John’s nice post has reminded me of the importance of repetitive series for Deleuze (an issue I also discuss here). Picking up on John’s discussion of the perception of colors, series play an important role in attempting to accounting for our use of predicates: in short, Deleuze will often place predicates within the context of a series of predicates – e.g., shades of blue. This pattern is most obvious in Deleuze’s Logic of Sense, where each chapter is titled “First Series of…” “Second Series of…” etc.… But why series?

Two short answers, which I’ll expand on below the fold: 1) a series of differences is precisely what provides, in good Spinozist fashion, the principle of sufficient reason for determinate phenomena; and 2) series in turn provide the metaphysics science needs.

Let us take a simple series of phenomena, E, E, E, E, etc. … Let us also assume there is no difference between the elements of the series. For Deleuze, however, each element, as an identifiable, determinate phenomenon, refers “to an inequality by which it is conditioned.” (DR 222). Thus every extrinsically distinct element presupposes an intensive difference, what Deleuze will call an “intensive quantum” (DI 88), and thus in the series E, E, E, E …, E itself presupposes the intensive quantum e-e’, and the element e presupposes ε-ε’, and so on ad infinitum. Deleuze will call this “state of infinitely doubled difference which resonates to infinity disparity,” which he then adds is “the sufficient reason of all phenomena, the condition of that which appears.” (DR 222; emphasis mine). One can picture this “state of infinitely doubled difference” by way of the graphs of Feigenbaum’s constant where functions approach chaos through period doubling:

Returning to the use of predicates, this difference or disparity that is the “sufficient reason of all phenomena” does not inhere in phenomena as their predicate, nor even as a separate or separable element, but it is rather the particularity of each element taken to the limit, or what Deleuze will call a “concrete universal.” For example, if we take a series of colors such as the several shades of blue one might find on a paint sample card at a hardware store, our tendency is indeed to consider each of these individual colors as a “shade of blue.” In other words, each particular color is differentiated from one another by a matter of degrees from one general color, blue, with these degrees running the spectrum from high to low saturation. Deleuze, however, argues that this is wrong. Following through on Bergson’s discussion of Revaisson (see DI 43), the universal is not an abstract concept distinct from each particular shade of blue, in which case we have an external difference, or a difference between the shades made possible by virtue of a universal that is external to them and of which they are varying degrees or shades. To the contrary, the concrete universal is the infinitely doubled difference that resonates and inheres within each appearing shade. In the case of a particular shade of blue, this concrete universal is “white light,” or it is the infinitely doubled difference (the far right of the above graph) that “makes the difference come out between the shades”; or,

…the different colors are no longer objects under a concept, but nuances or degrees of the concept itself. Degrees of difference itself, and not differences of degree. White light is still a universal, but a concrete universal, which gives us an understanding of the particular because it is the far end of the particular… (DI 43)

One can find further evidence for Deleuze’s metaphysics in Mark Wilson’s essay “Theory Façades,” (which can be gotten here) and in his subsequent book Wandering Significance. Wilson provides numerous examples, and with dizzying detail, to argue that throughout “scientific work” one finds that what is put to work in the effort to provide theoretical directives are “sheets of doctrine that do not truly cohere into unified doctrine in their own rights, but can merely appear as if they do if the qualities of their adjoining edges are not scrutinized scrupulously.” (“TF” p. 273) What may work well at one level and scale may begin to fail at a more detailed and enhanced level of description. As Wilson puts this in Wandering Significance,

…as our everyday descriptive terms become pressed to higher standards of accuracy or performance, as commonly occurs within industry or science, a finer and more perplexing grain of conflicting opinion begins to display itself within our applications of “hardness,” “force” and even “red.” (p. 7)

