I use an old challenge to motivate a new view. The old challenge is due to variation in our perceptions of secondary qualities. The challenge is to say whose perceptions are accurate. The new view is about how we manage to perceive secondary qualities, and thus manage to perceive them accurately or inaccurately. I call it perceptual structuralism. I first introduce the challenge and point out drawbacks with traditional responses. I spend the rest of the paper motivating and defending (...) a structuralist response. While I focus on color, both the challenge and the view generalize to the other secondary qualities. (shrink)

This paper contains four variations on Duhem's theme about the contrast between the abstract French mind and the concrete British mind. The first variation brings out the real contrast between two types of methods and their results: the A method or models and the C method or models. The second variation gives a critical discussion of the Callender-Cohen deflationary contruel of scientific representation. The third variation discusses Russell's structuralism in connection to the theme. And the fourth variation critically discusses (...) the relationship between models and fiction in connection to the distinction between the A-models and the C-models. A coda maps out without sufficiently detailed arguments the author's view on the nature of the C-models and why they, and only they, can be viewed as fully fictional. (shrink)

There is variation in how people perceive colors and other secondary qualities. The challenge of perceptual variation is to say whose perceptions are accurate. According to Sextus, Protagoras’ response is that all of our perceptions might be accurate. As this response is traditionally developed, it is difficult to explain color illusion and color constancy. This difficulty is due to a widespread assumption called perceptual atomism. This chapter argues that, if we want to develop Protagoras’ response, we need to give up (...) perceptual atomism. It ends with a brief sketch of an alternative called perceptual structuralism. (shrink)

The transition from the linguistics of codes, associated with structuralism and its neogrammarian ancestry, to a linguistics of discourses capable of seriously contemporary concerns has been a protracted transition. The average linguist has tended to find this transition somewhat confusing.

This study aims to corroborate Merleau-Ponty’s interpretations of fundamental ideas from Saussure’s linguistics by linking them to works that were independently elaborated by Jan Mukařovský, Czech structuralist aesthetician and literary theorist. I provide a comparative analysis of the two authors’ theories of language and their interpretations of thought as fundamentally determined by language. On this basis, I investigate how they conceive linguistic innovation and its translation into changes in the constituted language and other social codes and institutions. I explain how (...) they elaborate on Saussure’s idea of language as a system of oppositions by interpreting cultural innovation as a systematic variation of pre-established social norms and, similarly, linguistic innovation as gesturing within language. Connectedly, I show how Mukařovský’s works help clarify Merleau-Ponty’s focus on the gestural dimension of language. By discussing the two thinkers’ arguments in favour of linguistic innovation, I explore what could be called phenomenological limits of structuralism. (shrink)

. On a structuralist account of logic, the logical operators, as well as modal operators are defined by the specific ways that they interact with respect to implication. As a consequence, the same logical operator (conjunction, negation etc.) can appear to be very different with a variation in the implication relation of a structure. We illustrate this idea by showing that certain operators that are usually regarded as extra-logical concepts (Tarskian algebraic operations on theories, mereological sum, products and negates of (...) individuals, intuitionistic operations on mathematical problems, epistemic operations on certain belief states) are simply the logical operators that are deployed in different implication structures. That makes certain logical notions more omnipresent than one would think. (shrink)

This paper sets out to show how Eddington's early twenties case for variational derivatives significantly bears witness to a steady and consistent shift in focus from a resolute striving for objectivity towards “selective subjectivism” and structuralism. While framing his so-called “Hamiltonian derivatives” along the lines of previously available variational methods allowing to derive gravitational field equations from an action principle, Eddington assigned them a theoretical function of his own devising in The Mathematical Theory of Relativity (1923). I (...) make clear that two stages should be marked out in Eddington's train of thought if the meaning of such variational derivatives is to be adequately assessed. As far as they were originally intended to embody the mind's collusion with nature by linking atomicity of matter with atomicity of action, variational derivatives were at first assigned a dual role requiring of them not only to express mind's craving for permanence but also to tune up mind's privileged pattern to “Nature's own idea”. Whereas at a later stage, as affine field theory would provide a framework for world-building, such “Hamiltonian differentiation” would grow out of tune through gauge-invariance and, by disregarding how mathematical theory might precisely come into contact with actual world, would be turned into a mere heuristic device for structural knowledge. (shrink)

Cette contribution tente d'interroger les enjeux de l'usage de la référence à Descartes dans l'œuvre de Lyotard. Partant du constat que la référence prend ici la forme de lectures successives, très différentes du point de vue du style comme du point de vue du type de démonstration qu'elles viennent appuyer, on se propose de distinguer trois temps significatifs : -celui d'une lecture d'inspiration phénoménologique, mais également d'emblée critique vis-à-vis des présupposés ou des méthodes mises en œuvre par ces approches ; (...) -celui d'une lecture résolument ouverte aux mises en perspectives linguistiques, psychanalytiques et historiques ; -celui, enfin, d'une lecture qui s'arrête sur la « phrase » par laquelle se trouve « présenté » le je du Cogito, comme « destinateur désigné », et qui s'arrête sur les conditions de validité d'une thèse portant sur l'existence d'un tel « désigné ». Cette diversité d'approches pose elle-même le problème de l'unité ou de la « permanence » du « Descartes » auquel elles se réfèrent, en même temps que du statut de la référence à Descartes dans la philosophie contemporaine. (shrink)

The article attempts to critically reconsider some of the central motives of Tomáš Kulka’s aesthetics, especially his use of the term Gestalt and his concept of versions and alterations. In addition to his own objections, the author focuses on criticism of the above-mentioned parts of Kulka’s theory from the perspective of Czech structuralism and phenomenology.

