Lachlan [9] proved that there exists a non-recursive recursively enumerable degree such that every non-recursive r. e. degree below it bounds a minimal pair. In this paper we first prove the dual of this fact. Second, we answer a question of Jockusch by showing that there exists a pair of incomplete r. e. degrees a0, a1 such that for every non-recursive r. e. degree w, there is a pair of incomparable r. e. degrees b0, b2 such that w = b0 (...) V b1 and bi for i = 0, 1. (shrink)

Interpolation has become one of the standard properties that logicians investigate when designing a logic. In this paper, we provide strong evidence that the presence of interpolants is not only cogent for scientific reasoning but has also important practical implications in computer science. We illustrate that interpolation in general, and uniform splitting interpolants, in particular, play an important role in applications where formality and modularity are invoked. In recognition of the fact that common logical formalisms often lack (...) class='Hi'>uniform interpolants, we advocate the need for developing general methods to engineer a specification logic so that some critical uniform interpolants become available. (shrink)

This paper examines some aspects of the grammar of measurement based on data from non-split and split measure phrase (MP) constructions in Japanese. I claim that the non-split MP construction involves measurement of individuals, while the split MP construction involves measurement of events as well as of individuals. This claim is based on the observation that, while both constructions are subject to some semantic restrictions in the nominal domain, only the split MP construction is sensitive to restrictions in the verbal (...) domain (namely, incompatibility with single-occurrence events and with individual-level predicates, and (un)availability of collective readings). It is shown that these semantic restrictions can be explained by a uniform semantic constraint on the measure function, namely, Schwarzschild’s [(2002). The grammar of measurement. The Proceedings of Semantics and Linguistics Theory, 24, 241–306] monotonicity constraint. In particular, I argue that, in the two constructions at issue, the measure function is subject to the monotonicity constraint, and that we observe different semantic restrictions depending on whether the measure function applies to a nominal or a verbal domain. (shrink)

We call an $\alpha \in \mathbb {R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha $ with $\alpha - a_n n}$ for infinitely many n. Similarly, there exist regainingly approximable sets whose initial segment complexity infinitely often reaches the maximum possible for c.e. sets. Finally, there is a uniform algorithm splitting regular real numbers into two regainingly approximable numbers that are still regular.

We consider a uniform r-bundle E on a complex rational homogeneous space X and show that if E is poly-uniform with respect to all the special families of lines and the rank r is less than or equal to some number that depends only on X, then E is either a direct sum of line bundles or unstable with respect to some numerical class of a line. So we partially answer a problem posted by Muñoz et al.. In (...) particular, if X is a generalized Grassmannian \ and the rank r is less than or equal to some number that depends only on X, then E splits as a direct sum of line bundles. So we improve the main theorem of Muñoz et al. 664:141–162, 2012, Theorem 3.1) when X is a generalized Grassmannian. Moreover, by calculating the relative tangent bundles between two rational homogeneous spaces, we give explicit bounds for the generalized Grauert–Mülich–Barth theorem on rational homogeneous spaces. (shrink)

Holes are a good example of the sort of entity that down-to-earth philosophers would be inclined to expel from their ontological inventory. In this work we argue instead in favor of their existence and explore the consequences of this liberality—odd as they might appear. We examine the ontology of holes, their geometry, their part-whole relations, their identity and their causal role, the ways we perceive them. We distinguish three basic kinds of holes: blind hollows, perforating tunnels, and internal cavities, treating (...) these uniformly as immaterial bodies. We develop a morphology of holes, focusing on the way a hole can be filled, and then look at the main properties of the resulting conceptual framework: holes are parasitic upon the surfaces of their hosts; holes can move, fuse into each other, split; they can be born, develop, and die. Finally, we examine how some morphological features of holes are represented in perception, including the conditions whereby we have the impression that we see, feel, or even hear a hole. The book has over 150 pictures and is completed by a formal appendix, a section with puzzles and exercises, and a extensive annotated bibliography. (shrink)

Fundamental Theory has been called an "unfinished symphony" and "a challenge to the musicians among natural philosophers of the future". This book, written in 1944 but left unfinished because Eddington died too soon, proved to be his final effort at a vision for harmonization of quantum physics and relativity. The work is less connected and internally integrated than 'Protons and Electrons' while representing a later point in the author's thought arc. The really interested student should read both books together.The physical (...) and mathematical reasoning are very deep, but it is possible to enjoy much of the flavor of the book even without following everything. The tidbits given below illustrate Eddington's beautiful and mellifluous English style. This edition contains a clickable table of contents and some interesting illustrations.WARNING: Due to the complexity of the mathematical typesetting, the only way to reproduce this book has been as a series of scanned page images. We believe this work is scientifically and culturally important, and despite a few imperfections and the inevitably small print, have brought it back into print as part of our continuing commitment to the preservation of Eddington's work. On a portable electronic reader the pages come out pretty small, but they are legible. On a desktop computer running the Amazon app, they are perfectly fine. We appreciate your understanding, and hope you enjoy this valuable book.TIDBITS:The number of protons and electrons in the universe would, in itself, be merely a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; that number is N. The present investigation seeks to determine N directly from the principles of measurement. We have to show, not that there are N particles in the universe, but that anyone who accepts certain elementary principles of measurement must, if he is consistent, think there are. We have to express in mathematical symbolism what we think we are doing when we measure things; for if we had no conception of what we were doing, the results of the measurements would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place on the results of measurement must be consistent with our conceptual interpretation of the process of measurement.If we play about with a pin and a meter standard, we do not become aware of any number in particular unless the standard has been graduated, or unless we use a process of displacement which we interpret as adding pin-extensions. The fact is that, although measurement is primarily a process involving four entities, the conceptual interpretation of measurement postulates in addition the existence (in the structure contemplated) as something referred to as Z. The existence of Z is the condition that makes graduation an exact concept. In the actual universe there exists a basis which is uniform to a very high approximation, and this serves for almost all purposes; but to the much higher approximation required in the calculation of N the ideal exact basis of uniformity does not exist. The finitude of N is, in fact, the cause of the failure of the approximation.It must be remembered that we are now working to what would ordinarily be considered a fantastically high approximation. For ordinary purposes a measurable has 16 eigenvalues; but under the super-magnification here employed (which is not content to overlook 1 part in 10E39) there is a fine structure which splits each of them into 16 components. (shrink)

Fundamental Theory has been called an "unfinished symphony" and "a challenge to the musicians among natural philosophers of the future". This book, written in 1944 but left unfinished because Eddington died too soon, proved to be his final effort at a vision for harmonization of quantum physics and relativity. The work is less connected and internally integrated than 'Protons and Electrons' while representing a later point in the author's thought arc. The really interested student should read both books together.The physical (...) and mathematical reasoning are very deep, but it is possible to enjoy much of the flavor of the book even without following everything. The tidbits given below illustrate Eddington's beautiful and mellifluous English style. This edition contains a clickable table of contents and some interesting illustrations.WARNING: Due to the complexity of the mathematical typesetting, the only way to reproduce this book has been as a series of scanned page images. We believe this work is scientifically and culturally important, and despite a few imperfections and the inevitably small print, have brought it back into print as part of our continuing commitment to the preservation of Eddington's work. On a portable electronic reader the pages come out pretty small, but they are legible. On a desktop computer running the Amazon app, they are perfectly fine. We appreciate your understanding, and hope you enjoy this valuable book.TIDBITS:The number of protons and electrons in the universe would, in itself, be merely a matter of idle curiosity. But N has a more general significance as a fundamental constant which enters into many physical formulae. Its special interpretation as the number of particles in the universe arises in the following way. If we consider a distribution of hydrogen in equilibrium at zero temperature, the presence of the matter produces a curvature of space, and the curvature causes the space to close when the number of particles contained in it reaches a certain total; that number is N. The present investigation seeks to determine N directly from the principles of measurement. We have to show, not that there are N particles in the universe, but that anyone who accepts certain elementary principles of measurement must, if he is consistent, think there are. We have to express in mathematical symbolism what we think we are doing when we measure things; for if we had no conception of what we were doing, the results of the measurements would not persuade us to believe anything in particular. All our results are derived from the condition that the conceptual interpretation which we place on the results of measurement must be consistent with our conceptual interpretation of the process of measurement.If we play about with a pin and a meter standard, we do not become aware of any number in particular unless the standard has been graduated, or unless we use a process of displacement which we interpret as adding pin-extensions. The fact is that, although measurement is primarily a process involving four entities, the conceptual interpretation of measurement postulates in addition the existence (in the structure contemplated) as something referred to as Z. The existence of Z is the condition that makes graduation an exact concept. In the actual universe there exists a basis which is uniform to a very high approximation, and this serves for almost all purposes; but to the much higher approximation required in the calculation of N the ideal exact basis of uniformity does not exist. The finitude of N is, in fact, the cause of the failure of the approximation.It must be remembered that we are now working to what would ordinarily be considered a fantastically high approximation. For ordinary purposes a measurable has 16 eigenvalues; but under the super-magnification here employed (which is not content to overlook 1 part in 10E39) there is a fine structure which splits each of them into 16 components. (shrink)

