subota, 24. kolovoza 2013.

Christopher Vitale - Networkologies (blog)

Jako dobar interdisciplinarni teoretičar, od netvorkologije i kognitivnih studija do matematike za koju vrijede etička načela.

Christopher Vitale is Assistant Professor of Media Studies, M.A. Program in Media Studies, Pratt Institute, Brooklyn, NY. For more, see the website for Pratt’s M.A. Program in Media Studies.
Contact: cvitale-at-pratt-dot-edu
- Poststructuralism, Continental Philosophy, Complexity Studies, Theories of Networks, Queer Studies, Theories of Race and Culture, Cognitive Studies, Semiotics, Film and Visual Studies, and Comparative Modernist Literatures and Visual Cultures.
Networkologies: A New Philosophy of Networks for a Hyperconnected Age, Vol. I – From Diagram to World. Forthcoming, from Zer0 books, Fall 2012. For more, see here.
The Networked Mind: Cognitive Science, Artificial Intelligence, and Post-Structuralism.Book manuscript complete, now being readied for solicitation of publication. For more, see here.

Excerpts from the book manuscript of “Networkologies, Vol. I”

Speculations: The Journal of Speculative Realism, Vol. 1
Networkologies: A New Philosophy of Networks for A Hyperconnected Age is due to be published by Zer0 books this spring. Parts of the work in progress have been published, in two installments, in Speculations: The Journal of Speculative Realism, Vols. 1 & 2.
For links to the issues of Speculations, see here and here. Due to formatting issues, the first article is best accessed via pdf here. The articles do not need to be read in sequence, as they cover different issues. This first article is a general introduction to networks and their relation to philosophy. Much of this has been reworked in the final manuscript.
The second, more recent article, describes the metaphysical core of the networkological enterprise, as well as some of the applications to the physical world. For the page on this website with the entire text, see here. With some modifications, this article will become part of the final manuscript for Zer0.
Additional excerpts of the work in progress for Zer0 have been posted on this blog as regular posts, including here (on Networks and Emergence), here (on Networks and Complexity), here (on Networks and Extimacy), and here (On Networks and Parameters).


[For more information on the book length expansion of this manifesto, currently a work in progress, see here].
The network is increasingly one of the fundamental metaphors whereby we have described the character of our age. Despite this, there has yet to be a philosophy of networks. A Networkological approach aims to address this fact.
A Network is a diagram for the thinking of relation. This diagram can help us to understand the structure, dynamics, and potentials of our networked age.
Our age is one in which relation is increasing, reified entities are being reworked, and previously existent relations are becoming ever more evident. These changes, which have given rise to what might be called the ‘networked age,’ are partially due to the rise of the internet, the World Wide Web, global capitalism, etc. But this change cannot be reduced to the sum of its parts – change is the result of the interplay of material and ideal, actual and virtual.
The entire world can be viewed as composed of networks. A chair is a network, and so are atoms, concepts, words, societies, organisms, brains, economies, etc. Understanding the different styles and interactions between networks is the work that needs to be done to create a philosophy of networks.
To paraphrase a famous philosopher – “To those who look at the world networkedly, the world will look networkedly back.” This is the fundamental wager of the networkological project. The Networkological approach takes the notion of relation and works to elevate it to the notion of a concept, diagram, and project.
* * *
The Networkological approach is fundamentally a philosophy of relation. It does not deny the existence of isolated elements, so long as these are seen as ultimately related to the contexts and processes of their production. The Networkological approach is, however, against any theory which presupposes the fundamental division between mind and body, epistemology and ethics, social and natural, space and time, science and culture, or any approach which views any given binary opposition, reified entity, or limited list of terms as ultimate or fundamental. The only ultimate is the open, the background from which any network individuates and eventually must return.
The Networkological approach, as a philosophy of relation, is also necessarily aphilosophy of process, for relation is both spatial and temporal. These commitments are at once epistemological, ethical, ontological, and metaphysical. Any entity which has individuated itself from a background is necessarily related to that background, and to other entities which may be related at a higher level of abstraction. No entity is ever absolute, but rather an element of more encompassing frames of reference, and no product is ever more fundamental than the process of its production. Thus all networks are necessarily dynamic, that is, relational entities in process. As expressions of the whole from which they emerge, each entity and network are ultimately perspectives thereupon. The Networkological approach is therefore not only processural, but also holographic. Within the bounds of all that we know that exists, the Networkological approach is also, in a weak and relative sense, fractal in nature. That is, within the limits of the existent at either end in regard to the open, all networks are the product of networks at the micro-scale, and produce other networks at a macro-scale. From its ethico-epistemo-ontological commitments to relation, process, fractality, and holography, the Networkological approach articulates its relation to the wider world of nature, meaning, mind, and society.
The Networkological approach is therefore transgressive of traditional atomizations, distinctions, and reifications. The Networkological perspective is therefore also a method and a critique. Any reified entity or distinction will necessarily be broken down by a networkological critique, and re-related to the wider contexts within which it exists and from which it has emerged. Networkological critique blasts apart reified entities, revealing the dynamic networks contained within. Drawing inspiration from the methods of Deleuze, Simondon, Hegel, Marx, and Bergson, the goal is to demonstrate the relations hidden behind, beneath, within, and around what others view as elementary.
As a result, networkological critique is necessarily also transgressive of traditional disciplinary boundaries. It ranges freely from physics to metaphysics, societal analysis to abstract math, literature to art and culture, politics to ethology. It also is transgressive of the sharp division between word and image, or styles of writing or other modes of symbolic interchange.
Networkological texts are necessarily polyform, and seek to increase potential modes of relation between texts and their viewers. Networkological texts also aim to be use many different voices and forms of writing, such that many different types of viewers can access these texts. Reified categories which dictate what form of writing need be used to express certain types of ideas are simply not applicable to our networked age. That said, Networkological texts do not necessarily dispense with all forms of division or separation of elements within them. Rather, these texts often increase the atomization of their components so as to allow greater multiplicity of forms of (re)combination. In this manner Networkological texts, symbolic assemblages really, take the Brechtian imperatives in theater and apply them to the realm of theoretical text. Parts are separated out so as to both allow for multiple forms of their potential interrelation, while also breaking up any myth of the text as a unitary whole. Images, citations, captions, and written bits all float, and various textual, graphical, and organizational devices are deployed so as to the assist multiple linkages between the various parts. All reading thus becomes modeled on that which people already do on websites, full of surprise jumps and tunneling, thereby going through distraction to new forms of ideational proliferation and association. Networkological writing therefore aims to be viewed in a manner which is inherently multiple and complex.
The Networkological approach is closely aligned to many new movements within contemporary ‘continental’ philosophy. It has much in common with approaches such asspeculative realism and transcendental materialism. Due to the relational nature of a networkological approach, reified terms such as matter, energy, mind, knowledge, and consciousness are ultimately seen as derivative products of larger contexts and processes. As such, it necessarily has much in common with any approach which is fundamentally relational in nature.
The Networkological approach also has much in common with radical approaches to the broadening of the concept of media. This mediological approach is central to the project in question, as are the potential for a more networked notion of the intersection of media and semiotics might mean. In its analysis of any given media structure or signifying element, a network analysis will nevertheless break down any component into its networks of microfeatures, as well as its linkage to macronetworks. Worlds mediate themselves via their networked interrelations, and it is here that the commonalities between networkological and mediological approaches can be seen.
The Networkological approach, which frames itself via the notion of individuation at the border between the node and the link as they emerge from a given background, isultimately neither a philosophy of ‘the One’ or ‘the Two’, but of the ‘Oneand’ – the one which exceeds itself. Thus, it finds common ground with any approach to entities which finds them in the process of self-differing, becoming other. As the products of self-differing substance, networks are fundamentally dynamic in nature. Networks may thus shift in structure and form over time, and channel flows and entities within dynamic processes.
Much of the inspiration for the Networkological approach comes from the new sciences of complexity. Complexity studies examines the ways in which notions of emergence, non-linear dynamics, differential networked topologies, can allow new perspectives on what is at work in many previously underexplained scientific phenomenon. One of the major goals of the networkological approach is to extract the philosophical potentials from this emergent point of view. This is particularly essential in regard to the notion of emergence, whereby the radically new emerges from a whole which exceeds the sum of its parts. The science of complexity aims to track the manner in which such shifts occur, in particular by means such as fuzzy systems theory, complex network analysis, and genetic/evolutionary algorithms and multi-agent systems theories. These approaches are currently being applied widely beyond the domains of their origin, and are increasingly demonstrating a wide variety of scientific, philosophical, and cultural implications. From quantum indeterminacy to the emergence of mind from matter in neural networks, emergence is one of the primary manner in which networks bring novelty into the world.

The Networkological approach is also a theory of matter. Space and time are network phenomena, created due to the distribution of perspectives on what exists. Each perspective entails a view of the whole which emphasizes certain aspects over others. From the self-differing of what exists into bodies, space, and time, matter becomes multiplicity, giving rise to particles and fields, action and interaction. Matter comes to know itself as such via life, and overcome space and time via mind. Perspective, embodiment, space, and time are co-constitutive with the division of matter, as part of its self-differing. These divisions create bodies which, via perspective, relate to some elements more than others. These elements and the patterns they give rise to lead, in conscious entities, to concepts, and the combinatory of concepts to meanings. A Networked approach to semiotics works to understand the ways in which mind, matter, and meaning intertwine in ever more complex and nested networks whereby self-differing substance comes to know itself.
Networks are closely related to the notion of symmetry. Wherever there is a symmetry, even amongst otherwise radically heterogeneous elements, there is a network. When there is a symmetry between elements, physical or symbolic, each of these elements can be understood as elements of a set (when viewing the elements as a static network) or morphism (when viewing the elements as part of dynamic network). Symmetry takes many forms – for example, the radical disparation of a system in the process of changing form is composed of singularities which define its topology, and these singularities can also be seen as composing a radically heterogeneous network which gives shape to processes in/of a space and time. Physical laws and structures can also be understood as symmetries, as can the non-changing parts of any changing structure. Thus, the grammar in a language indicates a form of symmetry, as does the rules for addition as used in common mathematics. The expansion, contraction, alteration, and disparation of symmetries indicate the manner in which relative forms of invariance give structure to worlds of various sorts. Notions of symmetry and symmetry breaking are therefore crucial for understanding the manner in which networks, dynamic and otherwise, can be seen at work in the structure of the processes at work in physical, symbolic, and mathematical worlds.
Maths and Logics
Networks therefore also relate to mathematics and logic. According to many contemporary theorists of maths, which for networkology must always be thought in the plural, maths are composed of two fundamental gestures – the figure, or geometry (a relation within space), and the count, or number (a relation within time). All practical and applied maths can seen as networks of relations between aspects of these terms. As regards logics, another term which must always be thought in the plural, and relations between maths and logics, it is essential to remember that networks are composed of three primary structures: field, node, and link (and within networks nested within each other, the module). Each of these structures comes to be by a process of individuation. Set theory, the logical foundation of ‘modernist’ mathematics, focuses on nodes and their conditions of individuation within static networks, while category theory, the foundation of ‘postmodern’ mathematics, operates on the level of the link within dynamic networks. Both perspectives are ultimately limitations, and the networkological conception of a fuller logic must encompass both of these approaches within a structure which is potentially relational at all levels. Multi-valued, Fuzzy, and Intuitionist logics are steps in this direction, but ultimately the form of logic most germane to the networkological perspective is that presented in the dialectic of the Concept as presented in Hegel’s Logic, in which the node acts as the particular within the universal structured by the conditions of its individuation. From this logical conception of the node, a dynamic logical structure can be derived, and from there, the more particular logics, including of the propositional sort, needed to think specific aspects of the world.

Mind indicates a unique type of network, one which along with quantum phenomena, can overcome the separations inherent in networks of space and time. Rather than see mind and matter as radically distinct, the networkological approach to mind is based on the notion that what we self-conscious thought is complex emergent phenomena which develops the potential for mind within even the most fundamental building blocks of matter. To use the vocabulary of A.N. Whitehead, quantum events retain an interiority which prehends the world around them and react thereto. Such an interior reactivity to a perspectival and perceptual condensation of the world around it indicates the most basic form of mind, and the more developed forms of mind that we see in advanced organisms are simply more complex forms thereof. The philosophy of networks see no firm division between mind and matter. Both copermeate at all levels of scale.

The Networkological approach to thinking minds must take their fundamentally distributed and emergent nature into account. While psychoanalytic and psychological concepts may be of use to it, these often reify separations such as conscious or unconscious, ego or superego, etc. A Networked psychology needs to think in terms of nodes linked in nested hierarchies in ever more complex systems of interrelation. Thus, it becomes necessary to think of the manner in which perceptual and affective states are metabolized, reworked, and shattered, then cohere into networked nuclei within the psyche of individual, the collection of which forms dynamic schemas whereby subjects create patterns of filtering, emphasis, and regulation in relation to the world beyond them. Networked psychoogy needs to think in terms not only of nuclei but also fragments and flows, statics and dynamics, and the manner in which the psychic and the physical are fundamentally topologically related to one another.

