Note on Posthuman Resilience

On October 19, 2016, in Uncategorized, by enemyin1


This post is adapted from a paper presented at a workshop organised by the Open University’s PRiME (posthuman resilience in major emergencies) research group held in London, 18th-19th October 2016.


Resilience – understood as the capacity to recover from perturbations and resume “normal functioning” – appears seems to be a generic rather than domain specific property. It has a general application to complex systems at all scales and levels of complexity, and applies across the notional and contested divide between the natural and the artificial. It thus seems consonant with a “flat” posthuman world in which humans – rather than having privileged status – are just a distinctive being amongst other – similarly distinctive – beings.[1]

There are resilient individuals, resilient ecosystems, resilient institutions, and resilient software entities.[2]  It might seem, then, that resilience could provide a way of orienting ethics in a posthuman predicament” in which ontological domains are looking increasingly fragile or tenuous.

However, once we unhitch the concept from a domain, this ethics exhibits an indeterminacy akin to the massively indeterminate ethics of [posthuman] disconnection.

To see why this is so, I will consider C.S. Holling’s widely cited distinction between engineering and ecological resilience. A system exhibits engineering resilience if it tends to return quickly to a single stable state following some perturbing event. Systems that exhibit ecological resilience, by contrast, tend to be multistable: they can flip into a range of stable dynamic patterns (Holling 1996, 33).

For example, some semi-arid grasslands exhibit a dynamic balance between grasses with functionally distinct properties: one type resistant to drought and grazing herbivores due to long root systems, the other more photosynthetically efficient but more vulnerable to grazing and drought due to the greater concentration of surface biomass:

“The latter, productive but drought-sensitive grasses, have a competitive edge between bouts of grazing so long as drought does not occur. But, because of pressure from pulses of intense grazing, that competitive edge for a time shifts to the drought-resistant group of species. As a result of these shifts in competitive advantage, a diversity of grass species serves a set of interrelated functions— productivity on the one hand and drought protection on the other” (36).

This allows the ecosystem to exhibit functional diversity in the face of varying environmental pressures. While the intense grazing from herbivores comes in pulses, there are drought-free periods when the more efficient grasses have the edge. However, when such grasslands are used for ranching the constant but relatively light grazing give the more productive grasses a decisive edge. The ecosystem becomes “more productive in the short term but the species assemblage narrows to emphasise one functional type”. The ecosystem thus becomes specialised for a narrower range of functions – but also more vulnerable to drought. Ecological resilience is reduced in favour of short-term engineering resilience, but at the expense of its ability to withstand environmental contingencies over the longer term.

Ecological resilience is thus a measure of functional diversity – the ability to exist under a range of environmental conditions and subtend diverse functions in them (Holling 1996, 40). Accordingly, it a special case of the functional autonomy described in the psychology-free account of agency that supports the Disconnection Thesis. A highly functionally autonomous system is one that is highly capable of acquiring new functions and enlisting new values in other containing systems or environments (Roden 2014, 140).

Cultivating ecological resilience in natural or artificial systems is thus a question of engineering functional autonomy, thereby increasing the capacity of natural, artificial or social systems to accrue values and functions. However, this goal is ethically void in itself.

The Disconnection Thesis exhibits this problem in an extreme form. A posthuman would need to exhibit a high degree of functional autonomy in order to exist outside of the human socio-technical network but this abstract description tells us nothing about the implications of such an event, either for humans or posthumans.

For example, humans – in their current iterations – need planets. Really powerful posthumans might find packing mass down a gravity well inordinately wasteful.[3]

We can thus say little about the ethical value of posthuman lives – whether we should create them, or even become them – without precipitating a disconnection and seeing how things turn out. Even post-disconnection, there might be massive problems of radical interpretation for any human or merely transhuman ethicists still around (Roden 2014, 176-9).[4]

Any attempt to evaluate the posthuman is a necessarily irresponsible risk to the integrity of the species – necessary, since the technological trajectories of modernity could mean that we have no choice but to investigate possible lines of flight out of the human.

However, the same indeterminacy applies to ecological resilience. Since it is a form of functional autonomy it inherits its ethical vacuity.

Resilience sounds unproblematically good, but that is because the concept tends to be applied by thinkers to things that are already assumed to be values (e.g. resilient communities or environments). Once abstracted it over a flat posthuman universe it loses any specificity.