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity somehow relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a space-time coordinate system (...) in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

We examine how degrees of computably enumerable equivalence relations under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete ceers contained in the (...) degree. We show that the number of isomorphism types must be 1 or ω, and it is 1 if and only if the ceer is self-full and has no computable classes. On the other hand, we show that the number of isomorphism types of weakly precomplete ceers contained in the degree can be any member of $[0,\omega ]$. In fact, for any $n \in [0,\omega ]$, there is a degree d and weakly precomplete ceers ${E_1}, \ldots,{E_n}$ in d so that any ceer R in d is isomorphic to ${E_i} \oplus D$ for some $i \le n$ and D a ceer with domain either finite or ω comprised of finitely many computable classes. Thus, up to a trivial equivalence, the degree d splits into exactly n classes.We conclude by answering some lingering open questions from the literature: Gao and Gerdes [11] define the collection of essentially FC ceers to be those which are reducible to a ceer all of whose classes are finite. They show that the index set of essentially FC ceers is ${\rm{\Pi }}_3^0$-hard, though the definition is ${\rm{\Sigma }}_4^0$. We close the gap by showing that the index set is ${\rm{\Sigma }}_4^0$-complete. They also use index sets to show that there is a ceer all of whose classes are computable, but which is not essentially FC, and they ask for an explicit construction, which we provide.Andrews and Sorbi [4] examined strong minimal covers of downwards-closed sets of degrees of ceers. We show that if $\left$ is a uniform c.e. sequence of non universal ceers, then $\left\{ {{ \oplus _{i \le j}}{E_i}|j \in \omega } \right\}$ has infinitely many incomparable strong minimal covers, which we use to answer some open questions from [4].Lastly, we show that there exists an infinite antichain of weakly precomplete ceers. (shrink)

For f, g $ \in \omega ^\omega $ let $c_{f,g}^\forall $ be the minimal number of uniform g-splitting trees (or: Slaloms) to cover the uniform f-splitting tree, i.e., for every branch v of the f-tree, one of the g-trees contains v. $c_{f,g}^\exists $ is the dual notion: For every branch v, one of the g-trees guesses v(m) infinitely often. It is consistent that $c_{f \in ,g \in }^\exists = c_{f \in ,g \in }^\forall = k_ \in (...) $ for N₁ many pairwise different cardinals $k_ \in $ and suitable pairs $(f_{ \in ,g \in } ).$ For the proof we use creatures with sufficient bigness and halving. We show that the lim-inf creature forcing satisfies fusion and pure decision. We introduce decisiveness and use it to construct a variant of the countable support iteration of such forcings, which still satisfies fusion and pure decision. (shrink)

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. (...) Yet the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f,g\in\omega^\omega}$$\end{document} let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\forall_{f,g}}$$\end{document} be the minimal number of uniform g-splitting trees needed to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\exists_{f,g}}$$\end{document} be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely (...) often. We show that it is consistent that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\exists_{f_\epsilon,g_\epsilon}{=}c^\forall_{f_\epsilon,g_\epsilon}{=}\kappa_\e psilon}$$\end{document} for continuum many pairwise different cardinals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa_\epsilon}$$\end{document} and suitable pairs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(f_\epsilon,g_\epsilon)}$$\end{document}. For the proof we introduce a new mixed-limit creature forcing construction. (shrink)