A Networked aesthetic is based upon forms of artistic praxis which highlight aspects of the fundamental commitments of the Networkological perspective. Thus, art that is relational, holographic, fractal, or processural, or that indicates complexity or emergence in process, give body to a networked aesthetic. These concerns can be played out in multiple forms and in multiple media, so long as the reified nature of artistic praxis is undermined by the work in question.
The Networkological approach is also a praxis with a political component. The Networkological approach is fundamentally against the politics of fear and paranoia. It is an ethics which is also a politics. It is therefore anti-racist, anti-homophobic, anti-misogynist, and anti-anti-immigration/migration. Paranoid antagonisms of this sort ultimately keep networks from developing to their maximum potentials.
The Networkological approach thus takes a definite attitude in regard to the politics of life. Life is a complex network. In order to live more fully, we need to live at our most complex and most sustainable. Complexity and sustainability are the core tenets of a networked ethics. Racism, homophobia, misogyny, and anti-immigration and anti-migrancy all hinder the development of greater complexity and sustainability of this complexity.Extraction of surpluses from the natural and social worlds can also lead to the restriction of complexity and sustainability. The Networkological approach therefore is necessarily against contemporary forms of capitalism exploitation. The Networkological approach is in this sense an ethics, politics, economics, and ecology.

Based on what is stated above, we can formulate the basic principle of a networked ethics: Let all your networks operate at maximum robustness. The components of robustness are complexity and sustainability. And since all networks are ultimately connected via the open, all networks are your networks. Because the nature of this ethical approach is based on relation, it is fundamentally context specific, and is against rigid moral codifications. It is an ethics of life, one which requires specific agents to make specific judgments in specific contexts.
There are definite precursors, and in some cases, fellow travellers, to the Networkological approach. Some key predecessors include the following: Gilles Deleuze, Felix Guattari, Henri Bergson, Baruch Spinoza, G.W. Leibniz, Alfred North Whitehead, Gilbert Simondon, F.W.J. Schelling, John Dewey, The Stoics, Karl Marx, Jacques Lacan, Maurice Merleau-Ponty, G.W.F. Hegel, Alain Badiou, Slavoj Zizek, Yuri Lotman, Ernesto Laclau, R.W.D. Fairbairn, Guy Debord, Bernard Cache, Bruno Latour, Manuel Delanda, Brian Rotman, Graham Harman, Jonathan Beller, and the Complexity Theorists associated with the Santa Fe Institute in Santa Fe, New Mexico. While not all of these are necessarily complete theorists of relation, many have contributed to the structure of the contemporary Networkological perspective. In its commitment to relation, the Networkological aproach is generally anti-Kantian, as well as anti-Cartesian and anti-Platonic.
As regards fundamental philosophy, the Networkological approach views all views on the world as part of the great network of perspectives which gives rise to the diversity of what is. The Networkological approach is therefore necessarily partial, and finds its only justification in its relation to the larger project of life in its development at the particular time, place, culture, and situation of its emergence. Its ultimate foundation goes no further than this. As such, its relation to its foundation is most similar to that of emergence within complexity science.
The Networkological perspective views relation as at work at all levels of a network diagram – node, link, background, and, in the case of nested networks, module. Thus it is not only concerned with these entities as such, but their modes of relation and change, including notions such as the individuation/emergence of nodes, the topology of links, the nesting of networks within each other, and the different types of components, rules of individuation, structures of components, etc. Networks may be homogeneous or heterogeneous, material or conceptual, fluid or atomistic, hierarchical or distributed, continually changing or relatively static, etc. While networks in the world may reify any of these levels, or the structural forms any of these may take, the networkological approach needs view these as ultimately derivations of the potential forms a given network may take. While networks may take many forms, networkological analysis must be open to all the potentials within networks as such.
Networks can be thought of spatially, dynamically, and also genetically, that is, in relation to the logical process whereby a network emerges, or individuates, from its surroundings. Such an approach requires that we expand the basic structures of a network – background, node, link, (and module) into a typology of moments and relational configurations which ultimately derive, however, from the original tripartite structure. From such a perspective, the first stage of network development is that ofindifference, a state in which everything is possible, but nothing particular has taken shape. From this emerges an event, then events, and then series of events. When there are multiple events, either temporally or spatially, we can begin to speak of these events as indicating a structure which has begun to differentiate itself from its background. Such a structure indicates the presence of what Alain Badiou has called a ‘count-for-one’, in that when there is structure, one can begin to distinguish its parts. These parts may exceed the structure in question either partially or nearly completely, or be completely determined thereby, and the structure in question may be spatial or spatial and temporal. In regard to a given structure, the elements of which a structure is composed can be understood relationally as nodes within a network, and the conditions which determine which things count as a node determine the requirements of individuation within a given network. These nodes imply a structure/field which is structured by these nodes/elements, as well as a background from which nodes and field have emerged. The relations between nodes and a field are expressed by connections or links, and these links can take many forms – abstract, ideal, material, dynamic, etc. Links can also be gated or directional in a variety of ways, giving rise to structures of regulation, coregulation, resonance, and other effects whereby nodes interact within specific types of networks. Links can also connect nodes by means of a variety of meta-shapes, or topologies, such as chain, grid, star/hierarchy, distributed, or combinations thereof. By means of the types of separations between nodes, the space of a network, or netspace, is created. And by means of such netspace it becomes possible to determine relational rates of change, allowing a related nettime to emerge. Networks can connect to each other and constrain and contain each other. When networks or their parts indirectly influence each other by means of interactions between a shared or layered background, we speak of resonance.When networks contain or nest within each other, such that networks are partially or completely contained within other networks as their modules, or it the networks in question are composed of different matters, they may layer on top of each other. It must not be thought, however, that the terms just described, such as background, node, field, structure, link, topology, module, layer, or individuation are elements which exist separately from each other, for they are only defined relationally. That is, as some theorists have argued, a node is ‘where a network intersects itself’, or ‘ a node is a shortened link, a link an extended node.’ In many networks in process, we see network elements transforming into each other, and thus a network can only be understood from perspective of one’s own position within a network of reference. Networks are ultimately perspectival diagrams whereby relation can be understood. Ultimately, however, they are nothing more.

From such a perspective, all the world can be viewed as a network of one type of another, and all that is is a nested series of networks of different types, in different modes, etc. The Network is ultimately no more and no less than a diagram for thinking relation. It is a lens upon the world which may have much to tell us about our hyperconnected age.


© Christopher Vitale, 2009.

Article: “On The Metaphysics and Physics of the Networkological Endeavor: An Introduction”

[Note to the Reader: Here is the full text of the article published in Speculations: The Journal of Speculative Realism, Vol. 2.
The first section of this article describes the metaphysical core of the networkological endeavor. This is done by means of an articulation of the concept of the network diagram. This concept is composed of four primary elements, namely, the node, link, ground, and network/level, each of which is described in turn. This section will appear, with some degree of modification, in the book manuscript being finished for Zer0 books.
The second section of this article then goes on to begin to describe how a networkological approach can begin to be applied to some of the traditional notions of the physical world, such as matter, mind, space, time, extension, reality, knowledge, etc. This section will be reworked for the second volume of Networkologies, the draft of which this is currently a part.]

