David Albert claims that classical electromagnetic theory is not time reversal invariant. He acknowledges that all physics books say that it is, but claims they are ``simply wrong" because they rely on an incorrect account of how the time reversal operator acts on magnetic fields. On that account, electric fields are left intact by the operator, but magnetic fields are inverted. Albert sees no reason for the asymmetric treatment, and insists that neither field should be inverted. I argue, to the (...) contrary, that the inversion of magnetic fields makes good sense and is, in fact, forced by elementary geometric considerations. I also suggest a way of thinking about the time reversal invariance of classical electromagnetic theory -- one that makes use of the invariant (four-dimensional) formulation of the theory -- that makes no reference to magnetic fields at all. It is my hope that it will be of interest in its own right, Albert aside. It has the advantage that it allows for arbitrary curvature in the background spacetime structure, and is therefore suitable for the framework of general relativity. (The only assumption one needs is temporal orientability.). (shrink)

In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is ‐definable relative to the previous stages of the recursion. It is known that this principle is provable in. In the present note, we argue that a common formulation of effective transfinite recursion is too restrictive. We then propose a more liberal formulation, which appears very natural and is (...) still provable in. (shrink)

If there is a homeomorphic embedding of one set into another, the sets are said to be topologically comparable. Friedman and Hirst have shown that the topological comparability of countable closed subsets of the reals is equivalent to the subsystem of second order arithmetic denoted byATR 0. Here, this result is extended to countable closed locally compact subsets of arbitrary complete separable metric spaces. The extension uses an analogue of the one point compactification of ℝ.

Jean Baudrillard is one of the outstanding representatives both of French poststructuralism and postmodernism. Because of radical criticism it was not possible for him to establish a logically coherent theoretical system; the philosophical aspects of his work are specifically merged, therefore, into a critical asystematic fragmentarism, which is the subject of this work. From the critique of the political economy of the sign, through critiques of rationalism, reality, progress, truth, history to the theory of simulation, Baudrillard's specific para-concepts (fatal strategy, (...) symbolic exchange, seduction, hyperreality, pataphysics, etc.) are constantly fragmentarily present in the development of his thought. These concepts are Baudrillard's attempt at disengagement from modern philosophy and his new, unsystematic postmodern view of reality in general. In the analysis of binary metaphysical oppositions (reality-simulation, subject-object, knowledge-seduction, history-end, radical-irradical nihilism, metaphysics (God)-pataphysics), Baudrillard is radically exclusive through the arbitrary preference of one over the other concept. his ideas, it is possible to conclude that these dualistic antagonisms are also paradoxically compatible in his system, this compatibility is very close to the irrational mysticism of this thinker. This book is a clear and lucid presentation of this unique brand of postmodernism to English speaking scholarship. (shrink)

Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we prove that such (...) a graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed. (shrink)

We explore the problem of constructing maximal and unbounded filters on computable posets. We obtain both computability results and reverse mathematics results. A maximal filter is one that does not extend to a larger filter. We show that every computable poset has a \Delta^0_2 maximal filter, and there is a computable poset with no \Pi^0_1 or \Sigma^0_1 maximal filter. There is a computable poset on which every maximal filter is Turing complete. We obtain the reverse mathematics result that the principle (...) "every countable poset has a maximal filter" is equivalent to ACA₀ over RCA₀. An unbounded filter is a filter which achieves each of its lower bounds in the poset. We show that every computable poset has a \Sigma^0_1 unbounded filter, and there is a computable poset with no \Pi^0_1 unbounded filter. We show that there is a computable poset on which every unbounded filter is Turing complete, and the principle "every countable poset has an unbounded filter" is equivalent to ACA₀ over RCA₀. We obtain additional reverse mathematics results related to extending arbitrary filters to unbounded filters and forming the upward closures of subsets of computable posets. (shrink)

We analyze the axiomatic strength of the following theorem due to Rival and Sands [28] in the style of reverse mathematics. Every infinite partial order P of finite width contains an infinite chain C such that every element of P is either comparable with no element of C or with infinitely many elements of C. Our main results are the following. The Rival–Sands theorem for infinite partial orders of arbitrary finite width is equivalent to $\mathsf {I}\Sigma ^0_{2} + \mathsf (...) {ADS}$ over $\mathsf {RCA}_0$. For each fixed $k \geq 3$, the Rival–Sands theorem for infinite partial orders of width $\leq \!k$ is equivalent to $\mathsf {ADS}$ over $\mathsf {RCA}_0$. The Rival–Sands theorem for infinite partial orders that are decomposable into the union of two chains is equivalent to $\mathsf {SADS}$ over $\mathsf {RCA}_0$. Here $\mathsf {RCA}_0$ denotes the recursive comprehension axiomatic system, $\mathsf {I}\Sigma ^0_{2}$ denotes the $\Sigma ^0_2$ induction scheme, $\mathsf {ADS}$ denotes the ascending/descending sequence principle, and $\mathsf {SADS}$ denotes the stable ascending/descending sequence principle. To the best of our knowledge, these versions of the Rival–Sands theorem for partial orders are the first examples of theorems from the general mathematics literature whose strength is exactly characterized by $\mathsf {I}\Sigma ^0_{2} + \mathsf {ADS}$, by $\mathsf {ADS}$, and by $\mathsf {SADS}$. Furthermore, we give a new purely combinatorial result by extending the Rival–Sands theorem to infinite partial orders that do not have infinite antichains, and we show that this extension is equivalent to arithmetical comprehension over $\mathsf {RCA}_0$. (shrink)

Figure-Ground Duality in Humour: A Multi-Modal Perspective Creativity with words or pictures is not simply a matter of communicating a message, but of communicating it well, in a way that is effective, original and which defies convention. Effectiveness here pertains to the pragmatic goals of the communicator, and the extent to which these are achieved, while originality pertains to the manner in which the message is framed. Language, for instance, provides a wealth of conventions for framing a message; indeed, the (...) vast part of language is a solidified body of culturally received conventions, which fix the meaning of words and phrases and determine the contextual appropriateness of specific terms, topics and conversational strategies. To frame a message in a novel manner that stretches or even subverts these conventions, a communicator must imbue the elements of communication—whether words, gestures or pictorial elements—with additional meanings. This duality of meaning is not arbitrary, however, or communication cannot succeed. Rather, a creative communicator must draw out secondary meanings that are already implicit in the stock elements of communication, in a way that the audience can understand, appreciate and replicate. Duality thus lies at the heart of creative communication, allowing a communicator to say one thing and simultaneously convey another, secondary message that may augment or subvert the overt content of the communication. This mechanism, which draws out and gives prominence to that which is normally unseen or implicit, is Figure-Ground Reversal. (shrink)

Self-relevance has been demonstrated to impair instrumental learning. Compared to unfamiliar symbols associated with a friend, analogous stimuli linked with the self are learned more slowly. What is not yet understood, however, is whether this effect extends beyond arbitrary stimuli to material with intrinsically meaningful properties. Take, for example, stimulus valence an established moderator of self-bias. Does the desirability of to-be-learned material influence self-learning? Here, in conjunction with computational modelling (i.e. Reinforcement Learning Drift Diffusion Model analysis), a probabilistic selection (...) task was used to establish if and how stimulus valence (i.e. desirable/undesirable posters) impacts the acquisition of knowledge relating to object-ownership (i.e. owned-by-self vs. owned-by-friend). Several interesting results were observed. First, undesirable posters were learned more rapidly for self compared to friend, an effect that was reversed for desirable posters. Second, learning rates were accompanied by associated differences in reward sensitivity toward desirable and undesirable choice selections as a function of ownership. Third, decisional caution was greater for self-relevant (vs. friend relevant) responses. Collectively, these findings inform understanding of self-function and how valence and stimulus relevance mutually influence probabilistic learning. (shrink)

Lucette's suicide left me indifferent. This time I knew it was coming, but years ago, when I first read Ada, or Ardor, I also felt relatively indifferent (apart from the element of surprise) to learn about her sudden death. I was aware of my indifference at the time and was surprised at my (non)reaction. It surprised me yet again in my recent rereading of the novel. Manipulating and withholding the reader's engagement with the text and empathy toward a character may (...) have been part of the author's intention, of course. But for me, this lack of emotional engagement with Lucette's fate is emblematic of what I find problematic in Nabokov's admittedly brilliant novel: though intellectually challenging and aesthetically pleasing, Ada (unlike Lolita, for example) is not emotionally engaging. Of course, not all readers find such engagement an important feature of the reading experience, but I do. For this reader, its absence makes Ada (both with and without the italics) a gorgeous but empty shell.Ada's reader, activated by an urge to dig out buried clues, finds that deciphering a clue—aside from the joy to which it may give rise—contributes little to the characters’ reality, to the breadth and depth of their fictional humanity. Instead, Van and Ada remain, throughout the novel, more superhuman than human, endowed with almost supernatural excellences and perfections (their intellect, their looks, their way of life, their unique capacities and skills). Nabokov's heroes indeed bring to mind Nietzsche's Übermensch and the philosopher's critique of traditional ethics. It seems to me that his view of what constitutes human greatness is echoed in the charismatic figures of Van and Ada, whose outlook—an outlook privileging virtues such as aestheticism, intelligence, individuality, and human “greatness”—appears to embody a Nietzschean revaluation of values, privileging an aesthetic outlook on morality. As an amateur of Nabokov, therefore, I was surprised to see that very little has been written about this Nietzschean presence in Ada. An aesthetic revaluation of values is, however, what Ada delivers. As Michael Wood observes, “Nabokov would have hated the association [of his own name with Nietzsche's], but... the connection is not arbitrary.”While this association—whether it was intentional or not—surely contributes to the novel's intellectual breadth and complexity, it adds nothing to the psychology of its main characters. Instead, Van and Ada's übermenschliche qualities—their human “greatness”—seem to be inborn, part of their aristocratic nature, rather than acquired through transformative struggle. I suspect that it is this lack of transformation in the characters that undermines the reader's engagement with their fate. This lack makes Nabokov's family chronicle much less memorable than Tolstoy's.In the first sentence of Ada (“All happy families are more or less dissimilar; all unhappy ones are more or less alike”), Nabokov parodies by reversing the famous first sentence of Anna Karenina and thereby, as Robert Alter argues, reverses “the major thematic movement of the novel as a genre”: whereas Tolstoy's novel concerns lost illusions, Ada “is an attempt to return to paradise.” Nabokov's swing away from Tolstoy is startling and impressive but fails to convince me that the paradise inhabited by the happy Veens is superior to the lost illusions of the Karenins. Even in death, Anna is more alive than Ada. (shrink)

Affirmative action is standardly pursued in relation to admissions to prestigious universities, in hiring for prestigious jobs, and when it comes to being elected to parliament. Central to these forms of affirmative action is that they have to do with competitive goods. A good is competitive when, if we improve A’s chances of getting the good, we reduce B’s chances of obtaining the good. I call this Competitive Affirmative Action. I distinguish this from Non-competitive Affirmative Action. The latter has to (...) do with non-competitive goods, e.g., being granted early parole or freedom from arbitrary arrest. I argue that some of the most prominent objections against affirmative action—in particular, the reverse discrimination objection and the merit objection—speak less against Non-competitive Affirmative Action. And that some of the most prominent arguments in favor of affirmative action, insofar as they justify Competitive Affirmative Action, also justify Non-competitive Affirmative Action. (shrink)

We investigate which part of Brouwer’s Intuitionistic Mathematics is finitistically justifiable or guaranteed in Hilbert’s Finitism, in the same way as similar investigations on Classical Mathematics already done quite extensively in proof theory and reverse mathematics. While we already knew a contrast from the classical situation concerning the continuity principle, more contrasts turn out: we show that several principles are finitistically justifiable or guaranteed which are classically not. Among them are: fan theorem for decidable fans but arbitrary bars; continuity (...) principle and the axiom of choice both for arbitrary formulae; and $\Sigma _2$ induction and dependent choice. We also show that Markov’s principle MP does not change this situation; that neither does lesser limited principle of omniscience LLPO ; but that limited principle of omniscience LPO makes the situation completely classical. (shrink)