Put in the Deleuzian terms discussed above, the effort to produce accurate descriptions of phenomena encounters, with the increasing demands of more detailed and nuanced analysis, the substantive multiplicity or concrete universal that is the sufficient reason for the phenomena being described. The result is the failure of descriptive terms as these terms get pushed towards increasing particularity of detail; in short, as they are pushed toward the concrete universal that is “the far end of the particular.” (DI 43). What happens, Wilson argues, in our attempts to maintain “inferential headway” in the face of the difficulties that arise as the level of particularity increases, is that we often find it easier “to decompose the system’s overall behavior into descriptive fragments where the intractable complexities of the full problem become locally reduced to more tractable terms.” (TF pp. 273-4). Wilson offers the example of what happens when we attempt to use applied mathematics to understand the formation of spray on “the surface of a choppy ocean.” (WS p. 210, as are subsequent quotes). If the ocean is modeled as a continuous fluid, the partial differential equations will provide accurate descriptions to a point, but then it fails to track the phenomena for the equations continue “to plot an attached blob that never relinquishes its absurdly elongated umbilical tie to the mother ocean.” To offset this poor description, one solution is to run the model with an already detached blob that then separates from the ocean. This provides for a good description where the continuous model does not, but then the description is poor where the continuous model’s was good. If we combine the two models together, we can overlap them such that it provides a good description for the entire process. While this may be effective at providing an accurate description, Wilson argues that what is going on here is an exercise in “physics avoidance in that we do not directly describe the molecular processes that lead to drop separation, but merely cover the relevant region with an interpolating patch.” In other words, there is a repressed difference or boundary between the two patches that is then mistakenly held to be a unified account of water separation when it is not. Wilson is not arguing that no account of the water separation is possible. His argument is that an adequate account of the boundary where the different patches converge may well entail a complex mathematics beyond our ken at this point. As a result, and due largely to impatience, we are often tempted, Wilson claims, “to pretend as if our façade patchwork provides a wholly adequate descriptive framework solely on its own terms…” (TF 275)

Wilson’s point, however, and this is just what one would expect given the Deleuzian metaphysics and its use of the PSR, is that however detailed and nuanced the theoretical and mathematical description might be, there are underlying differences that subvert them as the level of description pushes to the “far end of the particular.” In other words, substantive multiplicity (or concrete universal) may be the sufficient reason for every phenomena, but it is also the reason our mathematical equations and theories which track phenomena will forever flirt with, and be challenged by the intensive differences that fail to be explicated and hence modeled by their equations. Wilson makes a very similar point in the early pages of Wandering Significance, and one quite in line with reading of Deleuze’s metaphysics offered here. Wilson argues that,

The main consideration that drives the argument of the book is the thesis that the often quirky behaviors of ordinary descriptive predicates derive, not merely from controllable human inattention or carelesseness, but from a basic unwillingness of the physical universe to sit still while we frame its descriptive picture. (WS 11)

The title/theme of the conference is “Deterritorializing Deleuze,” not Aberrant Monism, as some have come to think since the announcement for the conference in Copenhagen titled it as Aberrant Monism, though this is only my blog where I’ve had a page dedicated to the conference. When I return to the states at the end of the month I’ll launch a website dedicated just to next year’s conference, separating it entirely from my blog.

With the theme of deterritorializing Deleuze, one is left with many ways in which one can write a relevant paper. The point is one of attempting to think Deleuze beyond Deleuze, or to use Deleuze and Deleuzian concepts in ways that are in the spirit of Deleuze (and Guattari let us not forget), and hence engage with Deleuze’s work, while at the same time pushing Deleuze Studies in different directions.

When the new site is up I’ll post a link to it here. In the meantime, if anyone has any questions, feel free to contact me – jbell (at) selu (dot) edu.

Having read Protevi’s recent interview with Jason Stanley over at New APPS (here) I was reminded of a few insights I had had several years ago after reading Jason Stanley and Timothy Williamson’s excellent essay, “Knowing How” (Journal of Philosophy 98.8 [2001]) which in turn reminded me of Stanley’s book Knowledge and Practical Interests, which I’ve had but not read since I first came to it while working on what eventually became the Hume book. I’m now working my way through Stanley’s book, which is excellent, and remarkably lucid. Early on in the preface Stanley notes that the conclusions he draws in this book were found to be ‘unsurprising’ to ‘friends and family members more at home with non-analytic traditions.’ In particular, at least from my own perspective, I found this especially to be the case in Stanley’s critique of contextualism. The critique, in short, draws on what Stanley sees as a disanalogy between gradable expressions such as tall, really tall, flat, really flat, and knowledge attributions such as know, really know, etc. In the first case such expressions do draw much of their gradability from their context and this determines whether the attribution is correct or not, such that to attribute “really tall” might be appropriate when speaking of fifth graders but a completely different scale comes into play when speaking of professional basketball players or Tutsi tribesmen. The contextualists argue that it is the context that provides the appropriate scale for determining which attributions are appropriate. Stanley argues, however, that ‘attempts to treat “know” as a gradable expression’ in the same sense as tall, strong, etc., ‘fails’.