On the Metaphysics and Physics of the Networkological Endeavor: An Introduction

[diagrammatology: the network diagram]
ELEMENTS. The networkological project is an attempt to develop the potentials implicit in network diagrams, and in relation to networks in the wider world. Network diagrams are iconic signs whose relational form resonates, in varying degrees, with relational forms in networks in the world. The philosophical concept abstracted from the multiplicity of networks and network diagrams in the world is known as the network diagram. The three primary components, or elements, of the network diagram are the node, or individual, the link, or relation, and the ground, or context, from which these emerge. In addition, when a group of network elements are contained by other network elements, we see the manner in which what is considered an element of a network can also be a network as a whole in its own right. When network elements contain each other in this manner, we say that there is a difference in level of scale between the elements and whole network(s) in question. As far as we know about the structure of our universe, all networks are elements and all elements networks, depending on the level of scale, all the way up and down, up to and potentially including the open, at both the smallest and largest, most concrete and most abstract levels of scale. In this sense, we can say that the network diagram has three primary elements, namely, the node, link, and ground, as well as a supplementary element, which can be called the network, as a whole, or the level of scale, depending on one’s perspective. The network diagram thus takes the form of what will later be described in depth as a triandic structure, one inherent to the manner in which the oneand manifests in the threeand, as described by the concepts of the node, link, ground, and network/level. Networks elements arise in many forms in the world. When a node emerges from a ground, we say that it has individuated, and when a link emerges between nodes, it has connected them. Levels emerge within networks by means of the process of leveling, and grounds may give rise to or absorb any and/or all of these elements. Networks/levels, nodes, links, and grounds may be static or dynamic, heterogeneous or homogeneous. Nodes may encompass all of an element, or only an aspect thereof. Links may be uni-, bi-, or multi- directional, precise or fuzzy (indicative of what Ludwig Wittgenstein would call a ‘family resemblance’), single or multi-threaded, etc. Grounds may also be homo or hetero-geneous, flowing or static, and levels may take in groups of network elements or whole networks, may fold in various ways, etc. Networks include any and all of these permutations. From the diagrammatic germ described in this section—the threeandic formation of the node, link, ground (and level)—the entire networkological project springs.
DIAGRAM. The concept of the network diagram, and its associated concepts of network elements, are abstractions from networks in the world, and represent the networkological endeavor in its most abstract form. The concepts in question are clearly abstractions, and they collapse under the weight of this abstraction when taken to their extremes. However, as the source of generalization, abstraction has its uses, in that it can help us clarify in extreme form aspects of more concrete formations in the world. The first and foundational concept of networkological diagrammatology is that of the network diagram itself. The network diagram is both a concept and a diagram, for it is a concept of a sign, and the sign of a concept. A diagram is a sign which represents a concept, but the network diagram is a diagram which represents a concept which is also a sign. For unlike signs such as alphabetic or ideographic signs, network diagrams both say and show, they represent and perform relation. It is for this reason that the network diagram is both sign and concept, and while it cannot be easily drawn, for it is the concept of the network in its most abstract sense, and thus, abstracted from any particular form thereof, it can be described by means of the articulation of the relations between its component concepts.
NODE. The concept of the node in the network diagram represents the principle of unity. At a given level of scale within the network diagram, a node is without parts, completely identical to other nodes in the network, for in fact, each node is simply an instantiation, an ingression, of the node which is itself a concept within the concept known as the network diagram. It must be kept in mind, however, that no node can be a true unity, for true unity is an abstraction, for it would be without relation, and hence, we could have no experience of it. For this reason, we can say that the concept of the node is a form of unity- within-difference, or the one(and).
LINK. The concept of the link in the network diagram represents the principle of difference. Links hold apart that which they connect, and this is what is meant by difference, namely, disjunct-unity, or the two(and). When the concept of the link intersects that of the node, the result is the plurification of the node into nodes, for once there is a link, there are necessarily nodes rather than a node, and hence, a network rather than simply an element.
GROUND. The concept of the ground in the network diagram represents the principle of indistinction. Grounds are neither/nor, for they are neither fully inside a network nor outside of it, and in this sense, we can say that they are extimate to networks. This is not the only manner in which grounds are neither/nor, however, for they are also neither unified nor dispersed, neither nodes nor links, and while they may be the background of a network, depending on how that network is deployed in the world, they may also be the foreground. In the capacity of foreground, a ground functions as a node, just as when it functions as a background, the ground functions as a link, in that it links the network to the wider world. When the concept of the ground intersects with that of the node and the link, the result is the potential for change within the network articulated by the node and the link. Change always involves production or consumption, which are forms of transformation. For when nodes and links change, they do so by drawing upon the ground, or releasing into the ground, that which is produced or consumed in order to make this change occur. Some change may even lead to the emergence or dissolution of individual nodes or links. The concept of the ground deepens the difference presented by the concept of the link, developing disjunct- unity into self-differing, or the three(and), for it is by means of the interplay between nodes and links with the ground that networks can become different from themselves. Furthermore, grounds exist both inside and outside a given network, and in this sense, they allow the network to relate to the wider world. In this sense, we say that grounds are extimate (exterior yet intimate) to the networks of which they are a part. While links and nodes may exist in many networks at once, only grounds may be shared by networks, and in this sense, exist neither solely in one network nor another. And in this manner, we see how the neither/nor of the ground has the potential to deepen into the both/and of the level.
NETWORK/LEVEL. The concept of the network in the network diagram represents the principle of emergence, and for that reason this concept is doubled, for it is both the network as a whole, and the level as a part of another network as another whole. In this sense, we see the manner in which the notion of the network/level deepens the disjunct-unity of the link and the self-differing of the neither/nor of the ground into the emergence, or threeand, characteristic of the both/and of the network/ level. The concept of the network/level is both whole and part, it contains itself, and does so infinitely, and with infinite intensity. When the concept of the network/ level intersects with that of the node, level, and ground, it causes them to enter into a state of emergence. Such a state is doubly split, for emergence at any level implies a relation to a macro level which contains the level in question, and a micro level which is contained therein, thereby giving rise, in their intersection, to the meso level which unites them. Hence we see the split between meso- macro and meso-micro, as well as that between meso and macro-micro, which itself splits amongst itself, taking on thereby the form of a threeand. This self-containing threeand (split macro-micro, split between meso and macro-micro, split between meso-macro and meso- micro) has a form which mirrors the manner in which the network diagram can be considered as itself split between a threeand in which diversity contains unity (the level which contains the ground, link, node, and network), and one in which unity contains diversity (the network which contains the node, level, ground, and level). When the concept of the network/level intersects with the concept of the node, it transforms the pure unity of the node within itself, the lack of distinction between that which it unifies, into a disjunt-unity in which distinctions of various sorts may occur. When the concept of the network/level intersects with that of the link, the disjunct unity between nodes is transformed such that the relation between any network elements and/or networks can be seen as a form of link, thereby expanding the disjunct-unity of the link between self-differing and emergence. And when the concept of the network/level intersects with that of the ground, it transforms the self-differing of the ground into an emergence, in that any individuation, decomposition, and/or transformation of a network element in relation to a ground becomes the potential for an emergence of a network/level as well. However, the self-differing of the ground is also that which transforms the concept of the network into that of an emergence, or that of a level, for it is the self-differing of the concept of the ground which, as self-exceeding, pushes the concept of the network into the emergence of the level. The ground represents that which, as both inside and outside the network, exceeds it, and it is for this reason that the self-exceeding aspects of the network diagram, the –andic side which it bring to the three, is split between the concept of the ground and that of the network/level, while also finding itself in germ in the notion of the disjunct-unity within the concept of the link. The result is that disjunct-unity, self- differing, emergence and unity are necessarily various sides of the same, in that unity-in-difference, disjunct- unity, and self-differing, are all ultimately aspects of the manner in which the world emerges from within itself. While each emphasizes different aspects thereof, they are nevertheless all abstractions from the self-differing emergence of what is. And while emergence emphasizes levels, self-differing emphasizes grounds, and disjunct-union emphasizes links, and unity-in-difference emphasizes nodes, ultimately, these are all but sides of the oneand as it brings itself forth. Levels link networks, and are networks, for they allow for each network element to function as each other, depending on how they are related to other networks. That is, levels may link nodes and nodes, links and links, grounds and grounds, networks and networks, as well as any combination thereof. These structures, as described above, continue all the way down in networks in the world, at all levels of scale, and do so fractally. That is, the concept of the level describes the manner in which the oneandic nature of emergence manifests itself triandically, that is, as a fractal and holographic oneandic proliferation of threeands within threeands, at all levels of scale. The concept of the network/level show us the manner in which the concept of the network diagram describes the concept of relation, for it intertwines that of unity, disjunct-unity, self-differing, and emergence, thereby producing intertwined series of triands which give rise to the fractal, holographic, relational complexity of all that is.
THE ONEAND. By means of the relative degrees of reification of the oneand, as manifested in unity-in- difference, disjunct-unity, self-differing, and emergence, the oneand comes to emerge from within itself. It thereby produces relation, for it is relation in the process of its coming to be. And to the extent to which we can say that the degree of reification manifested by unity-in-difference is the most extreme present within the network diagram, we can say that the oneand in this guise cloaks itself, and does so in a manner which can be described as that of the one(and). The movement from oneand to one(and), then, describes the motion of the concept of the network diagram within itself. In addition, we can also say then that the concept of the link represents the notion of the two(and) (as well as the intermediate form of the self- exceeding binary of the twoand, as utilized by figures such as Bergson, Derrida, Luhman, Deleuze, etc.). And beyond this, the concept of the ground represents the notion of the three(and), and the level that of the threeand which opens onto the oneand itself. For it is by means of the plurivocity of the level, of the production of differences in kind from differences in degree, the movement from the indisctinction of the ground to the multiplicitous distinction of the level, that we see the emergence of the new within emergence itself, the production of the actual from within the potential. This process, which continually produces itself from itself, describes the manner in which the threeand manifests the oneand. For while the threeand is a concept extracted from a diagram, that is, a representation of aspects of the world, the oneand is the world, it is the world and the concept thereof, it is the process of the world in its self-exceeding, and the threeand is merely the means whereby it comes to know itself as relation, fractally, holographically, and immanently, at all levels of scale. All of what follows is simply a wager on the potential resonance between the concepts presented here and the wider world, such that the articulation of what follows is simply an unfolding into actuality of the potentials abstracted by the threeand of the diagram from its relation to the world, a process which must now effectively be reversed.
[matrixology: extension, self-differing, and worlding]
MATRIX. Matrixology is the study of how networks manifest in the world of experience. As a philosophy of relation, the networkological approach does not firmly separate ontology from epistemology, matter from mind. Following Baruch Spinoza, the networkological perspective grounds all that is in a single fundament, of which matter and mind are simply aspects. This fundament is called the oneand, or matrix, for it is within all, as well as that which gives rise to all, it is the emergent self-differing which gives rise to all existents. All forms of matter and mind are so many various incarnations of matrix, and matrix is within all of these and beyond them all. Matrix is the potential to be of all that is, as well as what potential becomes as it unfolds into the actual. When matrix has not come to be it is called potential, when it comes to actualize itself in a location it is called matter, and when matrix comes to experience itself, it is called mind. Mind and matter co-permeate, if at differing degrees of intensity and in different forms, at all levels of scale. For the networkological approach, and unlike the inheritors of René Descartes and Immanuel Kant, mind is not the exclusive province of humans or even animals, but something which ‘goes all the way down’ to the quantum level and potentially beyond. Unlike those who rigidly bifurcate the world into mind and matter, or subject and object, the networkological approach does not need to bridge a mind/body gap, for it sees none. Rather, its task is to explain the diversity of combinations of matter and mind that give rise to the varied phenomena in the world. Within matrix, there are several aspects of the oneand which manifest as the open, that is, as that which prevents matrix from ever being fully at one with itself, and whose avatars structure its modes of appearance, or matrixology, thereby giving rise to variety in the world. From an epistemological perspective, the open manifests itself as the undecideability of the fundamental obstacle in its varied forms. From an ontological perspective, the open takes the form of originary potential. And from the ethical point of view, the open takes the form of the call to maximum robustness. While these sides all present themselves, and will be explained in turn, they are all refractions of the same fundament, namely, the oneand of matrix in its process of emergent self-differing. The networkological approach, which frames itself relationally at the intersection difference and relation at the site of emergence, is thus ultimately neither a philosophy of ‘the One’ or ‘the Two’ but the one which exceeds itself, the one-and. Thus, it finds common ground with any approach to entities which finds them in the process of emergent self-differing, or becoming-other, for this is the necessary fundament for any truly relational philosophy. In the what that follows, the manner in which matter and mind intertwine within matrix as experience will be examined, first in its most general and abstract sense, and from there, in the varying ways in which forms of matrix emerge from one another, from the simplest to most complex. This examination of the ways in which matrix exceeds itself is what is what the networkological project calls matrixology.
EXTENSION. As matrix comes to be, it differentiates. While such differentiations may be stacked on top of each other in superposition, when matrix comes to be, it does so in ways that allows for differences which exclude each other. The result is an exclusive relation of a particular difference to matrix, segementing it and extending it within itself, producing spacing or distance within matrix, resulting in the genesis of separations, disjunctions, actualiztaion, and change. Such a process describes the manner in which matrix gives rise to the distribution of perspectives on what exists. Each perspective entails a view of the whole, one which emphasizes certain aspects over others, and this is what is meant by location. Each location is a node which links together the varied changing inputs of all that is, and perspective is the name given to the manner in which the location of an entity within an extended network determines, in relation to the nature of the entities in question, the strength of the impact of each on the other based influence based on the relative degree of separation between them. The emergent self-differing of matrix into localized perspectives is the result of the process whereby matrix comes to actualization, for it is only by means of this separation and self-distinction that matrix is able to localize, differentiate, experience itself, and appear to itself, and ultimately, these are various sides of the same. Most theorists today believe that our common universal matrix, or universe, originated within a singular formation often simply called ‘the big bang’ or ‘the singularity’. This originary matrix, from which all in our universe came to be, began at some point to self-differ, to shift from potentiality to increasingly complex forms of actualization. This process allowed for the growth within itself of what, following Whitehead, is called extension, namely, the opening within originary matrix that produces localization, perspective, and the relative mappings of changes therein, known as spacetime. Extension, spacetime, localization, and perspective are simply so many different ways of saying that the potentiality of the originary matrix began at some point to actualize, that is, to exclusively differentiate, and unfold into what we experience. Because our language is itself the product of an extended universe, it is ill equiped to describe the process of the coming to be of coming to be, of the genesis spacetime, unfolding, extension, actualization, etc., and it is for this reason that any attempt to do so must always use language against itself, fold back upon itself, etc. We can, however, describe this state at least negatively, and in relation to certain phenomena that exceed standard extended formations in our current context. At its furthest extent, we call all that we can experience, to the limits of our current spacetime horizon, the universe. However, the universe may also be part of a set of universes, or multiverse, which exist within a larger overall context, known as a megaverse. All of these are developments of the originary matrix which formed all of the current context within which we exist.
SPACETIME. Since the structure of spacetime networks differ according to the perspective of varied locations within the universe, there is a difference between what, following relativity theory, is called the proper time of an entity, that is, the experience of change as measured from the perspective of any given entity, while the change in time for a given entity as measured from the outside will be called a temporal mapping. Both of these are different, however, from the change of the universe as a whole, the ordering of which may be widely spatio- temporally different according to differing perspectives on the universe, and that from which all proper times, even if incompossible, emerge. Following Whitehead, we call this overall change, that from which proper times emerge, the creative advance of the universe. Building upon the distinction between proper time and creative advance, it is also worth conceptualizing the distinction between space as it is apprehended from a given location (called an inertial frame in relativity theory), and that as mapped from an outside location. We will call the first an entity’s proper space, and the apprehension of a space from an exterior location a spatial mapping. Space and time are ultimately abstractions, for it always takes time to move in space, and the changes which we use to apprehend movement can only be apprehended by motion in space. Even in everyday language, we say a voyage by car to another city is ‘an hour away,’ and we use the movement of a hand on an analog clock to describe changes in time. For this reason, the networkological project will generally speak of spacetime locations, rather than moments in time or locations in space. According to the theory of relativity, when one moves through spacetime, no matter how curved that spacetime may be, one’s own spacetime always seems flat, it is only that around one which seems curved. For in fact, only if one moves within flat, non-warped spacetime will one percieve the spacetime of its world not warp around it as its move. We will speak of an entity’s proper spacetime as the apprehension of time and space from path within spacetime of that entity, while the apprehension of spacetime from an exterior location will be called a spacetime mapping. Distortions in spacetime are never experienced directly, but only indirectly as one changes location in spacetime (which includes remaining in one location while the world around you changes, or moving in space while the world around you changes). This is because change is always relative (that is, any inertial frame of reference is equivalent to all others in relation to the laws of physics), and hence any entity can only experience changes in its own spacetime curvature indirectly by apprehending changes in the world beyond it.
POTENTIAL. All matrix has within it the potential for self-differing. Potential is emergence under the aspect of the future in the past (emergence that will have occurred), while the actual is emergence under the form of the past in the future (emergence which is always already different from what it was). From originary matrix to any bit of matter within the world, it is fundamentally unknowable whether the potential to be different present in any actualization is the result of mind or matter, or due to internal or external causes at a given localization in spacetime or level of scale. Some of the reasons for this are simply practical ramifications of the manner in which extension intertwines matrix within itself. It is logistically impossible to observe an entity from all spacetime locations, and at all levels of scale, and hence to know all the influences upon a matter, as well as all the hidden potentials therein in the future. What’s more, it is impossible to observe a matter from within, and thereby know the degree to which its decisions come from its form of filtering its influences, those influences itself, or some other, more fundamental source of differing such as originary potential. But to know another matter from within in this manner would be possible only by means of being that matter, which violates the very notion of matter itself. Beyond this, however, there is the issue of quantum fluctuations which, under the correct circumstances, could cascade up the series of networks in a given matter and tip the scales of a decision towards a given outcome. Researchers are relatively convinced of the fact that is impossible to know if, on a quantum level or below, there is some aspect of what is which renders matter itself fundamentally indeterminate. Within quantum mechanics, researchers still debate whether or not the fundamental indeterminacy of quantum fluctuations is due to the influence of minute shifts within the context of the quantum event in question, conveyed in a manner which is too delicate for our instruments to detect, or whether these fluctuations are the result of something present within the particles and sub-matters in question. Beyond this, there is no way to know, at least within contemporary science, whether or not there might not be influences which we simply cannot sense, which come from beyond the confines of our universe, simply because the universe is the horizon of our current experience. For all of these reasons, it makes sense to acknowledge the fact that all matrix has the power to surprise us, for in fact it has never ceased to do so. While it may behave in regular ways for the most part, it seems as if there is almost an inverse ratio between the level of precision with which we need to know it, and the degree to which we can know it. Let it suffice to say that we can understand matrix, particularly in general, but that in particular, it is nearly impossible to know, and we can call this impediment to knowledge, and the difficulties it gives rise to, the quandary of potential. And in the right conditions, all that we know can be given rise to by matrix no different than what we see before us in our everyday lives. All that is, or could be, exists as potential within any and all. The capacity for self-differing, in all its forms, is what is known by potential, and all matrix has this within it.
SELF-DIFFERING. For the networkological endeavor, matter is that within matrix which is able to actualize a difference, and mind is that within matrix which is able to experience difference as potential which it can then bring to actuality via action. When matrix is delocalized, however, it is pure potential. But as matrix comes to actualize itself, it comes to differ with itself, not merely potentially, but concretely, exclusively in relation to a location, and hence, actually, giving rise to both difference within matter, which is then experienced by mind, as well as difference experienced by mind and then actualized within matter. Mind and matter are the two aspects of matrix which allow this transition, this emergence, to occur. As a philosophy of relation-in-process, the networkological perspective does not fundamentally distinguish epistemology and ontology, subject and object, mind and matter, nor does it distinguish whether difference originates in the matter or mind sides of matrix. Matrix differentiates into matter and mind simultaneously as potential comes to actuality. Mind is the capacity within matrix to be affected by difference, just as matter is the capacity to be difference, and subjectivity and objectivity are, within conscious minds, simply higher-level echoes thereof. To ask which precedes or grounds the other is a false question, for matrix gives rise to these very distinctions in its coming to be (and later in this work, we will describe this false question by means of the notion of the obstacle of experience). All matrix has potential for self-differing, just as all matter has potential to be differently, and mind to experience differently. Self- differing, extension, and experience are three sides of the same manner in which matrix emerges from itself, grasping itself as experience, and giving rise to appearance from within itself.