Two central assumptions of current models of language acquisition were addressed in this study: (1) knowledge of linguistic structure is "mapped onto" earlier forms of non-linguistic knowledge; and (2) acquiring a language involves a continuous learning sequence from early gestural communication to linguistic expression. The acquisition of the first and second person pronouns ME and YOU was investigated in a longitudinal study of two deaf children of deaf parents learning American Sign Language (ASL) as a first language. Personal pronouns in (...) ASL are formed by pointing directly to the addressee (YOU) or self (I or ME), rather than by arbitrary symbols. Thus, personal pronouns in ASL resemble paralinguistic gestures that commonly accompany speech and are used prelinguistically by both hearing and deaf children beginning around 9 months. This provides a means for investigating the transition from prelinguistic gestural to linguistic expression when both gesture and language reside in the same modality.\nThe results indicate that deaf children acquired knowledge of personal pronouns over a period of time, displaying errors similar to those of hearing children despite the transparency of the pointing gestures. The children initially (ages 10 and 12 months) pointed to persons, objects, and locations. Both children then exhibited a long avoidance period, during which one function of the pointing gesture (pointing to self and others) dropped out completely. During this period their language and cognitive development were otherwise entirely normal, and they continued to use other types of pointing (e.g., to objects). When pointing to self and others returned, it was marked with errors typical of hearing children; one child exhibited consistent pronoun reversal errors, thinking the YOU point referred to herself, while the other child exhibited reversal errors inconsistently. Evidence from experimental tasks conducted with the first child revealed that pronoun errors occurred in comprehension as well. Full control of the ME and YOU pronouns was not achieved until 25-27 months, around the same time when hearing children master these forms. Thus, the study provides evidence for a discontinuity in the child's transition from prelinguistic to linguistic communication. It is argued that aspects of linguistic structure and its acquisition appear to involve distinct, language-specific knowledge. (shrink)

The appearance of consciousness in the universe remains one of the major mysteries unsolved by science or philosophy. Absent an agreed-upon definition of consciousness or even a convenient system to test theories of consciousness, a confusing heterogeneity of theories proliferate. In pursuit of clarifying this complicated discourse, we here interpret various frameworks for the scientific and philosophical study of consciousness through the lens of social insect evolutionary biology. To do so, we first discuss the notion of a forward test versus (...) a reverse test, analogous to the normal and revolutionary phases of the scientific process. Contemporary theories of consciousness are forward tests for consciousness, in that they strive to become a means to classify the level of consciousness of arbitrary states and systems. Yet no such theory of consciousness has earned sufficient confidence such that it might be actually used as a forward test in ambiguous settings. What is needed now is thus a legitimate reverse test for theories of consciousness, to provide internal and external calibration of different frameworks. A reverse test for consciousness would ideally look like a method for referencing theories of consciousness to a tractable model system. We introduce the Ant Colony Test as a rigorous reverse test for consciousness. We show that social insect colonies, though disaggregated collectives, fulfill many of the prerequisites for conscious awareness met by humans and honey bee workers. A long lineage of philosophically-neutral neurobehavioral, evolutionary, and ecological studies on social insect colonies can thus be redeployed for the study of consciousness in general. We suggest that the ACT can provide insight into the nature of consciousness, and highlight the ant colony as a model system for ethically performing clarifying experiments about consciousness. (shrink)

Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a dual (...) logic of partitions. That dual logic is described here. Partition logic is at the same mathematical level as subset logic since models for both are constructed from (partitions on or subsets of) arbitrary unstructured sets with no ordering relations, compatibility or accessibility relations, or topologies on the sets. Just as Boole developed logical finite probability theory as a quantitative treatment of subset logic, applying the analogous mathematical steps to partition logic yields a logical notion of entropy so that information theory can be refounded on partition logic. But the biggest application is that when partition logic and the accompanying logical information theory are "lifted" to complex vector spaces, then the mathematical framework of quantum mechanics is obtained. Partition logic models indefiniteness (i.e., numerical attributes on a set become more definite as the inverse-image partition becomes more refined) while subset logic models the definiteness of classical physics (an entity either definitely has a property or definitely does not). Hence partition logic provides the backstory so the old idea of "objective indefiniteness" in QM can be fleshed out to a full interpretation of quantum mechanics. (shrink)

The appearance of consciousness in the universe remains one of the major mysteries unsolved by science or philosophy. Absent an agreed-upon definition of consciousness or even a convenient system to test theories of consciousness, a confusing heterogeneity of theories proliferate. In pursuit of clarifying this complicated discourse, we here interpret various frameworks for the scientific and philosophical study of consciousness through the lens of social insect evolutionary biology. To do so, we first discuss the notion of a forward test versus (...) a reverse test, analogous to the normal and revolutionary phases of the scientific process. Contemporary theories of consciousness are forward tests for consciousness, in that they strive to become a means to classify the level of consciousness of arbitrary states and systems. Yet no such theory of consciousness has earned sufficient confidence such that it might be actually used as a forward test in ambiguous settings. What is needed now is thus a legitimate reverse test for theories of consciousness, to provide internal and external calibration of different frameworks. A reverse test for consciousness would ideally look like a method for referencing theories of consciousness to a tractable (and non-human) model system. We introduce the Ant Colony Test (ACT) as a rigorous reverse test for consciousness. We show that social insect colonies, though disaggregated collectives, fulfill many of the prerequisites for conscious awareness met by humans and honey bee workers. A long lineage of philosophically-neutral neurobehavioral, evolutionary, and ecological studies on social insect colonies can thus be redeployed for the study of consciousness in general. We suggest that the ACT can provide insight into the nature of consciousness, and highlight the ant colony as a model system for ethically performing clarifying experiments about consciousness. (shrink)

We examine the interdependence between individual and group behavior surrounding a somewhat arbitrary, real‐world decision: selecting a name for one’s child. Using a historical database of the names given to children over the last century in the United States, we find that naming choices are influenced by both the frequency of a name in the general population, and by its ‘‘momentum’’ in the recent past in the sense that names which are growing in popularity are preferentially chosen. This bias (...) toward rising names is a recent phenomena: In the early part of the 20th century, increasing popularity of a name from one time period to the next correlated with a decrease in future popularity. However, more recently this trend has reversed. We evaluate a number of formal models that detail how individual decision‐making strategies, played out in a large population of interacting agents, can explain these empirical observations. We argue that cognitive capacities for change detection, the encoding of frequency in memory, and biases toward novel or incongruous stimuli may interact with the behavior of other decision makers to determine the distribution and dynamics of cultural tokens such as names. (shrink)

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive (...) formulae are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Rhetoric and Power: An Inquiry into Foucault’s Critique of ConfessionDave TellOn October 10, 1979, Michel Foucault revised his thesis on confession. On that day, some three years after the publication of his magisterial treatment of confession in the first volume of The History of Sexuality, Foucault argued that the Pythagoreans, Stoics, and Epicureans had, before the advent of Christianity, their own practices of confession. Yet these practices, unlike their (...) Christian variants, were not complicit with practices of domination (OS 310, 312). In the context of Foucault’s thought theretofore, in which the confession consistently figured as an essential component in the exercise of modern power, this is a radical shift. In lectures given at both Berkeley and Dartmouth in the fall of 1980, Foucault made similar arguments. On these occasions he argued that Seneca’s De ira constituted a “stoic confession,” the object of which was to enable the subject to “live differently, better, more happily, than other people” (AB 210, 205). Judith Butler captures the gravity of the shift: “In the last years of his life, Foucault returned to the question of confession, reversing his earlier critique in the first volume of the History of Sexuality, where he indicts confession as a forcible extraction of sexual truth, a practice in the service of a regulatory power” (2005, 112).This reversal was short lived. Although Foucault would celebrate ancient Greek techniques of the self for the rest of his life, he would not [End Page 95] long refer to these techniques in terms of confession. Thus, in another reading of De ira, this one in March 1982, Foucault again noted that the Stoics have “confessional practices” that are “very close to what is found in Christianity” (Herm 482). This time, however, he insisted that the Stoic practices were fundamentally different: “However, all these elements seem to me to be profoundly different from what we should call ‘confession’ in the strict, or anyway, spiritual sense of the word” (Herm 365). In The Care of the Self, Foucault again conceded that De ira—what he now called “the most detailed description” of antique practices of the self—looked “at first glance” like a Christian confession, but he again maintained that it is something quite different: “The purpose of the examination is not therefore to discover one’s own guilt, down to its most trifling forms” (CS 61–62). Foucault concluded that the various “discourses of the self”—the confession and the Greek techniques of the self—could not be placed into a single category (see GE 250). Indeed, the “profound difference” (Herm 299) between these two discourses of the self was perhaps Foucault’s most repeated claim of the 1980s (see Herm 222, 237–44, 299, 308; GE 247–48; WS 237; AB 207–8; RFT 27; UP 89; CS 239; SS 5; FI 5, 12; FS 30, 35, 44, 87, 96, 97, 143–45, 147).It is worth asking why Foucault returned so consistently to the distinction between these two discursive forms. This question gains even more relevance for readers of this journal when we remember that, on at least two occasions, Foucault defined one of these forms, the ancient techniques of the self, in terms of its opposition to rhetoric: the techniques of the self, he claimed, are “nonrhetorical” (Herm 368; FS 20). Thus the question that drives this essay is not so much why Foucault attached such importance to the distinction but rather how rhetoric itself might differentiate the confession from the techniques of the self. Stated differently, Foucault’s work on the confession vis-à-vis the technologies of the self provides a valuable opportunity to study the role of rhetoric in Foucault’s thought—not because they are both rhetorical forms but, curiously, because Foucault insists that one is not.In order to foreground the work of rhetoric in Foucault’s thought, I situate his discourses of the self in the context of Nietzsche’s critique of metonymy. Although this may seem arbitrary, it gains initial plausibility from three facts. First, we know that Foucault understood rhetoric in terms of tropes (OT 84; Cooper 1988, 4). Second, we know too that Foucault had a deep... (shrink)

This paper presents a new explanation of how preferring the simplest theory compatible with experience assists one in finding the true answer to a scientific question when the answers are theories or models. Inquiry is portrayed as an unending game between science and nature in which the scientist aims to converge to the true theory on the basis of accumulating information. Simplicity is a topological invariant reflecting sequences of theory choices that nature can force an arbitrary, convergent scientist to (...) produce. It is demonstrated that among the methods that converge to the truth in an empirical problem, the ones that do so with a minimum number of reversals of opinion prior to convergence are exactly the ones that prefer simple theories. The approach explains not only simplicity tastes in model selection, but aspects of theory testing and the unwillingness of natural science to break symmetries without a reason. (shrink)

Freud proposes that in unconscious processing, logical connections are also (heavily) based upon phonological similarities. Repressed concerns, for example, would also be expressed by way of phonologic ambiguity. In order to investigate a possible unconscious influence of phonological similarity, 31 participants were submitted to a tachistoscopic subliminal priming experiment, with prime and target presented at 1ms. In the experimental condition, the prime and one of the 2 targets were phonological reversed forms of each other, though graphemically dissimilar (e.g., “nice” and (...) “sign”); in the control condition the targets were pseudo-randomly attributed to primes to which they don’t belong. The experimental task was to “blindly” pick the choice most similar to the prime. ERPs were measured with a focus on the N320, which is known to react selectively to phonological mismatch in supraliminal visual word presentations. The N320 amplitude-effects at the electrodes on the midline and at the left of the brain significantly predicted the participants’ net behavioral choices more than half a second later, while their subjective experience is one of arbitrariness. Moreover, the social desirability score (SDS) significantly correlates with both the behavioral and the N320 brain responses of the participants. It is proposed that in participants with low SDS the phonological target induces an expected reduction of N320 and this increases their probability to pick this target. In contrast, high defensive participants have a perplexed brain reaction upon the phonological target, with a negatively peaking N320 as compared to control and this leads them to avoid this target more often. Social desirability, which is understood as reflecting defensiveness, might also manifest itself as a defense against the (energy-consuming) ambiguity of language. The specificity of this study is that all of this is happening totally out of awareness and at the level of very elementary linguistic distinctions. (shrink)

Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes network, then every unambiguous causal conclusion produced by a consistent method from non-experimental data is subject to reversal as the sample size increases any finite number of times. That result, called the causal flipping theorem, extends prior results to the effect that causal (...) discovery cannot be reliable on a given sample size. We argue that since repeated flipping of causal conclusions is unavoidable in principle for consistent methods, the best possible discovery methods are consistent methods that retract their earlier conclusions no more than necessary. A series of simulations of various methods across a wide range of sample sizes illustrates concretely both the theorem and the principle of comparing methods in terms of retractions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Rhetoric and Power: An Inquiry into Foucault’s Critique of ConfessionDave TellOn October 10, 1979, Michel Foucault revised his thesis on confession. On that day, some three years after the publication of his magisterial treatment of confession in the first volume of The History of Sexuality, Foucault argued that the Pythagoreans, Stoics, and Epicureans had, before the advent of Christianity, their own practices of confession. Yet these practices, unlike their (...) Christian variants, were not complicit with practices of domination (OS 310, 312). In the context of Foucault’s thought theretofore, in which the confession consistently figured as an essential component in the exercise of modern power, this is a radical shift. In lectures given at both Berkeley and Dartmouth in the fall of 1980, Foucault made similar arguments. On these occasions he argued that Seneca’s De ira constituted a “stoic confession,” the object of which was to enable the subject to “live differently, better, more happily, than other people” (AB 210, 205). Judith Butler captures the gravity of the shift: “In the last years of his life, Foucault returned to the question of confession, reversing his earlier critique in the first volume of the History of Sexuality, where he indicts confession as a forcible extraction of sexual truth, a practice in the service of a regulatory power” (2005, 112).This reversal was short lived. Although Foucault would celebrate ancient Greek techniques of the self for the rest of his life, he would not [End Page 95] long refer to these techniques in terms of confession. Thus, in another reading of De ira, this one in March 1982, Foucault again noted that the Stoics have “confessional practices” that are “very close to what is found in Christianity” (Herm 482). This time, however, he insisted that the Stoic practices were fundamentally different: “However, all these elements seem to me to be profoundly different from what we should call ‘confession’ in the strict, or anyway, spiritual sense of the word” (Herm 365). In The Care of the Self, Foucault again conceded that De ira—what he now called “the most detailed description” of antique practices of the self—looked “at first glance” like a Christian confession, but he again maintained that it is something quite different: “The purpose of the examination is not therefore to discover one’s own guilt, down to its most trifling forms” (CS 61–62). Foucault concluded that the various “discourses of the self”—the confession and the Greek techniques of the self—could not be placed into a single category (see GE 250). Indeed, the “profound difference” (Herm 299) between these two discourses of the self was perhaps Foucault’s most repeated claim of the 1980s (see Herm 222, 237–44, 299, 308; GE 247–48; WS 237; AB 207–8; RFT 27; UP 89; CS 239; SS 5; FI 5, 12; FS 30, 35, 44, 87, 96, 97, 143–45, 147).It is worth asking why Foucault returned so consistently to the distinction between these two discursive forms. This question gains even more relevance for readers of this journal when we remember that, on at least two occasions, Foucault defined one of these forms, the ancient techniques of the self, in terms of its opposition to rhetoric: the techniques of the self, he claimed, are “nonrhetorical” (Herm 368; FS 20). Thus the question that drives this essay is not so much why Foucault attached such importance to the distinction but rather how rhetoric itself might differentiate the confession from the techniques of the self. Stated differently, Foucault’s work on the confession vis-à-vis the technologies of the self provides a valuable opportunity to study the role of rhetoric in Foucault’s thought—not because they are both rhetorical forms but, curiously, because Foucault insists that one is not.In order to foreground the work of rhetoric in Foucault’s thought, I situate his discourses of the self in the context of Nietzsche’s critique of metonymy. Although this may seem arbitrary, it gains initial plausibility from three facts. First, we know that Foucault understood rhetoric in terms of tropes (OT 84; Cooper 1988, 4). Second, we know too that Foucault had a deep... (shrink)

This article explores a distinctive representational strategy used in stop-motion animation: the object substitution. Using as its central example a children’s TV episode in which brushes stand in for dogs, it explains how this strategy produces a complex relationship between depiction and representation. The analysis highlights the pragmatic underpinnings of various theories of pictorial and cinematic representation, arguing that, in a substitution, depicted elements constitute explicatures and represented ones implicatures. Connecting this strategy to humans’ capacity for pareidolia (seeing things in (...) other things), it contends that an object substitution achieves its effects—and reconciles its marked incongruities—by prompting viewers to pleasurably reverse-engineer the far-fetched projective imagining that motivated its use. This process, which is a form of conceptual blending, is based on relations that are neither straightforwardly iconic nor purely arbitrary. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:“An Immoderate Taste for Truth”: Censoring History in Baudelaire’s “Les bijoux”E. S. Burt (bio)In May 1949, a French Court of Appeals reversed an 1857 decision condemning six poems from Les fleurs du mal for obscenity, in a signal case of a public lifting of a ban against some lyric poems. 1 Among the several interesting features of this case not the least is the decision to proceed against the (...) work in the first place. For lyric poetry does not appear an attractive target for censorship. Its subject matter and formalism remove it far enough from the experience of most readers that Gustave Flaubert, fresh from his troubles with the court over Madame Bovary, could express his surprise at the government’s attack: “This is new,” he wrote to Baudelaire, “this pursuit of a volume of verse.” While Flaubert’s comment was in point of fact inaccurate, he puts his finger on a problem worth considering. 2 Here we have a work that must seem naturally exempt from state intervention, by virtue of a deliberate retreat from risky political subjects, and it nonetheless did get censored by the state. Can anything be learned about “normal” state censorship from this exceptional case? [End Page 19]A key factor in the government’s decision to pursue the book, according to the prosecutor Pinard, was that these poems would prove accessible to a large audience: 3 “An immoral book that had no chance of being read or understood would not be pursued” [1208], he states. In his argument, as in the judgment by the court that the condemned poems “lead necessarily to the exciting of the senses by a coarse realism offensive to modesty” [1182], the assumption is that the work is extraordinarily available, its pictures immediately referable to ordinary experience. In the six condemned poems, language is judged to be not a veil but a tool, and a sex tool at that. “Despite an effort of style” [1182], the poetic situation—in most of the poems that of the boudoir—is painted in a language insufficiently flowery. 4A further interesting feature in the case is that when it comes up again, under DeGaulle’s Fourth Republic, the court summarily dismisses the 1857 judgment of coarse realism as just one possible interpretation, and a forced one at that. Instead, the 1949 court finds that the poems are self-referential, symbolic entities that do not represent ordinary experience:If some pictures, on account of their originality, were able to alarm some minds upon first publication and appeared to the first judges as offensive to morality, such an appraisal, attaching itself only to a realistic interpretation of the poems and neglecting their symbolic meaning, has proved to be of an arbitrary character, unratified by public opinion or by the judgment of the literary world.[St. John-Stevas 249]The shocking representations of 1857, outraging morality, are now understood to deliver the Wordsworthian “shock of mild surprise” by which we recognize the original work of art. In 1949, the poems are precious artifacts; their language is not realistic but symbolical; its sensuous forms reveal an inner, spiritual meaning.A crucial resemblance can be discerned between the actions taken by the two courts: both make their judgments in terms of a “reading pact,” a set of “artificial rules” [1206] that are presumed to govern reading and to have currency in the context. Les fleurs gets policed in the name of this generic purity, with the prosecutor Pinard calling “the judge... a sentinel who must not let the border be crossed” [1206] and the 1949 decision confirming the opinion of the literary world that the supposed transgression against public morality was in point of fact a transformation in the rules regulating the narrow confines of lyric poetry. 5This concern that texts be framed by a reading pact aimed at constraining their interpretation is worth considering in any discussion of censorship that wants to move from the level of pragmatics to that of theory. It leads to queries about the possibility of getting rid of state censorship entirely and about the state’s interest, as guardian and overseer of the archive, in the institutionalization and... (shrink)

The paper explicates a politicized conception of reality with the help of Michel Foucault’s critical project. I contend that Foucault’s genealogies of power problematize the relationship between ontology and politics. His idea of productive power incorporates a radical, ontological claim about the nature of reality: Reality as we know it is the result of social practices and struggles over truth and objectivity. Rather than translating the true ontology into the right politics, he reverses the argument. The radicality of his method (...) lies in showing how the ontological order of things is in itself the outcome of a political struggle: Ontology is politics that has forgotten itself. I argue that Foucault’s thought accomplishes the politicization of ontology with two key theoretical moves. The first is the contestation and provocation of all given and necessary ontological foundations. He affirms the ontological view that there is a discontinuity between reality and all ontological schemas that order it, and a subsequent indeterminacy of reason in establishing ultimate truths or foundations. After this initial step whereby ontology is denaturalized—made arbitrary or at least historically contingent—the way is open for explanations that treat the alternative and competing ontological frameworks as resulting from historical, linguistic and social practices of power. The second key move is thus the exposure of power relations and their constitutive role in our conception of reality. I conclude by considering the implications of Foucault’s politicization of ontology for our understanding of politics. (shrink)

The lessons of "logical empiricism" still need learning by scientific philosophers who continue to give ultimate descriptions of ultimate things. Even attempts to assign some basic transformative role to language must fail, as this role can always be reversed on some higher language level. Final philosophical characterizations of the universe collapse when we see their arbitrary linguistic nature. Similarly, the effort to force scientific philosophy into an ontology, as shown by a recent example, turns out to be only a (...) conventional way of talking, rather than a legitimate appeal to something in the universe. More vulnerable recent examples of scientific metaphysical descriptions of "reality" reveal a deceptive linguistic superfluity in no way necessary for science or scientific philosophy. Within the inevitable circularity of language, semantic analysis can still fasten to the goal of predictability; and predictability can do without uneconomical symbolism. (shrink)

In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is (...) possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects”. It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” of others, and the latter are “consequences” of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification. (shrink)

We show that a version of Ramsey’s theorem for trees for arbitrary exponents is equivalent to the subsystem ${{\sf ACA}^\prime_{0}}$ of reverse mathematics.

KANT'S CRITIQUE OF PURE REASON has been studied and analyzed over and over again in relation to its profound affinity with Newtonian science. But for the very reason that the putative validity of the transcendental arguments seems to depend upon this particular form of science as its ultimate model, the claim has been made repeatedly that Kant's philosophical stance can have no literal relevance to the actual problems thought germane to twentieth century physical science. Thus, the advent of the theory (...) of general relativity during the period from 1905 to 1916 has been seen almost unanimously as a sufficiently cogent refutation of some of the essential claims made by Kant regarding the nature of space and time. In the early days of the new theory, philosophers like Schlick, Reichenbach or Meyerson did their utmost to stress the unbridgeable nature of the gap separating the transcendental ideality of space and time from the metrical field used in general relativity. Indeed, the concept of metrical field may be seen as expressing an objective quality of reality because it could not exist at all if there were no phenomena related to matter. More recently, it has been argued that the fatal unrevisability of the Kantian categories necessarily means that the Kantian conception is annihilated and swallowed up by the relativistic one. The traditional distinction drawn by Kant between the form and the content of knowledge is itself reversed, in the sense that "for Kant, the formal components of knowledge are the most stable and objective elements," whereas according to the theory of relativity, "they are the most arbitrary and subjective elements" since the formal universality of the laws of nature depends upon arbitrary transformations of coordinates. This reversal, in turn, indicates that the form-content distinction has in effect been displaced by the very different distinction between the theoretical and the observational. At best, a high degree of correspondence has been accentuated, between the regulative validity of the Kantian a priori and the epistemological foundation underlying the principle of general relativity, inasmuch as the latter's vindication is seen to depend on arguments which are far from merely empirical. (shrink)

Merleau-Ponty: From Perspective to the Chiasm,the Epistemic Rigor of an AnalogyHere, we wish to take up the discussion of Merleau-Ponty’s notion of chiasm in light of the question of its status. Is it a matter of a metaphor without any cognitive value resulting from an analogical and arbitrary transfer from one domain to another, or is it a matter of a rigorous concept susceptible of being experimented upon, taken up again, or improved? If the latter is the case, what (...) is the nature of this concept? Is it descriptive, heuristic, or even logical? The question is worth asking insofar as it is not only the most orthodox positivists who may be likely to see, in this transfer of concept, nothing more than poetic license. Indeed, the most careful commentators authorized by Merleau-Ponty are in lockstep with the critics of his supposedly “literary” style. “Ambiguous” is thus the term, which more often describes Merleau-Ponty’s notions of encroachment, of reversibility, or even chiasm. First, we shall examine the function and the role of the concept of chiasm in Merleau-Ponty’s philosophy. We shall then establish its scope in order to be able to determine its exact status. It is only at the conclusion of this study that we will be able to show how this notion sheds light on Merleau-Ponty’s main concern, namely, to produce a counter-model of perspective and to promote a newcategory of relation – a concern which organizes the seemingly unrelated elements in his philosophy.Merleau-Ponty: dalla prospettiva al chiasma,il rigore epistemico di un’analogiaIntendiamo riprendere, in questa sede, la discussione sulla nozione di chiasma in Merleau-Ponty, alla luce di una domanda circa il suo statuto: si tratta di una metafora, priva di ogni valore cognitivo perché nata da un trasferimento analogico ed arbitrario da un campo semantico ad un altro, o si tratta di un concetto rigoroso, suscettibile di essere messo alla prova dell’esperienza e via via perfezionato? In tal caso, qual è la natura di questo concetto? È descrittiva, euristica, oppure logica? È interessante porre questa domanda dato che non sono solamente i positivisti più ortodossi, a vedere in questo trasferimento una semplice licenza poetica. In effetti, molti tra i commentatori più autorevoli di Merleau-Ponty aderiscono alle diverse critiche sollevate intorno alla presunta natura «letteraria» di questa espressione, e ritengono che il chiasma sia una semplice metafora. Interrogheremo innanzitutto la funzione e il ruolo di questo concetto nella filosofia di Merleau-Ponty al fine di determinarne l’esatto statuto. Solo al termine di questo studio preliminare potremo mostrare come questa nozione possa gettare nuova luce sulla preoccupazione principale di Merleau-Ponty, vero e proprio filo rosso che organizza in profondità tutti gli elementi apparentemente eterogenei della sua filosofia: vale a dire, il tentativo di produrre un contro-modello della prospettiva e una nuova categoria di relazione. (shrink)

