Aesthetics of Coherence in Politological Thought: Engaging Impredicativity
Simon Labrecque
University of Victoria


This essay approaches possible relationships between the fields of politological thought and logic. First, I claim that the logical problem of impredicativity (of self-referencing definitions, or of concepts that apply to themselves) offers a thought provoking site for unfolding a series of practical demands placed on students of politics (e.g. not presupposing your conclusions). Engaging this site in political and politological terms prompts a complex account of what goes on in logic, an alleged stronghold of coherence. This is significant insofar as self-described critical students of politics tend to hold fast to a simplified account of what logic is about, and quickly dismiss it as incoherent and violent. Second, trying to further texture what it can mean to take logic into account, I claim that the propositions formulated by Alfred North Whitehead on the interweaving of logical and aesthetic problems are relevant for apprehending the stakes of in/coherence at the time of writing. As two fields of "fundamental research," I think that logic and politological thought face similar challenges, especially in the form of the market-driven imperatives of productivity and usefulness. I propose that scholars working in those fields (and others) seriously consider possibilities of alliances.



Under this clumsy title, I would like to offer a few remarks on the importance of coherence and incoherence as co-constitutive notions operating in contemporary cultural, social, and political thought, and in what I will call politological thought. These remarks are deployed in two principal sections. Each addresses this general claim: in/coherences function both logically and aesthetically. Thinking the implications of qualifications of in/coherence requires the appreciation of compositions, and this is what logics and aesthetics involve. The first section deals with a strong demand in doctoral research, that of being both coherent, if not systematic, and that of being interesting, if not original. The problem of impredicativity can play a role in how this doubled demand is dealt with in politological compositions. The second section presents claims on in/coherence by Alfred North Whitehead. It considers the possibility, plausibility, and interest of challenging alliances.

A. Scholarship as Composition

1. Politological Thought

Importing a francophone usage, I name politology the scholarly study of political practices, and politologists (politologues) students of politics. I hold politological thought to be more adequate than political theory, political philosophy, and political thought, to name the practices with which I am concerned.

The expressions "political theory" and "political philosophy" are used in an intertwined series of claims on just what it is that a number of scholars are doing. Institutionally, political theory is a subfield of political science and political philosophy a subfield of philosophy that, in philosophy departments, often takes the form of moral philosophy. That politics has very little if anything to do with morality and ethics (a claim canonically attributed to Machiavelli's oeuvre, read as expressing the "rupture" marking Western modernity as such) has been held as the criteria according to which political theory and political philosophy differentiate themselves. The first welcomes the proposition as an axiom or lemma; the second tends to deplore its widespread if implicit acceptance. Another line of thought poses that political theory is a search for a, or for the demonstrably better explicative account of politics -- it thereby participates of the logic of social-scientific inquiry -- while political philosophy would hold fast to the thought that any criterion of betterness is already a political site involving historically contingent forms of life. In any case, these are well-trodden routes grasped through antagonistic metaphysics.

Political thought names something like a division of thinking itself (if there is such an "it"), and is thus not limited, in principle, to academic or scholarly practices. No one needs theorists or philosophers to think politics or to think politically. This proposition echoes Gilles Deleuze and Félix Guattari's assertion that

[philosophy] is not reflection, for nobody (personne) needs philosophy to reflect on anything: we (on) believe we give a lot to philosophy in making it the art of reflection, but we take everything away from it, since mathematicians as such have never awaited philosophers to reflect on mathematics, nor artists on painting or music; to say that they then become philosophers is a bad joke, given the extent to which their reflection belongs to [or is constitutive of] (appartient à) their respective creation (Deleuze and Guattari, 1991: 11; my translation).