DISTINCTION. Within the self-differing emergent extension of what is, stasis interpenetrates with change, and continuity with discontinuity. Extension gives rise to both differences in degree, or intension, and differences in kind, or emergence. Emergence, occurs when intensive differentiation differs with itself or the world around it. The result is that discontinuities arise in terms of space, time, matter, and mind, giving rise to analog/ continuous differences of degree, and digital/distinct/ discrete/discontinuous differences of kind. Were there no discontinuities, change would be limited in the extent that it could develop, and likewise, were there no continuities, there would be no opportunity for entities to interact and change thereby.
MIND. At a given level, any material entity or system has a series of inputs which affect it, from both micro-/ interior (sub-matters) and macro-/exterior levels of scale, and these then must be converted by the matter in question into actions. Mind is that which feels the influences upon it a given matter, experiences them, and then decides upon these influences, in light of its relevant potentials, by executing an action within its own matter. It must not be thought that mind is a magical substance that somehow inhabits matter in a ghostely manner. Rather, it is simply the manner in which matter relates to itself within experience. Mind can be thought of as the giant distributed thinking present within the brain of the universe of matter. Put differently, mind is that which processes the micro- and macro-level inputs within a matter, in light of the potentials relevant to that matter at its level of scale. That is, mind is the manner in which the micro folds into the macro, and the macro into the micro, at the level of the meso, and in relation to the potentials within that meso itself. This folding, beyond the three-dimesions of space and one of time, occurs in what can be thought of as a sort of fifth dimension material, that of mind. In this sense we can think of the intertwining of mind and matter, experience and action, macro and micro, as similar to a non-orientable twist within topological figures such as a cross-cap or Klein bottle. For there is no way that micro and macro levels of spacetime could intertwine within a meso-level of matter without in fact turning space inside out at the level of the meso, and mind is precisely this turning inside out of matter within itself, a doubling of matter which is yet still nothing but the same. Where is mind located? Perhaps this is a false question, for we live not in a world of matter, but of matrix, of which matter is simply one side, and one we only know indirectly through the experience provided by mind. However, in relation to that material side of what is, we can say that mind is both as if it were on the same level as matter, but also as if it were in a sense dimensionally orthogonal to it. Matrix is both mind and matter, and these can be thought of as two levels of matrix, but levels which do not relate to each other as macro and micro, but as meso to meso in different yet intertwined domains. That is, like the manner in which electrical and magnetic waves in the physical world are two sides of the same electromagnetic wave, but on different yet intertwined dimensional planes, so mind and matter are like two side of the same, on diferent yet intertwined planes. One is the plane of experience, or mind, the other the plane of action, or matter. However, while electromagnetic waves are one step out of phase with each other, changes within mind and matter remain in phase with each other. This is the sense in which mind is an interiority to matter, and yet, nothing but another aspect of that matter itself, for in fact, mind and matter are simply two sides of matrix, two sides of the same. Mind is what casts matter outside of itself, into the world of influence and experience, just as matter is that which localizes mind in the here and now of action. If energy is the potential within matter to configure itself differently, then mind is the potential within matter to understand itself, to split itself up and re-relate to itself based on differences in location within extension. While matter and energy are strictly convertible within physics, as two different forms of the same thing, mind can be thought of as matter to a higher power, an intensification of matter which is a difference in both degree and kind, even as it is simply nothing more than that matter itself under another aspect, a twist of matter within itself, in a sense. Likewise, the reverse can be thought of mind to a higher power, a concretization and actualization within localized extension, wrenching the plenum of influences into the here and now of action. This snake eating its own tail is matrix, and matter and mind are two sides of the snake, each turning themselves inside out within each other, two sides of the same.
WORLDS. Matrix, mind, and matter divide and link up to locations within extension according to networks of symmetry within the manner in which potential actualizes within what is. The result is that matrix differentiates, giving rise, along with spacetime, location, and perspective, to particular matrixal entities. Each of these entities has a matter side, known as ‘a’ matter, and a mind side, known as ‘a’ mind. Each side, in its way, is the condensation and/ or expansion of the other, each in its way, even as each is also the condensation and/or expansion of the whole, each in its way. That is, location, spacetime, matter, mind, extension, differentiation, and experience, actualization, and potential are all so many sides of the same process whereby matrix comes to emerge from itself. When mind is localized as ‘a’ mind by means of ‘a’ given matter, it takes up a particular position within spacetime, producing a unified perspective on what exists, and what this unified perspective presents to that mind is that mind’s world. Each world is a recasting and reworking of all that is into the graded series of appearances, the strength and positions of which is determined by the structure of spactime and the nature of the matters of both the mind in question the matrixal entities which form its contexts. Any given world indicates the manner in which the world appears to a matrixal entity composed of the matter, mind, and location in question. For self-conscious and conscious organisms, the world appears consciously via perception, but for simpler entities, the world is still experienced, but not in a manner which is conscious. Thus, while simple entities certainly have a world which appears to them, they cannot be said to know this, but only experience it. At all levels, a mind’s world is continually recreated as the context around that mind shifts.
WORLDASPECTS. The myriad of worlds or graspings of the world form aggregates and subaspects in a variety of ways. The combinations or sections of these give rise to aspects of the appearance of the world, known as worldaspects. There are varying types of worldaspects, suchasastatic/0-dimensionalworldpoint,a1-dimensional worldline, a 2-dimensional worldsheet, a 3-dimensional worldsolid, and a 4-dimensional worldhypersolid. A world is an intertwining of any or all of these into a complex and shifting whole. All worlds are the result of the manner in which matrix experiences or grasps itself, giving rise to experience as appearance by means of the process of self- grasping in self-differing known as worlding. If extension indicates the manner in which matrix differentiates, worlding is the manner in which matrix reconnects with itself in difference at higher and more abstract levels of emergence. Ultimately, we cannot know whether or not the manner in which a mind experiences its world corresonds to ‘what really is,’ for the world is never experienced in this manner, but only by given minds from given perspectives. In this sense, there is no ‘what really is.’ What’s more, it is impossible for any given mind to determine the degree to which what they experience is due to its own nature and location, or that of its contexts. This will later be described as the obstacle of experience. What there is, however, is intertwined series of worlds, and varying degrees in which these resonate with each other.
WORLDEVENTS. Each time a given mind or matter changes, this is known as an event. Any event always occurs in a given world, and as such, is a type of dynamic worldaspect which is also known as a worldevent. There are three varieties of worldevents which can be experienced by a given mind in relation to its world, namely, interior material events, exterior material events, and interior mental events. When a mind experiences an interior material event in its world, such an event is experienced as a shift within the sub-matters of the matter relevant to the mind in question. For example, when I say, “I’m hungry,” I say this because one of my sub-matters, namely, my stomach, has communicated to my consciousness the sensations associated with lack of food. An exterior material event occurs, however, when matters outside the matrixal entity in question change. For example, when I say “The kettle is boiling,” I am recognizing a shift in the matters outside of me. An interior mental event, however, cannot be known by any mind directly, but only indirectly, through a loop through other matters which are then experienced by the mind in question. For example, when I move my arm, the aspect of my mind that moves my arm does not experience this as an influence coming from outside it, simply because it is this. It can experience the movement of this arm afterwards, however, indirectly, by experiencing the sub- matters in question moving. Minds cannot experience themselves changing except by means of a loop through either interior or exterior matters. It is in this way that some complex organisms have developed special loops within their control systems, or brains, such that some aspect of the brains in question are there specifically to experience others, thereby giving rise to what is called ‘self-consciousness.’ Since the mind of any given matrixal entity is merely a processor of influences and actions at a higher level of scale, it cannot experience itself but indirectly, after a delay and by means of its effects. And while I have used examples above to describe this mechanism by means of conscious entities, the same can be said, in much simpler fashion, for simple entities which do not percieve the world, but are only affected by it. Thus, when a stone breaks, we see a cascade of internal material events that give rise to a set of influences on the matter of the stone. These are processed by the mind of the stone, which gives rise to an internal mental event, which manifests itself in the matter of the stone as a particular type of break. This break is experienced by the mind of the stone indirectly, by means of a shift in the influences of its sub-matters and exterior matters, for the matter of the stone is in many senses nothing more than the intertwining of these two levels within a given spacetime location. After the stone breaks, however, can we speak of the stone as a single matrixal entity, or rather, one which is now split or dispersed? These sorts of questions depend upon the networks of reference which are applied to the matrix in question, and this depends upon the manner in which the entity in question is apprehended a given entity. While it may be possible to say the stone now becomes a dispersed entity, or rather, multiple smaller entities, this all depends upon the manner in which the matrix involved is divided up into networks within the world of a matrixal entity which does the apprehending of such a split. There are, however, many dispersed matters in the world, with dispersed mental aspects, and they simply function differently than unified matters and minds. Since ultimately all matters and minds are divisions of matter and mind, just as all matrixal entities are divisions of matrix, the question is not whether or not a given division of the world into aspects and events is correct, but rather, what networks of reference and perspective is implied by a given division. For the networkological project, all divisions of matrix are possible, and no division is truer than any other, for any given division of matter, mind, and matrix into aspects is symptomatic and provisional, rather than ultimate. Aspects and events are simply aspects of all that is.
WORLDING. Worldaspects and worldevents may conjoin to create the larger entities of which a world are composed. When events line up in a series, generally, though not necessarily, due to the unifying aspects of a single spacetime location or a given entity, the world aspect this gives rise to is known as a worldline. Worldlines, like all worldaspects, can be disjunct or unified. For example, the series of American presidential elections gives rise to a disjunct worldline. A unified worldline is one which describes the appearance of continuity between the events in question. When such a continuity is seen from inside, this is known as an interior continuous worldline, and when seen from without, an exterior continuous worldline. A continuous interior worldline is known as a duration. Any interior worldline has a shifting dynamic context which corresponds to it, the inverse of that worldline, the aggregate of the worldslices which correspond to the interior events of which that interior worldline is composed. This inverted line is known as that worldline’s interior worldstructure. Each interior worldline may be complemented by a variety of exterior worldlines, which may not correspond in all degrees with that of the interior worldline. The same disjunct unity described here in regard to events and worldlines, can be seen at higher levels of scale in regard to worldsolids, worldhypersolids, etc. Each worldaspect may be unified or disjunct, has interior and exterior sides, has inverses, and is composed of sub-worldaspects and is part of aggregate worldaspects at higher levels of scale. Appearance occurs to minds via the intertwined worlds which matters give rise to. Worldaspects are fundamentally related to spacetime networks, for spacetime is itself simply an abstraction of the aspects of worldaspects which have to do with location within the shifting dynamics of the world.
REALITIES. Each matrixal entity has its own world, and each event shifts worldaspects in relation thereto. No world exists in isolation, however. When minds share a given context, physical or otherwise, they are likely to have strong similarities between the form of their worlds. Whenever there are multiple worlds layered on top of each other in this manner, the resulting network of worlds is known as a pluriverse. When a pluriverse is constructed by matters which share the same general spacetime context, we say that this pluriverse is a physically localized material pluriverse. Within any set of minds within a spacetime context, the zones of symmetry between their worlds give rise to what is known as a shared world, or reality. Any reality is dependent upon the minds which exist in it, and its parameters are set by the interaction between them and their contexts. Realities can be physical or mental, for the same strutural parameters apply, namely, the establishment of shared points of reference within conditions of flux. Worlds come in nested networks, while realities also come in nested networks, but also in varying degrees of fuzziness, and in varying forms of complexity, as determined by the worlds of which they are composed. The degree of fuzziness of a reality is indicated by the degree of asymmetry it contains. The higher the degree of asymmetry, the less the entities which compose this reality will be affected similarly by events which appear to them in their worlds, and therefore, it will be difficult for any sort of order or complexity to form. Some degree of symmetry within the basic reality shared by a group of entities is needed if order and complexity of any sort can emerge. For conscious organisms, the reality they share with other entities in their world must have relatively high degrees of symmetry for them to operate within that world in a manner which can support cause and effect in regard to their action, support learning, etc. Thus, there must not only be a relatively high degree of symmetry in regard to space, but also a very particular sort of asymmetry, known as directionality or the arrow of time, in which time moves in only one direction within its spacetime contexts. Such a condition is also necessary for the development of complexity, life, and other preconditions of consciousness. For self-conscious minds, the same requirements hold, if at higher levels of complexity.
REALITYASPECTS. Realities describe the the intertwining of worlds via matter and minds, such that realities are composites of the worlds they contain, in which the incompossible aspects of these worlds are recast as excesses which are fuzzily and extimately included within this reality. Realities, like worlds, can be divided into events, lines, sheets, solids, and contexts/structures of various sorts and degrees of complexity. The difference between them, however, is that worlds are inherently divided between interior and exterior sides, while a reality is always shared between entities, and emerges from the intertwining of interior and exterior world aspects. As such, there are internal and external sides of every entity and event, but no direct experience of mind enters into realities, where this does occur within worlds. This disjunction between world and reality is manifested as what will later be described as the obstacle of privacy, namely, the inability of one mind to experience what it is like inside another.
REALITYFORMING. How many worlds and realities are there? Ultimately, there are as many worlds as there are entities and events (which in their way are two sides of the same), and as many realities as there are networks of worlds. Just as worlds are networks, so are realities networks composed thereof, if differently. And in fact, all worlds are composed of realities, and all realities composed of worlds, down to and potentially including the quantum scale (where such distinctions become fuzzy), and it is the mind of a given matter which knits them together, each into the other, as it processes its relation to its context, or world. For ultimately, what a mind does is produce a world from a series of realities, just as matter shatters worlds back into semi-compossible realities, only to be recomposed by intertwined networks of minds at further stages in this cycle. In this sense, worlds and realities are differing aspects of the same. Both worlds and realities, however, are always exceeded by the world of which they represent graspings.
THE WORLD. All entities in a given universe ultimately share the same basic reality, known as the world. The world is a reality and world as well as universe, for it is both between and beyond these very categories. As the universe, the world is no different therefrom, for the universe is the manner in which it experiences itself, and hence, there is a difference in name and emphasis only. As a world, the world is the manner in which the universe experiences itself. As a reality, the world is extremely fuzzy, due to the extreme degree of difference between the realities of which it is composed.
MAPPING. Realities and their aspects appear to minds, if in a different manner than worlds and their aspects. Non-conscious minds are affected by their worlds, by they do not know them. Likewise, they are affected by the realities within which they exist and which they give rise to, for entities may grasp their worlds in manners which have symmetry between them, and lead to symmetries in the realities which form between them. Only conscious minds, however, posess the ability to recognize distinct entities, and by means interactions with entities repeated over spacetime, construct maps of the symmetries at work within the reality shared by entities in a particular zone of the world and the conscious mind in question. Doing this intentionally by means of a series of controlled interactions with these entities is known as reality testing, or experiment. Mapping is one key way in which conscious minds work to increase their sync with their worlds.
QUANDARY. All attempts to know matrix have limits. These derive from both the open, intertwined, and extended manner in which emergence manifests itself within the world, but also from the inherent difference between knowledge and understanding. When an attempt is made to capture aspects of the world within knowledge, its conceptual and representational form mesh better with some aspects of the world, but less with others. This is because aspects of the world may be relatively static, situated, and isolated for periods of time, even if they are ultimately necessarily relational in nature. When an attempt is made to fix these relatively reified aspects of the world in knowledge, entities which use these forms of knowledge to organize their relation to the world may do so without experiencing large difficulties coordinating their relation to the world, or within the systems of knowledge they produce. But as knowledge approaches more liminal, processural, emergent, extended, or otherwise unreifiable aspects of the world, the result is paradox, quandary, and infinite regress. This limit to knowledge is what is known as the fundamental obstacle. There are three sides to this obstacle. From an epistemological-diagrammatological perspective, the fundamental obstacle and its varied aspects are the result of what is known as the network paradox. Networks foreground aspects of the world, such that what is left out forms the network’s ground. Any attempt to know the ground in question results in the formation of a new network, but the same problem is ultimately reproduced within this new network formation. Even when an attempt is made to know the world via a series of nested and interlinked dynamic networks, there will always be that which grounds this complex meta- network, and which therefore connects it to the open. In this sense, the structure of inside, boundary, outside is found, if differently, in each of the fundamental obstacle’s manifestations, and these correspond in their way to node, link, and ground, respectively, with each node itself being composed of networks nested within it in turn. The infinite regresses which occur within paradox and quandary are a function of the manner in which the network paradox plays itself out in a wide variety of forms. From an ontological perspective, the fundamental obstacle appears as the quandary of emergence. Emergence is the name given to the self-containing aspects of the world. Since all the world is emergent, if in differing degrees of intensity and in different forms, this means that different aspects of the world will evidence the paradoxical nature of networks in differing degrees and in different forms. The intersection of the network paradox and the quandary of emergence give rise to the fundamental obstacle in its many appearances. However, there is also an ethical aspect to the fundamental obstacle as well, namely, the appeal of the other. Since emergence is fundamentally unknowable, giving rise to paradox within systems of knowledge in its wake, this means that all systems of knowledge must be seen as provisional tools to increase understanding, rather than ends in themselves. The world as emergent is continually in relational and in-process. This means that its otherness from what we know is continually appearing. Only when we continually listen to this appeal can we use knowledge in a manner which is less reifying, more relational, and hence, less paranoid in structure.
OBSTACLE. When attempts are made to know aspects of the world in ways which violate the network paradox, the result is one three types of error, namely, those of experience, distinction, and completion. When these errors arise, we say that the knowing system has fallen into the representational trap, and we can tell this has occurred because the actions of the knowing system in question which are based upon these errors will often fail to sync with the world in which they find themselves. Each of the three types of error lines up with one aspect of the network paradox, such that errors of experience are forms of overnoding, errors of distinction are forms of overlinking, and errors of completion are forms of overgrounding. When a knowing system acts as if a network it uses to know the world matches exactly the contents of a network in the world beyond it, we say that this is an error of experience. This manner of error is an attempt to reduce the oneand to the one(and). This error occurs due to three fundamental manifestations of the fundamental obstacle, namely, the obstacles of matter, privacy, and the context. That is, a knowing subject can never know whether or not its representation of the experience of a matter, other mind, or the context of any entity is the same as its representation thereof. When a knowing system acts as if the distinctions given rise to by means of the networks it uses to know the world matches exactly those in the world beyond it, we say that this is an error of disctinction. This manner of error is an attempt to reduce the twoand to the two(and). This error occurs due to three fundamental manifestations of the fundamental obstacle, namely, the obstacles of decision, experience, and complexity. That is, a knowing subject can never know whether or not the distinctions it makes by employing representational networks to know the world are the same as those in the world itself. Thus, when a subject attempts to distinguish between the contribution of its own networks and the world in regard to a given experience, the subject cannot know the degree to which this distinction is itself the result of the networks it employs or the experience in question. This is known as the obstacle of experience. Likewise, when a subject attempts to distinguish between it’s own contribution and those of one of its subminds when that mind makes a decision, the subject cannot know the degree to which the distinction is itself the result of the networks it employs, or of its submatters. This is known as the obstacle of decision. And in complex systems in the world, whenever a subject attempts to know the degree to which the complexity of a system as a whole is due to the contribution of the submatters in question, the system as a whole, or the potentials relevant to the system in question, the subject cannot know the degree to which the networks formed by means of the perspective taken by the subject in question informs such a judgement. This is known as the obstacle of complexity. And when a knowing subject acts as if it is able to know by means of its representational networks all that is about a given entity, we say that this is an error of completion. Errors of completion are attempts to reduce the threeand of the ground to the three(and). Thus, when a subject acts as if its representations of a system are complete, without taking into account the manner in which all matrix can differ from itself, depending upon the context, we say that there is a manifestation of the obstacle of potential. When a subject acts as if it can know all that is about the world as a whole, thereby reifying the world from process, we say that there is a manifestation of the obstacle of the world. And when a subject acts as if it can know all that there is about a system, thereby denying the relational nature of all that is, we say that there is a manifestation of the obstacle of aspect. Beyond all of these forms of obstacle, whenever any of the errors in question are made in a manner that applys to levels, we say that there is an error of leveling, and that there is a manifestation of the obstacle of level. The obstacle of level may manifest in all the other forms of error and obstacle, for it describes a form of overleveling, an attempt to reduce the threeand to the three(and) of the level. Often these errors intertwine, layer, and interpenetrate, and there are wide varieties of intermediary formations. The reasons for the obstacles described here will be developed in later sections. However, it must not be thought that these obstacles occur due to magical or transcendent reasons. Rather, they spring from the basic relational form of what is. It must also not be thought that these obstacles are merely hindrances. Rather, they describe the manner in which the world remains open. That is, each obstacle is also an opening, and describes the manner in which relational wholes are not closed to change and the new. The ramifications of these issues will be described in full in sections later in this work.