Merleau-Ponty: From Perspective to the Chiasm,the Epistemic Rigor of an AnalogyHere, we wish to take up the discussion of Merleau-Ponty’s notion of chiasm in light of the question of its status. Is it a matter of a metaphor without any cognitive value resulting from an analogical and arbitrary transfer from one domain to another, or is it a matter of a rigorous concept susceptible of being experimented upon, taken up again, or improved? If the latter is the case, what (...) is the nature of this concept? Is it descriptive, heuristic, or even logical? The question is worth asking insofar as it is not only the most orthodox positivists who may be likely to see, in this transfer of concept, nothing more than poetic license. Indeed, the most careful commentators authorized by Merleau-Ponty are in lockstep with the critics of his supposedly “literary” style. “Ambiguous” is thus the term, which more often describes Merleau-Ponty’s notions of encroachment, of reversibility, or even chiasm. First, we shall examine the function and the role of the concept of chiasm in Merleau-Ponty’s philosophy. We shall then establish its scope in order to be able to determine its exact status. It is only at the conclusion of this study that we will be able to show how this notion sheds light on Merleau-Ponty’s main concern, namely, to produce a counter-model of perspective and to promote a newcategory of relation – a concern which organizes the seemingly unrelated elements in his philosophy.Merleau-Ponty: dalla prospettiva al chiasma,il rigore epistemico di un’analogiaIntendiamo riprendere, in questa sede, la discussione sulla nozione di chiasma in Merleau-Ponty, alla luce di una domanda circa il suo statuto: si tratta di una metafora, priva di ogni valore cognitivo perché nata da un trasferimento analogico ed arbitrario da un campo semantico ad un altro, o si tratta di un concetto rigoroso, suscettibile di essere messo alla prova dell’esperienza e via via perfezionato? In tal caso, qual è la natura di questo concetto? È descrittiva, euristica, oppure logica? È interessante porre questa domanda dato che non sono solamente i positivisti più ortodossi, a vedere in questo trasferimento una semplice licenza poetica. In effetti, molti tra i commentatori più autorevoli di Merleau-Ponty aderiscono alle diverse critiche sollevate intorno alla presunta natura «letteraria» di questa espressione, e ritengono che il chiasma sia una semplice metafora. Interrogheremo innanzitutto la funzione e il ruolo di questo concetto nella filosofia di Merleau-Ponty al fine di determinarne l’esatto statuto. Solo al termine di questo studio preliminare potremo mostrare come questa nozione possa gettare nuova luce sulla preoccupazione principale di Merleau-Ponty, vero e proprio filo rosso che organizza in profondità tutti gli elementi apparentemente eterogenei della sua filosofia: vale a dire, il tentativo di produrre un contro-modello della prospettiva e una nuova categoria di relazione. (shrink)

Merleau-Ponty: From Perspective to the Chiasm,the Epistemic Rigor of an AnalogyHere, we wish to take up the discussion of Merleau-Ponty’s notion of chiasm in light of the question of its status. Is it a matter of a metaphor without any cognitive value resulting from an analogical and arbitrary transfer from one domain to another, or is it a matter of a rigorous concept susceptible of being experimented upon, taken up again, or improved? If the latter is the case, what (...) is the nature of this concept? Is it descriptive, heuristic, or even logical? The question is worth asking insofar as it is not only the most orthodox positivists who may be likely to see, in this transfer of concept, nothing more than poetic license. Indeed, the most careful commentators authorized by Merleau-Ponty are in lockstep with the critics of his supposedly “literary” style. “Ambiguous” is thus the term, which more often describes Merleau-Ponty’s notions of encroachment, of reversibility, or even chiasm. First, we shall examine the function and the role of the concept of chiasm in Merleau-Ponty’s philosophy. We shall then establish its scope in order to be able to determine its exact status. It is only at the conclusion of this study that we will be able to show how this notion sheds light on Merleau-Ponty’s main concern, namely, to produce a counter-model of perspective and to promote a newcategory of relation – a concern which organizes the seemingly unrelated elements in his philosophy.Merleau-Ponty: dalla prospettiva al chiasma,il rigore epistemico di un’analogiaIntendiamo riprendere, in questa sede, la discussione sulla nozione di chiasma in Merleau-Ponty, alla luce di una domanda circa il suo statuto: si tratta di una metafora, priva di ogni valore cognitivo perché nata da un trasferimento analogico ed arbitrario da un campo semantico ad un altro, o si tratta di un concetto rigoroso, suscettibile di essere messo alla prova dell’esperienza e via via perfezionato? In tal caso, qual è la natura di questo concetto? È descrittiva, euristica, oppure logica? È interessante porre questa domanda dato che non sono solamente i positivisti più ortodossi, a vedere in questo trasferimento una semplice licenza poetica. In effetti, molti tra i commentatori più autorevoli di Merleau-Ponty aderiscono alle diverse critiche sollevate intorno alla presunta natura «letteraria» di questa espressione, e ritengono che il chiasma sia una semplice metafora. Interrogheremo innanzitutto la funzione e il ruolo di questo concetto nella filosofia di Merleau-Ponty al fine di determinarne l’esatto statuto. Solo al termine di questo studio preliminare potremo mostrare come questa nozione possa gettare nuova luce sulla preoccupazione principale di Merleau-Ponty, vero e proprio filo rosso che organizza in profondità tutti gli elementi apparentemente eterogenei della sua filosofia: vale a dire, il tentativo di produrre un contro-modello della prospettiva e una nuova categoria di relazione. (shrink)

In this article I investigate the Confucian sense of responsibility from the framework of “moral economy,” understood as a causal relationship between one’s virtue and non-moral goods including political position/success, and “contingency,” the failure of moral economy, and argue that early Confucians’ astute understanding of the contingent nature of the political world enabled them to subscribe to the non-causal sense of responsibility. Contrary to the common argument that Heaven was invoked by the Confucians in order to shield themselves from responsibility (...) for their political failures, I argue that they imposed a more expanded sense of responsibility both on them and on the rulers, largely preoccupied with realpolitik. In their effort to restore moral economy between the ruler’s virtue and his political position in particular, I show Confucians engaged in what I call reverse moral economy, at the heart of which was to constrain the ruler’s arbitrary use of political power. (shrink)

There is a fact of the matter about the nature of the human will and whether it can be considered ‘free’. To investigate this fact is attempting to answer what can be termed the metaphysical question of free will. The M-question is not identical to the problem of free will. ‘The problem of free will’ is often presented as one of two distinct problems. The first problem is whether free will is possible given determinism or indeterminism. The second problem is (...) whether free will is necessary for responsibility and morals. I argue that in providing an answer to the M-question, one should disregard both of these problems. The two ‘problems of free will’ need not- and should not- yield any influence on the answer to the M-question. The normative claim, ‘that they should not’ is based on considerations of prudence recommending that care should be taken to avoid introducing elements that create arbitrary biases on subjects with which they may have no necessary connection. Traditionally theories of free will have taken either determinism or indeterminism as a precondition. However, we can do without a definite answer to the D/I-issue, if the answer provided to the Mquestion needs no precondition. This would make it compatible in a certain overarching way i.e. ‘supercompatible’. Do not confuse this idea with compatibilism. Rather supercompatibilism is a constraint, not a theory. Supercompatibilism is the doctrine that theories of free will should be broadly compatible with regard to the D/I-issue. Broad compatibility thus entails a threshold to the severity of the consequences any definite answer to the D/I-issue can have. A strong supercompatibilist accepts no consequences, and thus set the threshold at zero. In contrast, a weak supercompatibilist will have a higher threshold. She can accept that different outcomes of the D/I-issue prompt changes in her theory, as long as those changes are non-critical. Naturally one cannot be a supercompatibilist if any outcome on the D/I-issue makes one’s theory unfeasible. Prudency recommends supercompatibilism because presently the relation between either determinism or indeterminism and the M-question can at best be contingent. It can at best be contingent because either of the theses may eventually be discovered to be false. Since the matter is scientifically and theoretically unsettled, taking any outcome of the D/I-issue as a precondition will be the result of arbitrary convictions and preferences of the theorizer. I submit that the most prudent way to deal with this contingency is adopting supercompatibilism. Like with the D/I-issue, prudency recommends keeping the R/M-issue apart from the M-question. This prudency is based on asymmetrical influence between the R/M-issue and the M-question. It is possible to both pose and answer the question “do humans have any sort of free will?” without any reference to the R/M-issue. Therefore the answer to the M-question must be essentially independent of any conclusions regarding the R/M-issue. So, since the M-question is independent of whatever is the case on the R/M-issue, this cannot be allowed to influence the M-question. The independency the M-question from the R/M-issue is often overlooked, one reason for which might be because the reverse is not obviously the case. At least some theories on the R/M-issue could be affected by some answers to the M-question, but this is irrelevant to work on the M-question. What matters is that no theories from the R/M-issue can influence the answer to the M-question therefore the prudent scientist should avoid mention of the former from discussion of the latter. (shrink)

THIS PAPER IS THE CO-WINNER OF THE FRED BERGER PRIZE IN PHILOSOPHY OF LAW FOR THE 1999 AMERICAN PHILOSOPHICAL ASSOCIATION FOR THE BEST PUBLISHED PAPER IN THE PREVIOUS TWO YEARS. -/- The conflict between liberal legal theory and critical legal studies (CLS) is often framed as a matter of whether there is a theory of justice that the law should embody which all rational people could or must accept. In a divided society, the CLS critique of this view is overwhelming: (...) there is no such justice that can command universal assent. But the liberal critique of CLS, that it degenerates into an unpalatable moral relativism on which there is no non-arbitrary basis between a justice that underwrites forms of domination such as slavery and a justice that condemns such forms of domination is equally powerful and compelling. I show that there is a way to harmonize both views that is subject to empirical test. -/- First I show that the most widely accepted and influential formulation of liberal justice, John Rawls' Justice as Fairness, in. e.g, A Theory of Justice, cannot avoid the relativistic challenge because it would not be accepted, as a matter of sociological fact, by real people in a divided society once the "veil of Ignorance" is removed and real people step out from the Original Position. To put it differently, different reflective equilibria are inevitable in a divided society. Given the weight that Rawls properly puts on the realizability of a conception of justice and its stability in practice, this is a fatal objection. There can be no divided society that is "well ordered" in Rawls' sense, governed by a shared conception of justice and known to be so governed. -/- I then turn to the most powerful statement of the CLS view, Milton's Fisk's relativistic account in The State and Justice. For Fisk, justice is a compromise between what the dominant groups can compel and what the the subordinate groups will acquiesce to., There is no one such compromise in any given situation, so the account is in that sense relativistic, but more deeply, it is relativistic in that it offers no non-arbitrary, non-question begging way to choose between the official justice of, e.g., a slaveholding society and and the radical justice of the slaves, which has no place for slaveholders as a group or slavery as an institution.All that Fisk can offer is an arbitrary existential choice: I'm with the slaves. (Or the slaveowners.) Most of us would find this disconcerting or even unacceptable. -/- I show that Fisk's general sort of account can be modified to allow for an non-arbitrary choice. Given general facts about human nature, societies based on domination will produce resistance that over the long run will diminish or eliminate various forms of domination. Through a sort of ratchet effect, rights won will be hard if not impossible to reverse. Societies embodying forms of domination can therefore be compared on dimensions of stability: the more domination, the more resistance, and the less stability. Such societies are inferior on the dimension of justice to more emancipatory society on the terms of both kinds of justice, official and radical. -/- This is not question begging because regimes of domination incorporate stability no less than more emancipatory social orders. The choice between official justice embodying domination and radical justice that does not is not arbitrary because it is based on a shared commitment to long term stability. This offers an empirical test of which social orders are more justice, and a prediction that over time, domination will tend to decrease. (shrink)