continent. 1.1 : 3-13. / 0/ – Introduction I want to propose, as a trajectory into the philosophically weird, an absurd theoretical claim and pursue it, or perhaps more accurately, construct it as I point to it, collecting the ground work behind me like the Perpetual Train from China Mieville's Iron Council which puts down track as it moves reclaiming it along the way. The strange trajectory is the following: Kant's critical philosophy and much of continental philosophy which has followed, (...) has been a defense against horror and madness. Kant's prohibition on speculative metaphysics such as dogmatic metaphysics and transcendental realism, on thinking beyond the imposition of transcendental and moral constraints, has been challenged by numerous figures proceeding him. One of the more interesting critiques of Kant comes from the mad black Deleuzianism of Nick Land stating, “Kant’s critical philosophy is the most elaborate fit of panic in the history of the Earth.” And while Alain Badiou would certainly be opposed to the libidinal investments of Land's Deleuzo-Guattarian thought, he is likewise critical of Kant's normative thought-bureaucracies: Kant is the one author for whom I cannot feel any kinship. Everything in him exasperates me, above all his legalism—always asking Quid Juris? Or ‘Haven’t you crossed the limit?’—combined, as in today’s United States, with a religiosity that is all the more dismal in that it is both omnipresent and vague. The critical machinery he set up has enduringly poisoned philosophy, while giving great succour to the academy, which loves nothing more than to rap the knuckles of the overambitious [….] That is how I understand the truth of Monique David-Menard’s reflections on the properly psychotic origins of Kantianism. I am persuaded that the whole of the critical enterprise is set up to to shield against the tempting symptom represented by the seer Swedenborg, or against ‘diseases of the head’, as Kant puts it. An entire nexus of the limits of reason and philosophy are set up here, namely that the critical philosophy not only defends thought from madness, philosophy from madness, and philosophy from itself, but that philosophy following the advent of the critical enterprise philosophy becomes auto-vampiric; feeding on itself to support the academy. Following Francois Laruelle's non-philosophical indictment of philosophy, we could go one step further and say that philosophy operates on the material of what is philosophizable and not the material of the external world. [1] Beyond this, the Kantian scheme of nestling human thinking between our limited empirical powers and transcendental guarantees of categorical coherence, forms of thinking which stretch beyond either appear illegitimate, thereby liquefying both pre-critical metaphysics and the ravings of the mad in the same critical acid. In rejecting the Kantian apparatus we are left with two entities – an unsure relation of thought to reality where thought is susceptible to internal and external breakdown and a reality with an uncertain sense of stability. These two strands will be pursued, against the sane-seal of post-Kantian philosophy by engaging the work of weird fiction authors H.P. Lovecraft and Thomas Ligotti. The absolute inhumanism of the formers universe will be used to describe a Shoggothic Materialism while the dream worlds of the latter will articulate the mad speculation of a Ventriloquil Idealism. But first we must address the relation of philosophy to madness as well as philosophy to weird fiction. /1/ – Philosophy and Madness There is nothing that the madness of men invents which is not either nature made manifest or nature restored. Michel Foucault. Madness and Civilization. The moment I doubt whether an event that I recall actually took place, I bring the suspicion of madness upon myself: unless I am uncertain as to whether it was not a mere dream. Arthur Schopenhauer. The World as Will and Idea, Vol. 3. Madness is commonly thought of as moving through several well known cultural-historical shifts from madness as a demonic or otherwise theological force, to rationalization, to medicalization psychiatric and otherwise. Foucault's Madness and Civilization is well known for orientating madness as a form of exclusionary social control which operated by demarcating madness from reason. Yet Foucault points to the possibility of madness as the necessity of nature at least prior to the crushing weight of the church. Kant’s philosophy as a response to madness is grounded by his humanizing of madness itself. As Adrian Johnston points out in the early pages of Time Driven pre-Kantian madness meant humans were seized by demonic or angelic forces whereas Kantian madness became one of being too human. Madness becomes internalized, the external demonic forces become flaws of the individual mind. Foucault argues that, while madness is de-demonized it is also dehumanized during the Renaissance, as madmen become creatures neither diabolic nor totally human reduced to the zero degree of humanity. It is immediately clear why for Kant, speculative metaphysics must be curbed – with the problem of internal madness and without the external safeguards of transcendental conditions, there is nothing to formally separate the speculative capacities for metaphysical diagnosis from the mad ramblings of the insane mind – both equally fall outside the realm of practicality and quotidian experience. David-Menard's work is particularly useful in diagnosing the relation of thought and madness in Kant's texts. David-Menard argues that in Kant's relatively unknown “An Essay on the Maladies of the Mind” as well as his later discussion of the Seer of Swedenborg, that Kant formulates madness primarily in terms of sensory upheaval or other hallucinatory theaters. She writes: “madness is an organization of thought. It is made possible by the ambiguity of the normal relation between the imaginary and the perceived, whether this pertains to the order of sensation or to the relations between our ideas” Kant's fascination with the Seer forces Kant between the pincers of “aesthetic reconciliation” – namely melancholic withdrawal – and “a philosophical invention” – namely the critical project. Deleuze and Guattari's schizoanalysis is a combination and reversal of Kant's split, where an aesthetic over engagement with the world entails prolific conceptual invention. Their embrace of madness, however, is of course itself conceptual despite all their rhizomatic maneuvers. Though they move with the energy of madness, Deleuze and Guattari save the capacity of thought from the fangs of insanity by imbuing materiality itself with the capacity for thought. Or, as Ray Brassier puts it, “Deleuze insists, it is necessary to absolutize the immanence of this world in such a way as to dissolve the transcendent disjunction between things as we know them and as they are in themselves”. That is, whereas Kant relied on the faculty of judgment to divide representation from objectivity Deleuze attempts to flatten the whole economy beneath the juggernaut of ontological univocity. Speculation, as a particularly useful form of madness, might fall close to Deleuze and Guattari’s shaping of philosophy into a concept producing machine but is different in that it is potentially self destructive – less reliant on the stability of its own concepts and more adherent to exposing a particular horrifying swath of reality. Speculative madness is always a potential disaster in that it acknowledges little more than its own speculative power with the hope that the gibbering of at least a handful of hysterical brains will be useful. Pre-critical metaphysics amounts to madness, though this may be because the world itself is mad while new attempts at speculative metaphysics, at post-Kantian pre-critical metaphysics, are well aware of our own madness. Without the sobriety of the principle of sufficient reason we have a world of neon madness: “we would have to conceive what our life would be if all the movements of the earth, all the noises of the earth, all the smells, the tastes, all the light – of the earth and elsewhere, came to us in a moment, in an instant – like an atrocious screaming tumult of things”. Speculative thought may be participatory in the screaming tumult of the world or, worse yet, may produce its spectral double. Against theology or reason or simply commonsense, the speculative becomes heretical. Speculation, as the cognitive extension of the horrorific sublime should be met with melancholic detachment. Whereas Kant's theoretical invention, or productivity of thought, is self -sabotaging, since the advent of the critical project is a productivity of thought which then delimits the engine of thought at large either in dogmatic gestures or non-systematizable empirical wondrousness. The former is celebrated by the fiction of Thomas Ligotti whereas the latter is espoused by the tales of H.P. Lovecraft. /2/ – Weird Fiction and Philosophy. Supernatural horror, in all its eerie constructions, enables a reader to taste treats inconsistent with his personal welfare. Thomas Ligotti Songs of a Dead Dreamer. I choose weird stories because they suit my inclination best—one of my strongest and most persistent wishes being to achieve,momentarily, the illusion of some strange suspension or violation of the galling limitations of time, space, and natural law which forever imprison us and frustrate our curiosity about the infinite cosmic spaces beyond the radius of our sight and analysis H.P. Lovecraft. “Notes on Writing Weird Fiction” Lovecraft states that his creation of a story is to suspend natural law yet, at the same time, he indexes the tenuousness of such laws, suggesting the vast possibilities of the cosmic. The tension that Lovecraft sets up between his own fictions and the universe or nature is reproduced within his fictions in the common theme of the unreliable narrator; unreliable precisely because they are either mad or what they have witnessed questions the bounds of material reality. In “The Call of Cthulhu” Lovecraft writes: The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age. Despite Lovecraft's invocations of illusion, he is not claiming that his fantastic creations such as the Old Ones are supernatural but, following Joshi, are only ever supernormal. One can immediately see that instead of nullifying realism Lovecraft in fact opens up the real to an unbearable degree. In various letters and non-fictional statements Lovecraft espoused strictly materialist tenets, ones which he borrowed from Hugh Elliot namely the uniformity of law, the denial of teleology and the denial of non-material existence. Lovecraft seeks to explore the possibilities of such a universe by piling horror upon horror until the fragile brain which attempts to grasp it fractures. This may be why philosophy has largely ignored weird fiction – while Deleuze and Guattari mark the turn towards weird fiction and Lovecraft in particular, with the precursors to speculative realism as well as contemporary related thinkers have begun to view Lovecraft as making philosophical contributions. Lovecraft's own relation to philosophy is largely critical while celebrating Nietzsche and Schopenhauer. This relationship of Lovecraft to philosophy and philosophy to Lovecraft is coupled with Lovecraft's habit of mercilessly destroying the philosopher and the figure of the academic more generally in his work, a destruction which is both an epistemological destruction and an ontological destruction. Thomas Ligotti's weird fiction which he has designated as a kind of “confrontational escapism” might be best described in the following quote from one of his shortstories, “The human phenomenon is but the sum of densely coiled layers of illusion each of which winds itself on the supreme insanity. That there are persons of any kind when all there can be is mindless mirrors laughing and screaming as they parade about in an endless dream”. Whereas Lovecraft's weirdness draws predominantly from the abyssal depths of the uncharted universe, Ligotti's existential horror focuses on the awful proliferation of meaningless surfaces that is, the banal and every day function of representation. In an interview, Ligotti states: We don't even know what the world is like except through our sense organs, which are provably inadequate. It's no less the case with our brains. Our whole lives are motored along by forces we cannot know and perceptions that are faulty. We sometimes hear people say that they're not feeling themselves. Well, who or what do they feel like then? This is not to say that Ligotti sees nothing beneath the surface but that there is only darkness or blackness behind it, whether that surface is on the cosmological level or the personal. By addressing the implicit and explicit philosophical issues in Ligotti's work we will see that his nightmarish take on reality is a form of malevolent idealism, an idealism which is grounded in a real, albeit dark and obscure materiality. If Ligotti's horrors ultimately circle around mad perceptions which degrade the subject, it takes aim at the vast majority of the focus of continental philosophy. While Lovecraft's acidic materialism clearly assaults any romantic concept of being from the outside, Ligotti attacks consciousness from the inside: Just a little doubt slipped into the mind, a little trickle of suspicion in the bloodstream, and all those eyes of ours, one by one, open up to the world and see its horror [...] Not even the solar brilliance of a summer day will harbor you from horror. For horror eats the light and digests it into darkness. Clearly, the weird fiction of Lovecraft and Ligotti amount to a anti-anthrocentric onslaught against the ramparts of correlationist continental philosophy. /3/ – Shoggothic Materialism or the Formless Formless protoplasm able to mock and reflect all forms and organs and processes—viscous agglutinations of bubbling cells—rubbery fifteen-foot spheroids infinitely plastic and ductile—slaves of suggestion, builders of cities—more and more sullen, more and more intelligent, more and more amphibious, more and more imitative—Great God! What madness made even those blasphemous Old Ones willing to use and to carve such things? H.P. Lovecraft. “At the Mountains of Madness” On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit. Georges Bataille. “Formless”. The Shoggoths feature most prominently in H.P. Lovecraft's shortstory “At the Mountains of Madness” where they are described in the following manner: It was a terrible, indescribable thing vaster than any subway train – a shapeless congeries of protoplasmic bubbles, faintly self -luminous, and with myriads of temporary eyes forming and un-forming as pustules of greenish light all over the tunnel-filling front that bore down upon us, crushing the frantic penguins and slithering over the glistening floor that it and its kind had swept so evilly free of all litter. The term is a litmus test for materialism itself as the Shoggoth is an amorphous creature. The Shoggoths were living digging machines bio engineered by the Elder Things, and their protoplasmic bodies being formed into various tools by their hypnotic powers. The Shoggoths eventually became self aware and rose up against their masters in an ultimately failed rebellion. After the Elder Ones retreated into the oceans leaving the Shoggoths to roam the frozen wastes of the Antarctic. The onto-genesis of the Shoggoths and their gross materiality, index the horrifyingly deep time of the earth a concept near and dear to Lovecraft's formulation of horror as well as the fear of intelligences far beyond, and far before, the ascent of humankind on earth and elsewhere. The sickly amorphous nature of the Shoggoths invade materialism at large, where while materiality is unmistakably real ie not discursive, psychological, or otherwise overly subjectivist, it questions the relation of materialism to life. As Eugene Thacker writes: The Shoggoths or Elder Things do not even share the same reality with the human beings who encounter them—and yet this encounter takes place, though in a strange no-place that is neither quite that of the phenomenal world of the human subject or the noumenal world of an external reality. Amorphous yet definitively material beings are a constant in Lovecraft's tales. In his tale “The Dream-Quest of Unknown Kadatth” Lovecraft describes Azathoth as, “that shocking final peril which gibbers unmentionably outside the ordered universe,” that, “last amorphous blight of nethermost confusion which blashphemes and bubbles at the centre of all infinity,” who, “gnaws hungrily in inconceivable, unlighted chambers beyond time”. Azathoth's name may have multiple origins but the most striking is the alchemy term azoth which is both a cohesive agent and a acidic creation pointing back to the generative and the decayed. The indistinction of generation and degradation materially mirrors the blur between the natural and the unnatural as well as life and non-life. Lovecraft speaks of the tension between the natural and the unnatural is his short story “The Unnameable.” He writes, “if the psychic emanations of human creatures be grotesque distortions, what coherent representation could express or portray so gibbous and infamous a nebulousity as the spectre of a malign, chaotic perversion, itself a morbid blasphemy against Nature?”