Knowledge, in short, does not admit of differences of degree. Stanley is quite forthright on this point, arguing that ‘propositional knowledge ascriptions are not gradable at all.’ It is at this point where I begin to see connections with the Deleuzian theory I’m developing which argues that concepts are to be understood as intensive automata, where intensive is used, in the Deleuzian sense, in contrast to extensive, which involves differences of degree and/or differences of kind. As it comes together I may arrive at a Deleuzian theory of concepts Deleuze would find monstrous, but then this in its own way could be very Deleuzian. There are, however, some clear headwinds to such a project. For one thing, Deleuze and Deleuze and Guattari were uninterested in theories regarding propositional knowledge, quite unlike Stanley, and they found that in general these theories were built upon the most uninteresting of examples (e.g., “Scott is the author of Waverly,” “the cat is on the mat,” etc.). More crucially, perhaps, whereas Stanley sees his project as one that remains true to our common intuitions – as he puts it, “My philosophical tendency is to preserve as much as possible of common-sense intuition” – Deleuze, by contrast, seeks to create a philosophy and philosophical concepts that problematizes common sense, that makes the common of common sense the issue to be understood rather than taking it to be the given upon which everything else is to be understood. Despite these headwinds, it seems to me there are some significant connections and parallels to be drawn. When I get a rough draft finished I’ll post a link to it at this blog. I will also present what I come up with at the Deleuze Studies conference in Copenhagen and would be more than happy to talk about these and other Deleuze-related matters with those who are so inclined (preferably over coffee [morning] or beer [evening]).

I have followed the ongoing controversy in part because it brings to light a number of important issues in the philosophy profession that have been brought up within the comments – e.g., what is the status of special issues and the proper relationship between guest and general editors; the role of prestige and reputation in the field; the differing reactions among Anglophone (primarily American) and European philosophers, etc. As is my wont, I have found it interesting how history creeps in to a number of the arguments and justifications one makes for one’s stance. In short, one wants to be on the right side of history. That being said, there are a number of philosophers who believe the whole controversy is a tempest in a teacup at most or an outright witch hunt at worst. For them, there is insufficient evidence to tarnish the reputations of the editors and the journal that had been, prior to this incident, sterling. The very term “witch hunt,” which Philippe Huneman used to describe the prosecutorial approach of many to the actions of the editors-in-chief at Synthese, clearly brings with it an association of being on the wrong side of history. Who looks back upon the prosecutors at the Salem with trials, or at Joseph McCarthy’s hearings, and thinks ‘well done!’? But at the time it is not always clear whether one is on the right side of history. As events unfolded in Egypt a few months back, talking heads frequently chalked up the Obama administration’s cautious approach to the events by claiming that they wanted to come out on the right side of history; similarly, no doubt, for France and Britain with respect to Libya. But critics (take Putin for instance) argue that being militarily involved in Libya is being on the wrong side of history. Moving on to philosophy, Heidegger likely thought he was on the right side of history when he embraced the Nazi party and Hitler’s rise to power; and Descartes recognized, as he launched into his Meditations, that frequently in the past he was on the wrong side of history. Now of course he did not put it this way, but the temporal subsequently entered Descartes’ concept of the cogito in an important way (as Deleuze and Guattari also point out in What is Philosophy?), such that what one thinks one knows now may, with the passage of time, be revealed to be false. This was also an important aspect of Ladyman and Ross’s critique of traditional scientific realism (as I discuss here), whereby there are certain entities posited by today’s best theories which, by the lights of tomorrow’s best theories do not actually exist today, and since we can’t say which ones these are the best approach to scientific realism is to abandon the notion of entities (hence the title of their book, Every Thing Must Go) and urge instead the reality of patterns.