Journal of Mathematical Logic, Volume 23, Issue 02, August 2023. In mathematical logic there are two seemingly distinct kinds of principles called “reflection principles.” Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic reflection principles assert that every provable sentence from some complexity class is true. In this paper, we study connections between these two kinds of reflection principles in the setting of second-order arithmetic. We prove that, for (...) a large swathe of theories, [math]-model reflection is equivalent to the claim that arbitrary iterations of uniform [math] reflection along countable well-orderings are [math]-sound. This result yields uniform ordinal analyzes of theories with strength between [math] and [math]. The main technical novelty of our analysis is the introduction of the notion of the proof-theoretic dilator of a theory [math], which is the operator on countable ordinals that maps the order-type of [math] to the proof-theoretic ordinal of [math]. We obtain precise results about the growth of proof-theoretic dilators as a function of provable [math]-model reflection. This approach enables us to simultaneously obtain not only [math], [math] and [math] ordinals but also reverse-mathematical theorems for well-ordering principles. (shrink)

continent. 1.2 (2011): 78-91. This article consists of three parts. First, I will review the major themes of Quentin Meillassoux’s After Finitude . Since some of my readers will have read this book and others not, I will try to strike a balance between clear summary and fresh critique. Second, I discuss an unpublished book by Meillassoux unfamiliar to all readers of this article, except those scant few that may have gone digging in the microfilm archives of the École normale (...) supérieure. The book in question is Meillassoux’s revised doctoral dissertation L’Inexistence divine (or The Divine Inexistence ), with its seemingly bizarre vision of a God who does not yet exist but might exist in the future. Without literally accepting this view, I will claim that it is philosophically interesting in ways that even a hardened sceptic might be able to appreciate. Third and finally, I will speculate on the possible future of Meillassoux’s speculative materialism itself. And here I mean its future development not by Meillassoux, but by those readers who might be inspired by his book. Plato could never have predicted the emergence of Aristotle’s philosophy, despite the obvious debt of the latter to the former. Nor could Descartes have predicted Spinoza and Leibniz, nor Kant the German Idealists, and neither could Husserl in 1901 have foreseen the later emergence of Heidegger. How are the works of interesting philosophers transformed by later thinkers of comparable importance? While it may seem that there are countless ways to do this, I think there are only two basic ways in which this happens: you can radicalize your predecessors, or you can reverse them. I will close this article with a few words about these two methods, and try to imagine how Meillassoux might be radicalized or reversed by some future admirer. My view is that the more important thinkers are, the easier they are to radicalize or reverse. This helps explain why the great philosophers of the West have so often appeared in clusters, succeeding one another at relatively brief intervals during periods of especial ferment. 1. After Finitude After Finitude is unusually short for such an influential book of philosophy: running to just 178 pages in the original French, and an even more compact 128 pages in the English version, despite the introduction of roughly eight pages of new material for the English edition. Rather than summarizing Meillassoux’s book in the order he intended, I will focus on six points that strike me as the pillars of his debut book. Along the way, I will offer a few criticisms as well. The first pillar of the book is Meillassoux’s own term “correlationism.”1 Although he introduces this term as the name for an enemy, it is striking that Meillassoux remains impressed by correlationism much more than his fellow speculative realists are. This continued appreciation for his great enemy influences the shape of his own ontology. Is there a world outside our thinking of it, or does the world consist entirely in being thought? Traditionally, this dispute between realism and idealism has been dismissed in continental philosophy as a “pseudo-problem,” in a strategy pioneered by Husserl and extended by Heidegger. We cannot be realists, since following Kant we have no direct access to things-in-themselves. But neither are we idealists, since the human being is always already outside itself, aiming at objects in intentional experience, deeply engaged with practical implements, or stationed in some particular world-disclosing mood. The centuries-old dispute between realism and idealism is dissolved by saying that we cannot think either real or ideal in isolation from the other. There is neither human without world nor world without human, but only a primordial correlation or rapport between the two. This is what “correlationism” means: philosophy trapped in a permanent meditation on the human-world correlate, trying to find the best model of the correlate: is it language, intentionality, embodiment, or some other form of correlation between human and world? Among other problems, this generates some friction between philosophy and the literal meaning of science. When cosmologists say that the universe originated 13.5 billion years ago, they do not mean “13.5 billion years ago for us ,” but literally 13.5 billion years ago, well before conscious life existed, and thus at a time when there was no such thing as a correlate. Meillassoux also coins the term “ancestrality” (10) for the reality that predated the correlate, and later expands this term to “dia-chronicity,” (112) to refer to events occurring after the extinction of human beings no less than to those occurring before we existed. Up to this point, Meillassoux’s focus on ancestral entities existing prior to consciousness might seem like a straightforward realist who wants to unmask correlationism as just another form of idealism. Yet Meillassoux also admires the correlationist maneuver, which can obviously be traced back to Kant. Unlike a thinker such as Whitehead, Meillassoux feels no nostalgia for the pre-critical realism that came before Kant: “we cannot but be heirs of Kantianism,” he says (29). What impresses Meillassoux about correlationism is something both simple and familiar. If we attempt to think a tree outside thought, this is itself a thought . Any form of realism which thinks it can simply and directly address the world the way it is fails to escape the correlational circle, since the attempt to think something outside of thought is itself nothing other than a thought, and thereby collapses back into the very human-world correlate that it pretends to escape. For Meillassoux this step, suggested by Kant but first refined by the ensuing figures of German Idealism, marks decisive forward progress in the history of philosophy that must not be abolished. Any attempt to break free from the correlate must first acknowledge its mighty intellectual power. Realist though he may seem, Meillassoux’s works are filled with praise of such figures as Fichte and Hegel, not of so-called “naïve realists.” It is also the case that for Meillassoux, not all correlationisms are the same. The second pillar of his book is a distinction between various positions that I have termed “Meillassoux’s Spectrum,” though of course he is never so immodest as to name it after himself. He distinguishes between at least six different possible positions, and perhaps we could add even subtler variations if we wished. But in its simplest form, Meillassoux’s Spectrum allows for just four basic outlooks on the question of realism vs. anti-realism. Three of these are easy to understand, since we have already been discussing them. At one extreme is so-called “naïve realism,” which holds that a world exists outside the mind, and that we can know this world. Meillassoux rejects this naïve realism as having been overthrown by Kant’s critical philosophy. At the other extreme is subjective idealism, in which nothing exists outside the mind. For to think a dog outside thought immediately turns it into a thought, and therefore there cannot be anything outside; the very notion is meaningless. In between these two is what we have called correlationism. And here comes a crucial moment for Meillassoux, since he distinguishes between the two forms of “weak” and “strong” correlationism, and chooses the strong form as the launching pad for his own philosophy. Weak correlationism is easy to explain, since we all know it from the philosophy of Kant. The things-in-themselves can be thought but not known. They certainly must exist, since there cannot be appearances without something that appears. And we can think about them, which idealism holds to be impossible. They are simply unknowable due to the finitude of human thought. Strong correlationism is the new position introduced by Meillassoux (though he sees it at work in numerous twentieth century thinkers), midway between weak correlationism and subjective idealism. The major difference between the three positions is as follows. Weak correlationism says: “The things-in-themselves exist, but we cannot know them.” The subjective idealist says: “This is a contradiction in terms, since when we think the things-in-themselves, we already turn them into thoughts.” But the strong correlationist says: “Just because ‘things-in-themselves’ is a meaningless notion does not mean that they cannot exist. No one has ever traveled to the world-in-itself and come back to make a report on it. Thus, the fact that we cannot think things-in-themselves without contradiction does not prove that they do not exist anyway. There may be things-in-themselves, we simply are not capable of thinking them without contradiction form within the correlational circle.” This step is crucial for Meillassoux, since strong correlationism is the position he attempts to radicalize into his own new standpoint: speculative materialism. As I see it, this step of the argument fails. Strong correlationism cannot avoid collapsing into subjective idealism, since the statements of the strong correlationist are rendered meaningless from within. All three of the other positions in the Spectrum make perfectly good sense even for those who disagree with them. The naïve realist says that things-in-themselves exist and we can know them; the meaning of this statement is clear. The weak correlationist can say that things-in-themselves exist but lie forever beyond our grasp; this too makes perfect sense, even though the German Idealists try to show a contradiction at work here. We can also understand the claim of the subjective idealist that to think anything outside thought turns it into a thought, and that for this reason we cannot think the unthought. The strong correlationist, alone among the four, speaks nonsense . This person says “I cannot think the unthought without turning it into a thought, and yet the unthought might exist anyway.” But notice that the final phrase “the unthought might exist anyway” is fruitless for this purpose. For we have already heard that to think any unthought turns it into a thought. But now the strong correlationist wants to do two incompatible things simultaneously with this unthought. On the one hand, he neutralizes the unthought by showing that it instantly changes into just another thought. But on the other hand, he wants to appeal to the unthought as a haunting residue that might exist outside thought, thereby undercutting the absolute status of the human-world correlate found in idealism. But this is impossible. If you accept the argument that thinking the unthought turns it into a thought, you cannot also add “but maybe there is something outside that prevents this conversion from being absolutely true,” because this “something outside” is immediately converted into nothing but a thought for us. In short, Meillassoux here seems to be offering a kind of Zen koan: his “strong correlationism” is reminiscent of the gateless gate, or the sound of one hand clapping, or the command to punch Hegel in the jaw when meeting him on the road. We cannot at the same time both destroy the realist challenge of the things-in-themselves in order to undercut realism and reintroduce that very realist sense in order to undercut idealism. In a world where everything is instantly converted into thought, we cannot claim that there might be something extra-mental anyway, because this “might be something” is itself converted into a thought by the same rules that condemned dogs, trees, and houses to the idealist prison. This brings us to the third pillar of Meillassoux’s argument, which is the key to all the rest: the necessity of contingency. His strategy is to transform our supposed ignorance of things-in-themselves into an absolute knowledge that they exist without reason, and that the laws of nature can change at any time for no reason at all. In this way the cautious agnosticism of Kantian philosophies is avoided, but so is the collapse of reality into thought as found in German Idealism. Meillassoux does try to prove the existence of things-in-themselves existing outside thought; he simply holds that they must be proven after passing through the rigors of the correlationist challenge, not just arbitrarily decreed to exist in the manner of naïve realism. As he puts it, “Everything could actually collapse: from trees to stars, from stars to laws, from physical laws to logical laws; and this not by virtue of some superior law whereby everything is destined to perish, but by virtue of the absence of any superior law capable of preserving anything, no matter what, from perishing” (53). If idealism thinks that the human-world correlate is absolute, for Meillassoux it is the facticity of the correlate that is absolute. He tries to show this with a nice brief dialogue between five separate characters (55-59) which is covered in detail in my forthcoming book,2 but which I will simplify here for reasons of time. In this simplified version, we first imagine a dogmatic realist arguing with a dogmatic idealist. The realist says that we can know the truth about the things-in-themselves; the idealist counters that we can only the truth about thought, since all statements about reality must be turned into statements concerning our thoughts about reality. Here the correlationist enters and proclaims that both of these positions are equally dogmatic. For although we have access to nothing but thoughts, we cannot be sure that these thoughts are all that exist; there could be a reality outside thought, there is simply no way to know for sure. And this latter position is the one that Meillassoux attempts to transform from an agnostic, skeptical point into an ontological claim about the contingency of everything. Consider it this way. How does the correlationist defeat the idealist? The idealist holds that the existence of anything outside thought is impossible. The correlationist, by contrast, holds that something might exist outside the human-world correlate. But this “something might” has to be an absolute possibility. It cannot mean that “something outside thought might exist for thought ,” because that is what the idealist already says. No, the correlationist must mean that something might exist outside thought quite independently of thought. In other words, the correlationist says that idealism might be wrong, and this means it is absolutely true that idealism might be wrong. Thus, correlationism is no longer just a skeptical position. It holds that all the possibilities of the world are absolute possibilities. We have absolute knowledge that any of the possibilities about the existence or non-existence of things-in-themselves might be true, and this means that correlationism flips into Meillassoux’s own position: speculative materialism. As Meillassoux sees it, there are only two options here. Option A is to absolutize the human-world correlate, which is what the idealist does: there absolutely cannot be anything outside thought. Option B, by contrast, is to absolutize the facticity of the correlate: its character of simply being given to us, without any inherent necessity. The correlationist cannot have it both ways by saying: “there absolutely might be something outside thought, yet maybe this is absolutely impossible.” In other words, once we escape dogmatism we can only be idealists or speculative materialists, not correlationists. The human-world correlate is merely a fact, not an absolute necessity. But this facticity itself cannot be merely factical: it must be absolute. Here Meillassoux coins the French neologism factualité , which has been suitably translated into the English neologism “factiality.” (7, 122-3) Factialty means that for everything that exists, it is absolutely possible that it might be otherwise, not just that we cannot know whether or not it might be otherwise. Just as Kant transformed philosophy into a meditation on the categories governing human finitude, Meillassoux wishes to turn philosophy into a meditation on the necessary conditions of factiality, which he calls “figures”—a new technical term for him. (80) One such figure is that the law of non-contradiction must be true, and for an unusual reason. Since everything is proven to be contingent, nothing that exists can be contradictory, for whatever is contradictory has no opposite into which it might be transformed, and thus contingency would be impossible.3 Another such figure is that there must be something rather than nothing: for since contingency exists, something must exist in order to be contingent. It is a daring high-wire act, one that sacrifices realism to the correlational circle in order to rebuild it from out of its own ashes. Some might conclude that the lack of reason in things is a byproduct of the ignorance of finite humans, Meillassoux is making precisely the opposite point. For in fact, the doctrine of finitude usually leads directly to belief in a hidden reason. The fact that it lies beyond human comprehension merely increases our belief in this arbitrarily chosen concealed ground. By defending anew the concept of absolute knowledge Meillassoux evacuates the world of everything hidden. The reason for things having no reason is not that the reason is hidden, but that no reason exists. Thus, even while insisting on the necessity of non-contradiction, he rejects the other Leibnizian principle: sufficient reason. Everything simply is what it is, in purely immanent form, without deeply hidden causes. Or as Meillassoux puts it: “There is nothing beneath or beyond the manifest gratuitousness of the given—nothing but the limitless and lawless power of its destruction, emergence, or persistence” (63).The world is a “hyper-chaos”(64). But this is not the same thing as flux. For the chaos of the world is such that stability might occur just as easily as constant, turbulent change. Let’s now digress a bit, and return to the question of ancestrality, which Meillassoux transforms later in the book into “dia-chronicity.” Correlationism holds that all talk of a world outside the correlate is immediately recuperated by the correlate. The phrase “13.5 billion years ago” becomes “13.5 billion years ago for us ,” and the phrase “the universe following the extinction of humans” becomes “the universe following the extinction of humans for humans .” But notice that whether we talk about the world before or after humans, in both cases it is time that is used to challenge the correlate. Meillassoux has no interest in challenges that might be posed by space. For example, what about a vase in a lonely country house that topples to the floor and smashes when no one is there to watch it? Isn’t this also a challenge to correlationism, no less than the Big Bang or the heat death of the universe long after humans have vanished? In an eight-page supplement to the English translation of After Finitude ,4 possibly in response to my own 2007 review of the French original,5 Meillassoux bluntly denies that space is of any relevance to the question. Spatial distance is a merely harmless challenge to the human-world correlate. After all, even though no one is there in the lonely country house to witness the shattering of the vase, we can say that had there been an observer , that observer would have witnessed the toppling and destruction of the vase. For this event still occurs in a world in which the human-world correlate already exists, whereas the diachronicity of events both before and after the existence of humans makes it impossible to say that had there been an observer they would have witnessed the Big Bang occurring in such and such a fashion. However, it seems to me that Meillassoux merely asserts that the temporal simultaneity of our existence with that of the vase in the lonely country house is enough to render it harmless. It is true that the house does not exist prior to the correlate, but nonetheless it exists outside the correlate, and that is enough to make the same challenge. It is difficult to see why the “had there been an observer” maneuver succeeds in the case of a vase in the countryside in April 2011 but fails in the case of the Big Bang. This is not just a matter of nitpicking Meillassoux’s argumentative style: the fact that he bases his argument on time has at least two important consequences for his position. For in the first place, even though Meillassoux insists that the laws of nature are absolutely contingent, this turns out to be true only in a temporal sense. That is to say, it is a paradoxical feature of Meillassoux’s philosophy that he does allow for the existence of laws of nature, and simply believes that they can change at any moment without reason. Within any given moment, laws of nature do exist. He never suggests that different parts of the universe can have different laws at the same time, nor does he have any interest in the laws of part/whole composition that take place within any given instant. Could it be the case that rather than being made of gold atoms, a small chunk of gold could be made of silver atoms, cotton, horses, or that this same small piece of gold could be made of gigantic vaults filled with even more gold? These are not topics that draw Meillassoux’s attention, since he is focused solely on how the laws of nature might change or endure from one moment to the next . Another implication for Meillassoux’s system is that his concept of things-in-themselves turns out to be to be inadequate. For when he proves that things-in-themselves can exist without humans, this turns out to be true only in a temporal sense as well. Namely, things-in-themselves existed ten billion years ago, and they will continue to exist after all humans have succeeded in exterminating themselves. However, being able to exist before our births and after our deaths is just one small part of what it means to be a thing-in-itself. The more important part is that even if a thing is sitting on a table right now, in front of me, even if I stroke it lovingly or press my face up against it directly, I am still dealing only with a phenomenal version of the thing; the thing-in-itself continues to withdraw from all access. Yet no such thing is acknowledged by Meillassoux. For him finitude is a disaster, and absolute knowledge is in fact possible. Meillassoux’s thing-in-itself exists in independence only of the human lifespan , not of human knowledge. The fifth pillar of Meillassoux’s argument is his use of Cantor’s transfinite mathematics to show that even if the laws of nature are contingent, they need not be unstable, and thus we cannot use the apparent stability of nature to disprove his metaphysics of absolute contingency. What Cantor showed is that there are different sizes of infinity, and that all these infinities cannot be totalized in a single infinite number of infinities. Meillassoux sees this as crucial, since it allows him to discredit any “probabilistic” argument against his theory. The probabilistic argument (as defended quite clearly by Jean-René Vernes)6 would say this: given that the laws of nature seem so stable, it it is extremely improbable that there is no hidden reason for their remaining so stable. As Meillassoux sees it, probability is of value only when we can index an accessible total of cases. These can even be infinite: for example, there are an infinite number of points where a rope can break when stretched tight, but this does not stop us from calculating probabilities for various sections of the rope to break. By contrast, there is no way to sum up the number of possible laws of nature. For here there is no way to totalize; we cannot stand outside of nature and calculate the possible number of laws so as to determine the probabilities that any one of them might change. Therefore, although we can speak of probability when dealing with intraworldly events such as elections, horse races, and coin-flips, we cannot use the words “probable” or “improbable” when describing alterations at the level of nature as a whole. Rather than commenting on the validity of this argument and its use of Cantor, let me simply note that it once again creates a dualistic ontology. We already saw that Meillassoux treats time differently from space. In analogous fashion, he now treats the level of world differently from that of intraworldly events. The emergence of worlds is purely contingent and virtual and governed by no probability at all, while events within the world necessarily follow laws (even if these laws can change at any moment without reason), and thus their probabilities can be calculated. It is a strategy deeply reminiscent of Badiou’s (2005) own dualism between the normal “state of the situation” and the rare and intermittent “event.” The sixth and final pillar of Meillassoux’s book can be dealt with briefly, since we have already touched on it elsewhere. It comes at the very beginning of the book, when Meillassoux says that we must revive the distinction between primary and secondary qualities, and that the primary qualities are the ones that can be mathematized. He admits that he has not yet published a proof of this idea, though in fact it is already known as one of his primary doctrines. And here we encounter the familiar problem with Meillassoux’s inadequate conception of things-in-themselves. “Primary qualities” refers to those qualities that a thing has independently of its relations with us or anything else. But if the primary qualities can be mathematized, this means that they are not entirely independent of us, since our knowledge can get right to the bottom of them. The mathematized qualities of things are independent of us only in Meillassoux’s sense that they will still have those qualities even when all humans are dead. But to repeat, autonomy from the human lifespan is not the same as autonomy from human access. Here once more Meillassoux is concerned only with independence from the human-world correlate across time, not in any given instant. 