can safely predict the continued orbit of the planet (up to a certain point, at least, cf. the N-body problem) or the life of the sun, but not future science. But things are more complicated than that. What if foreseeing is literally what we could do? Consider, for instance, the possible future invention of time machines. This would make predictions about their future science not only possible in theory, but indeed achievable in practice. The argument against something like this would perhaps go along the lines of what Rescher says: «We could not possibly predict the substantive content of our future discoveries – those that result from our future cognitive choices. For to do so would be to transform them into present discoveries which, by hypothesis, they just are not» (Rescher 1999: 97). But is this really true? If it is, then time-travel into the future would seem to be made impossible on these purely conceptual or philosophical grounds, which would seem to contradict Rescher’s more general point. Another option is to say that such time-machines would change the future, so that if you went into the future and saw yourself going to a particular place at a particular time, you could decide to «invalidate» that future by going somewhere else instead. The same principle would then be valid for science. But notice that this is based on a thesis about time and free will which is hardly uncontroversial, let alone the only possible option. Who knows, we might find our theories, if not our intuitions, about free will profoundly changed by such an invention as a time-machine. So I see no conclusive reason why the users of such time-machines might not in principle be able to predict every scientific advance down to its smallest detail, simply by observing them happen. Drawing on Rescher’s own arguments, we simply have no way of knowing for sure whether this might happen or not. This could function in the same way as have been envisioned in arguments about time travel backwards in time. Such time travel is not logically impossible, many argue, but it requires that you for instance will not be able to go back in time and kill your then-to-be grandparents, simply because it didn’t happen. (David Lewis, for instance, has eloquently defended this.) We certainly have a greater propensity for considering the past unchangeable, whereas we consider the future to be open-ended, full of possibilities not staked out in advance. But who is to say we are not mistaken? Certainly not Rescher, because he could not rule it out completely on philosophical grounds (it is not contradictory to consider the future to be «already» decided), as that would again make him put philosophical limits on what science can or cannot do. In fact, Brian Greene, in his book The Fabric of the Cosmos, describes a way, implementing stable wormholes, in which time travel to the future and back could occur without violating any known physical laws.

Now, it seems important to notice that the position of the debate seems to have changed considerably compared to how Rescher sees it. If, as I believe, I have only drawn the consequences of what is already in Rescher’s text, then it seems as if he has not followed his premises through to what is the real stakes of the arguments. On the one hand, the possibility of time-travel, or some other scientifically tractable means of actually knowing the future, can hardly be ruled out by fiat. On the other hand,

The predictive inaccessibility of the future of the world (as best we can comprehend its nature) is clearly something that is not merely epistemic, something that does not just inhere in our own lack of information – our own ignorance. Rather, to the best of our understanding it roots in the very nature of things in a world whose dynamical development is subject to contingency. It is an aspect of reality as such – a result of the fact that presently existing conditions always encompass genuine contingency in that nature simply ‘has not yet made up its mind’ about the future – ‘has not yet decided’ at the present exactly and completely what the future is going to be like. (Rescher 1999: 90)

What does this mean? On the one hand, it seems to be saying that this inaccessibility is not just a result of our ignorance. On the other hand, it says that this is «as best we can comprehend its nature», and that seems to suggest that this might itself be just a temporary epistemic insufficiency. I would like to pull out what seems to me like the two most significant concepts involved here, that would need to be explored and clarified if the obscurities and contradictions of Rescher’s book were to be rectified: Contingency and time. In what follows, I will argue that only by adapting a specific metaphysical stance can Rescher hope to maintain his position on the limits of science. To do this I will refer to the arguments of the French philosopher Quentin Meillassoux.