The traditional practice of establishing morphological types and investigating morphological organization has found new support from evolutionary developmental biology (evo-devo), especially with respect to the notion of body plans. Despite recurring claims that typology is at odds with evolutionary thinking, evo-devo offers mechanistic explanations of the evolutionary origin, transformation, and evolvability of morphological organization. In parallel, philosophers have developed non-essentialist conceptions of natural kinds that permit kinds to exhibit variation and undergo change. This not only facilitates a construal of species (...) and higher taxa as natural kinds, but also broadens our perspective on the diversity of kinds found in biology. There are many different natural kinds relevant to the investigative and explanatory aims of evo-devo, including homologues and developmental modules. (shrink)

In identifying intrinsic molecular chance and extrinsic adaptive pressures as the only causally relevant factors in the process of evolution, the theoretical perspective of the Modern Synthesis had a major impact on the perceived tenability of an ontology of dispositional properties. However, since the late 1970s, an increasing number of evolutionary biologists have challenged the descriptive and explanatory adequacy of this “chance alone, extrinsic only” understanding of evolutionary change. Because morphological studies of homology, convergence, and teratology have revealed a space (...) of possible forms and phylogenetic trajectories that is considerably more restricted than expected, evo-devo has focused on the causal contribution of intrinsic developmental processes to the course of evolution. Evo-devo’s investigation into the developmental structure of the modality of morphology – including both the possibility and impossibility of organismal form – has led to the utilisation of a number of dispositional concepts that emphasise the tendency of the evolutionary process to change along certain routes. In this sense, and in contrast to the perspective of the Modern Synthesis, evo-devo can be described as a “science of dispositions.” This chapter discusses the recent philosophical literature on dispositional properties in evo-devo, exploring debates about both the metaphysical and epistemological aspects of the central dispositional concepts utilised in contemporary evo-devo and addressing the epistemological question of how dispositional properties challenge existing explanatory models in evolutionary biology. (shrink)

In this article, I attempt to restore the philosophical significance of that nonformalizable, noniterable, “singular’ element of natural language that I call “style.” I begin by critically addressing the exclusion of such instances of natural language by both semantics‐oriented logical analysis and a restricted variation of structuralist linguistics. Despite the obvious advantages – with regard to style – of ”pragmatic“approaches to language, such pragmatism merely returns to rule‐determination in the guise of “normativity.” Although style by definition resists any kind of (...) rule‐determination – whether posed in terms of semantics or intersubjective regulations of speech‐acts – there can be no consideration of language that ignores the persistence of style in natural language. In terms of cognition, any discursive agent understands more than allowed by either semantics or speech‐act theory. I ascribe this element of excessive signification to the role of style. My principal thesis is twofold: (1) a hermeneutic approach (exemplified by Schleiermacher) to literature should reveal the heuristically decisive role played by style in philosophy; and, more radically still, (2) style, in fact, may be crucially determinative of philosophical discourse in general. I suggest that a closer scrutiny of the lesser‐known works of Ludwig Wittgenstein, conventionally regarded as having dreamt of a “philosophy without style,” may consolidate the restoration of style's philosophical import. (shrink)

This paper proposes a concept of creativity that stems from a semiotic and linguistic theoretical perspective, in which the formal frame of reference for variation and linguistic change considers and evaluates both the process of general interaction and the contact of languages as a global phenomenon. This method proposes an analysis of creativity that ranges from reflections of ancient philosophy to a contemporary linguistic perspective, incorporates international ideologies, and identifies, within the dimensions of use and social sharing, the principle capable (...) of guiding potentially unlimited forms of linguistic creativity that are self-expressive and communicative, far beyond the grammatical patterns of regularity and norm. Interpreting the paradigm of creativity according to this model means placing the semiotic property in a position of prima inter pares, entrusted not only with the “role” of forming signs (words, sentences, texts), but the function of arbitraire, as a phenomenon of language creation. The following reading references the semiotic contribution of Tullio De Mauro, an Italian linguist who has contributed to the systematization of creativity, overcoming and synthesizing both Saussurian structuralism and Chomskyan generativism. (shrink)

The article analyzes a variation in the conditions of production of Gilles Deleuze’s philosophical thought based on joint production with Félix Guattari. The article is divided into three parts: firstly, we analyze the influence of structuralism on Deleuze’s work, mainly through the author’s own text on this current of thought and its influence on the construction of the notion of “idea” in Difference and Repetition. In a second movement, we analyze the appearance of the notion of “machines” in Guattari’s (...) work Psychoanalysis and Transversality and its protagonism in the authors’ first joint work, Anti-Oedipus. Finally, we analyze the role that machines play in defining concepts, in the authors’ latest joint work. In addition to methodological aspects, we argue that the variation from structuralism to machinism has epistemological and ontological ramifications, which are decisive for the authors’ reading. (shrink)

In this paper I wish to make some headway on understanding what \emph{kind} of problem the ``problem of time'' is, and offer a possible resolution---or, rather, a new way of understanding an old resolution. The response I give is a variation on a theme of Rovelli's \emph{evolving constants of motion} strategy. I argue that by giving correlation strategies a \emph{structuralist} basis, a number of objections to the standard account can be blunted. Moreover, I show that the account I offer provides (...) a suitable ontology for time in both classical and quantum canonical general relativity. (shrink)