Practices dealing with the qualification of political thought tend to affirm that any thinking whatever is political, or at least that thinking can and should be held to express political aspects, dimensions, affects, effects and conditions, and that a scholarly study of this political quality of any and all thinking is possible, plausible, and interesting. This is expressed through claims to the effect that thought is always embedded in and modulating relations of power and authority, distributions of sense-perception and sense-making, and that politics is a condition of thinking as a worldly activity. The polemical determinations of who is qualified and who and what are deemed unqualified to sense and express anything important for configurations of life in common when, where, and how, might be the question par excellence for practitioners and students of politics (Rancière, 1995). However, the study of explicit claims on politics is neither the whole of political thought, nor a simple part of practices of thought, if the latter are political by definition.

The delimitation of what practices are at issue -- of what exigencies and obligations they involve as practices (see Stengers, 2006) -- depends upon what is put under the equivocal terms theory, philosophy, and thought, and under the polemical qualifications political, apolitical, etc. It makes a difference, for instance, whether what is apprehended is "the political" as a foreclosed realm, or co-constitutive processes of politicization and depoliticization through which the problematization of a series of sites as politically important multiplicities requires the disqualification of others as politically insignificant. Using the term politological thought is to attempt to explicitly take into account the differentiation of scholarly and un-scholarly practices of political thought as a problematic process. This is a relevant move, as contemporary scholarship suggests that no epistemological "demarcation criterion" endures with authority, and that theory, philosophy, and thought are sites of politicization and depoliticization. This usage may prompt expressions of exigencies and obligations that are deemed important, politically and politologically.

Throughout universitary bubbles, one will encounter allegations that this or that account does not count as "proper scholarship," that this or that scholar (or discipline) by name is only that, an institutionally entitled writer (or field) doing something else than scholarship -- something akin to poetry, maybe, for those who equate this name with a lack of rigor; or something like philosophy, for those who underline the creative aspect of conceptual acts; or something akin to politics, for those who hold that scholarship requires an "objectivity" that prevents the constant application of a term like "political" to any practice taking politics as its subject. Once it is claimed that everything is political, is it not the case that nothing can then be held as becoming political in a strict sense? The proliferation of all-encompassing claims seems prevalent in "critical" scholarship. Is it not obvious that "proper" scholarship, for its part, demands a commitment to a type of coherence that rules out the generalized application of concepts to themselves, lest all that is iterated are tautologies? In contemporary conjunctures, is not the Academy (if "it" can be named in the singular) endangering an already unstable capacity to sustain claims to the production of important knowledge, while "the usefulness of useless knowledge" (Flexner, 1939) appears, or remains, at odds with the imperatives of the day? But is it not also clear that the most appealing politological compositions form challenging, circular accounts that seek to modulate what count as politically important matters?

2. Exemplifications

The above questions are, I believe, live problems for students of politics engaged in doctoral research who have to respond to the formal demands of pertinence, novelty, and rigor. The present remarks try to engage configurations of in/coherence in contemporary conjunctures because of a phrasing that insistently imposed itself while researching the workings of the notion of prevalence in Western politologies. This research, which is part of a broader project on aesthetics of politics and the problem of distributions of importance, can usefully exemplify what is at issue in considering scholarship as a practice of composition that relates to singular exigencies and obligations put under the signs of in/coherence.

From the inaugural (read: Greek) assumption that politics is about there being perceived rulers and ruled, to contemporary claims on the polemical, tactical, and dissensual character of occasions that qualify as politically significant, through the rhetorical trope of critique positing a dominant mode of thought that is then to be displaced, the endurance of the motif of necessarily transitory yet structurally inevitable prevalences is remarkable in Western politologies. Engaging this notion leads to the conclusion -- which is also the inspiration that prompted the engagement -- that prevalence is itself prevalent. As an example, take an apprehension of in/coherence drawn from the statements around which this conference is gathering. The "Narratives" thematic node has been presented thus:

Narratives form horizons of consciousness: while they open up some ways of relating, they simultaneously close off the possibility of others. Proposals around this theme explore how the norms of "good," i.e. coherent, narrative correspond to the dominant ideologies of our time (capitalism, neoliberalism, colonialism and so on). We also look for contributions that address the possibilities for new genres and narratives to reject the norms of efficiency and coherence. (csptconference2012.wordpress.com; my emphasis)