Work in Progress: “The Networked Mind: Cognitive Science, Artificial Intelligence, and Post- Structuralist Philosophy”

The Networked Mind: Cognitive Science, Artificial Intelligence, and Post-Structuralism
[Manuscript nearing completion, current length is 218 pgs. (103,000 words), expected date to be sent to potential publishers: Feb. 2012.]
How does matter emerge from mind?
The Networked Mind: Cognitive Science, Artificial Intelligence, and Post-Structuralist Philosophy shows how recent  developments in complexity studies, soft-computing, artificial intelligence, and cognitive neuroscience can help continental/post-structuralist philosophy conceive a new ‘image of thought’ beyond the dead-end cycle of binary paradigms and the perpetual critiques thereof. Contemporary post-structuralist approaches to the question ‘what is thought?’ are still haunted by the ghosts of the Manichean Cold War ideologies of cybernetics which were key to the development of structuralism and its the works of its critics, the latter of which form the foundation of much of contemporary theory.
By means of a genealogy of the role of the binary opposition in regard to theories of computation, the mind, and theory, The Networked Mind shows how binary paradigms emerged, and then examines new ‘soft’ computing technologies to show how binary models are being displaced within cutting edge computing and artificial intelligence research. Relational and networked oriented approaches at the level of units of computation (fuzzy systems theory), relations between units (artificial neural networks), and meta-relations between modules (genetic/evolutionary programming) provide models for non-binary thinking at the level of node, link, and module.
Relating these advances in computation back to analyses of the human brain, The Networked Mind then details how recent theorists have had remarkable success using these newer networked models to describe thought as a complex, networked phenomena which emerges from networks which are intertwined at multiple levels of scale. When applied beyond the brain to the larger networks within which the brain is embedded, such as the body, life-world, language, and culture, it becomes possible to see the world as a series of intertwined and nested layers of networks giving rise to the emergent phenomena we call evolution, culture, and even theory.
Framing the science of networks within the larger frame of complex systems theories,The Networked Mind shows precisely what non-binary thought looks like, concluding with an analysis of the ways non-binary thinking  requires us to recast aspects of contemporary theoretical practice.
Beyond simply describing networked thought, however, The Networked Mind also performs it, for its content is presented via a mode of graphic design intended to sync with the new forms of reading which have come about due to the rise of the internet. The text is therefore written in titled ‘nodes’ which can be read in linear fashion, or ‘surfed’ in a manner more common to the reading of websites. Supporting citations and images are often ’floated’ in the margins, to be linked or delinked from the main body of the text at will. Seeking to interface form and content, The Networked Mindaims to create a book-form which speaks to the modes of reading increasingly being deployed by texts in the age of the internet.
Written in language accessible to non-scientists, and graphically designed so that its form is as networked as its content, The Networked Mind provides a new image of thought for our networked age. The text is fully written, consists of approximately 100,000 words, and is undergoing final proofreading in preparation for solicitation of publication.
  • Chapter One: The Myth of the Binary Opposition. A genealogy of the binary opposition in contemporary society, presented by means of two intertwined trajectories. The first contextualizes the rise of binary thinking in contemporary thought, tracking the influence of cybernetics and the political mindset of the Cold War on early structuralist thought of the 1950′s and 60′s. While contemporary theory in its post-structuralist guises is often based on the critique of these binary models, it has yet to come up with a viable alternative. The second trajectory traces the rise of the binary paradigm in modern computing, from Leibniz to the development of mainframe computers in the postwar period. The contingent politico-social foundations at work in the binary paradigm, along with the history of successes whereby network models have begun to displace binary ones in contemporary artificial intelligence and ‘soft’ computing research shows the limits of the binary model, and the need to move on.
  • - Chapter Two: Beyond the Binary – ‘Soft’ Computing. New technologies collectively known by the name of ‘soft-computing’ are increasingly being used to displace binary approaches in contemporary computing research. In language accessible to the non-scientist, yet detailed enough to show what’s ‘under the hood,’ this chapter describes the ways in which non-binary approaches to the unit of computation (fuzzy systems theory), relations between units (artificial neural networks), and relations between groups of meta-units (genetic and evolutionary programming) provide entirely new paradigms whereby to think about how computers operate, how they are built, and the foundational assumptions of the discipline of computer science itself.
  • - Chapter Three: Networking the Brain. The brain is a network. Examining advances in cognitive neuroscience, this chapter will debunks the myth that neurons function like binary switches, or that groups of neurons function like the chips in modern serial computers. From there, this chapter shows how recent developments in complexity studies, along with the insights provided by soft and networked computing models described in the preceding chapter, have opened up new avenues for understanding the brain as a complex network that is continually working to sync with both itself and its relation to the outside world. Integrating cutting edge neuroscience with a tour of the work of a variety of  early twentieth century philosophers, such as John Dewey, Henri Bergson, and Maurice Merleau-Ponty, many of whose ideas on the brain are only now beginning to be confirmed, this chapter will show us how a networked approach to the brain can work to integrate science and philosophy within a new way of thinking about the very notion of thought itself.
  • - Chapter Four: Wideware. The brain is never truly alone, it is always within a world, and a networked model of the mind works to show how the brain is only the central node within an extended network of the mind in its world. Starting with an analysis of embodied cognition theorists, the chapter will show how many contemporary theorists argue that the mind ‘downloads’ much of its thinking to the physical structure of the human body. From there the chapter will describe how evolutionary linguists are increasingly convinced of the extent to which tool usage and language have and continue to mold the structure of the brain as its develops both in one lifetime and in our species as a whole. By examining all the extensions of the brain in our world – the brain’s ‘wideware’ – this chapter shows how the body, tools, and language are essential to understanding the networked brain and mind in relation to its world and culture as a whole.
  • - Chapter Five: Networking Thought. Tying the technical findings of the preceding chapters to the wider concerns of the introduction, this final chapter will argue the need for a networked theory of culture which can help us make sense of the increasingly relational demands of our current age. Using the work of a wide range of philosophers  and critics, including Richard Dawkins, Manuel Delanda, Alfred North Whitehead, Ernesto Laclau, and Guy Debord, this chapter ends by sketching what would be required to construct a comprehensive philosophy of networks to meet the needs of our hyperconnected age.