2. L’Inexistence divine In 1997, the same year in which he turned thirty years old, Meillassoux earned his doctorate at the École normale supériuere with a brazen dissertation entitled L’Inexistence divine ( The Divine Inexistence ). The work was substantially revised in 2003. But even then, with typical fastidiousness, Meillassoux decided that the work was not yet ready for press. It has now been scrapped in favor of some future, multi-volume work bearing the same title. While writing my book on Meillassoux for Edinburgh University Press, I was permitted to translate excerpts from this unpublished work for use as an appendix in my own book; in total, the appendix contains approximately twenty percent of Meillassoux’s 2003 manuscript, the first time any of it will be published in any language. Nonetheless, a portion of the argument was already tested in the article “Spectral Dilemma,” published in English in the journal Collapse (2008: 261-75). There the philosophical motives for the virtual God are already made clear. What troubles us most are early deaths, brutal deaths, deaths of especial injustice– the sorts of deaths in which the brutal twentieth century was so abundant. And here, neither the atheist nor the believer can help us. The atheist can offer nothing but a sad and cynical resignation when reflecting on the victims of these terrible crimes. The believer does little better, being unable to explain how God could have allowed such things to happen, due to the famous intractability of the problem of evil. The solution offered to this dilemma by Meillassoux is bold, and all the more so given that he emerges from such a deeply Leftist, materialist, and unreligious background. His solution is that God does not yet exist, and therefore is not blameworthy for these catastrophes. Given that everything is contingent in Meillassoux’s philosophy, this God and divine justice might never exist, but they can at least exist as an object of hope. Let’s begin by jumping to the end of L’Inexistence divine , where the alternatives are laid out so nicely. There are four basic attitudes that humans can have towards God, Meillassoux says. First, we can believe in God because he exists. This is the classical theist attitude, rejected for the simple reason that it would be amoral and blasphemous to believe in a God who allows children to be eaten by dogs, to use Dostoevsky’s example. Second, we can disbelieve in God because he does not exist: the classical atheist attitude. But this leads to sadness, cynicism, and a sneering contempt for the greatness of human capacity. The third option, rather more complex, is to disbelieve in God because he does exist: in other words, to exist in rebellion against God as the one who must be blamed for the evils of the earth. The examples here might range from Lucifer himself, to the more human figure of Captain Ahab in Melville’s Moby-Dick , to Werner Herzog’s even more recent catchphrase, “Every man for himself, and God against all.” That leaves only the fourth option: believing in God because he does not exist. Meillassoux closes his book by saying that the fourth option has now been tried (namely, in the course of his own book), and that now that all four have been specified, we must choose. The first reaction to this theory of the inexistent God will be laughter. Few readers will ever be literally convinced by it, and probably none will immediately be convinced by it. But if we ask ourselves why we laugh, the answer is because it sounds so improbable that an inexistent God might suddenly emerge and resurrect the dead. It obviously sounds more like a gullible theology than a rigorous piece of philosophical work. Yet two things need to be kept in mind. First, Meillassoux’s theories are hardly more unlikely than those of great philosophers of the past such as Plato, Plotinus, Avicenna, Malebranche, Spinoza, Leibniz, Nietzsche, or Whitehead. We read the great philosophers not because their systems are plausible in commonsense terms that can be measured by the laws of probability. Instead, we read them precisely because they shatter the existing framework of common sense and open up new window on the universe. Second, and even more importantly, Meillassoux has already rejected probability as a valid measuring stick in philosophy. Or rather, he accepts probability in the intra-worldly realm (where it is linked with potentiality), and rejects it at the level of the world itself (where potentiality is replaced with what he calls virtuality). The virtual God can appear at any moment for no reason at all, just as any other new configuration of laws of nature can appear: in a manner that the laws of probability cannot calculate. Responding to those who might ridicule the idea of a sudden emergence of God and a resurrection of the dead, Meillassoux cites Pascal, who asserts that the resurrection of the dead would be far less incredible than the fact that we were born in the first place. This shifts philosophy onto new ground. Rather than concerning ourselves with what is likely to happen in the world as we know it, we focus instead on the most important things that could happen. For this reason, the expected objection that a virtual God is no more likely to appear than a virtual unicorn or a virtual flying spaghetti monster misses the point. Unicorns and spaghetti monsters could also appear, just like any other non-contradictory thing. But these would just be novel bizarre entities among others, not the heralds of completely new worlds. For Meillassoux, the emergence of matter, life, and thought have been the three truly amazing advents of the world so far, each of them dependent on the advent(s) preceding them. As he sees it, there can be no greater intraworldly entity than the human beings who already exist, since nothing in the world is better than the absolute knowledge of which humans alone are capable. This means that the next great advent must be something that perfects human beings rather than superseding them. And this can only be the world of justice, in which the dead are resurrected and their horrible deaths partially cancelled (Meillassoux never considers the possibility of a God who would literally erase the pre-divine past so that it never happened at all). The only immortality worth having is an immortality of this life, not an existence in some ill-defined afterworld. Human existence, he holds, must always be governed by a “symbol” that gives us the “immanent and comprehensible inscription of values in a world.” And just as cosmic history made the three great contingent leaps of matter, life, and thought, with a leap to justice as the only one still to come, a similar structure occurs within human culture and its symbols, which consist so far of the cosmological, naturalistic, and historical symbols, with a “factial” symbol still to come. We can review each of these symbols briefly. The cosmological symbol refers to the ancient dualism between the terrestrial and celestial spheres. Here below everything is conflict, corruption, and decay; but in the heavens nothing is perishable, all movement is circular, and everything is arranged in mutual harmony. This symbol is ended by modern physics when Galileo discovers such blemishes as sunspots and craters on the moon, and when Newton integrates both celestial and terrestrial movement into a single gravitational law. Next comes the naturalistic or romantic symbol, in which perfection comes not from the sky but from nature itself. The world is filled with pretty flowers (Meillassoux claims that the ancients never discussed the beauty of flowers until Plotinus in the third century) and with living creatures naturally moved by pity, at least until society corrupts them. This symbol collapses in the face of reality as we know it, since pity is no more common than war, corruption, and violence. This brings us to the historical symbol, which only now is passing away. Bad things may happen, but history has an inner logic of its own, such that everything works out in the end. The ultimate form of the historical symbol is the economic symbol, whether in a Marxist or neo-liberal form. Just as the Marxist holds that the inner economic logic of the capitalists will inexorably lead them to self-destruction, the neo-liberal assumes that the sum total of individual selfish actions will lead, in the long run, to the greatest possible good. We worship the economy and let it guide history for us, just as the ancients worshipped celestial bodies and held them to be free from blemish. The final remaining symbol is the factial symbol, which Meillassoux hopes will now emerge. Factiality, we recall, is his term for the absolute contingency of everything that exists. Once we have grasped this absolute contingency, we are free to expect the dramatic advent of the coming fourth World: the world of justice, inaugurated by a virtual God and even mediated by a messianic human figure. There is the added feature, however, that this messiah must abandon all claims to special status once the messianic realm of justice is achieved. The messianic figure will then be no more special than any person on the street, since a reign of human equality will have arisen. Although this focus on human being might seem like a return to standard humanism, Meillassoux holds that human pre-eminence has never truly been maintained. Previously, humans have been treated as special only because they contemplate the Good, because they resemble their omnipotent creator, or because they happen to be the temporary victors in a cruel Darwinian death-match between millions of living species. For Meillassoux, by contrast, humans have value because they know the eternal. But it is not the eternal that is important, since this merely represents the blind, anonymous contingency of each thing. What is important is not knowledge of the eternal , but knowledge of the eternal. We should not admire Prometheus for stealing fire from the gods; Prometheus is simply as bad as all the gods, no matter how much he increased our power. Feuerbach and Marx were wrong to say that God is a projection of the human essence, since for Meillassoux the usual concept of God represents the degradation of the human essence. If the traditional God was allowed to inflict plagues and tsunamis on the human race, the Promethean human of the twentieth century simply assumes the right to inflict death camps and atomic fireballs instead. In this respect, we have simply begun to imitate the degradation of humanity that was formerly invested in an omnipotent and arbitrary God. In response to charges that absolute contingency might lead to political quietism, Meillassoux counters that the World of justice would mean nothing unless we had already hoped for it beforehand. A World of justice that came along at random would merely be an improved third World of thought: indeed, a perfect one. But it would have satisfied no craving, and would therefore have no redemptive power. For this reason, we must actively hope for the fourth World of justice for such a fourth World ever to arise. Not only justice, but beauty is dependent on such hope: for Meillassoux, who is here somewhat dependent on Kant, beauty means an accord between our human symbolization and the actual world, which could never be present in a World of the blessed any more than justice could. And just as a messianic figure is needed to incarnate our hope and then abandon power once the World of justice is realized, it is the figure of the child whose fragile contingency shows us a dignity and a demand for justice beyond all power. 3. Meillassoux Radicalized or Reversed Given the promising reception of Meillassoux’s first book, it would not be groundless to engage in early speculation about what it might take to earn him a place in the history of philosophy. Maybe this will never happen—who knows?—but quite possibly it will: his lucid argumentative methods and sheer philosophical imagination at least make him a good candidate to be read well into the future, especially following further elaboration in print of his mature system. Philosophy is often practiced as thought it were nothing more than the amassing of “knockdown arguments.” But this is no more insightful than saying that good architecture is the amassing of steal beams. It is true that poorly constructed building cannot stand for long, but sound construction is merely the first, indispensable step in building. In fact, I am inclined to say that what really makes a philosopher important is not being right, but being wrong . I mean this in a very specific sense. I once heard the interesting remark about twentieth century culture that “you have to remember that the sixties really happened in the seventies.” That is to say, it was in the 1970’s rather than the more honored 1960’s that civil rights, free love, long hair, and the rock and roll drug culture really took root. With respect to the history of philosophy, we might just as easily say: “you have to remember that Plato really happened in Aristotle,” that “Kant really happened in Hegel” or “Hume really happened in Kant,” or that “Husserl’s phenomenology first achieved its truth in Heidegger.” One becomes an important philosopher not by being right, but by attracting rebellious admirers who tell you that you are wrong , even as their own careers silently orbit around your own. To recruit faithful disciples may be comforting and flattering, but the greatest thinkers have generally had to experience refutation at the hands of their most talented heirs. For this reason, I would propose that we size up the magnitude of living thinkers not by deciding how many times they are right and wrong, but by asking instead: who would take the trouble to refute this author? For this reason I do not ask: “Is Meillassoux right?”, since I do not believe in the virtual God myself, nor am I convinced by any important aspect of Meillassoux’s philosophy. Instead, I ask if there are interesting ways to overturn him. Only by being overturned, by no longer remaining a contemporary, does one become a classic. Let’s begin with a simple model of refutation, which can be refined further at a later date once the basic point is established. One kind of refutation simply consists in saying: “This author is a complete idiot.” The refuter now walks away in celebration, and no link between the present and the future is built; all is reduced to rubble. But this sort of mediocre triumphalism is generally practiced by those who achieve little of their own, and is not especially interesting. Much more interesting is the sort of refutation that does not take its target to be a complete idiot. I would like to suggest that there are just two basic ways in which this can be done: radicalization and reversal . It has not escaped my notice that this is a fairly good match for the Deleuzian distinction between irony and humor. Whereas irony critiques and adopts the opposite principle of what it attacks, humor accepts what it confronts but pushes it into highly exaggerated form. The ironist is like the worker who sows chaos by rebeling and contradicting the boss, while the humorist is like the worker who follows orders to an absurdly literal degree, with equally chaotic results. Let’s start with a few examples. In Aristotle’s treatment of Plato, and Heidegger’s of Husserl, we find reversal. Plato’s eidei are transformed by Aristotle into mere secondary substances, and the individual worldly things despised by Plato become what is primary. For Husserl what is primary is whatever is present to consciousness, while for Heidegger this is precisely what is secondary, since the primary stuff of the world withdraws from any form of presence at all. As for radicalization, it is most easily found in the transformation of Kant by German Idealism: “Kant was right to wall off the things-in-themselves from human access, and simply should have realized that the thought of the Ding an sich is also a thought, and thereby the noumena are just special cases of the phenomena,” with much following from this discovery. It would also be easy to read Spinoza as a radicalizer of Descartes, and Berkeley and Hume as radicalized versions of Locke. Perhaps the distinction is now sufficiently clear. Admiring refutations are not those that say “Professor X is an idiot,” which is merely the flip side of the eager disciple’s fruitless “Professor X got everything right.” Instead, it will be some variant of one of the following two options: “Professor X is important, but got it backwards,” or “Professor X is important, but didn’t push things far enough.” In the history of philosophy these two latter cases have often been painful in purely human terms: Aristotle expresses sadness at refuting Plato, Kant is openly annoyed at Fichte, and Husserl feels betrayed and used by Heidegger. Rude handling from later figures almost seems to be the sine qua non of being a great philosopher. Now, it has already been claimed that Meillassoux is an emerging philosopher of the first importance, and by no less a figure than Alain Badiou: “It would be no exaggeration to say that Quentin Meillassoux has opened up a new path in the history of philosophy…” (Preface, vii). But rather than taking Badiou’s word for it, or rejecting his word, we might experiment by asking how Meillassoux could be radicalized or reversed. Are there interesting ways of doing this that might launch whole new schools of philosophy, unexpected or even condemned by Meillassoux himself? While no one can see the future, the present is poor when it is not riddled with virtual futures. The relation between philosophers and their predecessors and successors is always somewhat complicated, of course. But generally there is one central divergence at stake, which might be taken as the key to all the others. On this basis we could say that new thinkers primarily radicalize or primarily reverse the main ideas of their chief philosophical forerunner. There may be specific historical conditions and perhaps even personality traits connected with these two types, but this question can be left aside for now. More important for us is that radicalizers will generally be followed by reversers, and vice versa. Consider the textbook example of a reversal in the history of philosophy: Kant’s Copernican Revolution, which inverts the so-called dogmatic tradition that addresses the world itself, and makes the world revolve instead around the conditions by which it is known. While it is not completely impossible that Kant’s successors might have re-reversed this principle back into a new and stronger dogmatic realism, conditions were premature for such a move. Anyone doing this too early would likely have been an angry anti-Kantian reactionary rather than an original thinker in command of a genuinely new realist principle. The far more likely outcome is the one that actually happened: Kant’s reversal of his predecessors was viewed as incomplete, or as retaining lamentable bits of the traditional view, which despite his admirable breakthrough he was unable to shake off. This was the view of German Idealism, anyway. In similar fashion, Spinoza could also be viewed as a radicalizer of Descartes, who is equally accused of preserving various Scholastic dogmas in an otherwise radical project of philosophical reversal. The point is this: reversals in the history of thought tend to be followed soon thereafter by radicalizations of those reversals. The same may hold true in reverse: radicalizations might generally be followed by reversals, given that it is not always possible to be more radical than the radicals have already been. Consider the case of Husserl, who radicalizes Brentano’s early vagueness about what lies beyond immanent objectivity, and Twardowski’s assertion that there must be an external object lying outside the intentional content, by collapsing everything into the intentional sphere: there is no difference between the Berlin in my consciousness and the actual Berlin that is home to millions of people. It is difficult to see how one could be even more radical than Husserl’s idealist turn here. And thus the road is paved to Heidegger’s reversal of classical phenomenology, in which the key point is what lies deeper than any presence to consciousness: the Sein whose power and obscurity cannot be made exhaustively present, but only sends itself in historical epochs. In similar fashion we might also read Leibniz as a reverser of Spinoza’s radicalization, retrieving a strong sense of individual substance and a certain validity of what the Scholastics had said. Returning to Meillassoux, we might ask which kind of philosopher he is: a radicalizer or a reverser? At present, Meillassoux looks to me like a radicalizer (though for now his future remains shrouded in mist). He takes the correlationist tradition, which allows us to speak only of the relation between human and world, and tries to raise it into an even more extreme claim about the absolute contingency of everything. But whereas German Idealism did this by trying to collapse the distinction between thought and world entirely into the “thought” side, Meillassoux does it by trying to shift the non-absolute contingency of the thought-world correlate from epistemology to ontology. It is no longer a question of the inability of human knowledge to know what lies outside the correlate, but the inability of reality itself to be rooted in any definite laws. Furthermore, if we look at the various features of Meillassoux’s philosophy identified earlier tonight, all but one are already so radical that there is no obvious way to push them further. The one exception would be his claim that the world as a whole can change for no reason at any moment, coupled with the inconsistent claim that within a given world there are laws of nature that everything must follow. If gravitational attraction between all masses is a current law in our world, then for Meillassoux there can be no exceptions to this law for as long as it remains in force. A toppled vase will fall to the floor every time for sure,unless there is a cosmic change by which the laws of nature as a whole have altered. (This is reminiscent of the late medieval distinction between the absolute and ordained power of God, according to which God has the power to set or change the laws of nature, but not to contravene those laws locally once they are set.) On this point, to radicalize Meillassoux would simply be to say: there are no laws of nature even in the local sense. Everything that happens, even in the world here and now, is purely contingent and not governed by even a trace of law. And while this would be a more consistent development of Meillassoux’s thoughts on contingency, it is difficult to see how it could lead to a new philosophy. Instead, the admiring successors of Meillassoux are more likely to reverse one of his already sufficiently radical points. At least four candidates come to mind: *First, we have seen that Meillassoux thinks correlationism is challenged by a time before or after consciousness, but not by a space lying outside it. Perhaps this could be reversed into saying that spatial exteriority is the really crucial point. The arguments on this point are perhaps the least convincing in After Finitude (and do not even occur in the original French edition), and therefore it might be a candidate for the “blind spot” of which no philosopher is ever free. *Second, Meillassoux uses Cantor to claim that the contingency of laws of nature would not entail that they are unstable. A successor of Meillassoux might claim that it does make them unstable, and celebrate this fact. This person would then have to explain why common sense seems to encounter a relatively stable world despite its truly rampant instability. Whereas Meillassoux’s problem is to show how stability might exist despite contingency, this successor’s problem would be slightly different: to show why actual, full-blown instability might have the appearance of stability. *Third, Meillassoux claims that the primary qualities of things are those that can be mathematized. He might be reversed by a successor who says the opposite: the mathematizable qualities are the secondary ones, and the primary ones are those that elude symbolic formulation. While this is a perfectly valid possible objection to Meillassoux, it is one that is made in advance by some of his predecessors and is still made by some of his peers, making it less interesting for futurology than some of his other points. *Fourth and finally, whereas Meillassoux claims that God does not exist but might exist in the future, a successor might argue even more bizarrely that God has always existed but might vanish in the future. Let’s arbitrarily select the first of these possibilities, and imagine briefly where it might lead, if pursued in the future by admiring detractors. Meillassoux comes from the circle of Badiou, and some of Badiou’s most ardent admirers are found in Latin America. So, let’s imagine that towards mid-century some ingenious reversers of Meillassoux emerge in that portion of the Spanish-speaking world. Just for fun, let’s call them Castro and Chávez. And in order to avoid any confusion with the present-day politicians of those names, we will stipulate that Meillassoux’s great successors are both women. The philosopher Castro (we will suppose she comes from Peru) reverses Meillassoux’s argument that the ancestral or diachronic are what most threaten the human-world correlate. Instead, she claims that the diachronic does not threaten the correlate at all, and that we must instead look at space as what ruins the correlate and demands a strange new realism. What would such a philosophy look like? In order to determine this, we might ask what price Meillassoux pays for doing it the opposite way. As I see it, he pays in two separate ways. One is that laws of nature for him are contingent over time . The laws of nature apply to the universe as a whole at any given moment, and would be changed globally if they are ever changed at all. The second price he pays is that Meillassoux has no mereology , or theory of parts and wholes. Everything for him is on the level of the given, or immanent in experience, with the sole proviso that the laws governing this immanence might change without notice at any given moment. In reversing Meillassoux, Castro makes the following claims in the preface to her stunning debut book of 2045, The Cosmos and its Neighborhoods , rapidly translated from Spanish into all the languages of the world: Despite his brilliant analysis of the contingency of laws of nature over time, Meillassoux gets two important assumptions wrong. First, he allows for only one set of contingent laws to govern nature as a whole. Second, he allows laws to govern only the world that is immanent in experience, and thereby fails to explore the contingency among part-whole relations. In this book I will argue, first, that the laws of nature vary in any given instant between one region of the universe and the next; and second, that the world is made up of layers of parts and wholes that are also contingent with respect to one another. Those are the words of Castro. This may sound like a hopeless free-for-all of chaos, yet the book somehow succeeds in drawing some compelling deductions about how laws must vary from one place or level in the world to the next. Trapped in the limited horizon of 2011, and not yet inspired by the heavily balkanized political and technological situation of 2050 that somehow lends additional credence to Castro’s vision, we can only vaguely grasp what such a philosophy might look like. After this reversal of Meillassoux by Castro, the usual pattern leads us to expect a radicalization by Chávez, a young Argentine student of Castro. How could the already strange theories of Castro be radicalized? Perhaps as follows, in a disturbing new book entitled The Implosion of the Neighborhoods , which argues as follows: Castro was right to shift the Meillassouxian framework of contingency from time to space. However, in this respect she retained a surprisingly traditional opposition between the two. In this book I will show that time and space collapse into one another. This may sound too much like the discredited four-dimensional block universe of twentieth century physics and philosophy. However, the four-dimensional universe is a model biased in favor of space, merely adding an extra dimension to the commonsense spatial continuum while stipulating that the serial passage of time is an illusion. In this book I will argue instead for a one-dimensional space-time modeled after our experience of time, in which there is no simultaneous co-existence at all between different parts of the universe, or ‘neighborhoods’ as my esteemed teacher Castro has called them. Instead, the various portions of the universe link to one another by succession rather than by coexistence. Buenos Aires, New York, and Amsterdam do not exist simultaneously in the same landscape, but one after the other in the mind of some observer, and this observer can only be an observer much larger than any human. Against Meillassoux’s notion of a virtual God that does not exist now but might exist in the future, I will argue for an actual God that surveys the universe in sequence, thereby generating the illusion of spatial diversity and even the illusion of individual minds located within that diversity. Once this divine observer dies, the universe as a whole must perish. Again, these ideas are so bizarre that we of 2011 can barely comprehend them, just as Aristotle would have had a difficult time grasping the theories of Descartes. We could then perhaps imagine a further reversal of this theory, emanating from the intellectually resurgent Philippines of the twenty-second century. The Filipino School might argue that the universe is already dead, given the collapse of its spatial richness into the serial observations of a flimsy and mortal God. The virtual universe does not yet exist, but might exist in fully spatial form in the future, and this would require the death of God and the resulting liberation of God’s succession of images as independent, spatially situated realities. With a bit of sharpening, we might be able to make all of these imaginary thinkers more intuitively clear. Along with the history of philosophy, there might arise a new discipline generating imaginary futures for philosophy. The richness of Meillassoux’s system comes not from the fact that he is plausibly right about so many things, but because his philosophy offers such a treasury of bold statements ripe for being radicalized or reversed. He is a rich target for many still-unborn intellectual heirs, and this is what gives him the chance to be an important figure. NOTES 1. Quentin Meillassoux, After Finitude . Trans. R Brassier. (London: Continuum, 2008.) Page 5. The word “correlationism” does not appear in his doctoral thesis. As Meillassoux informed me in an email of February 8, 2011, he first coined this term in 2003 or 2004, while editing for publication a lecture he had given at the École normale supérieure on a day devoted to the theme of “Philosophy and Mathematics,” an event including Alain Badiou as one of the participants. 2. Graham Harman, Quentin Meillassoux: Philosophy in the Making . (Edinburgh: Edinburgh University Press, forthcoming 2011). 3. In an email of December 6, 2010, Meillassoux clarifies that in After Finitude he only deduces the impossibility of a “universal contradiction,” not of a determinate contradiction. In the same email he suggests that he can also prove the latter, though the proof is somewhat lengthier than the one found in After Finitude . 4. After Finitude (18-26), in the passage falling between the two sets of triple asterisks. These pages were sent by Meillassoux to translator Ray Brassier (in French) during the translation process, and do not appear in the original French version of the book. 5. Graham Harman, “Quentin Meillassoux: A New French Philosopher.” Philosophy Today 51.1 (2007): Pages 104-117. The passage where I raise the question of space can be found in the first column of page 107. 6. Vernes is first cited on p. 95 of After Finitude . See Jean-René Vernes, Critique de la raison aléatoire, ou Descartes contra Kant . (Paris: Aubier, 1982).  . (shrink)