Speculative Contingency

Let us recapitulate what priorities get Rescher into his awkward, contradictory position. It seems to me that the basic commitment Rescher sticks to throughout his book is a non-absolutist view of science, whether it is the possibility of science reaching the absolute, the total, complete truth, or the possibility of it encountering absolute limits to its progress. However, as we saw, there seems to be an absolute limit to science after all: predicting future science. And it even seems as if it is possible that this is not true, thus bringing us to the ironic conclusion that not only does Rescher actually posit an absolute limit to science, but the limit he posits is not necessarily a limit. Turning to the more general point, I believe this problem arises because it turns out that Rescher cannot afford to be a non-absolutist when it comes to non-absolutism itself. The open-endedness of science, its fallibilistic character, cannot itself be a thesis, a fallible proposal. Why? Because Rescher wants to maintain that the world of scientific discovery can always be more, be different than we think it is.

The interesting thing about Rescher, and what brings him very close to Meillassoux, is that he seems to feel forced, by the weight of the history of scientific revolutions, to adopt the view that there are not even contingently necessary limits to science. I can explain this better by comparing his position to Kant’s. According to Kant, science is limitless, and Rescher indeed uses Kant’s principle of question propagation as one of his main points when he argues for the impossibility of reaching a complete science. But there is a limit to this limitlessness in Kant. Kant and Rescher might perhaps agree on the fact that we never gain knowledge of «things in themselves», but only things as they appear to us, in our best scientific theories. (what Rescher calls «the epistemic gap between the apparent and the real» (Rescher 1999: 34).) But for Kant, there are certain specifications that have to be met for it to be possible for anything to become an object of experience. Without delving deeply into this, suffice it to say that Kant’s categories and forms of intuition (space and time) are unavoidable, and therefore anything that does not accord with them cannot be a scientific object, indeed it cannot be an object for us at all. These conditions of possible experience are themselves contingent, Kant says, but in so far as they are ours they are necessary, thus the before mentioned contingently necessary limits to science. This cannot apply to Rescher, because for him the conceptual and methodological innovations of science preclude any such a priori limitations. The ever-changing horizon of science sets temporary limits to what can be meaningfully and legitimately asked, but nothing substantial is set in stone.

As for Meillassoux, his philosophy aims to attack no less than all post-Kantian philosophy, which according to him can be broadly characterized as «correlationist». What unites all these correlationist philosophies is basically what we saw above, that Rescher and Kant agrees that we only ever know things as they appear to us. There is thus, in our theories, a correlation between us, as knowers, and the things known, and we have no access to things outside of this correlation. So, if Rescher endorses the basic view that Meillassoux attacks: how can their views be so close? As we shall see, this has to do with their emphasis on contingency. To show this, I will start by drawing attention again to a part of the quote referred to before: «the very nature of things in a world whose dynamical development is subject to contingency» (Rescher 1999: 90). And as I said in the comparison with Kant, for Rescher the same applies to our theories about the world. Now science and philosophy alike have traditionally been looking for necessity, whether for necessary laws of nature, sufficient reasons (as in Leibniz’ principle) or necessary conditions of experience. The question which remains undecided when it comes to Rescher is the one I referred to at the end of the last section: Is the contingency of the future of the world merely our current epistemic prejudice, or is it «in the very nature of things»?

For Meillassoux, it is the strong version of this claim, the contingency of the very nature of things, that must be upheld, and that promises to transform correlationist philosophies. In his more strictly philosophical discussion, it is the challenge of absolute idealism that brings correlationism into a position where it has to make this strong claim. Absolute idealism (Hegel is the main example for Meillassoux) asserts that, since any possible knowledge of things are knowledge of things as they appear to us, the possibility of knowing that the «thing in itself» might be different from the thing as it appears for us, is gone, since that already means knowing something about the thing in itself, and thus the boundary between what we can and cannot know is already overstepped by stating it. Therefore, the thing in itself collapses into the thing for us, and the correlation between our grasping of the world and the world is made necessary (through the Hegelian dialectic). This is not exactly the same as Rescher’s problem, which is that if the contingency of our scientific knowledge is itself contingent, absoluteness might be forthcoming. It is the move from our present to any present in the following quote which seems to require the strong version of the above claim: «The doctrine now at issue effectively holds that there is nothing cognitively privileged about our own position in time. It urges that there is nothing epistemically privileged about the present – any present, our own prominently included» (Rescher 1999: 37). A sort of cosmic Hegelianism of the universe coming to know itself through itself might be the link between the two problematics, as that can only be ruled out through the move from our present to any present. In fact, the possibility of a science which can answer all its questions, which Rescher downplays because this «might simply reflect the paucity of the range of explanatory questions Q(S) that it is in a position to contemplate» (Rescher 1999: 16), nicely encapsulates Meillassoux’ point, which is that the correlationist must maintain against the absolute idealist that such a correlation is as a whole merely contingent, and «erotetic completeness may well indicate poverty rather than wealth» (Rescher 1999: 17).

