hegel and nothing

Pure being is so indeterminate that it is not even being and so is nothing. This is one gloss on the basic Hegelian idea at the beginning of the Science of Logic. But what does it mean?

To achieve a correct understanding of this equation of pure being and nothing, we need to consider if it is required that we screen out properties that are indeterminate in the sense of not distinguishing between determinate beings. If everything were necessarily spatiotemporally located, for example, then being spatiotemporally located would be an indeterminate property in this sense. Yet something spatiotemporally located is not nothing, so we must be careful if we are going to suppose that the equation of pure being and nothingness rests on indeterminacy of this sort.

Why would we want to avoid this supposition? Well, insofar as we are capable of contrasting relative and absolute nothingness, it seems clear that the latter is incompatible with this sort of indeterminacy. So we have to get rid of this indeterminacy if we want to reach all the way through to absolute nothingness. And, if we take away all the indeterminate properties of pure being, as well as all the determinate ones, then we arguably don’t have a subject of predication at all, and that would seem equivalent to nothing in this absolute sense; or at least it would be if there were a workable notion of negation floating free of any predication.

Again, if we still have some indeterminate properties, e.g. self-identity, then we have probably not done enough to purify the concept of pure being so that it is capable of validating the equation with absolute nothingness. (That is, we have not done enough to destroy any means of distinguishing it from the latter.)

What prevents us from succeeding along these lines, then? The only barrier would be the inconceivability of absolute nothingness itself, which arises from the apparent inability to express any sort of negation without having that negation mean that something (and hence not nothing) is the case.

On the other hand, how do things stand if we adhere closely to the view that absolute nothingness is inconceivable? Then any negation of pure being would at least require that ‘being’ be taken equivocally, i.e. as something that could be wholly replaced by something else (and not by absolutely nothing). Yet, in this case, the being in question would clearly not be pure, because it would be determined against the being that negates it. Basically, as long as we take being to be an individual, it’s not going to be possible to completely purify it, even if we give up the goal of removing all its indeterminate properties (so as to equate it with absolute nothingness). Such a being would still be determined against every determinate thing, and thus be itself determinate (and so impure).

So to summarise: the purest being is impure and the most absolute nothing is relative.


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follow up on paradox and totality

Meillassoux deploys a stock Cantorian argument to conclude that there cannot be a totality of possibilities, i.e. a universal set of all possible ways the world could be. This takes place in the context of his attempt to disqualify an updated rendition of the old Kantian rejoinder to Hume (“If cinnabar were now red…”), according to which, on the supposition that contingency is the only necessity, we should expect to see frequent/constant variation of the so-called ‘laws of nature’. In their discussion of this problematic, Joshua Heller and Jon Cogburn suggest that Meillassoux should follow Graham Priest in accepting as true the various contradictions that arise at the limits of thought. They assert moreover that there is no middle path between an accessible paraconsistent totality and consistent plurality without totality. This is the dilemma they construct for Meillassoux, and that I wish to follow him in resisting.

Of course I readily agree that neither wilful ignorance nor complacent dismissal are acceptable responses to the paradoxes of totality. In fact it is basically axiomatic for me that dogmatic quietism is off the table: something significant, something revisionary, must be done. I take it to be true, furthermore, that there are no straight solutions to these paradoxes; only sceptical solutions, solutions that cede something significant to the ‘sceptic’ (i.e. the imagined propagator of the paradoxes). Having said this, there is an important sense in which existing sceptical solutions cede too much. In their eagerness to acknowledge the inexistence of problematic totalities like the universal set, they cede the ability to think in absolutely general terms at all, or to quantify universally and unrestrictedly. This is a mistake: to wed the generality of thought itself to the existence of paradoxical totalities is an unnecessary concession.

Thus my conclusion is that we need to find a place for pluralism somewhere within our response to the paradoxes, but without completely abrogating the viewpoint of absolute generality.