Since increasing resilience in this generalised sense increases functional autonomy it also implies an increase the complexity and unpredictability of the resulting systems. Thus – in a sense – nothing is less ecological than resilience when seen through a post-anthropocentric lens in which neither humans nor other organics have superlative value over other forms of life, posthuman or otherwise.

If ethics requires some commitment to a specific form of life – or as Claire Colebrook puts it – to a particular subject or speaker, then the ethics of resilience is a counter-ethics or anti-ethics since increasing resilience deterritorialises: it reduces dependence on specific forms of life or subjectivity.[5] Deterritorialization occurs where material or formal elements of an ordered assemblage (a territory) rupture their associations with a settled context generating new assemblages with new capacities, new rules or modes of functioning. As such, deterritorialization is not a process peculiar to the non-living or living, the social or technological domains. It is the ineluctable activity of nature operating “against itself”; threatening stable assemblages with anomalous relationships (Deleuze & Guattari 1988: 242–4).

If an ethics of resilience aims to increase the functional autonomy of entities without regard to their kind, then it is no more committed to improving the lot of creatures like ourselves than it is to cultivating a metal-storm of posthuman war machines. If it is predicated on the resilience of human bodies, lives or ecosystems, that is fine; but then it presupposes something more than just an ethics of resilience – perhaps an Aristotelian-humanist ethics, or a utilitarian one.

While this conclusion might seem perversely unhelpful, I prefer to think of it as salutary. It means that determining opportunities for resilient agency is always ethically problematic and requires that we take responsibility for decisions whose long-run implications will always exceed our capacity for calculation:

“We have perhaps always lived in a time of divergent, disrupted and diffuse systems of forces, in which the role of human decisions and perceptions is a contributing factor at best. Far from being resolved by returning to the figure of the bounded globe or subject of bios rather than zoe, all those features that one might wish to criticize in the bio-political global era can only be confronted by a non-global temporality and counter-ethics.” (Colebrook 2012a: 38)


Gao, J., Barzel, B., & Barabási, A. L. (2016). Universal resilience patterns in complex networks. Nature, 530(7590), 307-312.

Haraway, D. (1991), Simians, Cyborgs, and Women: The Reinvention of Nature. New York: Routledge.

Harman, G. 2008. “DeLanda’s Ontology: Assemblage and Realism”. Continental

Philosophy Review 41(3): 367–83.

Colebrook, C. 2012a. “A Globe of One’s Own: In Praise of the Flat Earth”. Substance: A Review of Theory & Literary Criticism 41(1): 30–9.

DeLanda, Manuel. 2002. Intensive Science and Virtual Philosophy. London: Continuum.

Delanda. 2006. A New Philosophy of Society: Assemblage Theory and Social Complexity. London: Continuum.

Deleuze, G. & F. Guattari 1988. A Thousand Plateaus: Capitalism and Schizophrenia. London: Athlone Press.

Collier, J. D. & C. A. Hooker 1999. “Complexly Organised Dynamical Systems”. Open Systems & Information Dynamics 6(3): 241–302.

Haraway, D. 1991. Simians, Cyborgs, and Women: The Reinvention of Nature. New York: Routledge.

Hayles, N. K. (1999), How We Became Posthuman: Virtual Bodies in Cybernetics, Literature, and Informatics. Chicago, IL: University of Chicago Press.

Holling, C.S., 1996. Engineering resilience versus ecological resilience. In: Schulze, P.

(Ed.), Engineering within Ecological Constraints. National Academy,

Washington, DC, USA, pp. 31–44.

Roden, David. 2012. “The Disconnection Thesis”. In The Singularity Hypothesis: A Scientific and Philosophical Assessment, A. Eden, J. Søraker, J. Moor & E. Steinhart (eds), 281–98. London: Springer.

Roden, David. 2013. “Nature’s Dark Domain: An Argument for a Naturalised Phenomenology”. Royal Institute of Philosophy Supplements 72: 169–88.

Roden, David. 2014. Posthuman Life: Philosophy at the Edge of the Human. London: Routledge.

Stross, C. 2006. Accelerando. New York: Ace.


[1] The philosopher Manuel Delanda refers to ontologies that reject a hierarchy between organizing form and a passive nature or “matter” as “flat ontologies”. Whereas a hierarchical ontology has categorical entities like essences to organise it, a flat universe is “made exclusively of unique, singular individuals, differing in spatio-temporal scale but not in ontological status” (DeLanda 2002, 58). The properties and the capacities of these entities are never imposed by transcendent entities but develop out of causal interactions between particulars at various scales. Importantly for the present discussion, a flat ontology recognizes no primacy of natural over artificial kinds (Harman 2008).