According to Meillassoux, the correlationist is thus pushed into a corner where he must maintain in order to preserve the contingency of its knowledge, that this contingency necessarily holds. I hope to have shown that this characterization is appropriate for Rescher, who finds himself forced into saying that it is in principle impossible to predict future science, in order to defend the claim that nothing is in principle impossible for science. There is only a short step from this to Meillassoux’ speculative materialism:

Speculative materialism asserts that, in order to maintain our ignorance of the necessity of correlation, we have to know that its contingency is necessary. In other words, if we can never know the necessity of anything, this is not because necessity is unknowable but because we know that only contingency necessarily exists. (Brassier 2007: 38)

Seemingly a small step, it is however a metaphysical starting point from which many surprising conclusion can perhaps be drawn. The key point is that this necessary contingency provides us with a philosophical access to the absolute; namely, the absolute contingency. This means that the contingency of things is an absolute truth, independent of our existence and our theories. It even goes beyond the certainty of the Cartesian cogito, because «what is necessary in the cogito is a conditional necessity: if I think, then I must be. But it is not an absolute necessity: it is not necessary that I should think» (Meillassoux 2007: 429). If I am correct, only this speculative realism can provide Rescher with a rigorous and non-contradictory version of his claims that stays true to his basic commitments; it can deny the possibility of insolubilia and deny the possibility of complete science. Thus, whether or not time-travel is possible, absolute contingency insures that such travels can never ascertain the limits of science once and for all. Time, for Meillassoux, is «absolute time (…) tantamount to a ‘hyper-chaos’ for which nothing is impossible, unless it be the production of a necessary being» (Brassier 2007: 39). The possibility of predicting future science might even give the predictions a conditional necessity, in the sense that if things go as they seemed to go, then necessarily this is what will happen. But that conditional will not itself be grounded in any ultimate reason; rather, its only ground is the absolute unreason of absolute contingency, meaning the real possibility that things can change for no reason at any moment. Though an absolute principle would generally seem anathema to Rescher, in this case, since it is the rejection of necessity that is being absolutized, it suits Rescher quite well. To adopt this position, Rescher would however have to abandon the possibility he outlines when discussing candidates for insolubilia, which is that it might be possible to adapt a teleological principle of «fittingness», of value, as the explanatory «end of the line» for certain basic facts about nature. This is not, in my opinion, a large sacrifice, as it seems to be much more in line with Rescher’s position as a whole to ground the basic conditional facts of nature (why there is something rather than nothing, etc.) on absolute contingency, rather than on some necessary teleological principle.

A possible counterargument in this case is that absolute contingency does not explain anything, that it is equivalent to saying «the reason is there is no reason». There are at least two rejoinders: One can use the same line of argument Rescher uses to defend the possibility of teleological explanations: who are you to be so sure what can and what cannot be a scientific explanation? The other maintains that in the absence of conditional necessity (it might, of course, turn out at a later point that a conditional necessity was involved after all), what could possibly be a better «reason» than appeal to an absolute principle, established by sound philosophical argument?

Thus, we arrive at a strange conclusion where Rescher can maintain his non-absolutist view of science, his claim that the limit of science is a nonentity, but only by grounding this view on the truth of an absolute metaphysical principle.

Brassier, R. 2007, “The Enigma of Realism: On Quentin Meillassoux’s After Finitude”, in Collapse II (ed. Robin Mackay), Urbanomic, Oxford, 15-55.

Greene, B. 2004, The Fabric of the Cosmos, Penguin Books, London.