We can call those who deny the ability to think in absolutely general terms generality relativists. This leads to a preliminary puzzle. For how is it that generality relativists manage to coherently express their viewpoint? Their view, taken straightforwardly, seems to require that, for any X, X is not an absolutely general thought. This however involves universal quantification over every X. The following, similar line of thought — taken from an interesting published correspondence between Patrick Grim and Alvin Plantinga — expresses the difficulty here clearly:

Were there a sound Cantorian argument with the conclusion that there can be no universal propositions — so the argument goes — it would require at least one universal proposition as a premise. But if sound, its conclusion would be true, and thus there could be no such proposition. If sound its premises would not all be true, and thus it would not be sound. There can then be no sound Cantorian argument with the conclusion that there can be no universal propositions.

Taken straightforwardly, generality relativism is inexpressible by its own lights. It is for this reason that sophisticated formulations of generality relativism do not straightforwardly deny absolute generality in this way. But then what exactly do they do? As far as I can see, they revert to a case by case treatment of individual concepts of totality, showing how each is paradoxical, but without ever ascending to the general conclusion that there is no such conception free of paradox.

Although we might raise further questions here, I am going to assume that the generality relativist has at least succeeded in formulating her disagreement in a way that constitutes a challenge from the viewpoint of the generality absolutist. After all, and in any case, we should want the latter to actually solve the paradoxes of totality, rather than sanguinely resting her entire case on the referential incoherence of denying totality. For this reason, I think that the dialectical subtleties surrounding generality relativism are a red herring: the generality absolutist should just focus on producing an understanding of totality that isn’t susceptible to refutation on the basis of familiar relativist strategies. At any rate, this is what I propose to do.

The paradoxes of totality are ontologically fecund: rather than locking us up in some cloistered epistemic space, the inexistence of higher totalities allows what is left behind to come clearly into focus; it enables absolute generality rather than foreclosing it — but only on the condition that what we are thus generalising about is conceived in a specific, and surprising, way.

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note on heller and cogburn’s meillassoux paper

Meillassoux’s insistence on both de-totalising the possible and simultaneously exploding correlationism is something that I am trying to preserve in my adaptation of his position. Of course I have since interpreted everything in my own way such that it is no longer fruitful (or easy) for me to articulate myself in terms of Meillassoux’s concepts and reference points. It is nevertheless great to come across work that makes real progress in doing the sort of thing I’d have to do if I were to attempt such an articulation. Thus I was happy to discover today a paper by Joshua Heller and Jon Cogburn entitled ‘Meillassoux’s Dilemma: Paradoxes of Totality After the Speculative Turn’. It is a very nice paper that seems to confirm my thinking and hunches on several points. I won’t try to cover all of the richness it includes, but I do want to comment briefly on their central thesis.

The tension between de-totalising the possible and exploding correlationism can be restated like this: we want there to be no totality of the possible, but we nevertheless want there to be a (consistent) totality of the actual. This turns out to be an extremely precarious balancing act; or, less optimistically, a dilemma. Cogburn and Heller quote the following salient passage from After Finitude:

This ignorance [of whether the possible can be totalized] suffices to expose the illegitimacy of extending aleatory reasoning beyond a totality that is already given in experience. Since we cannot decide a priori (i.e. through the use of logical-mathematical procedures alone) whether or not a totality of the possible exists, then we should restrict the claims of aleatory reasoning solely to objects of experience, rather than extending it – as Kant implicitly does in his objective deduction – to the very laws that govern our universe, as if we knew that the latter necessarily belongs to some greater Whole (Meillassoux 2008a, 105).

What is important to note here is that aleatory reasoning applies legitimately to experience for Meillassoux, which forms a totality, whereas possibility does not. Cogburn and Heller do not like this combination of attitudes: they see it as Meillassoux reverting to an oddly Kantian and correlationist attitude in his approach to modal space, and thus undermining his general critique of correlationism.

Here is a quick statement of their argument.