The philosophical understanding of the end of human history has a long tradition and, de­spite many different interpretations, gravitates towards two opposite versions. The opti­mistic version is symbolically presented in G.W.F. Hegel’s concept, while the pessimistic one can be found in the latest conceptual essays of the “late” V.S. Solovyov. This text is structured in a tonality that partly echoes that of the latter. Methodologically, it is based on the subject-centered strategy of existential philosophy and the variation of dialectics associated (...) with it. Thematically, it aims to reflect on the state of posthistory, a term that, according to the author, by virtue of its prefix “post-”, captures not only temporal shades of meaning (“after”), but also parodic ones. Every post-something parodies its own root, speculatively enhancing some meaningful aspects of it and hiding others. Posthistory di­minishes the social for the sake of the socio-technical and hypertrophies the political, which is already dominant in the historical process and its standard perception. The author focuses on the intellectual support of well-defined trends in modern social life and criti­cally analyzes theoretical constructions that fully (B. Latour) or partially (J.O. de La Met­trie) legitimize the reduction of the social to the socio-technical and subordinate, directly (K. Schmitt) or indirectly (S. Newman), the social to the political. While recognizing the weakness of modern society and agreeing with the importance of individual resistance to the negative tendencies that dominate it, the author emphasizes the positive signifi­cance of the individual’s self-identity – in contrast to post-structuralism and post-anar­chism – resulting from the individual’s power over himself. At the same time, the indivi­dual effort is considered insufficient to address the human condition. The prognosis for the posthistorical future is therefore pessimistic. But fortunately, earthly life – human life itself – is not limited to history and posthistory. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Desire and Monstrosity in the Disaster Film:Alfred Hitchcock's The BirdsDavid Humbert (bio)The theme of the relationship between desire and violence appears regularly in modern film criticism, and studies of this issue range in theoretical orientation from the Lacanian to the feminist.1 Though René Girard's view of this relationship is also regularly mentioned in studies of film violence, it is often with less than full appreciation of the way in (...) which it contradicts central features of structuralist and psychoanalytic approaches to film, approaches that, until recently, have dominated film theory. Furthermore, cinema is mentioned only in passing by Girard himself, sometimes derogatorily, while Girardian studies of films and film makers are relatively few and far between.2 One of the yardsticks by which René Girard demonstrates the validity of his theory of violence is the degree to which it illuminates key aspects of great literature that previously remained unexplained or were passed over in silence. The fundamental concepts of the scapegoat, the double, the rival, and triangular desire can be shown to illuminate similar interpretive lacunae in a wide variety of films of many genres.Alfred Hitchcock's The Birds3 is a case in point. I intend to argue the relevance of the mimetic theory of violence to this film largely as Girard does [End Page 87] himself in relation to works of literature, and hence with no pretense to originality. The theory of the scapegoat and triangular desire persuades because of the particular way it brings to view, and explains, previously unnoticed features of Hitchcock's films, notably The Birds. One must bear in mind, however, that, previous to The Birds, Hitchcock produced a remarkable body of work that is consistently (some would say obsessively) built upon the cluster of themes that Girard identifies with the scapegoat problem. For those who are familiar only with Hitchcock's later, more sensational work, like Psycho4 and The Birds, it may come as a surprise to discover that the director earlier produced films like I Confess5 or The Wrong Man,6 or Vertigo,7 in which the suspense is largely psychological, and in which themes of faith, romantic obsession, or moral conflict take center stage. The Birds is a variation on the works of the 1950s, rather than a completely new point of departure. It is an apocalyptic crystallization of the themes that had always preoccupied Hitchcock.The Birds is perhaps the only film by Hitchcock that envisions total societal breakdown, a disaster of the proportions of a medieval plague. Generally, Hitchcock's films are set in stable, if modern and troubled, societies in which there are at least more or less unquestioned social and economic orders. Flaws in these social orders, however, are evident in the small-scale disasters that happen to individuals in many of Hitchcock's scenarios. The Wrong Man focuses on the story of Manny Balestreros, who is wrongly identified as a criminal and has his life destroyed by a morally blind justice system. In Rope, the practitioners of a nihilistic thrill-kill are shown to be symptomatic of a pervasive moral and intellectual vacuum in contemporary society. Both these films and others by Hitchcock underline the need for morality and social order to withstand the irrational tendencies of human nature. Psycho, in particular, stresses the ambivalence of man in modern civilization. Norman Bates, it seems, is both the product of and yet the immoveable obstacle to the drive for civilization and order.In contrast to these films, The Birds is a film in which civilizational disaster is abrupt, all-consuming, and catastrophic. For no reason, out of the blue, birds collectively mass to attack human beings. The film is nothing more, some would argue, than one more film in the "revenge of nature" genre. But the attack of the birds is not a response called forth by a moral transgression. It is not a reciprocal act of violence, as the "revenge of nature" mode of interpretation would imply. In fact, the very randomness, irrationality, and suddenness of the attack is the key to understanding the film. The preeminent question is, as Slavoj Žižek puts it, "the stupid and... (shrink)