[2] Resilience can be contrasted with related concept: cohesion. A system is relatively cohesive if its structure causes it to exhibit unified dynamic behaviour in a wide range of contexts (Collier 1988). Systems like rocks, thunderstorms and cats are more cohesive across similar contexts than piles of sand, clouds or confraternities of cats.[2]

Resilience entails cohesion; it is a pre-requisite of resilience that systems exhibit stable dynamic behaviour over time. But not all cohesive systems are resilient. Resilience is a value-laden or norm-laden concept because it involves function ascription. If some entity has a function – for example, detecting the presence of a prey animal – it can perform at this role more or less well or fail in some way.

A rock exhibits cohesion. But a resilient system is also vulnerable. Things can go badly or well for it. It is, in this sense, that the resilience seems to imply a kind of ethics.

As characterised, both forms of resilience exhibit varieties of cohesion, since all that has been said concerns the way stable states are distributed through the “possibility spaces” describing a system’s dynamic behaviour. However, the distinction between single and multiple equilibria are what enable resilience and adaptation; not its defining features.


[3] This possibility is vividly portrayed in Charles Stross’ 2006 SF novel Accelerando. Accelerando begins in a 21st century in filled with speculative technologies and utopian aspirations but is largely set in a dystopian future in which the singularity has resulted in a world dominated by self-improving artificial intelligences. Its main protaganist, futurist and social innovator, Manfred Macx, opines near the beginning:

NASA are idiots. They want to send canned primates to Mars!” Manfred swallows a mouthful of beer, aggressively plonks his glass on the table: “Mars is just dumb mass at the bottom of a gravity well; there isn’t even a biosphere there. They should be working on uploading and solving the nanoassembly conformational problem instead. Then we could turn all the available dumb matter into computronium and use it for processing our thoughts. Long-term, it’s the only way to go. The solar system is a dead loss right now – dumb all over! Just measure the MIPS per milligram. If it isn’t thinking, it isn’t working. We need to start with the low-mass bodies, reconfigure them for our own use. Dismantle the moon! Dismantle Mars! Build masses of free-flying nanocomputing processor nodes exchanging data via laser link, each layer running off the waste heat of the next one in. Matrioshka brains, Russian doll Dyson spheres the size of solar systems. Teach dumb matter to do the Turing boogie! (Stross 2006, 15)

The novel is a parable about being careful what one wishes for. The AIs which come to run its world are “wide human descendants” of human corporations and automated legal systems, which achieved both sentience and a form of legal personhood back in the twenty-first. As one character ruefully observes, in this world the phrase “smart money” has taken on an entirely new meaning!

Eventually, these “corporate carnivores” – known by the epithet “Vile Offspring” – institute a new form of capitalism (Economics 2.0) in which supply and demand relationships are computed too rapidly for those burdened by a “narrative chain” of personal consciousness to keep up.

E 2.0 is so remorselessly efficient that it comes to dominate the major part of the solar system, whole planets pulverized and diverted to fast thinking dust clouds of smart matter “blooming” around the sun (Stross 2006: 208–10).

[4] (Continuing the previous footnote) how could we know whether Stross’ vile offspring were really vile, or morally considerable agents in their own right?


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Braidotti’s Vital Posthumanism

On October 21, 2013, in Uncategorized, by enemyin1

Bt-toxin-crystalsCritical Posthumanists argue that the idea of a universal human nature has lost its capacity to support our moral and epistemological commitments. The sources of this loss of foundational status are multiple according to writers like Donna Haraway, Katherine Hayles (1999), Neil Badmington (2003), Claire Colebrook and Rosi Braidotti. They include post-Darwinian naturalizations of life and mind that theoretically level differences between living and machinic systems and the more intimate ways of enmeshing living entities in systems of control and exploitation that flow from the new life and cognitive sciences. Latterly, writers such as Braidotti and Colebrook have argued that a politics oriented purely towards the rights and welfare of humans is incapable of addressing issues such as climate change or ecological depletion in the anthropocene era in which humans “have become a geological force capable of affecting all life on this planet” (Braidotti 2013: 66).

On the surface, this seems like a hyperbolic claim. If current global problems are a consequence of human regulation or mismanagement, then their solution will surely require human political and technological agency and institutions.

