As has been noted in discussions of Nelson Goodman’s theory of worldmaking, for Goodman worldmaking is always a product of various operations on pre-existing worlds—worlds are made from other worlds,[1] a stance which I will refer to as his ‘worldmaking thesis’. Moreover, Goodman’s orientation is marked by a skepticism (or perhaps an agnosticism [2]) about the difference between the multiple and the one—in the sense that, for Goodman, monism and pluralism are practically indistinguishable.[3] In this paper I will briefly consider some problems and alternatives to the strict dependency of forms of life on ‘well-made’ worlds—a dependency that appears to follow from many of Goodman’s characterizations. Starting from the recognition that some forms of life are uninhabitable and ‘worldless’—despite being clearly ‘made’ from other worlds—I will describe a hypothetical construct for this inhibition of worlds and its relation to a latent incompleteness in the logic of Goodman’s worldmaking framework. In articulating this world-inhibiting construct—which I describe as ‘statelessness’—I will explore how the threat of philosophical incoherence posed by logical and political incompleteness of the ‘stateless’ might be resolved through a spatialization of the worldmaking calculus.
In their mutual transformability, Goodman’s worlds might appear to be warding off incompleteness, implicitly supposing that worlds might be mutually transformed in perpetuo at a materially compatible level of abstraction. When considered in terms of the condition of mutual translatability/compatibility—i.e. the Goodmanian ‘worldmaking thesis’ that a world is always a remaking of another world—any given world may have a potential connection to a ‘future’ world as a material source for the latter’s composition. This is not to say that the worlds are all equally of the same ‘order’ (in the sense of first- or second-order logic, i.e. logical language and metalanguage), but rather that there is some possible morphism between them—or that there is no logical barrier of non-enumerability between the respective domains of their elements. I suggest that Goodman’s idea that worlds are always made (or ‘re-made’) out of other worlds risks philosophical incoherence—if the Goodmanian assumption of algebraic compatibility between worlds is not restrained, one confronts the logical issues posed by totality. [4]
While in principle logical incompleteness may be a valid consequence of a distinct philosophical orientation,[5] in Goodman’s case it threatens to be especially problematic because of Goodman’s agnosticism about any strong distinction between monism and pluralism. If monism and pluralism are functionally equivalent, and if any materially compatible class of world-models can be successively (whether transitively or not) deformed into any other world-model in that class, then one risks being left without any capacity for theorizing paradox or incompleteness—indeed, one disavows the problem of incompleteness. Patricia Reed renders the politico-logical problem at stake here in terms of “insuppressible frictions” existing within a world. Of the ever-present possibility of incompleteness in worlds, Reed writes: “Recognizing the threshold of insuppressible frictions germinating from within an existing world, are equal to making the incompleteness of that world intelligible. Correspondingly, to recognize the incompleteness of a world is to re-cognize its end.”[6] Reed approaches the problem of a world’s “end” from a temporal standpoint, speaking of a broader context of futurity. [7] Yet we can extend this idea of a world’s temporal “end” to what I will elaborate below as its ‘nontranslatability’—this is a world’s partial exit from the domain of the various functions of worldmaking operations. There is a situation in which a world’s material can no longer be called upon for further elaboration; it defies any status as origin and retreats from the image of thought and transitional state of identity that would be necessary for its form to be re-shaped into a different, other world. One example of this collapsed/collapsing world, I propose, is apprehended from within the condition I will call the condition of ‘statelessness.’
In an attempt to conceptualize points of incompleteness that get suppressed in Goodman’s system—when worldmaking uses operations that set-up false equivalence (i.e. material incompatibility / contrariety) between worlds—I will introduce the idea of statelessness as political and logical model of the translational failure between worlds. Being forced to navigate conditions that are continually materially incompatible with one’s subject position –i.e. conditions of perpetual contrariety—creates an experience of being without a world and of having a form of life for which no world can be built, despite being amidst various other world-forms. An example from the political realm is literal statelessness, in the sense of someone who has no national affiliation, such as when a country is no longer recognized in international law and an individual is a perpetual alien. However one can also consider ‘functional’ (effective, formal) statelessness the case of those who are criminalized by their own nations, perhaps forced to exist as refugees or otherwise perpetually hide. There are yet other cases of this ‘formal’ statelessness that can take place entirely internal to one political body—consider, for instance, when an individual’s existence gets continuously miscategorized by governing bodies. This is a form of chaos in which the bureaucratic frames of reference (each of which can reasonably stand as a distinct world) are constantly shifting—one frame is applied to a situation that was generated within another. This sounds abstract, but its real instances look like statelessness—one example is being falsely accused of a crime that really happened and bearing the prison sentence of some stranger who really did the transgression (and U.S. judicial history is rife with examples of this). Another example is an ill person who is criminalized because they are too poor to participate in the health system. In short, in this broad logico-political phenomenon of ‘statelessness’, the political body continually commutes one status into another; yet it always fails to apply a category of the adequate kind that would ‘solve’ the problem. This is a form of life, yet it cannot be inserted into the framework of a world despite the fact that it builds off the implicit structures provided by other worlds—It bends to them, responds to them, reflects and deflects them. How do we approach this state of perpetual expulsion from within Goodman’s system?