These lines describe coherence as a prevalent "norm" in cultural, social, and political thought, and implicitly, in politological thought. This is a polemical gesture, for one could just as well argue that the embracing of disarticulation, fragmentation, non-linearity, contingency, and the valorization of practices of displacement, disruption, interruption and suspension--"i.e. incoherence"?--have been texturing narration for decades, even centuries (e.g. Rancière, 2011). One might also advance that "the dominant ideologies of our time (capitalism, neoliberalism, colonialism and so on)" are deeply incoherent in one respect or another, and that they even "feed" on discrepancies, crisis, contradiction, etc. Such assertions make up a large part of what is published under the heading of critical scholarship, be it in sentences of the type "if we held a coherent view of x, then we would do y, not z," or when one endeavors to "reconstruct" an obscured coherence or to "expose" some incoherence. One could further claim that "the binary reduction of ‘coherence versus incoherence'" is the prevalent way in which in/coherence is thought in contemporary conjunctures -- unless what prevails, today, are attempts at bypassing this "binary reduction."

These considerations show just how assessing what mode of thought, expression, and action can be apprehended and qualified as prevalent (or dominant, hegemonic, crucial, etc.), if there is one, is the occasion of much polemics, a site of politics. If only in that sense, prevalence is prevalent in contemporary Western politological thought. Such a claim has a certain rhetorical force, but can it be reduced to "mere rhetoric"? Is it simply a symptomatic expression of a language-centered mode of scholarship that is itself prevalent in some "critical" circles and that could be made more significant, if only less attention was paid to wordings?

3. Impredicativity as a Problem

Claims like "prevalence is prevalent" make sense, although a certain sharpness of expression and style may be lacking. "Prevalence" functions as a subject and "prevalent" as its predicate. To know what difference it makes to use "prevalent" to qualify "prevalence," however, the latter must be constructed in a way that can account for this qualifying usage. In that sense, the two terms suppose one another. This construction must be capable of including the possibility of a historically prevalent character of prevalence. However, it can be argued that this reasoning is circular. Circular reasoning is held as a logical fallacy, a sign of incoherence. More broadly, "vicious circles" are matters of concern in doctoral research, not least because students risk facing the dismissive charge that a work is presupposing its conclusions. These claims are problematic, at the very least.

There exists a rather displeasing sounding substantive describing the relation of concepts being applied to or presupposing themselves: impredicativity. This notion is explicitly dealt with in fields that seldom seduce students of politics: mathematical logic and analytic philosophy (e.g. Landini, 2010; Linnebo, 2010; Cassou-Noguès, 2004). I contend that this is not a reason for dismissing it. Quite the opposite: I advance that engaging impredicativity can be useful to address the charges of in/coherence leveled against contemporary politologies, first because coherence tends to be deemed secured in, by, and through logical investigations, but also because this very attention to logic(s) might be qualified rather quickly as irrelevant by those interested in so-called pressing issues of violence and radical thinking on modes of expression. The problematic quality of impredicativity complicates these assumptions, if only because violences are indeed at play in logics.

I do not have the technical competence to present a systematic account of the stakes of impredicativity in mathematics and logic, nor to draw on such an account to assess the plausible magnitude of their "commonsensical" consequences for politology. I can, however, tell a story of the problematization of this notion, which I hold to hint at interesting avenues for further engagements with in/coherence.

Throughout the 19th century, the edifice of mathematics was troubled by the discovery -- or creation -- of consistent new, non-Euclidian geometries. They showed that what were once held as universal, atemporal and aspatial, truths were in fact constructed. In some of these geometries parallel lines could meet, for instance; the axioms of Euclid were only one set of axioms amongst many other possible, coherent ones. Mathematics showed itself to be a game with operative signs and symbols -- a rigorous game, but nonetheless only one among other equally valid, possible, and interesting ones. The foundations of arithmetic were soon put into question as well, following the development of set theory and the mathematics of infinities by Georg Cantor and others. The half-anxious, half-hopeful tonality of these investigations into the foundations of mathematics is exemplarily expressed in David Hilbert's 1900 address to the International Congress of Mathematicians in Paris (Hilbert, 1902). At that time, Cantor's set theory was found to lead to contradictions, or paradoxes, the most famous of which is called Russell's paradox (it halted Gottlob Frege's work on the foundation of arithmetic). Russell's paradox involves "the set of all sets that are not members of themselves": if this set is a member of itself, then it is not, for it is not not-a-member-of-itself; if it is not, then it is a member of the set of all sets that are not members of themselves, i.e. of itself.