But let’s just assume that there is something to the critical posthumanist’s deconstruction of the human subject and that, in consequence, we can no longer assume that the welfare and agency of human subjects should be the exclusive goal of politics. If this is right, then critical posthumanism needs to do more than pick over the vanishing traces of the human in philosophy, literature and art. It requires an ethics that is capable of formulating the options open to some appropriately capacious political constituency in our supposedly post-anthropocentric age.

Braidotti’s recent work The Posthuman is an attempt to formulate such an ethics. Braidotti acknowledges and accepts the levelling of the status of human subjectivity implied by developments in cognitive science and biology and the “analytic posthumanism” that falls out of this new ontological vision. However, she is impatient with what she perceives as a disabling vacillation and neutrality that easily follows from junking of human subject as the arbiter of the right and the good. She argues that a posthuman ethics and politics need to retain the idea of political subjectivity; an agency capable of constructing new forms of ethical community and experimenting with new modes of being:

In my view, a focus on subjectivity is necessary because this notion enables us to string together issues that are currently scattered across a number of domains. For instance, issues such as norms and values, forms of community bonding and social belonging as well as questions of political governance both assume and require a notion of the subject.

However, according to Braidotti, this is no longer the classical self-legislating subject of Kantian humanism. It is vital, polyvalent connection-maker constituted “in and by multiplicity” – by “multiple belongings”:

The relational capacity of the posthuman subject is not confined within our species, but it includes all non-anthropocentric elements. Living matter – including the flesh – intelligent and self-organizing but it is precisely because it is not disconnected from the rest of organic life.

‘Life’, far from being codified as the exclusive property or unalienable right of one species, the human, over all others or of being sacralised as a pre-established given, is posited as process, interactive and open ended. This vitalist approach to living matter displaces the boundary between the portion of life – both organic and discursive – that has traditionally been reserved for anthropos, that is to say bios, and the wider scope of animal and nonhuman life also known as zoe (Braidotti 2012: 60).

Thus posthuman subjectivity, for Braidotti, is not human but a tendency inherent in human and nonhuman living systems alike to affiliate with other living systems to form new functional assemblages. Clearly, not everything has the capacity to perform every function. Nonetheless, living systems can be co-opted by other systems for functions “God” never intended and Mother Nature never designed them for. As Haraway put it:  ‘No objects, spaces, or bodies are sacred in themselves; any component can be interfaced with any other if the proper standard, the proper code, can be constructed for processing signals in a common language’ (Haraway 1989: 187). There are no natural limits or functions for bodies or their parts, merely patterns of connection and operation that do not fall apart all at once.

Zoe . . . is the transversal force that cuts across and reconnects previously segregated species, categories and domains. Zoe-centered egalitarianism is, for me, the core of the post-anthropocentric turn: it is a materialist, secular, grounded and unsentimental response to the opportunistic trans-species commodification of Life that is the logic of advanced capitalism.

Of course, if anything can be co-opted for any function that its powers can sustain, one might ask how zoe can support a critique of advanced capitalism which, as Braidotti concedes, produces a form of the “posthuman” by radically disrupting the boundaries between humans, animals, species and technique. What could be greater expression of the zoe’s transversal potential than, say, Monsanto’s transgenic cotton Bollgard II? Bollgard II contains genes from the soil bacterium Bacillus thuringiensis that produce a toxin deadly to pests such as bollworm. Unless we believe that there is some Telos inherent to thuringiensis or to cotton that makes such transversal crossings aberrant – which Braidotti clearly does not – there appears to be no zoe-eyed perspective that could warrant her objection. Monsanto’s genetic engineers are just sensibly utilizing possibilities for connection that are already afforded by living systems but which cannot be realized without technological mediation (here via gene transfer technology). If the genes responsible for producing the toxin Bt in thuringiensis did not work in cotton and increase yields it would presumably not be the type used by the majority of farmers today (Ronald 2013).

Cognitive and biological capitalists like Google and Monsanto seem to incarnate the tendencies of zoe – conceived as a generalized possibility of connection – as much as the” not-for-profit” cyborg experimenters like Kevin Warwick or the publicly funded creators of HTML, Dolly the Sheep and Golden Rice. Doesn’t Google show us what a search engine can do?

We could object to Monsanto’s activities on the grounds that it has invidious social consequences or on the grounds that all technologies should be socially rather than corporately controlled. Neither of these arguments are obviously grounded in posthumanism or “zoe-centricism”  – Marxist humanists would presumably agree with the latter claim, for example.