Writing, the exigency of writing: no longer the writing that has always (through a necessity in no way avoidable) been in the service of the speech or thought that is called idealist (that is to say, moralizing), but rather the writing that through its own slowly liberated force (the aleatory force of absence) seems to devote itself solely to itself as something that remains without identity, and little by little brings forth possibilities that are entirely other: an anonymous, distracted, deferred, (...) and dispersed way of being in relation, by which everything is brought into question – and first of all the idea of God, of the Self, of the Subject, then of Truth and the One, then finally the idea of the Book and the Work so that this writing (understood in its enigmatic rigor), far from having the Book as its goal rather signals its end: a writing that could be said to be outside discourse, outside language. – Maurice Blanchot ( The Infinite Conversation , xi) The Compendium * Beginning with the idea and practice of writing, and moving to the subject or self, then to truth and the One, and arriving at the Book and the Work, Blanchot’s words reflect the trajectory of the following work of writing. True to the embeddedness of the subject in the work of writing, the term “Compendium” has been a metonym for me over the past few years as I have thought about the concept of totality alongside its expression in figures such as the One, the Whole, or the All. In the following I aim to share some of the content of this metonym, and to enrich it by making some distinctions. 1 Here the term “Compendium” will refer to a concept of totality that is ontological (pertaining to being, and the copula) and also textual (pertaining to the symbolic, and the signifier-signified relationship). The Compendium is a figure for thinking the world as a Book, in the broadest sense—an approach to reality that is by no means new, but one that is due for renewal. 2 In partial answer to the question of the Compendium we will say that the word ‘Compendium’ stands in for expressions which seek to totalize, or concepts which seek to approach the concept of ‘everything,’ particularly when these expressions are bound up in the question of the Book (both the book as a physical object and the Book as a metaphysical figure: a way of thinking about the work in and of writing). The question of the Compendium is strongly associated with the physical and metaphysical form of the Book, like the mysterious and symbolic books which are opened in the Biblical book of Revelation, the book of life and the book of death, which together constitute an important couplet. 3 Parataxis & Hypotaxis There are two helpful distinctions that will bring us closer to an answer to the question “What is a Compendium?” The first distinction is between two figures in and for writing: parataxis and hypotaxis . Typically paired in contrast to one another as literary techniques, with parataxis indicating a side-by-side placement of textual elements and hypotaxis referring to subordinate arrangements of textual elements, the two figures can be understood as having a philosophical significance in addition to their practical function as devices for writers. For us these two terms will remain between philosophical theory and writing practice, and serve as a perspective for our writing and creation of texts. Here I take texts to refer to anything from the concrete written words in a book, to the ontological text of the world that we experience. Parataxis , as a figural way of thinking about the ontological structure of texts, refers to texts which are tightly woven and interdependent – texts within which each sentence bears the weight of the entire work. Parataxis often involves repetition, great density, and fragility. One of the best examples of this sort of text is Theodor Adorno’s posthumous magnum opus , Aesthetic Theory . In addition to the text itself, the translation history of the book may also help us to better understand parataxis and its relation to hypotaxis . The final published version of Aesthetic Theory , in German, was a text that Adorno intended to revise and rewrite, but this intention was never realized because of his untimely death. Where the German text of Aesthetic Theory certainly exemplifies the concept of parataxis , the first English edition took this densely woven text and carved Adorno’s lengthy paragraphs and lengthy sentences into manageable ‘bite-sized’ pieces of English text. The first translator took further liberty and inserted headings and new paragraph breaks where there were none in the original. Aesthetic Theory was eventually retranslated by Robert Hullot-Kentor and is now available in a form that is much more faithful to the original work. 4 The pertinent idea that this translation history points to is the distinction between parataxis and hypotaxis . Where parataxis describes texts which are repetitive, densely woven, and often fragile, hypotaxis describes texts which are hierarchical and in which the primary relation is linear – the latter of which is very similar to the first English translation of Aesthetic Theory . On the other hand, the original German text that Adorno wrote was very dense, often repetitive, and contained long sections of text unbroken by paragraphs or headings. This example of parataxis was then turned towards hypotaxis through the initial translation which took a text that was, in many ways, nonhierarchical and nonlinear, and artificially subjected it to a hierarchy that was not its own (and here I take the word of Fredric Jameson who comments on the two translations in a note at the beginning of his book Late Marxism ). 5 The point here is not about translation, but rather the distinction between parataxis and hypotaxis precisely as they are figures for discourse, written or otherwise. The concept of parataxis looks far more postmodern and rhizomic than the concept of hypotaxis which remains very modern and arborescent. This is a more figural way of talking about the distinction. However, if we wanted to take a more precise and analytical approach we could say that on the level of form parataxis involves a relationship between sentences and paragraphs in which each part bears an equally crushing responsibility to present the whole content of the text. As well, on the level of content, parataxis requires that each concept in a work take on the full conceptual weight of the total work. Continuing the analysis, we could say that parataxis describes texts in which there is no (or very little) linear or causal move from antecedent to consequent, whether in content or form. Instead, parataxis describes texts which weave together concepts via conjugations or associations. The concept of hypotaxis , on the other hand, requires that texts submit themselves to hierarchy, one example of which is logical argumentation. The contingency of the conclusion upon premises in hypotaxis is certainly distinct from the repetition, re-presentation, and conjugation of concepts in parataxis , and I think that this is evident in the difference between the writing styles prevalent in contemporary Analytic philosophy and Continental philosophy. It is not the case that the distinction between parataxis and hypotaxis absolutely corresponds with the writing styles of Continental and Analytic philosophy (respectively). There are thinkers who take exception to this pattern, such as Badiou’s more formal approach in the discourse of Continental philosophy to give one example. However, when Analytic philosophy takes its writing lessons from the sciences, and seeks to do philosophy via the clean linear move from antecedent to consequent, then I think that Analytic philosophy writes with hypotaxis in mind. On the other hand, when Continental (particularly German and French) philosophy takes its writing lessons from narrative or poetry then Continental philosophy writes with parataxis in mind. It is not fair to say that all those writing Continental philosophy are looking to narrative and poetry for stylistic direction, just as it is not the case that all those writing Analytic philosophy have mathematics and science as their writing format, however there are some striking ways in which the differing epistemologies of Continental and Analytic philosophy encourage writing with parataxis and hypotaxis in mind (respectively). For some, writing with parataxis or hypotaxis in mind is a conscious decision and a product of stylistic self-consciousness, and for others it is an unconscious discursive and epistemic requirement that must be met in order to be involved in a particular discourse. Before moving on to our second distinction, and then an examination of the question of the Book, it is important to point out that both totality and figurations like the One, the Whole, and the All, come out of very human desires to totalize or to actualize our being-towards-totality. The relationship between identity and totality then can be construed, with Heidegger in mind, as striving toward wholeness, completion, or fulfillment, each of which is a quality of compendia. 6 Compilation & Selection The first distinction between parataxis and hypotaxis pertains to both form and content, and to both the mechanics of writing and the ideas to which writing refers. The second distinction pertains to both as well. In the process of writing and in the process of perception as well, there is a tension between compilation and selection . To begin with, in the work of theory-writing there is compilation, and this is because writing theory requires a broad perspective and certain measure of totalization. On the other hand, writing theory requires that the writer select an idea or a combination of ideas to individuate out of a radical and infinite multiplicity of identities and combinations. The concern here is not primarily for the writing of a theory about a specific idea, like a secondary work or a reference text. But rather the concern is with the writing of grand theories: Marx and Marxism, Derrida and Deconstruction, Husserl and Phenomenology, Sartre and Existentialism, Saussure and Structuralism —each of which strives along a trajectory towards being all-encompassing, whether it intends to or not. Today, we could even say that Speculative Realism has embarked on this journey, and perhaps now we could say that the discourse of Speculative Realism has reached the inevitable point after which a grand theory leaves the hands of its writer or writers and becomes a possession of the collective consciousness of the academy, or (perhaps now) the mass consciousness of the blogosphere—and this is a true pharmakon , a poison and a cure, a blessing and a curse. 7 When we write theory, whether the scope is that of a grand theory or a particular theory, we write in the tension between compilation (making good on the desire to be all encompassing) and selection (being required to decide and discern and to judge what is included in the work and what is deleted or appended or abridged or given over to ellipses). Generally speaking, the work of theory-writing often comes out of a desire to totalize, that is, to develop a theory of everything that is able to apprehend new experiences and ideas while still remaining whole. I grant that this is not a universal desire, and that not everyone who sits down to write a work (or book) of theory does so because of their will-to-totality, but it remains that this drive to totalize does condition a great many writers of theory (especially those who seek to develop grand theories like those mentioned previously). At the beginning of his book of interviews, Between Existentialism and Marxism , Sartre is quoted as saying, after completing the first volume of his Critique of Dialectical Reason : “I no longer feel the need to make long digressions in my books, as if I were forever chasing after my own philosophy. It will now be deposited in little coffins, and I will feel completely emptied and at peace—as I felt after Being and Nothingness . A feeling of emptiness: a writer is fortunate if he can attain such a state. For when one has nothing to say, one can say everything .” 8 This is where our two initial distinctions come to bear on the being-towards-totality as it is expressed in the concrete practice of writing: the first being between parataxis and hypotaxis , and the second being between compilation and selection. Where this second distinction is concerned there is a certain paradox at play given that selection is inescapable, and compilation is unachievable. Selection is inescapable (with the figure of the Compendium in mind) because, even when the imperative to compile is followed to excruciating lengths, selection still has the last word. This is why the Compendium is a figure rather than some material thing that can actually be accomplished or actualized. No matter how far one goes along with the will-to-archive and the will-to-compile, it is only ever a question of minimizing selection and never eliminating it. This leads to the second point, which is that total compilation is unachievable. The closest thing to total compilation that we have before us is the ontological and textual fabric of the world. Even in the case of the world, compilation cannot be enacted in a total fashion because of the need to include both the sphere of the actual and the sphere of the possible or potential. This as another way in which compilation is always-already selection, and further evidence that total compilation is practically impossible. Discursive Figuration and Total Writing Rather than figuration referring to a figure of speech or an image, here the term points to a way in which to think about the work of writing, both the work put into writing, and the work that is the result of writing: the finished yet incomplete final piece. As figures or figurations, the Book and the Compendium are ways of thinking about the work of writing and the human desire for the wholeness, completion, and fulfillment that are made manifest in the completed form of the book (whether a published or printed or saved document put to rest by the author). These two figures bear more strongly upon works that seek to be all-encompassing, and works that strive towards expressions of totality such as the One, the Whole, or the All. Moving on to the topic of the subtitle, and on a more prescriptive note, I would say that there is more hope for theory-writing to be found in parataxis than hypotaxis . Part of the reason for this claim is the poststructuralist critique of hierarchies, and yet another part is the compelling line of thinking called “weak thought” (in theology by John D. Caputo, and in philosophy by Gianni Vattimo, among others). 