In 1906, Henri Poincaré wrote: "the definitions that must be regarded as non predicative are those that contain a vicious circle" (1999: 163; my translation; emphasis in original). This assertion was made in a debate between Poincaré and Bertrand Russell, among others, on the form and provenance of logical paradoxes. As Oystein Linnebo (2010) puts it, "[a] definition is said to be impredicative if it generalizes over a totality to which the entity being defined belongs. Otherwise the definition is said to be predicative.. For Poincaré, the former are "illegitimate" in mathematics because "[a] definition that contains a vicious circle does not define anything (ne définit rien)" (1999: 164). In that sense, the expression "impredicative definition" is akin to a contradiction in terms. More precisely, such propositions should be excluded from the foundations of mathematics. In Principia Mathematica, Russell and his mentor, Alfred North Whitehead, shared this view while acknowledging that classical mathematics often rely on impredicative definitions. Their solution was to adopt the Axiom of Reducibility, which "says (loosely speaking) that every impredicative definition can be turned into a predicative one. However, this axiom has struck most people as intolerably ad hoc" (Linnebo, 2010).

Kurt Gödel, for his part, proved that Hilbert's project of a completely decidable and consistent formal system founding arithmetic was impossible, and he later argued that impredicativity is problematic only insofar as one adopts a "constructivistic (or nominalistic) standpoint" with regard to the existence of mathematical entities.

In this case there must clearly exist a definition (namely the description of the construction) which does not refer to a totality to which the object defined belongs, because the construction of a thing can certainly not be based on a totality of things to which the thing to be constructed itself belongs. If, however, it is a question of objects that exist independently of our constructions, there is nothing in the least absurd in the existence of totalities containing members, which can be described (i.e., uniquely characterized) only by reference to this totality.... It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence. They are in the same sense necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions and in both cases it is impossible to interpret the propositions one wants to assert about these entities as propositions about the "data," i.e., in the latter case the actually occurring sense perceptions. (Gödel, 1983 [1944]: 456-7)

It is now claimed that Gödel's defense of impredicativity "is the source of what is probably the dominant contemporary view on the matter," namely "that impredicative definitions are legitimate provided one holds a realist view of the entities in question" (Linnebo, 2010). In other words, something like a minimal pragmatic Platonism seems to prevail in mathematical practices. This Platonism is pragmatic, or better, Kantian, in that ultimate questions on the actual existence of mathematical objects "in themselves" are explicitly put aside, left unanswered, and might well be unanswerable -- what "truly" matters is that mathematical research can and does persist, under the sign of a forcefully enabling "as if" (als ob).

Despite its limited domain of "immediate" importance, the rejection of impredicative definitions and concepts is reiterated (if only by analogy) in multiple demands to expulse self-referencing notions and conclusions from scholarly research. The identification of a "vicious circle" might well be deemed a sufficient reason to refuse a piece of work as "proper scholarship" -- or tangentially, the fact that it will probably not, in practice, be deemed a sufficient reason, is arguably the sign that what is done nowadays under the name of scholarship, maybe especially in philosophy broadly understood, e.g. in UVic's Cultural, Social and Political Thought and similar interdisciplinary networks of thought, is deplorably unconcerned with the imperatives and rules of logic, in the singular [1]. But engaging impredicativity as it has been dealt with in mathematical logic also suggests that, if one is to hold a "coherent" constructivist or nominalist view, one would have -- at least according to logicians, and to Gödel in particular -- to find impredicativity problematic. The fact that impredicativity as such appears to be of no interest whatsoever in most politological research that claims for itself a constructivist or nominalist quality should thus raise the question of the limits of the coherence of such works: are they not ultimately realist or Platonist, in the image of Gödel's own philosophy? What would it mean to acknowledge this quality? It is my contention that the increased attention recently enjoyed by Whitehead's late works throughout contemporary "critical" politological networks counts as an expression of such an acknowledgment. After all, is not Whitehead's most famous proposition that "[t]he safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato" (Whitehead, 1978 [1929]: 30)?