This is not intended as a riff on skepticism regarding our knowledge of whether or not one is on the right side of history, but rather it brought to mind that the Synthese affair is a helpful example of Deleuze’s theory of events. As that which eludes the present state of affairs, being simultaneously past and future, the Synthese affair is an event that cannot be pinpointed to a present state of affairs but continually refers to the past – note the efforts of those who signed the petitions along with others to try to find out what actually happened, the facts that are already in the past – and to the future as people debate what to do, which course of action they believe is best, including whether or not to sign a petition, call for a boycott, or ignore the whole thing. Events are neither on the right or wrong side of history; they are, rather, the creativity that is the condition for the possibility of being judged to be on the right or wrong side of history. And yet these events are at the same time inseparable from what is the case, from existent states of affairs such as the status and institutional prestige of Synthese or Leiter’s blog, for instance (consider the non-response that would most certainly have followed had there been editorial misconduct at a little known journal and a seldom read blogger called for a boycott), the current state of the philosophy profession, and more germane to the Synthese affair there is the current state of scientific education in the United States along with the preponderance of the religious right and its largely willing embrace of intelligent design and the public policies that support it. It is in this context where events allow for the possibility of creating future judgments, of creating history, including the judgment that it was all for not. Around 300 people to this point have signed the petition in an effort to rectify a perceived wrong; time will tell if these efforts amount to much. I am one of those have signed the petition (it’s available here).

In this essay it will be argued that Deleuze’s theory of concepts can be fruitfully compared with automata theory (AT), and in particular a dynamical systems approach to the theory of cellular automata. The comparison of Deleuze’s thought with dynamical systems and complexity theory is a terrain that has been well traversed by John Protevi, Brian Massumi, Manuel Delanda, and Jeffrey Bell, but to date this approach has not taken on the task of exploring the possible connections with Deleuze’s theory of concepts, which is particularly important since Deleuze repeatedly argues that philosophy’s primary task is and ought to be concerned with the creation of concepts. Addressing Deleuze’s theory of concepts, which is in itself a neglected area of Deleuze scholarship, will thus clarify the distinctive role Deleuze believes philosophy can play.

By understanding Deleuze’s theory of concepts in light of automata theory this essay will set out to establish three important consequences. The first follows from a detailed analysis of the important role abstract machines play in carrying forth the computational processes between the progressive states of the automata, which will then be compared and contrasted with the understanding of abstract machines as found in the work of Deleuze (and Deleuze and Guattari). This comparison will allow us to clarify how conceptual automata (as we will refer to Deleuzian concepts in this essay) both engender and are engendered by abstract machines, and hence how concepts are dynamic systems. In turning to the second part of this essay we will show how a Deleuzian theory of concepts as conceptual automata relates to more traditional theories of the concept. On the one hand, we will show how a Humean-empiricist account of concepts as engendered by certain processes of association (that is, by certain computational rules in AT) is in line with our Deleuzian theory of concepts, a theory that thus demonstrates the continuing relevance of Hume for understanding Deleuze’s project. At the same time, however, conceptual automata are from the start connected to other concepts and to other abstract machines, or, to cite the closing lines of A Thousand Plateaus, ‘Every abstract machine is linked to other abstract machines, not only because they are inseparably political, economic, scientific, artistic, ecological, cosmic—perceptive, affective, active, thinking, physical, and semiotic—but because their various types are as intertwined as their operations are convergent. Mechanosphere.’ Thus, when Wilfred Sellars argues that ‘there is an important sense in which one has no concept pertaining to observable properties of physical objects in Space and Time unless one has them all,’ (Empiricism and the Philosophy of Mind, p. 45); or when Brandom argues that conceptual contents are ‘social achievements,’ by which he means that our ability to appreciate ‘the distinction between correct and incorrect application’ of concepts derives from the norms implicit to social practice (‘we have met the norms,’ Brandom argues, ‘and they are ours’ [I discuss this here, here, here, and here for a quick reading of McDowell's Mind and World]); in both cases we will find that our Deleuzian theory of concepts as conceptual automata will be quite compatible with these arguments. In other words, despite the widely held perception of there being a fundamental opposition between a Sellarsian/Brandomian theory of concepts and a Humean/empiricist account, we will show that not only does an understanding of concepts as automata not fall into the either/or alternatives of rationalist or empiricist accounts, but more importantly the Deleuzian theory set forth here offers a transcendental account in that it explicates the conditions for the possibility of these opposed alternatives, or for what will be called the intellectual mitosis (as I discuss here) inseparable from the bifurcation between empiricism and rationalism. The conclusions of the third and final section of this essay follow from those reached in the first two sections: namely, there is no priority given, in a Deleuzian account of thought and concepts, to human beings as conceivers, or to the thoughts and inferential arguments that are constructed and utilized by human cognizers. To the contrary, the Deleuzian theory offered here presumes a flat ontology of abstract machines. Conceptual processes and the inferential arguments of human thinkers are thus not privileged on this theory but are rather to be understood by the same theory of abstract machines and automata as is and can be used to account for any other determinate process. There is a reason, we shall see, why the final word of A Thousand Plateaus is Mechanosphere.