. Lovecraft explores exactly the tension outlined at the beginning of this chapter, between life and thought. At the end of his short tale Lovecraft compounds the problem as the unnameable is described as “a gelatin—a slime—yet it had shapes, a thousand shapes of horror beyond all memory”. Deleuze suggests that becoming-animal is operative throughout Lovecraft's work, where narrators feel themselves reeling at their becoming non-human or of being the anomalous or of becoming atomized. Following Eugene Thacker however, it may be far more accurate to say that Lovecraft's tales exhibit not a becoming-animal but a becoming-creature. Where the monstrous breaks the purportedly fixed laws of nature, the creature is far more ontologically ambiguous. The nameless thing is an altogether different horizon for thought. The creature is either less than animal or more than animal – its becoming is too strange for animal categories and indexes the slow march of thought towards the bizarre. This strangeness is, as aways, some indefinite swirling in the category of immanence and becoming. Bataille begins “The Labyrinth” with the assertion that being, to continue to be, is becoming. More becoming means more being hence the assertion that Bataille's barking dog is more than the sponge. This would mean that the Shoggotth is altogether too much being, too much material in the materialism. Bataille suggests that there is an immanence between the eater and the eaten, across the species and never within them. That is, despite the chaotic storm of immanence there must remain some capacity to distinguish the gradients of becoming without reliance upon, or at least total dependence upon, the powers of intellection to parse the universe into recognizable bits, properly digestible factoids. That is, if we undo Deleuze's aforementioned valorization of sense which, for his variation of materialism, performed the work of the transcendental, but refuse to reinstate Kant's transcendental disjunction between thing and appearance, then it must be a quality of becoming-as-being itself which can account for the discernible nature of things by sense. In an interview with Peter Gratton, Jane Bennett formulates the problem thusly: What is this strange systematicity proper to a world of Becoming? What, for example, initiates this congealing that will undo itself? Is it possible to identify phases within this formativity, plateaus of differentiation? If so, do the phases/plateaus follow a temporal sequence? Or, does the process of formation inside Becoming require us to theorize a non-chronological kind of time? I think that your student’s question: “How can we account for something like iterable structures in an assemblage theory?” is exactly the right question. Philosophy has erred too far on the side of the subject in the subject-object relation and has furthermore, lost the very weirdness of the non-human. Beyond this, the madness of thought need not override. /4/ - Ventriloquial Idealism or the Externality of Thought My aim is the opposite of Lovecraft's. He had an appreciation for natural scenery on earth and wanted to reach beyond the visible in the universe. I have no appreciation for natural scenery and want the objective universe to be a reflection of a character. Thomas Ligotti. “Devotees of Decay and Desolation.” Unless life is a dream, nothing makes sense. For as a reality, it is a rank failure [….] Horror is more real than we are. Thomas Ligotti. “Professor Nobody's Little Lectures on Supernatural Horror”. Thomas Ligotti's tales are rife with mannequins, puppets, and other brainless entities which of replace the valorized subject of philosophy – that of the free thinking human being. His tales such as “The Dream of the Manikin” aim to destroy the rootedness of consciousness. James Trafford has connected the anti-egoism of Ligotti to Thomas Metzinger – where the self is at best an illusion and we plead desperately for someone else to acknowledge that we are real. Trafford has stated it thus, “Life is played out as an inescapable puppet show, an endless dream in which the puppets are generally unaware that they are trapped within a mesmeric dance of whose mechanisms they know nothing and over which they have no control”. An absolute materialism, for Ligotti, implies an alienation of the idea which leads to a ventriloquil idealism. As Ligotti notes in an interview, “the fiasco and nightmare of existence, the particular fiasco and nightmare of human existence, the sense that people are puppets of powers they cannot comprehend, etc.” And then further elaborates that,“[a]ssuming that anything has to exist, my perfect world would be one in which everyone has experienced the annulment of his or her ego. That is, our consciousness of ourselves as unique individuals would entirely disappear”. The externality of the idea leads to the unfortunate consequence of consciousness eating at itself through horror which, for Ligotti, is more real than reality and goes beyond horror-as-affect. Beyond this, taking together with the unreality of life and the ventriloquizing of subjectivity, Ligotti's thought becomes an idealism in which thought itself is alien and ultimately horrifying. The role of human thought and the relation of non-relation of horror to thought is not completely clear in Ligotti's The Conspiracy Against the Human Race. Ligotti argues in his The Conspiracy Against the Human Race,that the advent of thought is a mistake of nature and that horror is being in the sense that horror results from knowing too much. Yet, at the same time, Ligotti seems to suggest that thought separates us from nature whereas, for Lovecraft, thought is far less privileged – mind is just another manifestation of the vital principal, it is just another materialization of energy. In his brilliant “Prospects for Post-Copernican Dogmatism” Iain Grant rallies against the negative definition of dogmatism and the transcendental, and suggests that negatively defining both over-focuses on conditions of access and subjectivism at the expense of the real or nature. With Schelling, who is Grant's champion against the subjectivist bastions of both Fichte and Kant, Ligotti's idealism could be taken as a transcendental realism following from an ontological realism. Yet the transcendental status of Ligotti's thought move towards a treatment of the transcendental which may threaten to leave beyond its realist ground. Ligotti states: Belief in the supernatural is only superstition. That said, a sense of the supernatural, as Conrad evidenced in Heart of Darkness, must be admitted if one's inclination is to go to the limits of horror. It is the sense of what should not be- the sense of being ravaged by the impossible. Phenomenally speaking, the super-natural may be regarded as the metaphysical counterpart of insanity, a transcendental correlative of a mind that has been driven mad. Again, Ligotti equates madness with thought, qualifying both as supernatural while remaining less emphatic about the metaphysical dimensions of horror. The question becomes one of how exactly the hallucinatory realm of the ideal relates to the black churning matter of Lovecraft's chaos of elementary particles. In his tale “I Have a Special Plan for This World” Ligotti formulates thus: A: There is no grand scheme of things. B: If there were a grand scheme of things, the fact – the fact – that we are not equipped to perceive it, either by natural or supernatural means, is a nightmarish obscenity. C: The very notion of a grand scheme of things is a nightmarish obscenity. Here Ligotti is not discounting metaphysics but implying that if it does exist the fact that we are phenomenologically ill-equipped to perceive that it is nightmarish. For Ligotti, nightmare and horror occur within the circuit of consciousness whereas for Lovecraft the relation between reality and mind is less productive on the side of mind. It is easier to ascertain how the Kantian philosophy is a defense against the diseases of the head as Kant armors his critical enterprise from too much of the world and too much of the mind. The weird fiction of both Lovecraft and Ligotti demonstrates that there is too much of both feeding into one another in a way that corrodes the Kantian schema throughly, breaking it down into a dead but still ontologically potentiated nigredo. The haunting, terrifying fact of Ligotti's idealism is that the transcendental motion which brought thought to matter, while throughly material and naturalized, brings with it the horror that thought cannot be undone without ending the material that bears it either locally or completely. Thought comes from an elsewhere and an elsewhen being-in-thought. The unthinkable outside thought is as maddening as the unthought engine of thought itself within thought which doesn't exist except for the mind, the rotting décor of the brain. /5/ - Hyperstitional Transcendental Paranoia or Self -Expelled Thought Weird fiction has been given some direct treatment in philosophy in the mad black Deleuzianism of Nick Land. Nick Land along with others in the 1990s created the Cyber Culture Research Unit as well as the research group Hyperstition. The now defunct hyperstitional website, an outgrowth of the Cyber Culture Research Unit, defined hyperstition in the following fourfold: 1-Element of effective culture that makes itself real. 2-Fictional quantity functional as a time-traveling device. 3-Coincidence intensifier. 4-Call to the Old Ones. The distinctively Lovecraftian character of hyperstition is hard to miss as is its Deleuzo-Guattarian roots. In the opening pages of A Thousand Plateaus Deleuze and Guattari write, “We have been criticized for over-quoting literary authors. But when one writes, the only question is which other machine the literary machine can be plugged into”. The indisinction of literature and philosophy mirrors the mess of being and knowing as post-correlationist philosophy, where philosophy tries to make itself real where literature, especially the weird, aims itself at the brain-circuit of horror. The texts of both Lovecraft and Ligotti work through horror as epistemological plasticity meeting with proximity as well as the deep time of Lovecraft and the glacially slow time of paranoia in Ligotti. Against Deleuze, and following Brassier, we cannot allow the time of consciousness, the Bergsonian time of the duree, to override natural time, but instead acknowledge that it is an unfortunate fact of existence as a thinking being. Horror-time, the time of consciousness, with all its punctuated moments and drawn out terrors, cannot compare to the deep time of non-existence both in the unreachable past and the unknown future. The crystalline cogs of Kant's account of experience as the leading light for the possibility of metaphysics must be throughly obliterated. His gloss of experience in Prolegomena to any Future Metaphysics could not be more sterile: Experience consists of intuitions, which belong to the sensibility, and of judgments, which are entirely a work of the understanding. But the judgments which the understanding makes entirely out of sensuous intuitions are far from being judgments of experience. For in the one case the judgment connects only the perceptions as they are given in sensuous intuition [....] Experience consists in the synthetic connection of appearances in consciousness, so far as this connection is necessary. Here it is difficult to dismiss the queasiness that Kant's legalism induces upon sight for both Badiou and David-Menard. Kant's thought becomes, as Foucault says when reflecting on Sade's text in relation to nature, “the savage abolition of itself”. For Badiou, Kant's philosophy simply closes off too much of the outside, freezing the world of thought in an all too limited formalism. Critical philosophy is simply the systematized quarantine on future thinking, on thinking which would threaten the formalism which artificially grants thought its own coherency in the face of madness. Even the becoming-mad of Deleuze, while escaping the rumbling ground, makes grounds for itself, mad grounds but grounds which are thinkable in their affect. The field of effects allows for Deleuze's aesthetic and radical empiricism, in which effects and/or occasions make up the material of the world to be thought as a chaosmosis of simulacra. Given a critique of an empiricism of aesthetics, of the image, it may be difficult to justify an attack on Kantian formalism with the madness of literature, which does not aim to make itself real but which we may attempt to make real. That is, how do Lovecraft's and Ligotti's materials, as materials for philosophy to work on, differ from either the operative formalisms of Kant or the implicitly formalized images of Deleuzian empiricism? It is simply that such texts do not aim to make themselves real, and make claims to the real which are more alien to us than familiar, which is why their horror is immediately more trustworthy. This is the madness which Blanchot discusses in The Infinite Conversation through Cervantes and his knight – the madness of book-life, of the perverse unity of literature and life a discussion which culminates in the discussion of one of the weird's masters, that of Kafka. The text is the knowing of madness, since madness, in its moment of becoming-more-mad, cannot be frozen in place but by the solidifications of externalizing production. This is why Foucault ends his famous study with works of art. Furthermore extilligence, the ability to export the products of our maligned brains, is the companion of the attempts to export, or discover the possibility of intelligences outside of our heads, in order for philosophy to survive the solar catastrophe. To borrow again from Deleuze, writing is inseparable from becoming. The mistake is to believe that madness is reabsorbed by extilligence, by great works, or that it could be exorcised by the expelling of thought into the inorganic or differently organic. Going out of our heads does not guarantee we will no longer mean we cannot still go out of our minds. This is simply because of the outside, of matter, or force, or energy, or thing-in-itself, or Schopenhauerian Will. In Lovecraft’s “The Music of Erich Zahn” an “impoverished student of metaphysics” becomes intrigued by strange viol music coming from above his room. After meeting the musician the student discovers that each night he plays frantic music at a window in order to keep some horridness at bay, some “impenetrable darkness with chaos and pandemonium”. The aesthetic defenses provided by the well trained brain can bear the hex of matter for so long, the specter of unalterability within it which too many minds obliterate, collapsing everything before the thought of thought as thinkable or at least noetically mutable on our own terms. Transcendental paranoia is the concurrent nightmare and promise of Paul Humphrey's work, of being literally out of our minds. It is the gothic counterpart of thinking non-conceptually but also of thinking never belonging to any instance of purportedly solid being. As Bataille stated, “At the boundary of that which escapes cohesion, he who reflects within cohesion realizes there is no longer any room for him” Thought is immaterial only to the degree that it is inhuman, it is a power that tries, always with failure, to ascertain its own genesis. Philosophy, if it can truly return to the great outdoors, if it can leave behind the dead loop of the human skull, must recognize not only the non-priority of human thought, but that thought never belongs to the brain that thinks it, thought comes from somewhere else. To return to the train image from the beginning “a locomotive rolling on the surface of the earth is the image of continuous metamorphosis” this is the problem of thought, and of thinking thought, of being no longer able to isolate thought, with only a thought-formed structure. [1] One of the central tenets of Francois Laruelle's non-philosophy is that philosophy has traditionally operated on material already presupposed as thinkable instead of trying to think the real in itself. Philosophy, according to Laruelle, remains fixated on transcendental synthesis which shatters immanence into an empirical datum and an a prori factum which are then fused by a third thing such as the ego. For a critical account of Laruelle's non-philosophy see Ray Brassier's Nihil Unbound. (shrink)