Meillassoux, Q. 2007, “Speculative Realism (Annex to Collapse II)” , in Collapse III  (ed. Robin Mackay), Urbanomic, Oxford, 307-451.

Rescher, N. 1999, The Limits of Science (revised edition), University of Pittsburgh Press, Pittsburgh.

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Meillassoux interview

An interesting Meillassoux interview (pdf) with Robin Mackay and Florian Hecker, published by Urbanomic. Their list of forthcoming publications is exhilarating, with the Nick Land collection, two books by Francois Laruelle, Reza Negarestani’s sequel to Cyclonopedia, and a work by Fernando Zalamea that promises to engage philosophically in more recent mathematical development, all scheduled for 2011 release.

À propos my previous remarks on dialetheism, this juxtaposition struck me:

Dialectics and paraconsistent logics would be shown to be studies of the ways in which the contradictions of thought produce effects in thought, rather than studies of the supposedly ontological contradictions which thought discovers in the surrounding world. (After Finitude, p. 79)

I remark that thought cannot be richer than reality: The capacity of thought cannot be richer than the capacity of realiy. (Urbanomic interview, p. 3)

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Apology for Obscurity

Obscurity, indeed, is painful to the mind as well as to the eye; but to bring light from obscurity, by whatever labour, must needs be delightful and rejoicing. – Hume, “An Enquiry Concerning Human Understanding”, sect. 1

And yet philosophy, to me, has always been about an attraction to obscurity. If ever I’ve had a religious impulse, surely that is it. But I’ve always experienced religion as expressing an attempted escape from the obscure, rather than  an attraction towards it. Art, on the other hand, yes; mathematics, yes; natural science, indeed; philosophy, certainly. 

If I feel any kinship to Bataille, it must be on this particular score – with obscurity as the excess of cognition. Like anyone with a penchant for ‘continental’ philosophy, I’ve been exasperated with the sheer ignorance evinced by most accusations of “charlatanery”, “postmodern relativism” and the like. But behind it, something else. Dan Sperber has, quite soberly, characterized as “the guru effect” the machinery behind the transformation of obscurity into perceived profundity. I won’t argue with his description as such, but merely say that it is written from the perspective of restricted economy. From the Pythagoreans, to Newton’s physical and alchemical preoccupations, to Freud and Lacan, there is surely something positively excessive and obscenely desirable in the intimation of obscurity, something well beyond the economy of “relevance”. This is what I found and cherished in Deleuze, the emphasis placed on the necessity and importance of the obscure distinctness of problems rather than the clear confusion of solutions. To write, and think, “only at the frontiers of our knowledge”, in the twilight of obscurity, Dunkelheit. To be honest, this is the affective reason I cannot fully appreciate the philosophy of object-oriented ontology and its account of the withdrawal of objects. My innermost desires and ambitions seem to draw me towards the obscure rather than the withdrawn. To me, nothing seems more worthy of exploration, as an object of theoretical interest and as a felt necessity and basin of ambivalent attraction. Like Borges and Lovecraft charting the affects of cognitive excess, or Werner Herzog’s encounter with the jungle, the Conquest of the Useless.

All I ever really wanted was a jungle, and a jungle I got. -Aesop Rock

And here I am, with a ph.d. fellowship in philosophy at the University of Oslo, about to embark on three years of research on Kant’s theory of inner sense. How fitting, then, that my main contention is the centrality of clarity and obscurity. What is clarity and obscurity for Kant? According to me: Logical symptoms of inner sensations, resulting from the self-affection, by our other faculties, of the faculty of inner sense. Sensations of consciousness, in both senses: Consciousness is a kind of sensation, and depending on its strength this sensation renders our representations relatively clear or obscure. But the reality which this sensation is a sensation of, is consciousness – that is, our faculty of consciousness, apperception.

Inner sense is famous for being one of the most obscure aspects of Kant’s theoretical philosophy. And the role of obscurity (and clarity) in Kant’s philosophy is practically unknown and uncharted. In other words, through some stroke of luck it seems my object of theoretical interest and my basin of attraction converge, and I can make a living pursuing it.