B. Whitehead and In/Coherence

1. Propositions

Alfred North Whitehead has been attracting a fair amount of scholarly attention in recent years. A number of "stars" of contemporary politological thought explicitly care for him -- especially for his late writings, after his "passage" from mathematics and epistemology to philosophy and cosmology -- in a way that seems irreducible to the researches in process studies, and especially process theology, that have been drawing on his work for decades (for a taste of the "stars'" engagement, see or listen to Butler, 2009; Latour, 2008; Stengers, Rorty, and Haraway, 2006; and Stengers, 2002). This should not be held against the British mathematician-philosopher. Of course, it should not be held as a sufficient reason to care either, even if the mapping of "influences", inspirations, and authorities that participate of configurations of contemporary politologies is a matter of concern for many students of politics and politological thought. I contend that Whitehead made interesting propositions on the problématique of in/coherence. This is why I wish to make them heard (or rather: read) accordingly -- if only for the sharpness of his style, Whitehead is worth citing at some length. I believe that taking his propositions into account might usefully inform the work of alliance-weaving that constitutes an important dimension of politological practices as political practices.

1.1 Process and Reality

To this day, Whitehead's is arguably the last philosophic system worthy of the name composed in the West. Process and Reality, first published in 1929, is the most rigorous expression of his "philosophy of organism" (Whitehead, 1978 [1929]). From the outset, in/coherence is a matter of concern:

This course of lectures is designed as an essay in Speculative Philosophy. Its first task must be to define "speculative philosophy," and to defend it as a method productive of important knowledge. Speculative Philosophy is the endeavour to frame a coherent, logical, necessary system of general ideas in terms of which every element of our experience can be interpreted. By this notion of "interpretation" I mean that everything of which we are conscious, as enjoyed, perceived, willed, or thought, shall have the character of a particular instance of the general scheme.... "Coherence," as here employed, means that the fundamental ideas, in terms of which the scheme is developed, presuppose each other so that in isolation they are meaningless. This requirement does not mean that they are definable in terms of each other; it means that what is indefinable in one such notion cannot be abstracted from its relevance to the other notions. It is the ideal of speculative philosophy that no entity can be conceived in complete abstraction from the system of the universe, and that it is the business of speculative philosophy to exhibit this truth. This character is its coherence. (3; my emphasis)

By specifying that his use of the term coherence "does not mean that [the fundamental ideas of the scheme] are definable in terms of each other," but that they nonetheless "presuppose each other so that in isolation they are meaningless," Whitehead both acknowledges and addresses the problem of impredicativity as it may apply to philosophical propositions, and not only to mathematical definitions. His are ontological, even cosmological claims: there exists a system or scheme of general ideas that can account for every instance of experience -- he is composing one, and calling for the composition of a multiplicity of others. It should be noted, however, that Whitehead considers that "the chief error in philosophy is overstatement. The aim at generalization is sound, but the estimate of success is exaggerated" (7). The two main forms of overstatement are (a) what he famously called "the fallacy of misplaced concreteness," and (b) "a false estimate of logical procedure in respect to certainty, and in respect to premises," which is explained by how "[p]hilosophy has been misled by the example of mathematics" in denying that "the accurate expression of the final generalities is the goal of discussion and not its origin" (8). If "[t]here is no first principle which is in itself unknowable, not to be captured by a flash of insight," it is also the case that "[p|hilosophers can never hope to finally formulate these metaphysical first principles. Weakness of insight and deficiencies of language stand in the way inexorably" (4). The road traveled by Whitehead diverges radically, here, from that of other mathematician-philosophers who defend so-called analytic philosophy against its supposedly "irrational" outsides!