At the Leiter blog there was an interesting thread (here) concerning Philip Kitcher’s recent essay, “Philosophy Inside Out” (here). Given the current state of support for philosophy (or lack thereof) within the academy, it was not surprising that many of the comments were in support of Kitcher’s basic claim that philosophy ought to reconsider or reflect upon its core mission, although not everyone agreed with how such a reconsideration would look in practice, or what has put philosophy into the state it is in.

Kitcher’s basic argument stems from his reading of Dewey, who he ‘take[s] to be the most important philosopher of the twentieth century.’ In particular, Kitcher analogizes much of the “core” work that is most highly valued in philosophy today, by which Kitcher means epistemology, philosophy of language, and philosophy of mind, with placing the highest musical value upon those who can perform an ‘ornamented Quadruple Temolo 41 with an extra trill.’ In short, much of the core work in philosophy Kitcher claims is increasingly devoted to making finer and finer distinctions, the relevance of which is apparent to an ever-dwindling number of fellow neo-scholastics (referring here to Ladyman and Ross’s critique of contemporary analytic metaphysics, as discussed here). The overall message: it’s no wonder philosophy programs are at risk. It’s time to take stock of what we philosophers are doing and whether it is worth doing.

The necessary corrective, as Kitcher sees it, is to follow Dewey and to address issues and problems that have a ‘far broader, and more readily comprehensible, significance.’ Even mathematics and the natural sciences, despite delving into technical knowledge and minutiae that may seem far removed from issues of broader significance is able, nonetheless, to realize this broader significance, Kitcher claims, ‘at least in outline, [in] a sequence of steps.’ Where my interest in this debate was piqued was with Kitcher’s Deweyan understanding of philosophical problems. Kitcher cites the following relevant passage from Dewey:

The fact that philosophical problems arise because of widespread and widely felt difficulties in social practice is disguised because philosophers become a specialized class which uses a technical language, unlike the vocabulary in which the direct difficulties are stated (from Democracy and Education, p. 328).

Philosophical problems thus arise from what is common and hence ought, in the end, to be discussed and addressed in a manner that can effectively resolve these ‘widely felt difficulties in social practice.’ Natural science, for example, presumably addresses the widely felt need for understanding one’s world, and thus even the most technical and arcane of scientific practices are simply steps away from being seen as addressing these widely felt concerns, and hence science is able to be vindicated as relevant. The same is not the case for philosophy today, Kitcher claims (echoing Dewey).

Despite my admiration for Dewey – I would agree Dewey is one of the most important philosophers of the twentieth century – I disagree with the Deweyan understanding of philosophical problems, though not for the same reasons that were most frequently expressed in the comments to Leiter’s post. Ted Sider, for instance, states his difficulties with Kitcher’s understanding of philosophy as follows: “Going deeply into details, working vertically rather than horizontally, isn’t as glamorous as making sweeping connections. But what a superficial field philosophy would be, if we were all synoptic seers of broad visions! The great figures in the history of philosophy were certainly no strangers to the trenches.” The synoptic seers with broad visions are important, but so too are the philosophers who work in the trenches, working vertically, delving into the details and establishing connections and weeding out false paths and connections. Sider’s concern is that if we follow the Deweyan approach we may lack the patience necessary to sort through the necessary details and connections in a way that may keep us from making hasty, ‘sweeping connections’. The implication for Sider appears to be that the vertical, in the trench philosophizing, is complementary to and perhaps a prerequesite to the best horizontal philosophizing. Vertical philosophizing is thus not at odds with Dewey’s concerns for addressing ‘widely felt difficulties in social practice,’ but merely highlights the need for patience and recommends we be cautious against a rush to relevance, or a rush to MATTER as Sider puts it.