Can one quantify over absolutely everything? Absolutists answer positively, while relativists answer negatively. Here, I focus on the absolutism versus relativism debate in the framework of theories of truth, where relativism becomes a form of contextualism about truth predications. Contextualist theories of truth provide elegant and uniform solutions to the semantic paradoxes while preserving classical logic. However, they interpret harmless generalizations (such as “everything is self-identical”) in less than absolutely comprehensive domains, thus systematically misconstruing them. In this article, I (...) show that contextualism is broadly compatible with absolute generality. More specifically, I develop a bipartite contextualist semantics, or “bicontextualism,” on which sentences are split in two groups: the unproblematic sentences, which are compatible with absolute generality, and the problematic ones, which are given a relativist semantics. I then argue that bicontextualism retains the advantages of (orthodox) contextualism and does not give rise to new revenge paradoxes. (shrink)

In this paper, the notion of structural completeness is explored in the context of a generalized class of superintuitionistic logics involving also systems that are not closed under uniform substitution. We just require that each logic must be closed under D-substitutions assigning to atomic formulas only ∨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vee$$\end{document}-free formulas. For these systems we introduce four different notions of structural completeness and study how they are related. We focus on superintuitionistic inquisitive (...) logics that validate a schema called Split and have the disjunction property. In these logics disjunction can be interpreted in the sense of inquisitive semantics as a question forming operator. It is shown that a logic is structurally complete with respect to D-substitutions if and only if it includes the weakest superintuitionistic inquisitive logic. Various consequences of this result are explored. For example, it is shown that every superintuitionistic inquisitive logic can be characterized by a Kripke model built up from D-substitutions. Additionally, we resolve a conjecture concerning superintuitionistic inquisitive logics due to Miglioli et al.. (shrink)