Whitehead addresses in/coherence, and detaches it from strictly logical concerns, by describing how it operates in the practices of philosophical thought:

The requirement of coherence is the great preservative of rationalistic sanity. But the validity of its criticism is not always admitted. If we consider philosophical controversies, we shall find that disputants tend to require coherence from their adversaries, and to grant dispensations to themselves. It has been remarked that a system of philosophy is never refuted; it is only abandoned. The reason is that logical contradictions, except as temporary slips of the mind -- plentiful, though temporary -- are the most gratuitous of errors; and usually they are trivial. Thus, after criticism, systems do not exhibit mere illogicalities. They suffer from inadequacy and incoherence. Failure to include some obvious elements of experience in the scope of the system is met by boldly denying the facts. Also while a philosophical system retains any charm of novelty, it enjoys a plenary indulgence for its failures in coherence. But after a system has acquired orthodoxy, and is taught with authority, it receives a sharper criticism. Its denials and its incoherences are found intolerable, and a reaction sets in./ Incoherence is the arbitrary disconnection of first principles. In modern philosophy Descartes' two kinds of substance, corporeal and mental, illustrate incoherence.... [T]his [Cartesian] system makes a virtue of its incoherence. (6)

For Whitehead, "[t]he attraction of Spinoza's philosophy lies in its modification of Descartes' position into greater coherence." The scheme he is himself composing, "[t]he philosophy of organism[,] is closely allied to Spinoza's scheme of thought. But it differs by the abandonment of the subject-predicate forms of thought, so far as concerns the presupposition that this form is a direct embodiment of the most ultimate characterization of fact" (7). The application of the fundamental propositions of first-order predicate logic to accounts of experience would, on the contrary, reinforce this form of thought which has shown to be inadequate in many respects.

In Whitehead's system, the "ultimate which is actual in virtue of its accidents" is named "creativity." The universe is populated by actual entities and eternal objects. Coherence plays a crucial part in this ontological claim: from a neutrino to a gale, from individual humans to a murmuration, to cohere -- in an almost etymological sense, i.e. co-haerere, "together-stick" -- is the prevalent mode of processual existence. This is the sense of coherence involved in the 22nd (of 27) "category of explanation": "(xxii) That an actual entity by functioning in respect to itself plays diverse rôles in self-formation without losing its self-identity. It is self-creative; and in its process of creation transforms its diversity of rôles into one coherent rôle. Thus ‘becoming' is the transformation of incoherence into coherence, and in each particular instance ceases with this attainment" (25; my emphasis). The next category of explanation reads: "(xxiii) That this self-functioning is the real internal constitution of an actual entity. It is the ‘immediacy' of the actual entity. An actual entity is called the ‘subject' of its own immediacy." These are the types of claims that are of interest for contemporary politologists such as Judith Butler. More generally, "[t]he coherence, which the system seeks to preserve, is the discovery that the process, or concrescence, of any one actual entity involves the other actual entities among its components. In this way the obvious solidarity of the world receives its explanation" (7). This claim evokes Leibniz's proposition, in the Monadology, that any individual monad expresses the entire world. It explains the attention that Deleuzian scholars like Isabelle Stengers have been paying to Whitehead. But what can be done with these propositions in politological thought?

1.2 Modes of Thought

"Thinking with Whitehead" (Stengers, 2002), politically, remains a path to be explored, a spoor to pursue. This is one of the (surely, far too numerous) avenues I am attempting to explore in my doctoral dissertation-to-come. The work is tentatively titled Aesthetics of Politics: Refolding Distributions of Importance. In a nutshell, it argues (a) that the problem of importance, of what matters and what does not matter politically, is a "point of heresy" in politological thought, a question through which different accounts, theories, philosophies, sociologies, etc., differentiate themselves, and (b) that an aesthetics of politics, i.e. the historically constructed distributions of what is visible and invisible, sayable and unsayble, thinkable and unthinkable, and of who is deemed to have the competence to see and the capacity to think and say anything that matters for configurations of life in common, act as prerequisites in the determination of distributions of political importance and unimportance. Different politologies constitute different modes of political thought operating through both logical and aesthetic concerns.