Projected Texts: “The Networked Image: Lacan, Deleuze, Film, and Beyond” and “Nodularities: Towards a Networked Culture”

Currently the two manuscripts The Networked Mind and Networkologies are in final proofreading stages, and are just about ready to be sent out to start the process of soliciting publication. While I fully expect there will be various changes which will be needed to be made before these appear in print, and while I certainly plan a bit of rest, I have two additional projects which I’m currently at the point of dreaming up.
Unlike the other works, however, these are only at the ‘sketch’ stage of development, and no text has been written. However, both will be to some extent based on either courses I already teach, and in which I have found a good primary source lacking, or on texts I have already to some extent written. Nevertheless, I foresee the development of these two projects as a multi-year process.
* * *
The Networked Image: Lacan, Deleuze, Film and Beyond
The purpose of this book will be to introduce, in highly accessible language Lacanian and Deleuzian film theory, followed by a networkological synthesis of these which can be applied to more contemporary forms of images as well. The text will be written in clear, accessible language, and will work to serve as a general introduction to Lacan, Deleuze, and the networkological approach from the vantage point of contemporary cultures of the image.
My goal is that this text will also be useful for students in classes I’ve taught in which a usable and visually oriented introduction to psychoanalytic film theory (particularly of the Lacanian and Zizekian variety), as well as Deleuzian theories of the image, has been lacking. Much of this book will be based on class lectures I’ve done for my graduate course Cinema and Time. Readings of filmic and other media texts will be woven throughout to provide illustration to the points made, with extended readings in particular of time-travel and time-loop films such as The Prestige (Christopher Nolan), Donnie Darko (Richard Kelley), Mullholland Drive (David Lynch), Oldboy and Cut(Park-Chan Wook), Primer (Shane Carruth), Solaris (Andrei Tarkovsky), etc.
There will also be an appendix to The Networked Image, called Media, Semiotics, Networks: An Introduction to Semiotics. This short text, of which preliminary drafts of sections have already been written, will work to provide an extremely basic introduction to semiotics, and its relation to media studies and theories of networks, for absolute beginners. Much of this short text will be based on lectures I do for first year undergraduates as part of an introductory course I give on semiotics and the visual image.
For a taste of what’s to come, see the sidebar of the blog, where I have a section of mini-essays entitled “Mini-Essays: Full Online Guide to Reading Deleuze’s Cinema Books.”
* * *
Nodularities: Networks and Culture
This second major project will work to integrate a wide variety of written texts from various sources to examine the way in which networks and culture intertwine. More than just a series of essays, this text will use formal experimentation at the level of graphic design, as well as a series of common themes between the essays to develop a networked approach to a wide variety of cultural issues. The nodularity, or medium-length text, which will anchor this work will be a reworked version of my dissertation project on Richard Bruce Nugent, the only openly ‘gay’ author of the Harlem Renaissance. My work on Nugent was what originally got me fascinated in networks, because while writing my dissertation it seemed that networks were the only way to make sense of the intertwined and multiply constellatory project I was developing out of my graduate work in literature, philosophy, and visual culture.
This nodularity will weave Nugent’s polyform visual works with the crystalline narration at work in his experimental fictions to describe the manner in which his texts deform the primary narratives used to make sense of a figure like him, namely, those proposed by queer studies, African-American studies, and modernist studies. Nugent’s work provides us with a symptomatic node excluded from all these but uniting them by means of this exclusion, thereby allowing us to turn this constellation on its head. In the process, the constellations of race, sexuality, and post-modernism can be put into contact with the node of Nugent’s work to create a crystal which shatters many of the expectations for the future which impact our current age. Interwoven with this anchor text will be reworked versions of many of the more extended posts presented on this blog, as well as new nodularities that emerge to weave this all together between now and then.
The goal will be to show that the networkological approach is not only a philosophy, but also a theory of culture and cultural critique. The other essays will range widely an touch on issues such as masculinity, math education, activism and media strategy, and a wide variety of additional concerns, all woven together by means of the general approach to networks and culture which will be extrapolated out of the central Nugent essay to link it to the surrounding nodular texts.
* * *
Once again, these two major projects are in sketch stage, but since they are built from teaching and/or texts which have already partially been accomplished, these seem to be very doable projects upon which I can likely begin work sometime during the next academic year. My hope is to begin producing some first draft text for The Networked Image at some point in Spring 2011.
At some point I would also like to write on the relation between networks and philosophy of math, as well as networks and political economy. These, however, will require extended research before I can even think of sketching out these potential future projects.