This abstract condition of ‘statelessness’ is not fundamentally an experience of being ‘outside’—it is a condition of movement, of transversal motion, rather than exclusion. Were we to reason about the Goodman’s ‘worldmaking thesis’ along the lines of a world wrought by exclusion, we might risk invoking a private language fallacy (for instance, if we understood ‘nontranslatability’ as an unintelligible world) while trying to critique Goodman’s worldmaking thesis. This is not, however, what I aim to do here, and I would acknowledge that an argument relying on the unintelligibility of a possible world would suffer from being circular. (For, by Goodman’s lights, we might assume that a world that can’t be made intelligible is simply moot to begin with.) By contrast, the abyss of the Goodmanian picture I’m describing is not a state of exception but rather the chimera of form—a shifting sand of continually changing paradigms. To the extent that the stateless position appears compatible with the political or logical frameworks it exceeds, it is a diagonalized compatibility, in the sense of a forcing of correspondences between domains of different orders that do not have mathematical grounding. The individual becomes this diagonal excess. Just as Badiou describes the “diagonal” generating a space of “excess”,[8] the stateless individual assumes the paradoxical position of being both outside and excessive relative to the inside of the world or system. After being rendered in the first, he is judged by the second, then condemned to live in the third, being passed along through a labyrinth of incongruous models. This is different than Agamben’s picture of the logic of exception. My view of statelessness instead formalizes the ‘excluded’ element of the political world as a residue of other worlds—‘excluded’ individuals are transverse elements rather than ‘encamped’ elements that are paradoxically inside and outside. [9] Moreover, this transversality formalizes someone who is denied futurity (cf. Patricia Reed), as I will describe below.
Crucially, ‘statelessness’ here is a form of life constructed through various other worlds, but being unconstitutable as a world through any of them, and existing only as a residual excess. Given this basic notion of ‘statelessness’, I now hope to show how this limit case can be addressed by incorporating a spatial, topological logic into the Goodmanian picture. To the extent that Goodman’s idea of worldmaking presupposes some translatability between worlds, we can hypothetically draw up an implicit calculus up of worldmaking. Suppose we did draw up this calculus, consisting of all the possible algebraic operations Goodman draws up in his Ways of Worldmaking (supplementation, ordering, weighting, and so on[10]). This would be a calculus for the transmutation of any one world into another. As I suggested above, Goodman’s model of formalizing worlds, which highlights continuity in the world (i.e., logically, completeness, which Goodman tends to render in the terminology of the “well-made world”[11]) and, generally, homomorphism between different world-structures, can be understood as topological or spatial in nature—in addition to the algebraic character granted by its calculus of transmutations. Drawing out a latent but suppressed presence of a ‘topological’ facet of Goodman’s worldmaking model is, I suggest, the key to mitigating the threat of false equivalence in his model-theoretic transformations. Furthermore, it opens a way to dealing with the problem of ‘statelessness’ that I have set forth above.
Sustaining Goodman’s various commitments requires philosophical instruments for moderating between what Hintikka has distinguished as “language as calculus” and “language as a universal medium”. [12] Goodman’s ‘worldmaking thesis’ approximates a “language as calculus” orientation, for reasons already discussed. Conversely, his thesis about the indistinguishability of monism and pluralism is more compatible with an approach to “language as universal medium” orientation. I suggest that these views do not in fact have to be diametrically opposed. Hintikka notes of this distinction, “The term ‘language as calculus’ serves to highlight the claim that language is reinterpretable like a calculus”. [13] A consequence of Goodman’s thesis seems to be, in part, that interpretation is itself mereological—it creates part-whole relations between things, and can render changes in mereological distribution and scale—for instance, between localities to totalities. It is in this sense that Goodman can reasonably say that monism and pluralism blend together in his view. On a basic level, the Goodmanian requirement of a calculus is universal—’language’ is precisely an instrumentalization of language, its use as a calculus. Language qua calculus is the ‘universal medium’ for Goodman, in addition to being an operator of mereological redistribution.