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Mathematics as the Non-Object?

The existence axiom at the basis of ZF set theory postulates the existence of the empty set, the set without elements. But being without elements, thus also without parts, the empty set qua mathematical cannot be an object according to OOO (Object-Oriented Ontology), since an object is defined on the basis of specific relations (emergence, submergence) between the whole and its parts. It cannot even be a pseudo-object, since a pseudo-object is also defined on the basis of specific relations (lack of emergence, etc) between the whole and its parts. (See this post for a summary of Graham Harman’s views on objects and pseudo-objects).

Insofar as one can construct basically the whole of mathematics out of ZF set theory, it might seem as if mathematical structures in general are neither objects nor pseudo-objects. So what are they? What is mathematics, according to OOO?

In itself, classifying mathematics as non-objective need not be a problem. For instance, the point that mathematics is not “objective” and has no objects is central to Badiou’s account of mathematics. In fact, it is a precondition for his central claim that mathematics is ontology. Mathematical structures are not objects, they are the being of objects. For object-oriented ontology, on the other hand, it must mean that mathematics has no place within ontology. Of course, there are many ontologies which do not include mathematics and mathematical objects. But object-oriented ontology includes societies, ideas, phonemes, organizations, and so much else (not by coincidence can it be referred to as promiscuous ontology), so it is fairly surprising that it does not seem to include mathematics!

I do not mean, of course, that it does not include mathematics at all. It obviously does. Mathematics qua signs, for instance the name of the empty set, ø, is presumably an object. So is mathematics qua scientific practice, mathematics qua mental and physical ideas and constructions, and so on. But mathematics qua mathematics is, I suspect, not. If this is correct, then OOO is reductionistic with respect to mathematics, insofar as the existence of the subject matter of mathematics cannot be affirmed as such, but only as something else, whether signs, ideas, physical patterns, practices, or something else.

I’m fully aware that I’ve drastically simplified things here, basically reducing the mathematics-OOO interface to the encounter between the statements “the empty set exists” and “an object has parts”. My primary wish is to see the partisans of object-oriented ontology engage with mathematics, and I would be perfectly happy to stand corrected. As per now, whereas I am not convinced by either Badiou’s or Meillassoux’ account of mathematics (though seeing as Meillassoux has not yet published his thoughts on mathematics I can hardly expect to, in his case), when it comes to OOO I have only the vaguest idea of what their account would even be, as this post no doubt shows.

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Badiou, Hegel, and the Infinite – part I: Introduction

Meditation 15 of Badiou’s Being and Event is one of the most forbidding encounters of that book, pitching the Hegelian doctrine – or, more precisely, doctrines – of the infinite against Badiou’s own Cantorian conception. Keeping both these competing views in focus while attempting to grasp their precise differences and perhaps even adjudicate between them….. I remember someone stating that reading Difference and Repetition is intellectually akin to running into the ocean – splashing out those exhilarating first few steps before you abruptly come to a halt and tumble into the deep water of “sink or swim” – but I’ve read this meditation a few times before, and each time it feels more akin to running into a brick wall. And so, previously, I’ve settled for the bland “Badiou thinks Hegel cannot do justice to the mathematical infinite” conclusion. Which is clearly unsatisfactory in the long run, so this post is a first effort at dismantling the “wall” aspect of those nine pages.

Some of the obvious  – too obvious – disagreements between Badiou and Hegel can be stated at the outset, simply to get a preliminary grasp of the battlefield:

Hegel thinks that infinity is 1) generated, i.e., immanently derived from the dialectical process, and 2) ‘good’, i.e., qualitative, so it is the qualitative essence of quantity that constitutes its true infinity.

Badiou, on the other hand, thinks that infinity is 1) postulated, i.e., that the existence of an infinite set must be axiomatically decided upon, and 2) ‘bad’, i.e., quantitative, since Cantorian infinity allows for “the very proliferation that Hegel imagined one could reduce” (B&E, 170).