  1. They construe Meillassoux’s rejection of correlational finitude in terms of Graham Priest’s Domain Principle, which says that claims of the form ‘all sets are so and so’ only have determinate sense if there is a determinate totality over which the quantifier (‘all’) ranges. More explicitly: correlational finitude is defined by Cogburn and Heller as the position that we cannot coherently conceive (“self-subsistent”) totalities or absolutes. They claim that, given the Domain Principle, this view illicitly requires reference to the actual totality of spacetime, and so is self-defeating. They take the felicity of their reconstruction as evidence for concluding that Meillassoux is actually committed to the Domain Principle (or else is reasoning fallaciously in his refutation of correlationism).
  2. Commitment to the Domain Principle is, however, in tension with de-totalising possibility. Hence the dilemma. The tension comes from the fact that, given the Domain Principle, when we quantify over possibilities we therefore incur commitment to the totality of possibility. Meillassoux has to quantify over possibilities in order to formulate and express his metaphysics of contingency. Hence…

Perhaps the best feature of Cogburn and Heller’s paper is the way it tries to simplify the dialectic by reducing the number of live options on the table. Specifically, one must, in their view, choose either inconsistent totality or consistent plurality. The importance they assign to the Domain Principle also seems instructive to me. However, in trying to simplify the dialectic in this way, they have ipso facto had to lay a number of cards on the table. I am happy they have done this, and I hope the dogmatic nature of the rest of this post – where I simply list my disagreements more or less without defense – does not come off as negative or dismissive.

First, it is not clear to me that Meillassoux really wants to use the Domain Principle as part of his refutation of correlationism. I suppose this is an easy point to make, since Cogburn and Heller are explicitly offering a reconstruction rather than a straightforward interpretation of what Meillassoux really wanted to argue. Nevertheless, this Priestian offering looks to me like a Trojan Horse that is best left outside the city.

In any case, even if Meillassoux does want to use the Domain Principle, we can still argue on behalf of actual totality without having to appeal to it. Maybe in so doing we lose the ability to meet the correlationist on her own terms, but then I think we had best not try to do that anyway; better to simply resolve the paradoxes of totality. To try to generate this solution (as it were) directly  from the conditions of correlationism itself, and thus preserve a sort of neo-Cartesian, anhypothetical purity – this strikes me as a bridge too far.

I think the Domain Principle is pretty dubious. This can be guessed, I suggest, from the uses Priest puts it to. In particular, he uses it to bolster his Hegelian view that potential infinity requires actual infinity. This is an exact inversion of my own approach that is intended to rest heavily on the viability of potential infinity (which I compare with Meillassoux’s virtuality rather that his potentiality) as part of a consistent response to the paradoxes of totality. On my model, the same thing allows us to both successfully balance the explosion of correlationism (taken in the deflated sense implied above) with the de-totalization of the possible, and articulate the metaphysics of contingency: namely the finitude of actual totality. This basic gesture then informs all of my other disagreements with Cogburn and Heller. In particular, I disagree with – or would seek to interpret extremely carefully – the view that talking about possibility requires quantifying over possibilities. And I agree with Markus Gabriel that possible worlds semantics are actually a hindrance in the way of our correctly understanding the nature of modality.

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more on waghorn

Just a little more to add to my previous post.

Consider the following argument:

  1. Set theoretical paradoxes such as Russell’s paradox show that we can’t consistently quantify over absolutely everything.
  2. If we had a consistent concept of absolutely everything, then we could consistently quantify over absolutely everything.
  3. We don’t have a consistent concept of absolutely everything (from 1 and 2).
  4. We can’t consistently understand nothingness as the negation of absolutely everything if we don’t have a consistent concept of absolutely everything.
  5. Hence, we can’t consistently understand nothingness as the negation of absolutely everything (from 3 and 4).

Waghorn presents this argument (though not quite in this way) in his book Nothingness and the Meaning of Life (p. 60 onwards)There are three independent premises: 1, 2, and 4. Premise 4 doesn’t strike me as worth arguing over, so I will focus on premises 1 and 2 instead. (For the rest of this post, I abbreviate ‘consistent concept of absolutely everything’ to ‘concept of totality’, except where otherwise noted.)

Premise 2: We can distinguish conceiving something and being able to quantify over it, but with regard to totality these two things usually go together. In particular, if we treat the existential quantifier as implying an ontology of discreet individuals that is at odds with the phenomena of vagueness and indeterminacy, then we can motivate drawing this distinction. This is gestured at by Gabriel in Fields of Sense (p. 104), and it is also a feature of Patrick Grim’s more recent work on totality, which is an attempt to escape from the straight-jacket he had created for himself in The Incomplete Universe. Nevertheless, I am going to assume this premise is true or irrelevantly false for present purposes.