However, we can find the traces of a zoe-centered argument in Deleuzean ethics explored in the essay “The Ethics of Becoming Imperceptible” (Braidotti 2006). This argues for an ethics oriented towards enabling entities to actualize their powers to their fullest “sustainable” extent. A becoming or actualization of power is sustainable if the assemblage or agency exercising it can do so without “destroying” the systems that makes its exercise possible. Thus an affirmative posthuman ethics follows Nietzsche in making it possible for subjects to exercise their powers to the edge but not beyond, where that exercise falters or where the system exercising it falls apart.

To live intensely and be alive to the nth degree pushes us to the extreme edge of mortality. This has implications for the question of the limits, which are in-built in the very embodied and embedded structure of the subject. The limits are those of one’s endurance – in the double sense of lasting in time and bearing the pain of confronting ‘Life” as zoe. The ethical subject is one that can bear this confrontation, cracking up a bit but without having its physical or affective intensity destroyed by it. Ethics consists in re-working the pain into threshold of sustainability, when and if possible: cracking, but holding it, still.

So Capitalism can be criticized from the zoe-centric position if it constrains powers that could be more fully realized in a different system of social organization. For Braidotti, the capitalist posthuman is constrained by the demands of possessive individualism and accumulation.

The perversity of advanced capitalism, and its undeniable success, consists in reattaching the potential for experimentation with new subject formations back to an overinflated notion of possessive individualism . . ., tied  to the profit principle. This is precisely the opposite direction from the non-profit experimentations with intensity, which I defend in my theory of posthuman subjectivity. The opportunistic political economy of bio-genetic capitalism turns Life/zoe – that is to say human and non-human intelligent matter – into a commodity for trade and profit (Braidotti 2013: 60-61).

Thus she supports “non-profit” experiments with contemporary subjectivity that show what “contemporary, biotechnologically mediated bodies are capable of doing” while resisting the neo-liberal appropriation of living entities as tradable commodities.

Whether the constraint claim is true depends on whether an independent non-capitalist posthuman (in Braidotti’s sense of the term) is possible or whether significant posthuman experimentation – particularly those involving sophisticated technologies like AI or Brain Computer Interfaces – will depend on the continued existence of a global capitalist technical system to support it. I admit to being agnostic about this. While modern technologies such as gene transfer do not seem essentially capitalist, there is little evidence to date that a noncapitalist system could develop them or their concomitant forms of hybridized “posthuman” more prolifically.

Nonetheless, there seems to be a significant ethical claim at issue here that can be used independently of its applicability to the critique of contemporary capitalism.

For example, I have recently argued for an overlap or convergence between critical posthumanism and Speculative Posthumanism: the claim that descendants of current humans could cease to be human by virtue of a history of technical augmentation (SP). Braidotti’s ethics of sustainability is pertinent here because SP in its strong form is also post-anthropocentric – it denies that posthuman possibility is structured a priori by human modes of thought or discourse – and because it defines the posthuman in terms of its power to escape from a socio-technical system organized around human-dependent ends (Roden 2012). The technological offspring described by SP will need to be functionally autonomous insofar as they will have to develop their own ends or modes of existence outside or beyond the human space of ends. Reaching “posthuman escape velocity” will require the cultivation and expression of powers in ways that are sustainable for such entities. This presupposes, of course, that we can have a conception of a subject or agent that is grounded in their embodied capacities or powers rather than general principles applicable to human agency. Understanding its ethical valence thus requires an affirmative conception of these powers that is not dependent on overhanging  anthropocentric ideas such as moral autonomy. Braidotti’s ethics of sustainability thus suggests some potentially viable terms of reference for formulating an ethics of becoming posthuman in the speculative sense.


Badmington, N. (2003) ‘Theorizing Posthumanism’, Cultural Critique 53 (Winter): 10-27.

Braidotti, R (2006), ‘The Ethics of Becoming Imperceptible”, in Deleuze and Philosophy, ed. Constantin Boundas, Edinburgh University Press: Edinburgh, 2006, pp. 133-159.

Braidotti, R (2013), The Posthuman, Cambridge: Polity Press.

Colebrook, Claire 2012a.), “A Globe of One’s Own: In Praise of the Flat Earth.” Substance: A Review of Theory & Literary Criticism 41 (1): 30–39.

Colebrook, Claire (2012b.), “Not Symbiosis, Not Now: Why Anthropogenic Change Is Not Really Human.” Oxford Lit Review 34 (2): 185–209.