A Deleuzian understanding of philosophical problems, by contrast, is in many ways completely opposed to Dewey’s (which may justify for many the sense that Deleuze’s thought is irrelevant). When Deleuze and Guattari, in What is Philosophy?, argue that opinions are ‘the object of a struggle or an exchange’ and that this ‘is the Western democratic, popular conception of philosophy as providing pleasant or aggressive dinner conversations at Mr. Rorty’s,’ it becomes quite clear that the task of philosophy is not, primarily, one of addressing problems in a way that can be seen as responding to ‘widely felt difficulties.’ Far from it, once philosophers actually sit down to discuss their work, or argue about what one or the other is doing, they have ceased to be addressing philosophical problems and are instead focusing on that which is by its nature common since it is that which can be exchanged in a give and take of discussion. Deleuze was no doubt aware that he was echoing Nietzsche’s sentiments as expressed here in Beyond Good and Evil:

In all souls a like number of frequently recurring experiences have gained the upper hand over those occurring more rarely: about these matters people understand one another rapidly and always more rapidly—the history of language is the history of a process of abbreviation; on the basis of this quick comprehension people always unite closer and closer. The greater the danger, the greater is the need of agreeing quickly and readily about what is necessary; not to misunderstand one another in danger—that is what cannot at all be dispensed with in intercourse. Beyond Good and Evil §268

Moving from what we agree to be our widely shared difficulties and then back to what can be widely comprehended, as is Dewey’s model, thus bypasses the importance and significance of what happens in between (au mileu), and it is here where Deleuze believes philosophical problems lie and where their problematizing effects emerge. It is here as well where the significance of Dewey’s experimental pragmatism emerges, and thus where we see both that the quick lumping of Dewey with pragmatism (and his thereby being promptly dismissed) misses the point and that Dewey is indeed one of the most important philosophers of the twentieth century. For Deleuze what happens between the common understanding of a pressing problem and the common recognition of its solution is the philosophical concept. With this in mind, it is worth quoting Deleuze and Guattari at length:

Every philosopher runs away when he or she hears someone say, “Let’s discuss this.” Discussions are fine for roundtable talks, but philosophy throws its numbered dice on another table. The best one can say about [philosophical] discussions is that they take things no farther, since the participants never talk about the same thing. Of what concern is it to philosophy that someone has such a view, and thinks this or that, if the problems at stake are not stated? And when they are stated, it is no longer a matter of discussing but rather one of creating concepts for the undiscussible problem posed. Communication always comes too early or too late, and when it comes to creating, conversation is always superfluous. WP 28

We can now better situate the Deleuzian approach relative to Kitcher and Sider (although I could equally well use Timothy Williamson, among others). Put simply, Deleuze is addressing different problems and creating different concepts. Unlike Kitcher, the Deleuzian problematic is not a matter of engaging in a free, open discourse regarding widely shared problems in order to attain widely perceived, and relevant, solutions. Nor, and unlike Sider and Williamson (et. al.), is the problem one of creating a more finely tuned and accurate (i.e., true) logical representation of the processes associated with epistemology, mind, and language. Deleuze might not go so far as to compare this effort to adding a trill to the Quadruple Tremolo 41, but he may very well see logic as Spinoza did – that is, as useful for mental hygiene and fitness. At the same time, the problem for Deleuze is not one of establishing communicative rationality or consensus. The Deleuzian problematic is to create concepts, full stop. In doing this, or at least in doing this well, philosophy problematizes both the common and the representable – this is the sense in which concepts are related to an ‘undiscussible problem’. The creation of concepts also problematizes accepted methodologies, or the presumed means whereby one sets about addressing and resolving problems. In fact, in creating concepts one creates the means of resolving them, but in a way often at odds with, or problematic in relation to, already established methodologies. This is where the philosophical effort to create concepts is of a piece with historical ontology (as I discuss here and here). This effort is the key to philosophy’s relevance for it is only in problematizing established orthodoxies whereby the tools to address problems in the manner that was Dewey’s concern become available; and yet, echoing Ted Sider’s concerns, philosophy cannot set out to create the tools that MATTER, tools that satisfactorily address a set of established and predetermining needs and concerns. Philosophy ‘throws its numbered dice on another table,’ and for this reason, among others, a central and enduring problem of philosophy will be its relevance.