9 The consequences of these two convictions are such that if one is to strongly assert the truth of a grand theory without leaving the realm of hierarchy-critique and weak thought, then one must write paradoxically with parataxis in mind, and in so doing write weakly and non-hierarchically. This does not mean avoiding a sort of topography or topology when writing theory, rather it means avoiding both subjugation and oppression in thought by pursuing a nonviolent sort of ontology. In order to do this, theory writing does not present itself as an exercise in logical analysis where one mechanically moves from a set of premises (via contingency) to the inevitable conclusion (via necessity). Instead, theory approaches the idea of a Compendium. Given that the figural Compendium places parataxis and compilation above hypotaxis and selection, then the question becomes: is placing one part of a binary term before another not just another way of selecting, or another expression of hypotaxis ? Counter to the urge to resign oneself to the reign of selection, with some qualification one can nonetheless write without deciding whether selection and hypotaxis should be subservient to compilation and parataxis (which is to say that writing-without-decision is somewhere between and beyond possibility and impossibility). This dilemma can be disarmed by stating that theory writing is not about primacy, and not about having-decided-beforehand, both stylistically and also where content is concerned. This is the paradox of writing: always striving along a trajectory ( telos ) towards totality via parataxis and compilation, but always being drawn back to finitude and making selections, and placing one idea before another with hypotaxis in mind. In light of this paradox, the question of the Compendium as a figure for discourse and a figural Book has resonance with Jacques Derrida’s essay on Edmund Jabès’ Book of Questions , found in his Writing and Difference . The Question of the Book “Little by little the book will finish me.” 10 Derrida quotes Jabès, and proceeds to outline the reflexive relationship between the author of the book and the book itself, each of which are subjected to the other through a sort of chiasmus, both ontological and textual (not that the two are entirely separable). The Book, for Derrida like Blanchot in the introductory quotation, “infinitely reflects itself” and “develops as a painful questioning of its own possibility”, and in light of this we can draw an association with the painful tension between the practical reality of selection and the ideal trajectory of compilation. 11 This tension in writing, between the will to total compilation and the necessity of abridgment, is an ontological tension between part and whole just as it is a textual tension between signifier and signified. The ontological tension in writing that Derrida expresses in his essay on Jabès is between everything and nothing – a contradiction which Derrida finds in Jabès’ Book of Questions and also in the divine, in God. When one writes between compilation and selection one writes towards totality, and here we can follow Derrida who states that the lapse in signification, presumably in the signifier-signified discrepancy, is a “ rupture with totality itself” and furthermore that this lapse cannot be rectified through deductive reason or even philosophical discourse. 12 This rupture with totality, found in the troubled relation between signifier and signified, can also tell us a lot about the Book and about writing. Given an understanding of writing as an ontological act that strives towards (but never accomplishes) totality, we can see the written book as the manifested and given body of that striving. Perhaps in other disciplines or even other schools of philosophy there is a cultural climate within which the article is prized above the book, but I am fairly confident, especially when referring to the grand theories of Continental thought, that there is a respect for the book as a uniquely meaningful object capable of apprehending totality. Derrida writes, Between the too warm flesh of the literal event and the cold skin of the concept runs meaning. This is how it enters into the book. Everything enters into, transpires in the book. This is why the book is never finite. It always remains suffering and vigilant. 13 Here the vitality of the literal event is compromised by the deadening weight of the concept, and the figure of the Book assists in this lapse of meaning. The Book is a totalizing object, much like the figure of the Compendium, and yet this totalization lacks its final object of completed totality both because the figural Book is necessarily incomplete, and because the physical book is always-already a product of selection. Instead of achieving its end of being a place where everything takes place, it suffers from the lapse of writing, the discrepancy between event and concept. Derrida continues his exposition on Jabès by bringing to light yet another reflexive relation, a reversal of the relationship between the Book and the world. Derrida writes that, for Jabès, “the book is not in the world, but the world is in the book.” 14 In addition to what was stated before, I take figuration to mean that the concepts employed, such as the Book or the Compendium, are not subject to the supposed rigor of analysis that is so prized by Enlightenment or Capitalist realisms. The figure of the Book and the figure of the Compendium cannot be held accountable to standards imported from scientific method, given an understanding that these standards require a concept to be replicable, consistent, falsifiable, measurable, and so on… This is an important point to make, especially in the present atmosphere within which theory must justify itself under conditions that are not its own. Instead of being held to these standards, figuration serves as a way in which to think about writing that leaves thought open to idealistic speculation, imperfect analogies, and most importantly the ever-present gain and loss that occur in the relationship between thought and being. By extension the figural way of addressing writing indulges in enough generalization to accommodate the excess/lack relationship between the ideal form of the Book or the Compendium, and the manifested and given body of a text (as it is practically completed and closed). Here we speak against the hostile atmosphere which would have theory submit itself to hierarchical rigor, rather than Blanchot’s “enigmatic rigor”, by being explicit about the discursive conditions and epistemic conditions under which theory operates. To write with parataxis in mind is, to a certain degree, to write with weakness as one’s methodology (with weak thought being in opposition to hypotaxis and hierarchy as much as weak thought can be in opposition to anything). Rather than asserting the strength of hierarchical theory, and rather than employing antagonistic argumentation with the goal of refutation different discursive and epistemic conditions for theory writing must be cultivated (and these are by no means new). First the critical and theoretical spirit reveals itself as being concerned with the task of complication—especially the complication and critique of binaries, dichotomies, dualities, polarities, paradoxes, parallaxes, hybridities, and especially antinomies. Second, theory positions itself as a sort of showing or revealing, rather than being ultimately focused on coming to full agreement or disagreement. This is where figuration can help theory-writing, both by placing emphasis on teleologies and trajectories (like parataxis and compilation), and by shifting focus away from pure primacy, power, or absolute origin. Figuration then, assists theory writing by placing the concern of theory outside of the concerns of the hard or soft sciences, and into the realm of thought or the idea. To speak of ‘the’ Compendium or ‘the’ Book, here, is to generalize not regarding the perfect form of the Compendium or Book, but to engage speculatively with an abstract idea which remains singular and yet complicated by multiplicity. The question of the Book that Derrida asks through Jabès is a question of everything and nothing, totality and nonbeing, and this question is a concern for writing and a concern for the figure of the Compendium so defined by the tension between compilation and selection, and parataxis and hypotaxis . On the note of nonbeing, we can look to the final page of Derrida’s first essay on Jabès in Writing and Difference and notice the introduction of his neologism, différance (with an ‘a’). Derrida writes: Life negates itself in literature only so that it may survive better. So that it may be better. It does not negate itself any more than it affirms itself: it differs from itself, defers itself, and writes itself as différance . Books are always books of life (the archetype would be the Book of Life kept by the God of the Jews) or of afterlife (the archetype would be the Books of the Dead kept by the Egyptians). 15 This introduction of différance into the equation of the Book, alongside ontological affirmation and negation, hearkens back to the discussion of the symbolic lapse earlier in his essay. Differing and deferring, the Book is always a Book of Life and a figure for the intersection of the vital (life) and the total in writing. In a way, the writer of the Book may be someone who lives life, and in another way the writer of the book-as-object may be someone who engages in the act of writing, both practically (by inscribing words on paper, or typing script on a computer) and ontologically or symbolically (by investing their existence and inexistence into a work worthy of the figural Book). In addition to the writer as writer, the writer also serves as an editor, and the editorial role alongside the idea of the Compendium shows the editor to be one who collects and compiles, while being restrained by eventual selection and decision. Beyond this the editor of works and texts, in both the Book and the world, is engaged in a process of inscribing notation—of annotating (on) the Compendium. Eternal commentary is a feature of the textual Compendium, just as open-ended totality describes the ontological Compendium. The writer as writer does not simply write texts, but rather engages in a profoundly ontological act of inscribing their existence into the world, and the writer as editor does not merely annotate or alter texts as they are, but rather comments upon the text of the world. In/Conclusion So as we create texts, and as we write and create theory, let us be and remain attentive to the figure of the Compendium and the figure of the Book. These two concurrent metonymies are essential for total writing (grand theories, etc.), and may be forgettable for those concerned with fragmentary or hierarchical writing (which are valid in their own right). From the ontological and symbolic text of the world and phenomenological experience, to concrete texts such as books or mixed media, the figure of the Compendium and the figure of the Book are important for the actualization of the human will to be all-encompassing. The figure of the Compendium teaches writers of theory that the repetition, density, and fragility of parataxis offers a strong sort of weakness which does not become yet another variety of oppressive and hegemonic thought. Rather than write with hypotaxis in mind, subjugating one thought to another via cause and effect or antecedent and consequent, I would hope that theory-writing could guiltlessly indulge in the dialectical and contradictory conjugation of ideas, and take this as a legitimate methodology. Rather than being ashamed of showing resonances or giving way to abridgment or ellipses, it is my own authorial (but not authoritative) conviction that one need not give up on totalizing and constructing grand theories because of the fact that complete totalization is impossible, and one need not give up on totalizing and constructing grand theories because of the worry of violence, for the Book and the Compendium lack their completed object and are ever incomplete trajectories. NOTES * UPDATED 7/19/13: we've updated the HTML version to reflect the (correct) PDF version. Our apologies to the author—eds. 1. I would like extend thanks to Dr. Peter Schwenger of the University of Western Ontario for his comments on this paper and his hospitality as it was presented as a Theory Session at the Centre for Theory and Criticism on October 26th 2012. I would also like to thank Andrew Weiss for conversation and critique. 2. I should clarify my use of the term ‘figure’ at the outset. Given the use of the term by Jean-Francois Lyotard in Discourse, Figure (and also Gilles Deleuze in Francis Bacon ), I should state clearly that my use of the term will not correspond to the term ‘figure’ understood as the representation of an object. Instead, my use of the term ‘figure’ and its variations (‘figural’, ‘figurative’, ‘figuration’) will refer to the illustrative or metaphorical use of the Compendium or the Book as models or ways of thinking about writing and discourse. 3. Cf. Revelations 20:12-15. 4. Theodor Adorno, Aesthetic Theory , Trans. Robert Hullot-Kentor (London & New York: Continuum Press, 1997). 5. Fredric Jameson, Late Marxism: Adorno, or the Persistence of the Dialectic (London & New York: Verso, 1990), ix-x. 6. I have written about this concept of being-towards-totality elsewhere in two pieces of writing: the first is called Notes on the Compendium (an unfinished draft) which addresses some very wide theoretical concerns, being structured as a sort of itinerary or archive, and the second is Dialectics Unbound (Punctum Books, 2013) which outlines a concept of totality without the violence of totalization. While these works are more concerned with ontological totality, here I would like to focus on the idea of the Compendium as a textual totality. 7. Cf. Louis Morelle, “Speculative Realism: After Finitude and Beyond, A vade mecum” in Speculations: Journal of Speculative Realism . Issue 3 (Brooklyn, New York: Punctum Books, 2012), 241-272. 8. Jean-Paul Sartre, Between Existentialism and Marxism . Trans. John Matthews (London & New York: Verso, 1974), 9. 9. Cf. John D. Caputo, The Weakness of God (Indiana: Indiana University Press, 2006). 10. Jacques Derrida, “Edmond Jabès and the Question of the Book” in Writing and Difference . Trans. Alan Bass (Chicago: University of Chicago Press, 1978), 65. 11. Ibid, 65. 12. Ibid, 71. 13. Ibid, 75. 14. Ibid, 76. 15. Ibid, 78. (shrink)