Tractatus Logico-Pilosophicus, the only book published during Ludwig Wittgenstein's lifetime , has since attracted the imagination of generations of philosophers as a work of great philosophical genius. Nonetheless, even today, more than eighty years later, philosophers are struggling to reconcile its diverse themes within a single, coherent picture. The present work is an attempt to meet this challenge. ;Wittgenstein considered the single proposition as a concrete model for the fact. The challenge is to show how a system of propositions can (...) serve as a model of reality. My work concentrates on three pillars of the logic of the Tractatus: the picture theory, negation as "reversal of sense," the independence of elementary propositions. Using a simple scenario of the ordering of objects or letters on a line, I examine the conflict generated by the attempt to adequately accommodate all three themes and offer my own solution. My solution brings implications to the problem of negation and to the Tractatus's thesis that the possibilities of logical space are spanned by the possible configurations of the ultimately simple objects. One such implication, which stands in contrast to the common reading, is that in atomic facts we have 'complex objects' as constituents. ;The resolution offered, furthermore, exposes an intrinsic difficulty in the Tractatus, for which I have reserved the term arbitrary choice. The difficulty is manifested in the lack of assurance---from the perspective of logic---that a concept-word will preserve its 'standard' meaning when it is reapplied or when its scope of application varies. In this I uncover the seed of central themes in Wittgenstein's later philosophy, e.g. the rule-following argument, as present already in the Tractatus. ;In the concluding chapter, I suggest a new account for the nature of the proposition by connecting the analysis offered in the Tractatus with the subject of time and motion. The picture with which the work concludes then considers language not as corresponding to reality, but as engaged or synchronized with reality---if you will, it is a picture of language and reality in a dance. (shrink)