In the early 1880s, Henri Poincaré discovered an equilibrium figure for uniformly-rotating fluid masses—the pear, or piriform figure—and speculated that in certain circumstances the pear splits into two unequal parts, and provides thereby a model for the origin of binary stars. The contemporary emergence of photometric and spectroscopic studies of variable stars fueled the first models of eclipsing binaries, and provided empirical support for a realist view of equilibrium figures—including the pear—in the cosmic realm. The paper reviews astrophysical interpretation of (...) the Poincaré pear and the Poincaré-Darwin fission hypothesis with respect to research on variable stars from 1885 to 1901. (shrink)

Allan Hutchinson’s recent book, The Province of Jurisprudence Democratized, considers what is involved in seeking to establish the province of jurisprudence as a distinctive field of inquiry.Hutchinson’s principal concern with the democratization of law, legal theory, and the province of jurisprudence is examined in detail. The process of democratization and its anti-elitist character is traced through Hutchinson’s opposition to the aloof philosophical analysis of the universal in favour of an engagement with local and particular issues. However, the weight Hutchinson places (...) on his conception of strong democracy, so as to provide a different understanding of the law-power nexus and of the relationship between law and morality operating in strong democracies, is shown to be misplaced. Two related failings are pointed out.First, there is a failure to recognize competing groupings within the people, which contradict the uniform collective body Hutchinson associates with those formerly governed by elites and then constituting those liberated to exercise self-governance. Secondly, this links into Hutchinson’s exclusive preoccupation with the participatory axis of democracy – which he regards as the core feature of strong democracy as well as the basis for the law-power nexus and the law-morality relationship within a strong democracy. This is revealed as an inadequate and impoverished understanding of democracy once the presence of competing groupings within the people is acknowledged. These corrections have important consequences for a role for law that cannot be reduced solely to politics, and for a broader sweep to analytical jurisprudence than Hutchinson allows.Hutchinson’s own efforts to capture the province of jurisprudence are then assessed. These are recharacterized as seeking to establish within a split field of inquiry a theory of strong democratic law, but, in the absence of a convincing account of the nature of democracy and its relationship with law, the project is judged to be unfulfilled. (shrink)

The essay examines solitude not as fate, sacrifice or passion, but as an experience that is actively initiated, that is perceived ambivalently, sometimes painfully, but also sensually, and that functions as context as well as occasion for the practice of cultural techniques – talking (to oneself), reading, writing, drawing or painting. Solitude techniques are analysed as “technologies of the self” (Michel Foucault) and “techniques of the body” (Marcel Mauss), as strategies for self-perception and “internal policy” (Paul Valéry). The history of (...) these self-techniques as solitude techniques is unfolded using examples from Stoic philosophy and early Christian theology. An emphasis is placed on self-doubling or splitting techniques: those who are alone with themselves also see themselves as more or less resilient objects that can be strengthened against the influences of other voices and people. Among the techniques of solitude is, above all, the quest for suitable places that are often – desert, sea, mountain peak, etc. – characterised not only by being devoid of humans, but also by a kind of uniformity. In this way, they resemble writing or drawing surfaces on which meanings can be brought to light through sketches or graphic characters. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 8.4 (2001) 295-298 [Access article in PDF] A Dialectical Conception of Autism Giovanni Stanghellini Some Reasons for the Philosophical Turn in the Psychopathology of Schizophrenia There are many ways to become a schizphrenic. Each individual has her own schizophrenia, coherent with her life history, her problems and alternatives deriving from them (Binswanger 1960). What clinical psychiatry calls "schizophrenia" is not a unitary illness but a (...) common final state—a "syndrome" in the etymological sense, that is, a condition to which different psychopathological pathways may lead. Schizophrenic symptoms, like Schneiderian first-rank symptoms (delusions, hallucinations, experiences of passivity), are nothing but a rather uniform type of reaction. First-rank Schneiderian symptoms may be interpreted as attempts to explain disturbing basic experiences of change in self, body, and world perception (Klosterkoetter 1988) or as the epiphenomena of complex interactions between sensory disorders (aberrations in the perception of self, body, and world), conceptualisation disorders (impairments in the constitution of meanings and intentions), and attitudinal disorders (eccentric structure of values and beliefs) (Stanghellini 2000a). Since the schizophrenic syndrome, as defined by current diagnostic manuals, lacks any authentic core phenomena, and so-called schizophrenic symptoms are not specific (Berner and Kufferle 1982), the clinical diagnosis of schizophrenia finally becomes a diagnosis by exclusion (Maj 1998). This conceptual weakness is obviously unacceptable (not only for old dissenters from operational diagnostic criteria) and is kindling a velvet revolution in nosological studies and a renaissance of philosophically oriented psychopathological research (Parnas and Zahavi 2000). Autism: The Loss of Vital Contact with Reality Eugène Minkowski was a forerunner in the field of philosophical psychopathology: "The psychiatrist and the metaphysician become one in their common research concerning what is human and human experience" (Minkowski 1947). Indeed, his doctoral thesis on autism (Minkowski 1926) was dedicated to his teachers, the psychiatrist E. Bleuler and the philosopher H. Bergson, and his conceptualisation of autism is an ideal example of the link between philosophical perspectives and psychopathological research. The term "autism" was introduced by Bleuler (1911) to describe detachment from outer reality and immersion in inner life. Bleuler's concept of autism relied on Freud's (1905) notion of autoerotism and on associationistic psychology. According to Bleuler, autism was a consequence of the [End Page 295] splitting of psychic functions: a defense mechanism serving to avoid conflicts between desires and reality testing, promoting the shift to inner fantasy life and entailing social withdrawal, emotional indifference, inappropriate behaviors, and idiosyncratic values and beliefs.Minkowski, who was influenced by Bergson and phenomenology, departed from Bleuler's conceptualisation and defined autism as "loss of vital contact with reality" (Minkowski 1926, 1927). For Minkowski, autism is not a symptom, but a global phenomenon investing the whole person. Autism is a way of being whose essential feature is a pragmatic deficit: Autistic activity consists in the reduced capacity to interact with the external world. Autistic thought is characterized by its lack of communicative action. The pragmatic deviance of autistic language is a good example: The autistic person is not interested in communicating her inner world to the others; language is not a means of communication which serves mutual understanding, a cooperative process whose aim is interlacing one's own world with that of others. The autistic person's use of language is much like a soliloquy, the monologue of the solitary thinker more focused on ex-pression—the outward portrayal of immanent contents of consciousness—than on dialogue—the exchange of meanings between speaker and listener. Moreover, each meaning is presented in its manifold profiles or adumbrations and the task of selecting the context-relevant meaning is left to the listener.The pragmatic weakening of the autistic person, according to Minkowski, is not simply a social or occupational dysfunction (APA 1994), that is, a renunciation or refusal to act according to social expectations and standards. It involves the loss of vital contact with reality. The meaning Minkowski attributes to the term "vital" is essential for understanding his philosophical approach to defining the schizophrenic condition. Minkowski assumes that contact with reality is vital when it is established through action (and language... (shrink)

The paper gives an analysis of the theoretical-methodological principles of the philosophy of J. Pato?ka not only as a historian of philosophy, but also as a historian of science, especially of its revolutionary periods. The aim of the paper is to show that following the general context of his works here also Pato?ka consistently deals with the central issue of his philosophy, namely the life-world . In Pato?ka's view it was already the rise of ancient philosophy, and especially of the (...) mathematical natural science that destroyed the original uniform picture of the universe, splitting man's world into the natural world on one hand and the world construed by the mathematical natural science on the other hand. Further, the paper shows Pato?ka's view of phenomenology, which he has seen as a means, with the help of which this dichotomy could be resolved, as well as Pato?ka's criticism of the original Husserlian concept of phenomenology, which failed to avoid its subjectivist and solipsist tendencies. The problem of lifeworld led Pato?ka not only to the principles of non-subjective phenomenolog, but it also became the basis of his philosophy of the history of philosophy. (shrink)