This book deals with the relationship between feminism and liberalism in theory and practice. The author argues that rather than seeing liberalism as exclusionary of women's specificity, as many contemporary feminists do, we should look at variations in liberalism, and in particular at its democratization in the nineteenth century and how feminists have used liberalism as a resource. Liberalism is analyzed using a post-structuralist theory of hegemony: texts of liberal political philosophy are deconstructed to show how the term "women" is (...) used as an "undecidable" in the Derridean sense to produce the opposition between feminine private and masculine public spheres; these texts are then linked to liberal-democratic social and political practices, including feminism as a social movement. (shrink)

The processes underwriting the acquisition of culture remain unclear. How are shared habits, norms, and expectations learned and maintained with precision and reliability across large-scale sociocultural ensembles? Is there a unifying account of the mechanisms involved in the acquisition of culture? Notions such as “shared expectations,” the “selective patterning of attention and behaviour,” “cultural evolution,” “cultural inheritance,” and “implicit learning” are the main candidates to underpin a unifying account of cognition and the acquisition of culture; however, their interactions require greater (...) specification and clarification. In this article, we integrate these candidates using the variational (free-energy) approach to human cognition and culture in theoretical neuroscience. We describe the construction by humans of social niches that afford epistemic resources called cultural affordances. We argue that human agents learn the shared habits, norms, and expectations of their culture through immersive participation in patterned cultural practices that selectively pattern attention and behaviour. We call this process “thinking through other minds” (TTOM) – in effect, the process of inferring other agents’ expectations about the world and how to behave in social context. We argue that for humans, information from and about other people's expectations constitutes the primary domain of statistical regularities that humans leverage to predict and organize behaviour. The integrative model we offer has implications that can advance theories of cognition, enculturation, adaptation, and psychopathology. Crucially, this formal (variational) treatment seeks to resolve key debates in current cognitive science, such as the distinction between internalist and externalist accounts of theory of mind abilities and the more fundamental distinction between dynamical and representational accounts of enactivism. (shrink)