Both these disagreements can be found more generally in Badiou’s engagement with the philosophical and mathematical tradition. For instance, Badiou likewise criticizes Dedkind’s attempted deduction of the existence of the infinite, in Number and Numbers, ch. 4. (“Now, just like the empty set, or zero, the infinite will not be deduced: we have to decide its existence axiomatically” (N&N, 44). And the qualitative conception of infinity is something Badiou takes the philosophical tradition in general to task for, seeing in it a latent religiosity.

We must immediately complicate the above assertions, however, for they do not adequately represent Badiou’s particular line of argumentation in meditation 15. It might, from the above, seem as if Badiou gainsays any deduction of the infinite, and that he opposes the proper, quantitative infinite to the spurious qualitative infinite. But in fact, Badiou does not object to Hegel’s deduction of the good qualitative infinite. And in fact, Badiou recognizes that there is not, in Hegel, a simple dichotomy between qualitative and quantitative infinity, but rather a fourfold of infinities: the bad qualitative infinity, the good qualitative infinity, the bad quantitative infinity, and the good quantitative infinity.

What Badiou seems to argue is 1) that Hegel cannot properly ground the third infinity, the bad quantitative infinity: “One must recognize that the repetition of the One in number cannot arise from the interiority of the negative” (B&E, 169). 2) That in any case, what Hegel puts forward as the fourth infinity, the good quantitative infinity, cannot properly be called “infinity” at all: “I have no quarrel with there being a qualitative essence of quantity, but why name it ‘infinity’?” (B&E, 169).

I must therefore demur from Hallward when he writes, in Badiou: A Subject to Truth, that “The crux of Badiou’s argument is that without tacit recognition of the disjunctive decision to affirm the infinite, the good, ‘qualitative’ infinity cannot join up with a properly quantitative notion of infinity at all.” (173). The problem is not that there are two different infinities, and they cannot be joined. Rather, the problem is as follows: there are two dialectics, quality and quantity, which Hegel connects by means of a “fragile verbal footbridge thrown from one side to the other: ‘infinity’.” (B&E, 170) But this footbridge is fragile indeed: It is in fact merely verbal, since on one side it is anchored to an ungrounded hallucination – the Hegelian ‘good quantitative infinity’.

I’ll try, next, to investigate more in detail Badiou’s analysis of Hegel, and perhaps even delve properly into the Science of Logic to see whether his objections can be met from a Hegelian standpoint.

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The Limits of Entropy

In this post, Levi Bryant argues that object-oriented ontology takes into account the problem of entropy in a way that classical structuralism is unable to.

This seems to me a plausible claim, one that I will not dispute. Rather, I am interested in the ramifications of bringing entropy into an object-oriented ontology. I realize of course that these ramifications are far from obvious or settled (which is why I’m interested). But entropy seems to be one of those problematic concepts where the boundaries between metaphysics and science is less than clear, and even more interestingly, I have a feeling that the concept of entropy might very well attract philosophy towards ideas it does not want.

For instance, I have one latent worry concerning the compatibility of scientific conceptions of entropy and object-oriented ontology: Recent physics consider entropy to have a limit, a maximum, and claims that this maximum is in fact evinced by black holes. What does this imply? According to wikipedia, at least, it suggests that “matter itself cannot be subdivided infinitely many times and there must be an ultimate level of fundamental particles” (see this article). And it is indeed difficult to see how an entropy limit would not signify a limit in the degrees of freedom of the components of the entropic system, and each such basic, uncomposed degree of freedom signify something like a fundamental particle or a discrete state of such a particle (or could it be asymptotical?)

From what I know about the object-oriented ontologists like Bryant and Harman, they do not look favorably upon materialism and atomism, so I suppose that they are not eager to embrace entropy limits either. But what are the options? Deleuze’s account and critique of “thermodynamical illusion” (in chapter 5 of Difference and Repetition)?

In any case, I would like to propose black holes as one of the paradigm cases of “object”; not because they are typical but precisely because they are such extreme tests of any theory of objects. You have a theory of objects, you should at some point plug “black hole” into the litanizer and see what results come out. Any bias towards anthropocentrism or common sense should have a good chance of being exposed.

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