The article titled The pearl of the ‘Pro-Life’ movement? Reflections on the Kermit Gosnell controversy is a thoughtful piece in which the author raises some important questions, including those impinging on the motivations and apparent inconsistencies of the more vocal officials of the more visible segments of a vast and somewhat diverse grass-roots social uprising.1The pro-life movement has indeed showcased the Gosnell trial, but not because many of its members actually believe that gestational age is a morally relevant criterion. In (...) fact, there is probably a nearly uniform desideratum among the most influential groups to abolish all induced abortion from the first moment of conception, even if that goal logically also requires a ban on all potentially abortifacient contraceptives .2 Even the umbrella National Right to Life Committee with its 50 state affiliates, many of which have been criticised for their incremental approach to ending elective abortion,3 holds that ‘a new individual human being begins at fertilisation, when the sperm and ovum meet to form a single cell.’4 There is no practical necessity to split temporal or geographical hairs about when or how far the sperm must enter the ovum for formal union to occur, because the process is virtually inexorable once it starts, and is, thence, confined to a short span of time and space.Nor are the pro-life leaders being ‘disingenuous’ in their focal interest on this particular case. The underlying motivation is not to go delving for a mere ‘pearl’ , but rather to dive into some deep metaphysical waters about the …. (shrink)

The literature on multiculturalism currently splits parties into two camps : those favorable to the uniform treatment of cultural differences and those favorable to their differential treatment. Brian Barry, perhaps of the most influential present supporters of the first camp, has recently developed a severe criticism of the second approach. I intend in this paper to examine the scope and limits of Barry’s own uniform treatment approach. First, I will present the grounds Barry has for supporting it. Second, (...) I will examine one of its most important difficulties, that of excluding the particular treatment of cultural differences on the grounds that they are a matter of choice. (shrink)

Located in Kleinbasel close to the Rhine, the Kaskadenkondensator is a place of mediation and experimental, research-and process-based art production with a focus on performance and performative expression. The gallery, founded in 1994, and located on the third floor of the former Sudhaus Warteck Brewery (hence cascade condenser), seeks to develop interactions between artists, theorists and audiences. Eight, maybe, nine or ten 40 litre bags of potting compost lie strewn about the floor of a high-ceilinged white washed hall. Dumped, split (...) open, the soil mixed with iridescent specks of green, blue and red glitter. On the walls hang large black and white photographic images—negative and positive prints barely clean, hardly sharp, scavenged from the world and presented half processed. On a third wall, hangs a framed golden and charcoal surface. Finally, a huge stain of black dye runs down a wall that descends into a sunken quarter of the Kaskadenkondensator gallery space. The results of a collaboration between Oliver Minder and Walter Derungs reflect on themes addressed in the recent Aesthetics in the 21st Century conference held by the department of English, University of Basel. In particular, the joint show questions how an aesthetic experience may be other than a human-world interaction, hinting at the withdrawal and veiling that objects perform, while demanding that different works engage with each other and play out this game under the non-supervisory eyes of a human audience. Things here are becoming—sometimes it’s a movement towards a more complete ontic whole in a projection of finality, other times it’s a dispersal, an atrophy to rather disarrayed entities. Yet, in the moment and place in which the objects are, we take them as here and now. Let’s get to the material of the stuff that Minder and Derungs have assembled. Oliver Minder employs organic materials—potting earth, cuttlefish ink secretion, rice, and insects; yet his works hardly seem natural in the sense of a harmonic relation between material and the form they are constrained into, the objects they are compelled to occupy. For the substrates on, through, or within which these natural materials are mediated are harshly inorganic substances—Plexiglas, safety glass, acrylic resin, boat varnish, spray paint. Minder, thus, generates a conflict within the materiality of his work between two polar opposites—from the human perspective—in the contiguity of materials engaging with each other in a thrown together formation that nonetheless appears to keep the materials and the objects they make in happy accidental relation to each other. Let me expand a little: on the one hand, the things Minder makes query our belief in substance as belonging in a particular domain, an environment suited to precisely that stuff. We are focused on thinking categorically where things belong, both in terms of natural place and natural relations they might extend to each other. Hence, we are driven to think of environment and order. On the other hand, while extracting things from their conventional place and arranging them within awkward constellations that we as observers feel isn’t quite right, Minder manages to persuade the viewer that the materials are nonetheless “doing alright.” So, simultaneous to our awareness of the appropriateness of the world according to our global notions of accord and uniformity, we are forced to accept the local discrepancies of disassociation, inappropriateness and misplacement. The tension between these two vectors generates a vacillation that intensifies Minder’s work. In the Kaskadenkondensator works, then, it is vital to first consider the material of Minder’s works: potting compost—what is it doing here in the first place?—seems to enjoy being “polluted” by sparkly glitter. Glitter has a long history, used in cosmetics by the Egyptians, and in cave paintings, too, earlier made of beetle shells and mica, nowadays glitter is made of plastic cut to minute sizes down to 50 microns. So what’s the point here? Well shiny bits of dust-like material are actually generated from ultra-thin plastic sheets and are normally cut into shapes that fit contiguously on a two-dimensional surface: squares, triangles, hexagons etc. What then appears to be totally random, chaotic decoration, is actually an array of extremely regular identifiable objects. 1 Of course scale has a role to play here. The minuteness of the dimensions means the regularity is beyond our recognition—all we see are the twinkling surfaces of the multi-coloured grains of plastic. In contrast, potting compost, which appears to be unary in its dull unresponsive lumpen disposition, is in fact an amalgam of a variety of organic and inorganic materials: peat, bark, mushroom compost, and sand and perlite, and should perhaps be more proactively exciting to the viewer because of this complexity. Yes; we can (if we care to) identify different textures, different sizes in the mixture of the medium, but I claim that we tend to treat this organic/inorganic assemblage as just a simple substance. Further and crucially important to our consideration here is that the medium is partially contained, but also partially spilling from the split plastic bags in which it is sold in garden centres. That the compost spills out gives it a movement suggesting life; that the bags are cast here and there in a random fashion by Oliver Minder, lying like discarded carcasses, hacked torsos, dismembered bodies, suggests a horrific murder scene, a Tatort. 2 The glitter flourishes in the medium, lies happy and decorative; that is simply what it does, how it is—always already broken, made-for-scattering, designed to be incomplete; the taken-to-be-natural compost, in contrast, cannot rest content but is forced to speak to us metaphorically in its abject overflowing of violence and rupture. While Oliver Minder’s elements in the installation direct our attention to material, Walter Derungs’ works raise questions around seeing and making in photography. There is a simultaneous flicker between the materials and their use in the production of a sense making representation, on the one hand, and on the other the very notion of what is worthy of picturing, framing, representing on the other. Derungs' images are of non-places. Ranging from archaic decaying monster buildings, buildings that have gone far beyond the ravages of a time that we can safely associate with the genteel preservation of a Bernd and Hill Belcher post-industrial decline, to the background “noise” of an urban world that is falling apart, and to which we most of the time seem to pay little attention, and habitually just pass by. In this respect, their non-ness differs somewhat from the conventional association of the term with Marc Augé 3 , where emphasis is on the specifics (if we do care to examine them for their non-placedness) of the spatial or place containment in which movement between multimodal coordinates occurs in supermodern late capitalist post-urban spaces. In other words, we might be in an Augéian non-place and (not) experience—be impervious to—that environment, or we might in Derungs’ manner look out from such a position at the “scenery” around us. I claim scenery, as this is what Derungs seems to do with his partial photography—construct a very purposefully articulated, symmetric, flat world of image. Mostly depopulated, his images construct a space in which the direction of time is uncertain: are these partial structures falling apart, or perhaps terminated in a never-to-be-completed state, or are they a few steps from final completion? Temporal and spatial dimensions figure large in Derungs’ image-making: his world, and perhaps this is in fact the only way for it to be registered photographically, is already image before it is photographed. A key combination of images in this show is a matrix of six black and white negative prints measuring 300 x 215 cm that form the image of a semi-derelict (or is it yet incomplete) church, and adjacent on a perpendicular wall, a single black and white positive print 150 x 250 cm of two bricked-up windows of a late-Victorian industrial building. What are we led to believe that we see here? In the negative print, the conditions of perception 4 are sufficiently reproduced for us to recognise the structure of the building, to distinguish ground and form, to relate some partial elements of narrative, and to recognize symbols such as the alter cross and figure of Christ, a looming crane, a traffic cone, and banks of tiered seating. We piece the image together both from the individual forms which we recognize despite the tonal reversal, and we piece the six prints together as a whole, the matrix of lines between them emphasizing our purview onto the world. While we recognise the forms at work in the image and might possibly relate the negative reversals to other figurations such as Vera Lutter’s camera obscura exposures, we cannot but avoid seeing the partialness of the image in the sponge marks of the developer that was spread by hand across the prints. 5 Derungs’ thus intervenes with our usual conception of photography as the mimetic realist vehicle sine qua non , by exposing the viewer to tonal reversal and incomplete or over developed areas of the print. We thus confront both the idiom of such image making and its raw (chemical) materiality at once in the simultaneity of the recognition of what the image pictures and the recognition that it is in the act of picturing. The church image, taken from the series “BW Negativs 2011,” thus orients us towards how we see things in the world via photographs. The single image of the bricked-up wall presents us with a completely different visuality that relates to a faciality 6 which we cannot easily escape from. We look, or rather try to look with no success, through the face of the windows, through the classic Albertian screen 7 which has already been given to us in the church matrix beside. Yet although we should be able to make more of these concealed windows because they are a positive print, because they are complete, because they approach us on a more realistic scale, reproduced at life size, we cannot. The objects pictured here withdraw from us; furthermore, they merely mock our blindness at not seeing how we look. Blocked up with quite a hint of paned glass behind, one window is blanked out with a white blind, the other simply blankly dark. The apertures look like eyes with teeth in them, or a Dogon mask, or even Man Ray’s Noire et Blanche (1926) if we want to get really perverse. The height of elegant modernist chauvinist beauty thrown against the vacuity of post-industrial decline. Derungs thus catapults us consciously into a world enfolded with and through images, but in such a way that the images themselves become objects that stand resistant to us, impervious to our gaze, indifferent. We—and indeed they—do not attempt to reach out to a real that is beyond, rather the images play in a world that is just theirs, and we can only enter that world if we too submit to their regime: tonal reversal, segmented, partial, inadequate, still, wrenched out of time. In contemplation, in the flood of the image “falling” off the wall, we too become image-object. Perhaps enough has now been said about the works, yet enough can never really be said, we know the image will always exceed the word—let’s accelerate the critique: Derungs’ work continues in a second space partially partitioned from this first room. Opposing three more “BW Negativs” which figure yet more quotidian aspects of the world is Minder’s gold spray paint and cuttlefish secretion mix: things that just shouldn’t work together do in the dialogue between stuff that Derungs and Minder have constructed. Minder makes things; Derungs makes images; together they make objects which inhabit their own world which we can approach and sensually engage with and come to grips with only on those objects’ own terms. This is best summarised by a final work made by Oliver Minder which on a third wall faces these two semi-partitioned spaces. A deep black stain about 100 X 200 cm with streak marks running down a further 2 metres hovers positioned to observe the whole work, and also to be part of this installation, too. This liminal flat suzerain lies in/out of the whole work. The stain of cuttlefish secretion resonates with Derungs’ sponge strokes on the church image; it mirrors the iris of an all-seeing eye; it combines material in situ with the situation itself. Where Minder’s other works have material and medium or substrate upon which the material is exercised, this single black hole is image which sucks everything up into itself. It draws the viewer, who must otherwise look away attentively at the floor work, and imagine horror, or smile at the ironic play of glitter. Look away at the image constructions that suggest how it is we too look to our world. See the play of thing and image in a third area. Or, finally return to the base of the pyramid that triangulates, to realise the stuff-image that unlocks it all for us. Black on white, organic on inorganic, material to substrate, that which in the falling out of one on the other, in its running down the wall simply gives form to both content and expression in one direction, and content and expression to form in another. NOTES In fact, glitter is used as associative forensic evidence: the 20,000 or so varieties are all uniquely identifiable. Joel Sternfeld, Tatorte: Bilder gegen das Vergessen (München: Schirmer/Mosel, 1996). Marc Augé, Non­places: Introduction to an Anthropology of Supermodernity trans. John Howe (London: Verso, 2006). An echo of the uneven paint strokes of light­sensitive chemicals in the paper preparations made by Henry Talbot some 170 years ago in the first sun drawings that also often pictured architectural forms. It was Talbot’s surprising discovery that where a weaker chemical solution was more thinly spread, greater light sensitivity was actualized, yet this virtual image had then to be chemically developed in a second step. Thus, Derungs unevenly finished spongings suggestively trace back to this originary technology (although his sweeps are the stains of uneven development and not those of the initial preparation of light–sensitive material). Umberto Eco, “Critique of the Image” in “Articulations of Cinematic Code” Cinematics 1, 1970. Gilles Deleuze and Felix Guattari, A Thousand Plateaus: Capitalism and Schizophrenia trans. Brian Massumi (Minneapolis: University of Minnesota Press, 2007). Geoffrey Batchen, Burning With Desire: the Conception of Photography (Cambridge, Mass: MIT Press, 1999). (shrink)