Premise 1: In general, Waghorn thinks that many responses to Russell’s paradox are philosophically ad hoc because they turn the spade as soon as they succeed in removing the threat of paradox from the realm of mathematical activity. Thus one common approach mentioned by Waghorn, the von-Neumann-Bernays-Gödel axiomatisation of set theory, stipulates that collections beyond a certain size are not sets but ‘proper classes’, which by definition cannot be members of themselves (here the notion is formalised, unlike in ZF). Waghorn’s sentiment, which I am sympathetic towards, is that mere technical solutions like this are not (philosophically) illuminating, and thus inadequate. That is one reason why I appreciate Grim’s book so much: he shows how to amplify the felt cogency of the paradoxes of totality beyond attempts to quarantine it within set theory or mathematical thought more generally. The paradoxes of totality are rightly taken as paradoxes of thought as such, not merely mathematical or logical paradoxes.

Although it isn’t completely clear what philosophical illumination actually requires in this case, to count as satisfactory a solution ought to have some independent motivation behind it. Now, the motivation behind my own solution is quite rhizomatic and multifarious, but can at least be hinted at with the following:

a) Nothingness is both conceivable and possible.

b) Being is finite.

c) There are no abstract objects.

These can be taken as mutually reinforcing but also as receiving independent inputs. (Note that b and c are the pillars of Goodman and Quine’s famous 1947 paper ‘Steps Towards a Constructive Nominalism’.) Listing all these inputs and connections would be time-consuming, but one thing we can see straightaway is this: Waghorn’s claim, that the paradoxes of totality preclude the conceivability of nothingness, arguably rests on the premise that there are abstract objects, since arguably these paradoxes require abstract objects to work. He is effectively claiming, then, that the existence of abstract objects is more probable than the ability to conceive totality. Actually, to be more precise, he is committed to the stronger premise that the existence of the subset of abstract objects necessary to express the paradoxes of totality is more probable than the truth of the proposition ‘we can conceive totality’. That however does not seem plausible to me.

To be fair, it is common to hold that the sort of nominalism demanded as minimally necessary to avoid the paradoxes of totality precludes the conceivability of totality. In other words, we must eschew all thought of totality in order to avoid paradox. Thus Geoffrey Hellman argues (in his paper ‘Against Absolutely Everything’) that the phenomenon of indefinite extensibility – which Waghorn rightly emphasises in his book – forces us away from a Platonist philosophy of mathematics and leads to the inconceivability of totality. He calls the latter, following standard usage, generality relativism. However, as Hellman notes, neither the indefinite extensibility of concepts like ‘ordinal’ and ‘set’, nor nominalism as such, imply generality relativism. Further arguments are needed. In general, it shouldn’t be that surprising to find that, after we prune the ontological bush there is nothing preventing us from quantifying over the totality that remains, so that premise 1 of the above argument is false. (Again, contrast this with the view that we must eschew all thought of totality in order to avoid paradox.)

Of course, I am sweeping under the rug for the time being the question of what happens to mathematics when we start gleefully pruning the ontological bush in this manner! Looking at the fate of Quine and Goodman’s early project, for example, it should be clear that my approach does require a degree of optimism.


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may update…

At present this blog is as acting as a sort of placeholder for future input, so for those of you who are still following, please bear with me! At the moment I am working a heavy teaching load, which doesn’t leave much time for independent study or writing; and in any case my ideas are — even without external interference — slow to develop.

Nevertheless, I recently had a chance to read through Nicholas Waghorn’s Nothingness and the Meaning of Life, which is probably the most exhaustive examination of the concept of nothingness that covers both analytic and continental philosophy. One could with profit read it as a companion text to Markus Gabriel’s Fields of Sense, since it develops a kindred line of thought, one that attempts to block the conceivability of both nothingness and totality (the one following from the other). The comparison is also instructive in the following way: Waghorn is acutely aware of the performative tension involved in his investigation, and has written a book with a truly tortured reflexivity to it (you have to read into it a bit before you fully realise this).