This is a critical review of the book Variational Approach to Gravity Field Theories - From Newton to Einstein and Beyond (2017), written by the Italian astrophysicist Alberto Vecchiato. In his work, Vecchiato shows that physics, as we know it, can be built up from simple mathematical models that become more complex step by step by gradually introducing new principles. The reader is invited to follow the steps that lead from classical physics to relativity and to understand how this (...) happens and why. Moreover, while presenting the variational approach to gravity field theories in a clear and elegant manner, Vecchiato shows a constant worry in leading the readers in such a way that they understand the relevance of what the author considers to be the most powerful technique and unifying concept of theoretical physics - and how it works. Each chapter is enriched with exercises, of which a step-by-step solution is offered, so that the reader can gain a real insight into the topic presented and follow the reading as fruitfully as possible. The most innovative aspect of the book, however, is not the rigorousness and the clarity of the treatment of the variational approach, but rather the point of view that Vecchiato keeps and that the reader is led to endorse too: physics is a human enterprise, prone to error and open to improvement, and not a complete and definite system of truths about our world. (shrink)

A new method for evaluating aircraft engine monitoring data is proposed. Commonly, prognostics and health management systems use knowledge of the degradation processes of certain engine components together with professional expert opinion to predict the Remaining Useful Life (RUL). New data-driven approaches have emerged to provide accurate diagnostics without relying on such costly processes. However, most of them lack an explanatory component to understand model learning and/or the nature of the data. A solution based on a novel recurrent version of (...) a VAE is proposed in this paper to overcome this gap. The latent space learned by the model, trained with data from sensors placed in different parts of these engines, is exploited to build a self-explanatory map that can visually evaluate the rate of deterioration of the engines. Besides, a simple regressor model is built on top of the learned features of the encoder in order to numerically predict the RUL. As a result, remarkable prognostic accuracy is achieved, outperforming most of the novel and state-of-the-art approaches on the available modular aero-propulsion system simulation data (C-MAPSS dataset) from NASA. In addition, a practical real-world application is included for Turbofan engine data. This study shows that the proposed prognostic and explainable framework presents a promising new approach. (shrink)

The aim of this paper is twofold: (1) to assess whether the construct of neural representations plays an explanatory role under the variational free-energy principle and its corollary process theory, active inference; and (2) if so, to assess which philosophical stance - in relation to the ontological and epistemological status of representations - is most appropriate. We focus on non-realist (deflationary and fictionalist-instrumentalist) approaches. We consider a deflationary account of mental representation, according to which the explanatorily relevant contents of (...) neural representations are mathematical, rather than cognitive, and a fictionalist or instrumentalist account, according to which representations are scientifically useful fictions that serve explanatory (and other) aims. After reviewing the free-energy principle and active inference, we argue that the model of adaptive phenotypes under the free-energy principle can be used to furnish a formal semantics, enabling us to assign semantic content to specific phenotypic states (the internal states of a Markovian system that exists far from equilibrium). We propose a modified fictionalist account: an organism-centered fictionalism or instrumentalism. We argue that, under the free-energy principle, pursuing even a deflationary account of the content of neural representations licenses the appeal to the kind of semantic content involved in the aboutness or intentionality of cognitive systems; our position is thus coherent with, but rests on distinct assumptions from, the realist position. We argue that the free-energy principle thereby explains the aboutness or intentionality in living systems and hence their capacity to parse their sensory stream using an ontology or set of semantic factors. (shrink)

This book is the first to provide a sustained, coherent analysis of Foucault's work as a whole. To demonstrate the sense in which Foucault's work is beyond structuralism and hermeneutics, the authors unfold a careful, analytical exposition of his oeuvre. They argue that during the of Foucault's work became a sustained and largely successful effort to develop a new method - "interpretative analytics" - capable of explaining both the logic of structuralism's claim to be an objective science and (...) the apparent validity of the hermeneutical counterclaim that the human sciences can proceed only by understanding the deepest meaning of the subject and his tradition. (shrink)

Due to the inherent chaotic and fractal dynamics in the price series of Bitcoin, this paper proposes a two-stage Bitcoin price prediction model by combining the advantage of variational mode decomposition and technical analysis. VMD eliminates the noise signals and stochastic volatility in the price data by decomposing the data into variational mode functions, while technical analysis uses statistical trends obtained from past trading activity and price changes to construct technical indicators. The support vector regression accepts input from (...) a hybrid of technical indicators and reconstructed variational mode functions. The model is trained, validated, and tested in a period characterized by unprecedented economic turmoil due to the COVID-19 pandemic, allowing the evaluation of the model in the presence of the pandemic. The constructed hybrid model outperforms the single SVR model that uses only TI and rVMF as features. The ability to predict a minute intraday Bitcoin price has a huge propensity to reduce investors’ exposure to risk and provides better assurances of annualized returns. (shrink)

A simple random walk model has been shown by Gaveauet al. to give rise to the Klein-Gordon equation under analytic continuation. This absolutely most probable path implies that the components of the Dirac wave function have a common phase; the influence of spin on the motion is neglected. There is a nonclassical path of relative maximum likelihood which satisfies the constraint that the probability density coincide with the quantum mechanical definition. In three space dimensions, and in the presence of electromagnetic (...) interaction, the Lagrangian for this optimal, nonclassical path coincides with the Lagrangian of the Dirac particle. The nonrelativistic, or diffusion, limit is shown to be a formal consequence of Einstein's dynamical equilibrium condition; the continuity equation reduces to the same diffusion equation derived from Schrödinger's equation. The relativistic, massless limit, which would describe a neutrino, is comparable (in the sense of analytic continuation) to a nonviscous liquid whose molecules possess internal degrees of freedom. (shrink)