To put this in clearer terms less specific to Hintikka’s distinction, the mitigation and compatibilization between calculus and universal medium I am proposing for Goodman’s view are akin to what Badiou outlines when he discusses how ‘locales’ operate in the context of his Logic of Worlds. Summarizing this structure in his Second Manifesto of Philosophy, he writes: “There exist many structures of this type that are not isomorphic. This diverse group is caught up in a tension between algebra and topology—between the theory of operations and that of localizations—which I have long believed to be at the core of all dialectical thought.” [14] Similarly, Patricia Reeds’s work on navigation between localities and the ‘big world’, or nested scales within the planetary, also enacts mathematical resources that enact “the dialectic between the discrete (or the particular) and the continuous (or the global)”. [15] She goes on to say, “for both thinkers [Glissant and Grothendieck], coming from disparate fields, there is no pitting of the discrete against the continuous. They each refuse this false choice, and put their efforts towards the articulation of a relational glue that upholds both discrete and continuous scales simultaneously… this results in a picture of situatedness as discretely located, but also, crucially, as inextricable from the continuous or nonuniform totality”. [16]
Ultimately, Goodman’s views on worldmaking are easier to accept if we allow that logical forms of worldmaking to form certain spaces among and through which we can navigate. This topological view also helps formulate the specific plight of ‘statelessness’, which is the transversal movement and perpetual displacement I described above. It is in this sense that we can understand the ‘stateless’ condition I have described as being a form of life that holds no space, has no space for itself, and has no position. Further, it is in this a-topological sense that statelessness can be a form of life and yet not a world—its not being a world is connected to its unnavigability, its placelessness, its non-localizability. It is, as Badiou would say in Heideggerian fashion: “not there”. [17] One problem of the ‘stateless’ world is, as Reed as put it,[18] its inevitable end—a result of its confrontation with incompleteness. In charting Goodman’s processes of worldmaking and world transformation, one has to be wary of false equivalences, in which case one would end up in a situation that Patricia Reed might categorize as inhospitable and without futurity. [19] Points of false equivalence might even be considered symptoms of the loss of Badiouian continuity offered by truths and truth-procedures. As all finite time horizons close, in the absence of futurity, one looks to the eternal, and one candidate for these is a Badiouian truth/truth-procedure[20]–one possible route to palliate the threat of ‘statelessness’ in the process of worldmaking.
In summary, in this paper, I raised the question of how we can accept Goodman’s ‘worldmaking thesis’— i.e. that the creation of a new world is always the remaking of an existing world—given that there exists a ‘stateless’ possibility of a worldless form of life created through a conjunction of other worlds. Through examples of political forms, I conceptualized how these ‘stateless’ forms of life might be inhibited from being constituted into a new world precisely due to the impingements of the already existing ones. Turning back to Goodman’s fundamental assumptions, I explained that his philosophical orientation risks being incoherent unless one can create for his system a way of mediating between ‘language as calculus’ and ‘language as universal medium.’ To do this, I considered a Grothendieck-like orientation for localizing and mediating between continuous and discrete, as well as introducing the idea that interpretation of language in Goodman’s picture has mereological potency. This led to a new rendition of worldmaking in which logical formations are also topological formations, allowing for redistributions of the logical and topological domains of worlding. In this sense too, we can note that the worldless ‘stateless’ life exists on a deserted, unlocalizable ‘plane of immanence’. [21] We know from history and our social life in the present that there exist non-worlds where the hyper-presence of separately coherent frames combine to create an indecipherable formalism—a nightmare condition that sends one continually reeling across various systems, not seen or registered or understood by any of them. Particular logics cohere to certain logical spaces. ‘Statelessness’ is not a null concept, but simply a state of immanent worldlessness, a groundless whirlwind above an immanent plane of logical space. In considering the latent spatiality of logical form we can start to imagine an alternative to such formalized anarchy.
References
[1] Goodman, Nelson. “Words, Works, Worlds”, In: Ways of Worldmaking. US: Hackett Publishing, 1978. p. 61: “Worldmaking as we know it always starts from worlds already on hand; the making is a remaking.”