A recurrent theme in Waghorn’s book is that we don’t have a concept of (absolute) nothingness. The reasoning here is simple and yet mysterious to me: we can’t characterise nothingness, since it does not have any properties. To which we can immediately add: to assert that we can’t characterise nothingness is also to characterise it (p. 162), which illustrates in nuce why Waghorn’s approach contorts itself into an indefinite regress. Another way to put the basic claim is like this: to say that nothingness is not some X is necessarily to say that nothingness is a Y such that Y ≠ X. It is mysterious to me why, underneath every refusal to countenance the conceivability or possibility of nothingness, there appears finally this premise, like Plato’s ghost.


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two new papers…

My first paper, ‘Why not Nothing? Meillassoux’s Second Figure of Factiality and Metaphysical Nihilism’ has been published in the journal Speculations; it can be found here.

My second paper ‘Markus Gabriel Against the World’ has also been published in the journal Sophia; it can be found here.

In my next paper, I will try to push further into the philosophical and (broadly speaking) logical motivations for thinking of being as finite and contingent.

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global anti-representationalism and ‘the world’

Huw Price distinguishes between subject naturalism and object naturalism as follows. Object naturalism is the view that all that exists is the world as studied by science (i.e. the physical world), and that scientific knowledge is the only genuine knowledge. By accepting object naturalism we take on the challenge of accommodating within this framework the existence and knowledge of such things as moral facts, aesthetic facts, mathematical facts, modal facts, etc., which seem to have no place in the natural or physical world.

pricePrice calls his own view subject naturalism (amongst other names), and takes it to be prior to and independent of object naturalism. Subject naturalism is initially described simply as the view that we ought to start with ourselves qua objects of scientific investigation (when thinking about how to navigate the problem of accommodation just described).* Although object naturalists should take themselves to be subject naturalists, the reverse need not true, Price observes.

*(Notice that Price’s starting point is the primacy of science, i.e. of the scientific perspective under a particular interpretation. One question to ask here is how Price motivates this privileging of the framework or language game of science, given the global nature of the anti-representationalism he defends. Sure, science is privileged by its own lights, but why do these lights take precedence? How do we even give pragmatic explanations in the case of a global anti-representationalism, given that we cannot treat science as representational when it offers e.g., evolutionary explanations?)

The basic idea behind subject naturalism turns out to be this: when considering the various placement/accommodation problems (e.g. how to place moral/mathematical/etc. facts in the world), we ought to understand ourselves as starting with linguistic and psychological data, not with objects, properties, qualities etc. Roughly, we begin in the formal rather than the material mode, and according to Price that is where we should stay. This is Price’s anti-metaphysical or Carnapian streak, which I am sounding out in this post. As he sees it, the problem of how to naturalistically accommodate a plurality of linguistic usages or practices is not only prima facie more tractable than that of accommodating seemingly non-natural objects or parts of reality (such as modal facts), but it scratches the same itch, or close enough, that classical metaphysics scratches.

My interest in Price has to do with the nature of the pluralism he defends, as I am very much interested in the common association of naturalism with ontological univocity and monism, and how this plays out with regard to the question of the existence of the world (i.e. the totality, the domain of all domains, etc.), a question also posed recently by Markus Gabriel.

Somewhat like Gabriel, Price denies that the world, under a certain specific interpretation which I’ll now state, exists. Price contends that the common conception of the world runs together two distinct things: the world qua totality of facts, on the one hand, and the world qua natural environment or physical universe, on the other. To undo this problematic association, we must first learn to understand facts without reference to semantic notions like truth, reference, etc. This move is de-totalising insofar as it refocuses our attention on the plurality of possible, functionally distinct assertoric language games, a plurality that cannot be unified because it lacks a common measure (we are told).* Science and ethics are examples here. In connection with this point, it should be emphasised that Price’s pluralism is not ontological in the sense of involving multiple ontological realms. In other words, we’re not duplicating object domains construed in the material mode, as if there were a deep plurality in the ontological furniture of the world, but simply acknowledging the wide variety of different things we do with words.