Haraway, Donna (1989), ‘A Manifesto for Cyborgs: Science, Technology, and Socialist Feminism in the 1980s’. Coming to Terms, Elizabeth Weed (ed.), London: Routledge, 173-204.

Hayles, K. N. (1999) How We Became Posthuman: Virtual Bodies in Cybernetics, Literature, and Informatics. Chicago: University of Chicago Press.

Roden, D. (2010). ‘Deconstruction and excision in philosophical posthumanism’. The Journal of Evolution & Technology, 21(1), 27-36.

Roden, D. (2012). ‘The Disconnection Thesis’. In Singularity Hypotheses (pp. 281-298). Springer Berlin Heidelberg.

Roden, D. (2013). ‘Nature’s Dark domain: an argument for a naturalized phenomenology’. Royal Institute of Philosophy Supplement, 72, 169-188.

Roden, R (2014). Posthuman Life: philosophy at the edge of the human. Acumen Publishing.


Autonomous Systems Quotes

On January 23, 2013, in Uncategorized, by enemyin1

“Unlike physical or chemical dissipative structures, in which patterns of dynamic order form spontaneously, but whose stability relies almost completely on externally-imposed boundary conditions, autonomous systems build and actively maintain most of their own boundary conditions, making possible a robust far-from-equilibrium dynamic behavior.”

“A big stone in the river holds water from flowing, and some bacteria ferment milk to produce yoghourt. Although both systems do something, we do not call the stone an agent. The difference between the two cases is not in the degree of change operated by one or the other, but in the consequence of that change: only in the latter case does the change contribute to the maintenance of the performer of the action.”

Ruiz-Mirazo, Kepa & Moreno, Alvaro (2012). “Autonomy in evolution: from minimal to complex life”. Synthese 185 (1), 33-34.

Autopoiesis and closure Q&A

On March 17, 2011, in Uncategorized, by enemyin1

Dark Chemistry has an interesting and thought provoking post about autopoiesis and objects here. This is not an area I know well and I’m happy to be put right, but I’ve a few newbie thoughts and questions about some of the concepts applied by fans of Luhmann, Varela, etc.

I accept that some processes can have the appearance of formal closure insofar as each stage requires a result of some earlier or later stage of the process (chicken-egg-chicken). Social processes and some biochemical processes exhibit this property (Collier 2006). Moreover, they depend on the maintenance of boundaries between inside and outside while also contributing to that maintenance in certain cases. However, there seem to be obvious cases where system maintenance depends on boundary permeability as well. E.g. Merleau-Ponty’s blind man has extended the boundaries of his self when he uses his cane (self seeps into exo-self). So complex systems need boundary maintenance and process closure up to a point, but they also need to be open enough to exploit resources and couple with other systems. So I’m not quite ready to buy the idea that process closure is the only ontologically salient fact when thinking about whether object-hood implies absolute closure and separation or something messier and by degree like Collier’s notion of ‘cohesion’ (Ibid.).

DC’s references to object-oriented programming is interesting – I think Robert Jackson has also discussed this from time to time over at Algorithm and Contingency. My Java is a bit rusty, but isn’t computational encapsulation an artifact at the level of code – a convenient way of thinking about computational structures by allocating proprietary methods to objects? Any algorithm that can be written OO style can be written procedurally (more messily and less debuggably) without encapsulating objects and their methods. So the unity of computational objects is notional and practical, not ontological.

Finally, I’m not clear about the free use of terms like ‘recursion’ and ‘self-reference’ in discussions of autopoiesis. If I define something recursively using a successor relation – e.g.:

1) If fx, then f(s(x))

2) f(0)

This tells us that 0 is f and that any successor of an f is an f. By mathematical induction, then, we can show that all entities – 0, s(0), s(s(0)), s(s(s(0))), etc. –  in the domain of quantification for which the successor relation is defined are f.

There is obviously a sense in which the recursive part of the definition defines fx in terms of itself. But this is not a case of self-reference. No part of the definition mentions another part.

True, the I could append a clause using quotes saying that this is a definition of ‘f’ – “Df ‘f'” – but this would be a way of informing someone that this is a definition of a predicate f, and is not part of the recursion.

Self-reference and recursion are different. The one is a semantic relation between a thing and itself while the latter is a syntactic relation whereby a composite contains instances of itself (self-similarity).

I suppose the obvious rejoinder to this is that I should get round to reading Luhmann, et al. at some point!

Collier, John (2006), ‘Autonomy and Process Closure as the Basis for Functionality’, Annals of the New York Academy of Sciences, Vol 901, 208-290.