[2] Ibid., p. 2: “…the issue between monism and pluralism tends to evaporate under analysis. If there is but one world, it embraces a multiplicity of contrasting aspects; if there are many worlds, the collection of them all is one. The one world may be taken as many, or the many worlds taken as one; whether one or many depends on the ways of taking.”
[3] See above footnote and associated passage.
[4] Cf. the discussion in “Introduction” of: Livingston, Paul M. The Politics of Logic: Badiou, Wittgenstein, and the Consequences of Formalism. New York and London: Routledge, 2012. pp. 3-64.
[5] Ibid. Livingston defines a class of philosophical orientations that admit incompleteness at the “Generic”—in which he includes Badiou’s framework. The thrust of my paper essentially assumes that Goodman, though often appearing to be a constructivist, in fact gains coherence through a generic framework. Goodman is not a definitively generic thinker, but his project might be rendered through an oscillation between constructivism and generic orientations.
[6] Reed, Patricia. “The End of a World and its Pedagogies”, Making & Breaking, Issue 02, 2021. p. 2.
[7] Ibid.: “…every seemingly ‘complete’ world is underwritten by a particular configuration of futurity that legislates a degree of continuous dynamism within those futural parameters.”
[8] Badiou, Alain. Briefings on Existence: A Short Treatise on Transitory Ontology. NY: SUNY Press, 2006. p. [Not legible or identified in scan]: “…mathematical thought returns unto itself under the constraint of a real sticking point or the inevitable emergence of an impossible point within its own field. This sticking point can be… of a paradoxical nature triggering excess…”
[9] Compare Agamben’s notion of ‘state of exception’ and his notion of the ‘camp.’
[10] Goodman, Nelson. “Words, Works, Worlds”, In: Ways of Worldmaking. US: Hackett Publishing, 1978.
[11] Cf. Goodman, Nelson. “Things”. In: Of Mind and Other Matters. Cambridge, MA: Harvard University Press, 1984. pp. 30-39, “Notes on the Well-Made World”.
[12] For an account of this distinction, cf. Hintikka, Jaako. “Is Truth Ineffable?”. In: Lingua Universalis vs. Calculus Ratiocinator: An Ultimate Presupposition of Twentieht-Century Philosophy. Republished in Jaako Hintikka Selected Papers, Volume 2, Dordrecht: Springer Science + Business Media, 1997. pp. 20-45.
[13] Ibid., p. 25.
[14] Badiou, Alain. Second Manifesto on Philosophy. Trans. Louise Burchill. Cambridge and New York: Polity Press. p. 39
[15] Reed, Patricia. “Orientation in a Big World: On the Necessity of Horizonless Perspectives”, e-flux journal, no. 101, Summer 2019. p. 5.
[16] Ibid.
[17] Badiou, Alain. Second Manifesto on Philosophy. Trans. Louise Burchill. Cambridge and New York: Polity Press. p. 30: “Let us take any multiplicity…. there is the fact that this multiplicity is there. Hegel was right to join a doctrine of being-there to his doctrine of pure being. The fact that a multiple is in some way localized, such that the multiple-indifference of its being is assigned to a world, goes beyond the resource of this multiple-being as thought by mathematics. A sort of impetus, topological in essence, prevents the multiple from being merely what it is since, as what appears, it is there that it has to be what it is.”
[18] Reed, Patricia. “The End of a World and its Pedagogies”, Making & Breaking, Issue 02, 2021. p. 2.
[19] Ibid. Cf. Reed’s discussion of “underlying futural structures” and “futural parameters”.
[20] Badiou, Alain. Second Manifesto on Philosophy. Trans. Louise Burchill. Cambridge and New York: Polity Press. p. 24:” Truths, and truths alone, unify worlds. They transfix the disparate composites of bodies and languages in such a way that, for a split second or sometimes longer, these are, as it were, welded together. This is why all truths introduce, within the play of established opinions, a sudden change of scale. That which is One in terms of mundane closure attains, through the welding of worlds, a vast superior unity.
[21] Cf. Prado, Bento Jr. “The Plane of Immanence and Life”. In: Khalfa, Jean, ed. Introduction to the Philosophy of Deleuze. London and New York: Continuum, 1999. pp.9-25. Additionally, what I refer to as ‘unlocalizability’ might be compared to the Deleuzian concept of ‘deterritorialization’.