*(I compare this plurality with Gabriel’s plurality of fields of sense.)

A related type of ontological pluralism is the view that there are multiple distinct existential quantifiers. Does Price accept pluralism of this sort? It appears he wants to have it both ways here. On the one hand, a key part of his position is the denial that all declarative utterances or assertions are descriptive or representational in nature. Like the quasi-realist, Price holds that at least some statements can be considered truth-apt (in a suitably deflated sense of ‘true’) even though they are not strictly speaking descriptive (since there are no object-naturalistically respectable properties, objects, qualities etc. for them to describe).

However, on the other hand, there are two ways in which Price’s view is at least prima facie more monistic than the quasi-realist.

rudolf_carnap_3First. In the capital ‘R’ sense of Representation, Price denies that any statements are strictly descriptive, which is why his anti-representationalism (i.e. his ‘expressivism’, though that is a misleading term), is global rather than local. (To clarify, what anti-representationalism means here is that we explain e.g. moral truth in broadly pragmatic terms, eschewing appeal to semantic notions like truth or reference at the explanatory level. This reflects the vaguely internal realist flavour of the project.) What this means is that the bifurcation between strictly and non-strictly descriptive statements falls by the wayside.

Second. Apparently moving in the other direction, although this bi-furcation is given up, another is put in its place, involving a distinction between internal and external representations. However, as with Kant’s internalisation of the mind-world relation, this is not heterogeneity on the same level as before. Rather, the functional plurality Price is at pains to emphasise is placed on a foundation different from that of local anti-representationalists such as Blackburn; a foundation that, at least from a certain viewpoint, seems to militate against the unbridledness of that plurality. Specifically, Price’s functional plurality is underwritten by a unified account of assertion à la Brandom (see e.g. EPR p. 31). This balancing of unity and plurality yields a vaguely Carnapian framework-relative understanding of univocity and ontological monism.

It seems to me that there is something problematic about this result, which I can only gesture vaguely at here.* To start with, Price interestingly wonders whether Brandom’s claim that assertion is the fundamental language game is at odds with the functional pluralism of local anti-representationalism (e.g. quasi-realism). In response to this query, Price assures us that whilst assertion may be fundamental, it nevertheless has multiple functionally distinct applications. He presents the unity here in as sparse terms as he can muster. But how sparse must it be to avoid commitment to monism? Hasn’t Price ceded the crucial point by allowing a single account of assertion to range over everything like this? Price himself leaves the matter open as a problem requiring further investigation.

*(Gabriel also tries to mimic univocity in a related manner, with similarly unsatisfying results in my opinion.)

At any rate, the general issue (or what I take to be the general issue) is apparent in Price’s discussion of Carnap and Quine on the question of ontology. We know that Quine objected against Carnap that, rather than thinking of metaphysics and ontological monism as requiring an impossible standing outside of all frameworks or language games, we can think of them as involving instead a single existential quantifier corresponding to a single framework or game that encompasses everything, such that ontological questions are both maximally general and yet nevertheless framework internal. This sets Price to the task of defending Carnap’s assumption that linguistic plurality is somehow de jure recalcitrant to this homogenising of the existential quantifier. And here again Price argues that pragmatic plurality, that is, the multiplicity of different things we do with language, either entirely or mostly escapes the reach of Quine’s objection. It is the same logical device, this way of thinking allows us to admit, but used in a variety of different ways. The variety is what is salient, Price wants us to think, not the sameness. But once again I am dubious that unity and plurality can be balanced in this way, short of just accepting monism. Isn’t Price just giving us monism with a tolerant face? To be fair, Price’s response to this does seem plausible against the specifically Quinean considerations in favour of monism that he has in mind (see his paper on Carnap and the ghost of metaphysics for more), but these aren’t the only considerations available. In particular, it seems to me that the problematic status of the negation of absolute generality, as reflected especially in indefinite extensibility arguments for generality relativism, represents a more difficult obstacle for the intrepid pluralist. More on this, perhaps, in a later post.

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