Post-Foundational Mathematics as (Met)a-Gaming

Mathematics is a fundamentally human activity, and a semiotic one at that, which is to say, it is an activity of making and using signs in relation to the wider world of practices whereby humans relate to their worlds. While this might seem obvious, most working mathematicians self-identify as Platonists, which is to say, they take the position that they are working with realities which are “really there,” “mathematical objects” which are able to be discovered by means of techniques modelled on that of the discovery of physical objects in nature. Mathematical objects, which is to say, things like numbers and geometrical figures, are ideal entities whose contours are wrenched from the fabric of the ideal itself by means of the techniques of logico-mathematical proof. All of which is to say, even if there were no physical world, the truths of mathematics are “really there,” as if God given, hence the term Platonism, often worn with pride by mathematicians today. The locus classicus of this position is that of Leopold Kronkeker, in 1893 when he famously said that “God made the natural numbers, all the rest is the work of man.”
Nevertheless, Kroneker was responding to the foundations crisis which was beginning to shake the tree of mathematics. For example, logicists like Gottlob Frege had attempted to “found” mathematics upon the basis of its subsumption to the “rules of thought” articulated in his new logical calculi. The problem with this, however, is the at it hardly did what Frege intended, which is to say, to “ground” mathematics, and hence show its absolute necessity in “all possible worlds” (to use a term from Leibniz), but rather, to reveal just how ungrounded the seemingly incontrovertible world of mathematics actually was. When combined with the set theoretics developed by Georg Cantor, or the slippery attempts to ground number from linear continua as described by Richard Dedekind, it seemed as if just as mathematics had radically increased in power and rigor during the nineteenth century, it had also revealed in the process that perhaps despite or by means of this very power, it was all illusion, a slight of hand. Did the Emperor have clothes? Kroneker believed that blind faith was the answer, and so do many mathematicians today.
And of course, if one works far from the limits of the mathematical enterprise, which is to say, far from the applied aspects of mathematics which find themselve continually in dialgue with the physical world and its non-mathematical impingements upon the edifice of pure mathematics, then one is safe from these issues. Likewise, if one doesn’t stray too far into the realm of the pure, to the foundations of mathematics itself, one is also able to skirt around the issues of how precisely mathematics derives its authority or internal consistency. It is the in the “dirty middle” realm, from which both the shores of the physical world and the purely ideal world are both distant horizons, that the terrain of mathematics appears boundless. But at the shores, the issue becomes muddier indeed.
And this is what the foundations crisis that shook the mathematical world at the start of the century revealed. Some argued, with Hilbert, that mathematics was purely about signs, and was merely a game, and hence, should not be compared to the physical world. Any need for grounding was then moot, because mathematics grounded itself, circularly, and needed no justification beyond this. It’s own internal consistency made it a form of sophisticated play, and if it was useful in the world beyond mathematics, then so be it, but this was ultimately, accidental and not something worth the time of mathematicians. This “formalist” approach, however, simply ignored the fact that the engine of mathematical creativty had not only come from within, but without. The radical developments within mathematics during the early 19th century, for example, the great works of Leonard Euler, were often spurred by attempts to solve problems from mechanics, which is to say, very practical issues which engineering posed to the lofty realm of math, and to which it could not answer. Even analysis, the great discovery of Newton and Leibniz, had been wrested from the gods of mathematics by means of the push of the attempt to describe accurately the motion of heavenly bodies, not to mention the behavior of mundane physical objects. Whatever mathematics is, it is hardly pure.In contrast to this we see the Intuitionism proposed by L.E.J. Brouwer, who argued that mathematics should simply get rid of anything that couldn’t be grasped by the intuition of the mind as purely abstract nonsense. Brouwer attempted to “construct” mathematics on the intuitions of the mind, producing an analogy to the manner in which the mind intuits the objects of the physical world and the manner whereby it intuits the ideal realm of mathematical entities. A highly influential early twenteith century movement, one based to a large degree in Neo-Kantian ideas of scientific method and practice, Intuitionism largely fell out of favor, along with formalism, even as the limits of pure Platonist and applied approaches found their own limits in Goedel’s famous “incompleteness theorums” of 1929-31.
In contrast to this we see the Intuitionism proposed by L.E.J. Brouwer, who argued that mathematics should simply get rid of anything that couldn’t be grasped by the intuition of the mind as purely abstract nonsense. Brouwer attempted to “construct” mathematics on the intuitions of the mind, producing an analogy to the manner in which the mind intuits the objects of the physical world and the manner whereby it intuits the ideal realm of mathematical entities. A highly influential early twenteith century movement, one based to a large degree in Neo-Kantian ideas of scientific method and practice, Intuitionism largely fell out of favor, along with formalism, even as the limits of pure Platonist and applied approaches found their own limits in Goedel’s famous “incompleteness theorums” of 1929-31.
Goedel’s singular accomplishment was to put all four of these approaches to grounding math – Platonic idealism, Physical Realism, Intuitionist Neo-Kantian Subjectivism, and Objective Structuralist Formalism – to rest as aspects of the insoluability of the same problem. That is, math simply could not be grounded from within, nor could it be grounded from without without proving itself ultimately both grounded and ungrounded, and in fact, both and neither, from a mathematical point of view, in the process. What Goedel essentially did, then, was show that the very notion of “grounding,” at least as this notion was being framed by mathematicians of his time, was part of the problem. That is, mathematicians who wanted to ground mathematics from within, as the insurer of its own truth, would find only circularity, but no ability to say if this circularity applied to anything beyond math. Those who wanted to ground mathematics in something beyond math, such as the physical world or human intuition, or even the workings of ultimately meaningless signs, would find that all they could prove by means of the tools provided by math, from within at least, was that mathematics relied on something beyond it, but no way of showing the need of this, or the need of any relation to a particular grounding or another, by solely mathematical means. That is, to ground math with something beyond it (ie: human activity, human signs, human intuition, god), would require actually bringing something outside of math inside of math. And that would produce contradiction.
Circularity or contradiction, the result would be incompletion or incoherence, respectively. The final option, oscillation or inconsistency, was simply what most working mathematicians did, which is, to use whichever options made math “work best” in a given local instance, and leave “grounding” for some other time. What Goedel did was show that Hilbert’s famous dictum that math must prove itself “consistent, coherent, and complete” by its own means, which is to say, by means of mathematics, is simply not possible, and that this is not simply an accident, but part of the very structure of the way mathematics itself works. Goedel showed that math had its own limits.
Of course, some of this might seem like common sense. Math always counts (numbers) or draws (geometry) something which is not math itself. If I see a group of animals and count them, and label them “four dogs,” the dogs and the number “four” are fundamentally different things. Math is always both about and not about mathematics. When math tries to eliminate any aspect of it which is not math, or which is math, the result will always be, at least from wtihin math, paradox. So it is with any signifying practice. The same can be said about language. A dog is not the same as the word “dog,” and ultimately, one cannot “ground” the relation between the two, at least from wtihin language, without producing paradoxes. Just as Goedel showed this within mathematics, so Jacques Derrida famously demonstrated by means of linguistic deconstruction, and Ludwig Wittgenstein in his own way nearly thirty something years before. The fact that Goedel, Wittgenstein, and Derrida share what can be seen as variations of the same insight in different fields, one which resonates strongly with that of Heisenberg in physics, is likely perhaps not accident.
Naturalistic Mathematics?
If mathematics cannot ground itself, perhaps it can ground itself in the fact that humans devised mathematics. That is, it is a signifying practice, like that of language, whereby humans describe aspects of their world so as to interact with them. Mathematics is a special type of language, but language nevertheless. Of course, most working mathematicians are likely not to like this, because it subordinates their activities to something, anything. But there is no unsubordinated position from which to view the world, we are always mediated in our relation to anything and everything, and likely, are nothing but mediations of mediations all the way down, fractally and holographically. That is, any notion that there is some ‘God’s Eye Perspective’ from which to survey the world seems singularly outdated as any other simplistic form of faith in the unbiased. All is perspective, and mathematics is simply one amongst others. It is useful, of course, but so is language, our bodies, our brains, etc. Each of these has been viewed by its partisans as the singular, privileged lens on the world, and each can be decentered by others. Why mathematics should be any different is beyond me.
Rather, we live in a world of networks, each of which supports the others, culture and nature, language and physics, human and animal, living and non-living, each an aspect of a wider whole which supersedes them all. Whether we call this whole experience, or the universe, these are also simply aspects of it, attempts to describe the whole. And as Goedel showed in his way, Derrida in his, and Heisenberg yet another, the attempt of any system to grasp the whole from within it is likely to founder in paradox. In mathematics, of course, this is the famous paradox of the barber, Bertrand Russell’s attempt to articulate the issue of the “set of all sets.”
That said, these problems all become less of an issue if we say something like mathematics is a human signifying practice, which is useful in its domain in relation to others. Of course, this begs the question of what use means, but since humans are those who determine that which is useful to them, and are also the originators of any math we have ever known, then we could perhaps say that mathematics reflects aspects of what humans value in the world. That is, mathematics has helped humans do the sorts of things they value, one form of which is mathematics. While some enjoy doing math for its own sake, the urge to do something like mathematics does seem to find its impetus in practical activity, which is to say, the attempt to describe the world so as to be able to do things in relation to it. There is no question that both pure and applied mathematics have given rise to new forms of mathematics, but as some of the more “naturalistic” philosophers of mathematics today have argued, math is always between the physical and the ideal, with one foot in each, dirty and impure to the core. That is, it is a form of media, just like language, or the body. A lens on the world of experience, if a particular one, like yet different from all other media in this way.
While naturalistic approaches to mathematics are in the minority among working mathematicians, and even philosophers of mathematics, it seems to be the only approach to mathematics which takes into account its foundations crisis mid-century. If it dethrones mathematics from its attempt to imagine itself as the queen of the sciences, well, let it join philosophy and every other dethroned discipline which aimed for such a role. For perhaps it is the very desire for centrality which is the problem rather than attempt to “find” a solution, for it seems to give rise to paradoxes, whereby the very fabric of, well, something, call it the world or otherwise, resists. Physics, linguistics, mathematics, the foundations crises of many disciplines of the twentieth century, they all seem to indicate that the center does not hold, and yet, centerlessly, they still do many things. Naturalism attempts to start from this, from activity in the world, and human activity at that, rather than ideal foundations, be they ideal in the classical sense, or the materialist inversions thereof.
Post-Structuralist Approaches to Mathematical Gaming
If mathematics is a human activity, then perhaps it may be possible to philosophize about it in regard to this perspective on it. Certainly mathematicians refer to specific “things,” which they describe with symbols which they manipulate. These signifieds of mathematics are represented by signifiers, which is to say, the graphs and equations scratched on paper, computer screen, and chalk-board as “representing” something generally called “mathematical.” If “mathematical objects” are signifieds, meanings, that which are described and represented by mathematical signs, considered as signifiers, then perhaps we can think of mathematics as a specialized type of language, and the practice of mathematics as a type of writing and speech. Certainly not one which is meaningless, as Hilbert famously argued. No, mathematics seems to be about the world as much as about itself, just as any language, and yet, it is a very particular sort of language at that.
As any language, mathematics can be considered, as Wittgenstein famously argued, a game. That is, it has rules, and people get quite heated if you break them, even if the rules of the game are always being changed from within as you go. Good moves in the game, in fact, change the very nature of the game itself, and in doing so, change what it means to play, the players, etc. In this manner, the rules of mathematical play are like that of linguistic play, which is to say, mathematics has a grammar, just like natural languages do, even if this grammar works differently than those of natural language. But this grammar is a grammar nevertheless. And so, a (post)structuralist analysis of mathematics is not only possible, but I would say, desirable.
Structuralism viewed languages as composed of utterances, often described as “parole,” in relation to structuring categories which were implicit yet made sense of utterances, or “langue.” There are, of course, several types of langue working in any given language. For example, in a natural language such as English, there is the langue of the semantics of the language, which is to say, the meanings of words, systematized in a dictionary, which a competent speaker of English would need to understand to “make sense” of a given utterance. Just as one couldn’t make sense of a sentence such as “The cat is on the mat” without knowing, for example, what it means to “sit,” likewise, one cannot make much sense of a mathematical sentence such as “x – 5 = 17” unless one knows the meaning of what “5” means, and how this mathematical “word” differs from that of “17.” While it is necessary to bring in forms of semiotics which deal in diagrams to describe how this could be applied to notions such as geometry, the semiotics of C.S. Peirce seems more than adequate to the task.
Below the level of semantics, or the meanings of words, are the deeper structures, whose which determine the ways in which these can be linked to each other. A word like “is” in “The cat is on the mat” presents a word which is really not merely a word, but a word which represents grammar, or syntax, which is the foundation out of which word meanings arrive, for it provides the fundamental and implicit categories which all the meanings of words to take form. And so, if one was to look up any word in a dictionary, one would find that the word “is” equivalent to this or that meaning. “Is” is both a word and a meta-word, so to speak, and this is what is meant by langue in relation to parole. Just as knowledge of the meaning of a term at a given level is necessary to understand an utterance, so is the meaning of the meanings which describe the meanings of these words, which is to say, the rules of the game as well as the particular move being made. And so, if one doesn’t understand what “is” is, then understanding the particular meaning of “The cat is on the mat” is likely impossible. The same with grammar markers in mathematics, such as “=,” which ultimately, is very similar to saying “is” in a natural language such as English.
As is likely apparent from the preceding, recurcsion is operative here, not only at each level, but at any level. That is, each and any utterance/parole is related to a langue, which itself is a parole in relation to at least one other langue, and this repeats fractally. This is the contribution to this sort of structural approach made by post-structuralism, namely, the attempt to show the paradox of any attempt to find an ultimate foundation at work in such an analysis. And so, rather than argue that a notion such as “is” represents a “deep structure” of the language of mathematics, and hence, in some way, the world itself, a post-structuralist approach uses relatively similar methods to show that the process can be carried on infinitely, with no ultimate ground in sight, or, if one wants, arbitrarily ended for convenience sake. But any attempt at ultimate ground will give rise to something like infinite regress, which is to say, incompletion, arbitrary end, or incoherence, or some mixture, which is to say, inconsistency. Post-structuralism and Goedel are on the same page on this one.
Mathematical Meta-Gaming
From a post-structuralist perspective, then, it becomes possible to say that mathematics has objects, which are meanings within its semantics. These objects are things such as numbers and shapes, or any of the other entities which mathematics attempts to “treat.” When mathematics deals with combinations as if they were “things,” which is the discipline of combinatorics, then we know we are in the realm of mathematical semantics. These things are then linked together to produce utterances, according to the rules of grammar implicit to the “game” of mathematics.
The sorts of utterances vary, however. Some are simple equations, such as “x – 5 = 17,” which are then transformable, by a known series of procedures, into “x=12,” such that it becomes possible to state that these two are themselve “equal.” There are procedures here, such as “solving” equations, which are the utterances. And these procedures produce the grammar whereby mathematical equations are transformed, one into the other.
But then there are meta-mathematical utterances, and these are proofs. A mathematical proof makes use of procedures within the language of mathematics to create utterances which attempt to alter the way the game is played. This is, for example, not all that different from the role of argument in philosophy. A philosopher might argue, for example, that we shouldn’t think of reason or god as this or that. Ultimately, the philosophers is using words to impact the way we use words, just as a proof indicates the ways in which a mathematician uses math to impact the way math is done. Of course, the goal is ultimately to impact the way people think about math, but seeing as mind-reading isn’t yet possible, the only way we’d know how people think is how they act, which is to say, how they “do” math, and a proof may aim at how people think, but ultimately, it only manifests its effects in how people “do” math. The same could be said of the role of argument in philosophy.
None of which is to say, of course, that I haven’t been doing precisely this in what I’ve already said. In fact, the preceding paragraphs are simply arguments, attempts to impact the way the game of philosophy of mathematics is done, from within it. And this sort of meta-gaming is part of how the game is played, even if the results of this are always uncertain, which is to say, incomplete, inconsistent, or incoherent, at least from within the game as it currently stands. But games evolve, and meta-gaming is how this happens, in math and language as much as any other sort of gaming. And so, if I decide all of a sudden that a bishop can now jump, but only over rooks, in chess, and this move catches on, and becomes part of the new rules amongst the “community” of chess gamers world wide, then I have made an utterance, not within the game, but also not beyond it. In a sense, I’ve made a meta-utterance or meta-move in regard to the game, thereby altering its grammar from within.
Mathematics does this all the time. In fact, that is precisely what Goedel did, and what others do when they “invent” new mathematics. Those meta-moves which catch on become movements, such as “category theory,” or meta-meta-movements, such as “post-foundationalist mathematics.” None of which is to say that the meta-games precede the games, since there was no such thing as “post-foundationalist mathematics,” or even the need for this, before the foundations crises. Sometimes the meta-games pre-exist, because they have already been called into existence (ie: people have been talking about the grammars of languages for quite a long time), while other times, they are produced, even giving rise to new layers in between existing layers.
In a similar manner, mathematicians can give rise to new objects. Certainly “category theory” has not only given rise to new mathematical grammars within and beyond it, but also, new mathematical objects, such as “functors” or “categories.” The field of abstract algebra, of which category theory is simply one form, in fact is the branch of mathematics which works to deal abstractly with various sorts of ways of relating objects and grammars to produce utterances and meta-utterances. From its start in set theory, modern algebra developed into group theory and beyond, and by means of Emmy Noether around the time of Goedel, because the meta-mathematical enterprise it is today. If Goedel destroyed the hope of a single meta-mathematics, Noether proved that the true name of foundations was “many,” even if meta- as a notion was only ever “one” in relation to a particular location. Noether showed that grammars and objects have plural ways of relating. And from such a perspective, it becomes possible to see that foundations are things, but verbs, processes of continually founding and refounding, which is to say, relating to levels of micro- and macro- scale within a given level of practice, semiotic or otherwise.
It is for this reason that many have turned to category theory as a possible inheritor to set-theory, as a possible “post-foundational” foundation for mathematics. What is so incredibly slippery about category theory is that it defines its objects, grammars, and moves relationally. That is, the very meaning of an object is what you can do with it, and these “moves” give rise to the very categories of objects in question, and vice-versa. That is, object, category, and move are interdependently defined, collapsing the distinction between utterance and meta-utterance, such that all utterance is meta-utterance and vice-versa. All of which is a way of saying that the constructedness and reconstructedness is not hidden behind a smokescreen of “this is the way things really are.” Category theory is a mathematics, not of being, such as set theory, but rather, a mathematics of relation.
There are, however, other potential post-foundational discourses. Fernando Zalamea has, in recent works such as “Synthetic Philosophy of Mathematics,” argued that sheaf theory can play this role in a way different from that of category theory. Sheaf theory, a form of mathematics which works to extract invariants from particular transits between mathematical objects in transformation, is fundamentally a mathematics of the in-between. It is a mathematics which extracts from particular motions particular symmetries, and like group theory, then works to put these to work themselves in transit between local and general. For example, sheaf theory may attempt to describe the ways in which particular figures can be sliced and re-glued to themselves in ways which maintain coherency even when that figure is transformed in a particular way, and to then learn from this possible insights which can be applied to different yet related types of slicing, re-gluing, and transformation. In many senses, sheaf theory is a meta-analytic formation, which is to say, it takes the sorts of tools of decomposition and recomposition, analysis and synthesis, seen in notions such as differentiation and integration, and generalizes them to ever wider terrain.
Sheaf theory is then a mathematics of transits, of the temporary reification of an aspect of a transit, only to reapply this to another. In this sense, the objects, categories, and grammars are also relationally interdetermining, and the relation between utterance and meta-utterance are constructed and reconstructed continually, as with category theory. One difference, however, is that category theory is ultimately a logical enterprise, and doesn’t get into the specifics of particular figures and their equations, but rather, attempts to describe the logical grammar “beneath” the mathematical language used to describe and manipulate these. In a sense, then, one could say that category theory and sheaf theory are both instantiations of post-foundational foundations of mathematical practice, but in regard to differing aspects of the mathematical enterprise. Category theory is a meta-gamic approach to logic, while sheaf theory plays this role in regard to transformation within a particular field which already has instantiated categories of objects, categories, and grammars (ie: figures, types, and rules to regulate transformations).
None of this is to say that category theory is “more” foundational, but rather, it is more abstract, and this is different. Abstraction here indicates that this is a further move away from the physical world, and closer to the ideal, which is simply the realm stripped of specifics. Between a relatively “concrete” aspect of the world, such as a stone, there is the abstract representation of this, such as the word “stone,” or the number “1” which can be used to count this stone. Category theory leans to the latter side, and sheaf theory the other, but depending on the particular pole one is using to base one’s practice at a given moment, be this the concrete or the abstract pole, or any other for that matter, then the “foundational” orientation of one’s meta-gamic practice will proceed differently. Foundations are always foundationing, and as such, one always creates and recreates them by means of meta-gamic moves. The whole point of a post-foundational foundationalism is that it aims to produce the potential for foundations everywhere, rather than prohibit them, less this simply become foundationalism in reverse. The hope isn’t to proscribe foundations, but to liberate them, and in the process, practices, from the straight-jacket of both foundationalism and its evil twin, anti-foundationalism. Post-foundationalism, on the contrary, embraces creativity, which is to say in relation to mathematics, the potential production of new mathematical games and meta-games to give rise to new ways of descriging our potential relations to the world.
Foundations as Foundationings: Or, Mathematico-(Meta)gamic Ethics
If abstract and concrete are two poles which can help us orient in this process, these two should be seen as merely categories produced by meta-gamic moves, and hardly necessary, but produced and reproduced at each and any moment in which they are operative. Just as Zalamea finds this set of polarities useful, I also find those of the human body helpful. That is, if all mathematics can be constructed as the product of human activity, then perhaps, as with natural language, it makes use of categories which can be seen as potentially deriving from the form of our embodiment. Natural languages, for example, have nouns, adjectives, linking words (ie: prepositions), and verbs, four primary parts of speech, and some theorists, including Gilles Deleuze, have argued that these can be seen as the result of the ways in which human embodiment in the world makes use of things, qualities/categories, forms of relation, and actions, which is to say, nouns, adjectives, ‘linking words’ (ie: of, on, in, is, therefore), and verbs. The grammar of human language, then, can be seen as a way of representing some of the primary categories which humans have, by means of the media of their bodies, extracted from their worlds of experience. None of which is to say that these categories are necessary, but rather, that they are produced and reproduced, continually, by gaming and meta-gaming in the worlds of our experience, with language being one of the effects thereof.
From such a perspective, it might not be far-fetched to argue something similar about mathematics. That is, there are mathematical objects, which function like nouns, and categories of these, which are similar to adjectives, giving rise to semantics from the relation between these. From here, utterances and meta-utterances formed by means of these objects and their meta-linkages in categories, utterances, and meta-utterances give rise to modes of relation, which are represented alongside the objects and categories within utterances and meta-utterances by means of “linking words” which represent within these grammartical structure. But all of these are ultimately the result, sedimentation, and reification, if only partial, of the processes which give rise to these. Mathematics and meta-mathematics, two sides of the same, ultimately, like a language and its grammar, are processes of gaming and meta-gaming.
Thinking in these terms also allows for mathematical gamings to be linked up to philosophical notions as well. Set-theory, then, is clearly, as Alain Badiou has argued, the mathematics of being, and as such, has fundamental resonance with the philosophical notion of ontology, even as category theory seems to be something like a mathematics of relation. Sheaf theory seems an attempt to describe something like a mathematics of becoming, of the transits between the figural and the numerical, and within each. If, as Brian Rotman has argued, geometry is the language of space, and algebra the language of counting, it becomes possible to see these as so many layers of semantics and syntax in relation to each other, and yet, also permeated by that often forgotten stepchild of linguistics, which is to say, pragmatics. There is no vocabulary or grammar without a context which makes these relevant and meaningful. Without something like human bodies in something like a world of experience which has particular structures of space and time such as we know them, it is unlikely that anything like mathematical grammar or vocabulary, let alone those of natural languages, would make any sense. Likewise with what we tend to think of as constituting proof or argument.
By framing languages as composed of semantic vocabularies of objects, linked in syntactic categories which produce series of potential relations between these, which are grasped in meta-syntatic categories which are the grammars of that language which ultimately articulate the pragmatic linkage of that language to its contexts beyond itself, then what gives rise to all of this? Creation, it would seem, but also recreation. Math emerged from our world, and continues to reemerge from it, as does language. Semantics, syntactics, and pragmatics are simply aspects of this continual process of recreation. And if this essay attempts to do anything, it is to deconstruct attempts to hide the manner in which recreation, which is to say, emergence, is the ever present potential within any and all, here and now.
Mathematics and language, just as with any other sedimentation of our actions into representations thereof, are simply ossifications which stand out from our practices, which we then treat as if “real,” which is to say, as if necessary. And yet, they are only ever produced and reproduced by our actions, even as these are only ever produced and reproduced by that of our contexts in turn. We are networked, linked nodes of praxis within others, at potentially infinite levels of scale. And yet, within our particular zones of this, there remains the potential to give rise to effects which ripple widely beyond, leading, under the right contextual conditions, to the potential for cascades which give rise to a sea-change in how things are done.
There will always be those who will try to control the way things are done, who will try to close off our sense that, to quote the revolutionaries of the past, “beneath the stones, the beach,” or, in more contemporary idiom, that our world is only ever of our own making and remaking. No one entity can ever shift the whole, and yet, any one entity can sit at the fulcrum of others and provide the critical shift in a grain of sand that creates a massive change. Or participate in structuring such a set of conditions so that something else can provide that final push.
There are times, of course, in which it is necessary to restrict the manner in which things recreate themselves, for in fact, too much change can dissolve and destroy. But our world has almost never been in danger of such things, and when it has, it is the chaotic dissolution has nearly always served to reproduce the deeper aims of control. But creativity, radical creativity, doesn’t care if it is the center of the world, but only that it resonates with the creativity within it in its own way, amplifying the power of liberation and emergence, being emergence itself, even if towards an end beyond it. The reason for this, of course, is that emergence knows no fruit, it is its own reward. As anyone who has ever created anything knows, creation is powerful stuff.
Mathematics is a form of creation. If god created the natural numbers, and humans created god or are god, or even tap into some aspect of the godlike nature of creativity within fabric of the world as such, that which has never yet ceased to surprise us with its novelty, then by creating new mathematics, we allow the world to recreate itself through us. And in doing this, we learn something deep about ourselves, and about the manner in which we emerge from the world in and through things like mathematics. Human languages aren’t thinks, they are emergences and reemergences, as are we, as is, it seems, the universe from some primordial singularity.
While the end of this essay may seem far from questions of mathematics, the reason for going to such metaphysical issues is to make the point that they are omnipresent, and that reification obscures this, with control and petrification as the result and aim. Liberation and emergence can also be result and aim, and both are self-potentiating tendencies, as paradoxical as anything described by Godel, but dynamic beyond such at attempt to grasp it in snapshots. None of which is to say that we need dispense with reification, but rather, that we simply need not be seduced by its productions as being anything ultimate. Rather, there is always a play of natura and naturans, to use Spinozist terminology, or to cite Schelling, producer and produced. Forgetting that the produced is only a product and not the producer is the classic means of taking the present and its products as necessary. Those in control of our world have always relied on the stability of appearances to maintain the notion that the world has to be as it is.
While creation for its own sake can dissolve all that’s good in the world if taken to its limits, our world has always erred on the side of reification for its own sake, minimal necessary creativity to avoid ossification. This of course makes sense in world in which survival is that of the fittest. But in a world in which we can now feed everyone, in which the worst predators humans face are other humans and their products, the very evolutionary situation has changed, and so, our ability to survive depends on us unlearning the very lessons that evolution evolved into us to survive the brutal period of biological evolution. Surviving cultural evolution is the next step, and this requires walking backwards the paranoia we needed to develop out of the primordial oceans.
All the games we play, from mathematics to baseball, politics to economics, these are all human products, and products of the world beyond this in turn. Those creations and recreations we give rise to reveal what we value. And so often, we tend to forget that we have choices. Of course, if we are to truly make choices, we have to deal with the meta-gamic question of what we value, and why. To avoid precisely such meta-gamic questioning, it is often easier to simply pretend that our world is not even partially of our own making, and that our agency is small indeed. But while our agency is distributed and relational, it is hardly small.
The ethics of this essay is that of emergence, neither creation for its own sake, thereby giving rise to chaos, nor consolidation and control for its own sake, giving rise to stasis. Because our world overvalues the second, course correction would seem to value a shift to the other side, to novelty, but again, this should hardly be seen as necessary, only situational.
Mathematics has in fact engaged in a radical move towards creativity during the twentieth century, and put the seduction of reification behind it after the foundations crisis of the early part of the century, itself potentially a reflection of so many other crises of foundations early in the century, and their often violent repercussions. Foundations are always foundationings. They are statements of value and valuation, but if one looks for the values underpinning one’s values, there is only ever refraction to the whole, because the whole notion of value itself is simply the manner in which one is able to relate a particular move within a particular game to the meta-game played at the level of a given whole. The ultimate meta-meta-game, however, something like the world or experience, is precisely what the question of value addresses, and the answer is only ever inconsistent, incoherent, or incomplete. And yet, the creations and recreations we give rise to in the way we game and meta-game in relation to this is what makes everything worthwhile.
And if there is something that gives value to meta-gaming as such, it seems to be the emergence of (meta)gaming as such, and its continued emergence, the robust complexity of the games playable within the larger gamespacetime. Everything in our world worth valuing, after all, seems to only exist contextually within such situations. Life, for example, or the love which it can give rise to, these depend upon the complexity, and robust sustainable complexity, of the systems which give rise to them. Look at the best within the game, and use it as a guide to establish new guidelines for future gaming and meta-gaming, and continually readjust.
For games without rules, such as life or love, it’s always about values, and values are always about the relation of moves to the context of the whole, which is always in the process of emergence. But is that emergence getting better, and in a manner which is seems to lead to that in the future? Perhaps that is the best we can ask. If there is an ethics to (meta)games such as mathematics, perhaps it is in praxes like these. And while many may balk at the notion that math could ever have an ethics, there is no action in the world which does express values and valuation, and hence, have an ethical component. Humans value things in the world which allow them to continue to live and grow, which is to say, to recreate their ability to create and recreate. We eat food, build buildings for shelter, and create things like mathematics, and in doing so, we expend our energy and time, things we value, in the process. We value mathematics, and as such, it is an expression of our value, valuation, and values, even humans themselves are expressions of the value, valuation, and values of the contexts which produced us in turn.
There is an ethics to every move in every game, including language and mathematics. I’d like to think that emergence is, ultimately, the only way to imagine winning, which is to say, to emerge more robustly in relation to any and all in one’s context. An ethics of emergence, with ramifications for all gaming and (meta)gaming, including the creation and recreation of mathematical worlds.