The ideas of Jewish Messianism and libertarian utopia hold a decisive place in the work of Franz Kafka and while it is possible to recognise the selective tendency which links them, their orientation derives from radical negativity. The sympathy for libertarian utopianism which led Kafka to become involved in the activities of Prague anarchist circles in 1919-1922 did not take on the same form in his novels and short stories. In them it is purely negative, a critique of a world (...) devoid of freedom, of the meticulous absurd and arbitrary logic of some all-powerful "apparatus". The structural homology with "negative theology" is striking: in both cases the positive reverse of the established world - a libertarian utopia or messianic redemption - is totally lacking and it is this absence that defines the life of people as fallen, lost or devoid of meaning. The subconscious selective tendency between the two "negative" configurations leads to a convergence which can be seen in the structure of the novels (The Trial, The Castle) and short stories: this is what the crushing of the individual and the total refutation of freedom indicates - the redemption of the world. (shrink)

David Hilbert’s distinction between mathematics and metamathematics assumes mathematics is not metamathematics, cardinality of mathematics is less than cardinality of metamathematics, and metamathematics contains mathematics. Only by abandoning the last renders these characteristics consistent. Every set identifiable only in a metaset, following Kurt Gödel, the metaset is convertible into the set by translation of its constituents into constituents of the set, rendering the set indistinguishable from the metaset. Reversing Kurt Gödel, the set is convertible into the metaset by translation of (...) its constituents into constituents of themetaset, rendering the set indistinguishable from the metaset. Set being indistinguishable from metaset, the set of mathematics is unidentifiable as constituent of the set of metamathematics. Only inductively by exclusive resolution of all constituents of the set of all disjunctives of the sets of mathematics and metamathematics is the set of mathematics identifiable. Generated is endless arbitrary qualification of mathematical identity exhibited in continual proofsof its axioms. Understood as clarification, when everything is unique, no concealed contradiction is contained. Constituted is the endless non-repeating digit to the left of the decimal of an algebraic unknown number. Manifest is casuistry, now neither objective nor specious identity, but instead necessary subjective identity distinguishing sets. (shrink)

Kruskal proved that finite trees are well-quasi-ordered by hom(e)omorphic embeddability. Friedman observed that this statement is not provable in predicative analysis. Friedman also proposed (see in [Simpson]) some stronger variants of the Kruskal theorem dealing with finite labeled trees under home(e)omorphic embeddability with a certain gap-condition, where labels are arbitrary finite ordinals from a fixed initial segment of ω. The corresponding limit statement, expressing that for all initial segments of ω these labeled trees are well-quasi-ordered, is provable in Π (...) 1 1 -CA, but not in the analogous theory Π 1 1 -CA 0 with induction restricted to sets. Schutte and Simpson proved that the one-dimensional case of Friedman's limit statement dealing with finite labeled intervals is not provable in Peano arithmetic. However, Friedman's gap-condition fails for finite trees labeled with transfinite ordinals. In [Gordeev 1] I proposed another gap-condition and proved the resulting one-dimensional modified statements for all (countable) transfinite ordinal-labels. The corresponding universal modified one-dimensional statement UM 1 is provable in (in fact, is equivalent to) the familiar theory ATR 0 whose proof-theoretic ordinal is Γ 0 . In [Gordeev 1] I also announced that, in the general case of arbitrarily-branching finite trees labeled with transfinite ordinals, in the proof-theoretic sense the hierarchy of the limit modified statements $\mathbf{M}_{ (which are denoted by LM λ in the present note) is as strong as the hierarchy of the familiar theories of iterated inductive definitions (more precisely, see [Gordeev 1, Concluding Remark 3]). In this note I present a "positive" proof of the full universal modified statement UM, together with a short proof of the crucial "reverse" results which is based on Okada's interpretation of the well-established ordinal notations of Buchholz corresponding to the theories of iterated inductive definitions. Formally the results are summarized in $\S5$ below. (shrink)

Our target article argued that a genetically specified Universal Grammar (UG), capturing arbitrary properties of languages, is not tenable on evolutionary grounds, and that the close fit between language and language learners arises because language is shaped by the brain, rather than the reverse. Few commentaries defend a genetically specified UG. Some commentators argue that we underestimate the importance of processes of cultural transmission; some propose additional cognitive and brain mechanisms that may constrain language and perhaps differentiate humans from (...) nonhuman primates; and others argue that we overstate or understate the case against co-evolution of language genes. In engaging with these issues, we suggest that a new synthesis concerning the relationship between brains, genes, and language may be emerging. (shrink)

The crucial phase of speciation is argued to be the evolution of mating cross-incompatibility (prezygotic incompatibility) between the genotypes distinguishing the prospective species populations. Based on this idea, a single-locus model of speciation is presented, which is shown to be biologically plausible and may help to settle the controversy as to the biological significance of single-locus modes of speciation. The model involves three alleles, two of which characterize in homozygous state the prospective species populations and in heterozygous state their hybrids. (...) The third allele represents a mutant which is equivalent to one of the first two alleles with the exception that it inhibits mating with carriers of the third allele. This third allele is fixed in one population and immigrates into a second population which contains the mutant inhibiting matings with members of the former population. Migration in the reverse direction does not occur. Proceeding from a widely applicable concept of fitness and mating preference it is shown that postzygotic incompatibility (hybrid or heterozygote disadvantage) alone suffices to trigger evolutionary replacement of the extant mating relations in the population receiving immigrants by any arbitrary degree of prezygotic incompatibility. This corroborates Wallace's hypothesis and emphasizes the potential biological relevance of speciation by reinforcement (parapatric speciation) at single gene loci. (shrink)

Combining techniques of the first author and Shelah with ideas of Magidor, we show how to get a model in which, for fixed but arbitrary finite n, the first n strongly compact cardinals κ 1 ,..., κ n are so that κ i for i = 1,..., n is both the i th measurable cardinal and κ + i supercompact. This generalizes an unpublished theorem of Magidor and answers a question of Apter and Shelah.

We show that a version of Ramsey’s theorem for trees for arbitrary exponents is equivalent to the subsystem \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\sf ACA}^\prime_{0}}$$\end{document} of reverse mathematics.

In this paper I begin by extending two results of Solovay; the first characterizes the possible Turing degrees of models of True Arithmetic (TA), the complete first-order theory of the standard model of PA, while the second characterizes the possible Turing degrees of arbitrary completions of P. I extend these two results to characterize the possible Turing degrees of m-diagrams of models of TA and of arbitrary complete extensions of PA. I next give a construction showing that the (...) conditions Solovay identified for his characterization of degrees of models of arbitrary completions of PA cannot be dropped (I showed that these conditions cannot be simplified in the paper. (shrink)