Whitehead's Modes of Thought (1968 [1938]) is a useful site for this research because of the manners in which it constructs an original notion of importance that is irreducible to the languages of (inter-)subjective judgments, decisions, and valuations. Since the latter languages are arguably prevalent in contemporary politologies -- to the question: what counts politically?, the most widely accepted response is: it all depends on what more or less relational individual human subjects think on the matter -- I feel I have to ask if and how these accounts can be accounted for otherwise than by themselves; in other words, I have to ask if I can avoid impredicativity in the story I am exploring and composing. Whitehead's notion of importance is presented as one of those "ultimate" notions "incapable of analysis in terms of factors more far-reaching than themselves" (1968: 1). It is thought-provoking precisely because it is relevant, in principle, for an indefinite multiplicity of processual entities that include but are not limited to humans; it can, for example, account for the nonhumans "within" or "between" humans; cells, atoms, bacteria or ideas; this virus imports for that cell, here and now. This notion of importance is itself important, I argue, when one takes into account recent attempts at "including nonhumans in political theory" (Stengers, 2010; see also the works of Bruno Latour, Eugene Thacker, Michel Serres, Peter Sloterdijk, and Gilles Deleuze). If this importance has its logic, it is first and foremost an aesthetical notion.

Why insist on aesthetics? Is this not a gesture that has continuously been leading to the avoidance of real-pressing-political-issues, and not least away from urgent questions about violence and the problem of its (if "it" is an "it") minimization, redirection, modulation, etc.? There is an argument to be made about the aesthetic quality of violence, insofar as what is at issue under this term are relationships between sense and sense, sense-perception and sense-making, configurations of prevalence, emancipation, temperament, friction, endurance, etc. In other words, violence is experienced, and most Western politologies rely on an (Kantian) apprehension of experience as an aesthetic matter, if only because experience "necessarily" occurs "in space and time," or through spaces-times. There is another, related argument to be made about the violence of aesthetics, with regard to how manners, styles, or elegance, for instance, participate of modulations of violence, of forces of affection, perception, conceptualization, etc. The disconnection of violence and aesthetic is arbitrary, in that sense, as is the disconnection of violence and logic; indeed, there exists a type of violence related to the positing of a singular, universally valid logic, of one form of coherence and one prevalent mode of expression that all propositions should conform to.

Whitehead's Modes of Thought is again useful for engaging this relationship between logic and aesthetics, if only because he suggests that "the analogy between aesthetics and logic is one of the undeveloped topics of philosophy" (1968: 60).

In the first place, they are both concerned with the enjoyment of a composition, as derived from the interconnections of its factors. There is one whole, arising from the interplay of many details. The importance arises from the vivid grasp of the interdependence of the one and the many. If either side of this antithesis sinks into the background, there is trivialization of experience, logical and aesthetic. The distinction between logic and aesthetic consists in the degree of abstraction involved. Logic concentrates attention upon high abstraction, and aesthetics keeps as close to the concrete as the necessities of finite understanding permit. Thus logic and aesthetics are the two extremes of the dilemma of the finite mentality in its partial penetration of the infinite. (60-61)

Whitehead ends his first three lectures by continuing this reflection. Note that if coherence was characterized as "the great preservative of rationalistic sanity," these remarks mobilize the arguably related lexicon of understanding-as-penetration:

By reason of the greater concreteness of the aesthetic experience, it is a wider topic than that of the logical experience. Indeed, when the topic of aesthetics has been sufficiently explored, it is doubtful whether there will be anything left over for discussion. But this doubt is unjustified. For the essence of great experience is penetration into the unknown, the unexperienced. Both logic and aesthetics concentrate on the closed fact. Our lives are passed in the experience of disclosure. As we lose this sense of disclosure, we are shedding that mode of functioning which is the soul. We are descending to mere conformity with the average of the past. Complete conformity means the loss of life. There remains the barren existence of inorganic nature.... There is one moral to be drawn. Apart from detail, and apart from system, a philosophic outlook is the very foundation of thought and of life. The sort of ideas we attend to, and the sort of ideas which we push into the negligible background, govern our hopes, our fears, our control of behaviour. As we think, we live. This is why the assemblage of philosophic ideas is more than a specialist study. It moulds our type of civilization. (62-3)

Beyond the liberal politics of civilization privileged by Whitehead himself, I believe his writings can be interesting actants in the formation of contemporary alliances.

2. Concluding Alliances

These remarks have been concerned with indicating some avenues of thought around in/coherence by complicating what counts as a scholarly account, when the demands of pertinence, novelty and rigor put on doctoral research are formally reiterated, while in practice what will count as scholarship worthy of the name (of a diploma) remains a contingent matter, and surely not the most important one, politically. Engaging impredicativity shows that even in the fields of logic and mathematics, perceived as strongholds of coherence and rigor, the legitimacy of different modes of thought and expression is a highly polemical site. Presenting some of Whitehead's propositions around in/coherence has suggested the usefulness of considering this problématique on different planes: epistemological, cosmological, aesthetical -- political. In his 1900 address, Hilbert began by addressing the question of what is a good problem. His response was about aesthetics: "a mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock at our efforts. It should be to us a guide post on the mazy paths to hidden truths, and ultimately a reminder of our pleasure in the successful solution" (1902, 438). Practices of composition play a crucial role in scholarship, in why it is sometimes deemed worth it to persist, and sometimes not. The fact that a mathematician-philosopher writes: "I see no reason to believe that the stretch of Bertrand Russell's mind, or of Wittgenstein's mind, or of Carnap's mind, has attained the limits of insight or expression possible in the evolution of intelligent beings. They are bright boys, good representatives of a stage of rationalism, but nothing more" (Whitehead 2011 [1936], 72), suggests that alliances might be possible with those working in fields we sometimes like to dismiss.

This is particularly important in a series of conjunctures -- let's say: at the time of writing -- marked by ceaselessly reiterated demands for productivity and usefulness, or rather, for very particular types of productivity and usefulness, tailored to market imperatives -- or to very particular interpretations thereof. Politological thought, logic, and a multiplicity of other fields of research and knowledge production appear to me to be in the same boat.

Notes

[1] A version of this argument has been insistently reiterated by French philosopher Jacques Bouveresse, especially in his short, incisive treaty Prodiges et vertiges de l'analogie. De l'abus des belles-lettres dans la pensée (1999), published in the aftermaths of the "Sokal Affair." This book is concerned with the defenses mounted by the writers-philosophers attacked by the physicist. Bouveresse sees their counter-attack as a form of obscurantism, privileging affects and seduction over clarity of expression and rationality of principles. Interestingly, Bouveresse takes as his principal site of argumentation the uses (and abuses) of Gödel's incompleteness theorems in the "postmodern" thought of people like Régis Debray. In this respect, it is noteworthy that Gödel himself seemed much more open than Bouveresse appears to be to the analogical use of his theorems in relation to philosophical, social, and religious problems, i.e. outside the restricted field of strictly defined formal systems: "Analogy in general is, for Gödel, a totally serious mode of reasoning. The logician also believes in the existence of the devil, of which he at least proves the possibility on the basis of his incompleteness theorem" (Cassou-Noguès 2007, 39; my translation -- this book is based upon researches into Gödel's archived notes at the Institute of Advanced Studies, Princeton).

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Bio

Simon Labrecque is a PhD candidate in political science and cultural, social, and political thought at the University of Victoria. His doctoral research concerns the problem of the importance of what matters and what does not matter politically and the aesthetics of politics that act as this distinction's prerequisite.

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