This study investigated the impact of three prior distributions: matched, standard vague, and hierarchical in Bayesian estimation parameter recovery in two and one parameter models. Two Bayesian estimation methods were utilized: Markov chain Monte Carlo (MCMC) and the relatively new, Variational Bayesian (VB). Conditional (CML) and Marginal Maximum Likelihood (MML) estimates were used as baseline methods for comparison. Vague priors produced large errors or convergence issues and are not recommended. For both MCMC and VB, the hierarchical and matched priors (...) showed the lowest root mean squared errors (RMSEs) for ability estimates; RMSEs of difficulty estimates were similar across estimation methods. For the standard errors (SEs), MCMC-hierarchical displayed the largest values across most conditions. SEs from the VB estimation were among the lowest in all but one case. Overall, VB-hierarchical, VB-matched, and MCMC-matched performed best. VB with hierarchical priors are recommended in terms of their accuracy, and cost and (subsequently) time effectiveness. (shrink)

Günter Wagner’s Homology, Genes, and Evolutionary Innovation collects and synthesizes a vast array of empirical data, theoretical models, and conceptual analysis to set out a progressive research program with a central theoretical commitment: the genetic theory of homology. This research program diverges from standard approaches in evolutionary biology, provides sharpened contours to explanations of the origin of novelty, and expands the conceptual repertoire of evolutionary developmental biology. I concentrate on four aspects of the book in this essay review: the genetic (...) theory of homology and character identity networks; the implications for how we explain evolutionary novelties; the expanded set of concepts surrounding homology, and the epistemological conflicts between Wagner’s viewpoint and functionally-oriented evolutionary biology, as well as differences with other Evo–devo researchers. Together these have ramifications for how we interpret different explanatory approaches to evolutionary phenomena and understand relationships between the usefulness of concepts and the reality they represent. (shrink)

Darwinists classify biological traits either by their ancestry (homology) or by their adaptive role. Only the latter can provide traditional natural kinds, but only the former is practicable. Process structuralists exploit this embarrassment to argue for non-Darwinian classifications in terms of underlying developmental mechanisms. This new taxonomy will also explain phylogenetic inertia and developmental constraint. I argue that Darwinian homologies are natural kinds despite having historical essences and being spatio-temporally restricted. Furthermore, process structuralist explanations of biological form require an unwarranted (...) assumption about the space of developmental possibility. (shrink)

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined. The weighted rough variational coefficient similarity measures between the rough ideal alternative and each alternative are xxxxx calculated to find the best alternative. The ranking order of all the alternatives can be determined by using the numerical values of similarity measures. Finally, an illustrative example (...) has been provided to show the effectiveness and validity of the proposed approach. Comparisons of decision results of existing rough similarity measures have been provided. (shrink)

The current study reports on a variational pragmatic comparison of compliments and compliment responses between Egyptian and Saudi Arabic. Data were collected by using Discourse Completion Tasks from 443 Egyptian and 428 Saudi undergraduates, and were analyzed using adaptations of Yuan’s and Herbert’s models. The results reveal significant differences in politeness management between Egyptian and Saudi youth, particularly with Egyptians producing more explicit compliment strategies and Saudis showing stronger preference for implicit compliment strategies and combination patterns. Less difference is (...) noted in compliment responses with only Egyptians exhibiting higher use of additional strategies. The findings are interpreted in light of politeness theory and the interplay between cultural values and linguistic behavior. (shrink)

According to realist structuralism, mathematical objects are places in abstract structures. We argue that in spite of its many attractions, realist structuralism must be rejected. For, first, mathematical structures typically contain intra-structurally indiscernible places. Second, any account of place-identity available to the realist structuralist entails that intra-structurally indiscernible places are identical. Since for her mathematical singular terms denote places in structures, she would have to say, for example, that 1 = − 1 in the group (Z, +). We (...) call this the identity problem and conclude that nominalism is presently the safest route for the structuralist. (shrink)

Category theory has become central to certain aspects of theoretical physics. Bain has recently argued that this has significance for ontic structural realism. We argue against this claim. In so doing, we uncover two pervasive forms of category-theoretic generalization. We call these ‘generalization by duality’ and ‘generalization by categorifying physical processes’. We describe in detail how these arise, and explain their significance using detailed examples. We show that their significance is two-fold: the articulation of high-level physical concepts, and the generation (...) of new models. 1 Introduction2 Categories and Structuralism 2.1 Categories: abstract and concrete 2.2 Structuralism: simple and ontic3 Bain’s Two Strategies 3.1 A first strategy for defending Objectless 3.2 A second strategy for defending Objectless4 Two Forms of Categorical Generalization 4.1 Generalization by duality 4.2 Generalization by categorification 4.3 The role of category theory in physics5 Conclusion. (shrink)

Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles of (...) one, the finite element method nevertheless succeeds in obtaining its legitimacy from the other. (shrink)

Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true (...) of the other. I suggest that ‘i’ functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike Connotea Del.icio.us What's this? (shrink)

A version of the permutation argument in the philosophy of mathematics leads to the thesis that mathematical terms, contrary to appearances, are not genuine singular terms referring to individual objects; they are purely schematic or variables. By postulating ‘ante-rem structures’, the ante-rem structuralist aims to defuse the permutation argument and retain the referentiality of mathematical terms. This paper presents two semantic problems for the ante- rem view: (1) ante-rem structures are themselves subject to the permutation argument; (2) the ante-rem structuralist (...) fails to explain reference in a way that makes her account different to, and privileged over, that of her eliminativist rivals. Both problems undercut the motivation behind ante-rem structuralism. (shrink)

Structural realist interpretations of generally relativistic spacetimes have recently come to enjoy a remarkable degree of popularity among philosophers. I present a challenge to these structuralist interpretations that arises from considering cosmological models in general relativity. As a consequence of their high degree of spacetime symmetry, these models resist a structuralist interpretation. I then evaluate the various strategies available to the structuralist to react to this challenge. †To contact the author, please write to: Department of Philosophy, 9500 Gilman Drive, 0119, (...) University of California, San Diego, La Jolla, CA 92093‐0119; e‐mail: [email protected]. (shrink)