On Description, Or Beyond the Linguistic Turn, Post-scriptum

[This is a post-script to a series of posts. For earlier posts, see here.]
It may be said that in what has preceded, we have in fact simply played the deconstructionist game, played with words, and not really moved beyond the linguistic turn, that it was all slight of hand. Now, of course it was slight of hand. But let us be clear about what we have just done.
Philosophy is the shift from practice to the meta-, the moment of reflexivity, it is the practice of raising the question of what we are doing in practice. Such a move always produces loss but also gain, loss of the immediacy of the original practice, but new perspective. The presuppositions, constitutive outsides of the practice are revealed by means of the creation of new ones, and in fact, the former and latter are in fact two sides of the same.
Deconstruction is the name of the destructive part of this gesture, just as description is the name of the constructive part. Destruction and creation, two sides of life. In between, there are moments of practice, moments in which there is no thought as to the meta, and these are moments of certainty, or at least, relative certainty. If this certainty is too strong, we have apodicticism and paranoia, while if this certainty is too weak, we deconstruct without reconstructing. Descriptivism is certainty in the process of description, that which allows for interplay between creation and destruction, description and deconstruction, by means and through a sly descriptivist application of apodicticity, if according to its own terms.
For whenever deconstruction destroys, we must not lose sight of the fact that it also produces. The deconstructive gesture operates by means of a shifting of the terrain, and this new terrain is produced only by means of the destruction of the old. Each deconstruction has its own presuppositions, and these do not merely lurk there, but are also created each time a deconstruction is performed. In this sense, deconstruction is a creative act, if one which often cloaks itself. Likewise, description is also destructive, if in a cloaked manner. Descriptivism is the process, however, which works to bring them together in a manner which works.
Language, which has been at the forefront of so many deconstructive assaults on the apodictic, is not the end all and be all of deconstruction, though as the medium in which philosophy is generally performed, it has a privileged relation to the meta- of philosophical practice. And language is little other than the creative destruction of an elsewhere. For the deitic gesture, the indicative of the pointing finger, “I am talking about that,” is itself as destructive as it is creative, for it destroys the finger to the extent it creates the “that” in question. So it is with any philosophy. Philosophy is the reflection on a practice. In reflecting, it turns the practice into an object for thought, destroys the immediacy, the surety of that practice, even as it creates the immediacy and surety in its own practice as philosophy.
We have simply shifted our terrain, and in the process, creatively destroyed our own foundations. We have used a slight of hand to shift the terms of the game. Philosophy has never benn anything but, nor self-reflection, nor language. We string words together in a sentence, each one partially obliterating the ones before it while creating new meanings for them in the process. We keep speaking to creatively destroy what we have already said. We change the terrain of our arguments to creatively destroy new ways of acting in the world.
So it should come as no surprise that in my own description of descriptivism, I kept changing terrain. At each jump, I creatively destroyed the last, showing the ways in which descriptivism could relate to a variety of contexts, how it unravelled in those contexts, and in relation to the creative unravelling of other terms like apodicticism and deconstruction. But I didn’t relate it explicitely to other terms, like dog or cabbage or mustard or steel. Descriptivism relates much better to apodicticism and deconstruction, to philosophy and reflexivity, than to salt or wood or stone. While I could’ve tied descriptivism to these more concrete terms, there is more distance, more labor is required, more stretching to do. And this distance between terms creates gradations, terrains, forces, attractions. Each deconstruction is like a topographical intervention, a leveling of a particular hill in a landscape, yet one which always gives rise to a hill somewhere else, for the terrain is simply the flip side, the moebius strip-like refraction, of the act of walking.
That is, the descriptions and unravellings are always specific, always situated, and the particulars of the situation provide traction, force, and movement. Each metaphor is related by gradation to some over others, wood is closer to tree than it is to stone or Immanuel Kant. Deconstruction is always local, and so is creation. One never ends up without something to stand on so long as one keeps speaking.
For in fact, I always choose to deconstruct a particular term over others in a given discursive situation. Those which I deconstruct provide space in a discourse which is always already being filled by others. The terrain moves under our feet. That which I do not deconstruct, namely, the words I use to do the deconstructing, provide the scaffolding for what remains, and the grounds for the next round of creative destruction.
Which is why the issue with deconstruction isn’t so much language, but rather, of faith. Deconstructionists are creators who have lost a degree of faith in the potential of the world to create itself anew, just as apodictics are those who are scared of the potential of the world to create itself anew. Descriptivists, on the contrary, keep saying yes to the creative powers of life, they have faith in description, enough to describe again, and then to describe again yet again. Having faith in description means not being overly attached to any, it means being ok with swimming in a constantly fluid domain.
Of course, life gives us little choice but to swim in such fluidity, life is fluid whether we like it or not. Deconstruction and apodicticity are means of defense against a game we must play whether we like it or not. And in this sense, deconstruction and apodicticity are always already forms of description, but they are in a sense less honest about what they do. For the apodictic constantly redescribes their justifications for what appear to be the same descriptions of the world, but underneath the appearance of stasis, all is actually continually having to modify itself in the effort to remain the same in changing circumstances. Likewise, deconstruction continually must deconstruct the new forms of description which come its way as the world changes.
We are all descriptivists, in this sense, anyway. And yet the apodictic and the deconstructionist waste so much time and energy, the first creating defenses against new creation, and the second destroying them the second it has created them.
Descriptivism, however, has its eye on sync. Sync with itself, with the world, and with its own self-redescription in its process. Sync conserves as much of creation as is possible, for it creates and destroys in the name of creation. And of course it can always already be destroyed from within. The question isn’t whether or not you can unravell it from within. The question is in how you play the game.
And game it is. Life, language, they are all a slight of hand, a continual pulling out of the rug beneath our own feet. This is time, change, becoming, saying, doing. But it’s all in how you play the game.
And how slowly. In the time between the saying and the unravelling, metaphor gives rise to the new via description. Metaphor, always nested, networked, into specific relations in a specific topography in a specific terrain. Which move do you make, and how fast or how slow, in a give region? Which way do you shift the gradients, which way do you push or pull yourself in given situation.
Your move.

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