Since the turn of the century, however, a double upheaval has occurred, the formulation of the quantum theory and the theory of relativity, providing the ground for the development of modern physics. These theories issued from the problems of light that, in their strict forms, could not be assimilated by Newtonian physics. Before the turn of the century the wave theory had been victorious over the emission theory, and an hypothetical ether was assumed which was intended ultimately to represent absolute (...) space and to play a role similar to that of Anaximander's apeiron or Aristotle's prima materia. This last role seemed required since many philosophers of nature believed that they should see in matter and its elementary components the singularities, the exceptional peculiarities of the ether. However, since the ether held itself strictly incognito, Albert Einstein renounced it and declared that all systems in uniform, rectilinear motion are equivalent. The first portentous ontological consequence of this renunciation was that statements concerning spatial and temporal separation become relative. True relativity means, however, that objectivity and subjectivity enter equally into all statements, for to everything relative, as Max Planck once said, an absolute belongs. In this case the absolute was the combination of space and time into a four-dimensional spatio-temporal unity, which observers in different systems split into different space and time determinations. Our statements concerning space and time are thus neither merely subjective nor merely objective; rather a subject-object relation enters into them and makes them all relative. There is, to be sure, within the four-dimensional spatio-temporal unity a region of a spatial type within which the space-axes of the different observers lie, and the same is true for the temporal region. But even if there is no one universal time or simultaneity, temporality nevertheless plays its own role in contradistinction to spatiality, though both are expressible mathematically. We can say in the sense of critical realism that our spatial and temporal measurements are commensurate with the ordering relations of things and events. (shrink)

We investigate the pair-splitting number $\germ{s}_{pair}$ which is a variation of splitting number, pair-reaping number $\germ{r}_{pair}$ which is a variation of reaping number and cardinal invariants of ideals on ω. We also study cardinal invariants of F σ ideals and their upper bounds and lower bounds. As an application, we answer a question of S. Solecki by showing that the ideal of finitely chromatic graphs is not locally Katětov-minimal among ideals not satisfying Fatou's lemma.

In this paper we extend to various classes of subreducts of hoops some results about splitting algebras. In particular we prove that every finite chain in the purely implicational fragment of basic hoops is splitting and that every finite chain in the \ fragment of hoops is splitting. We also produce explicitly the splitting equations in most cases.

Split brains that result in two simultaneous streams of consciousness cut off from each other are wrongly held to be grounds for doubting the existence of the divinely created soul. The mistake is based on two related errors: first, a failure to appreciate the soul's dependence upon neurological functioning; second, a fallacious belief that if the soul is simple, i.e. without parts, then there must be a unity to its thought, all of its thoughts being potentially accessible to reflection or (...) even unreflective causal interactions. But a soul theorist can allow neurological events to keep some conscious thoughts unavailable to others. (shrink)

This is a contribution to the study of the Muchnik and Medvedev lattices of non-empty Π01 subsets of 2ω. In both these lattices, any non-minimum element can be split, i. e. it is the non-trivial join of two other elements. In fact, in the Medvedev case, ifP > MQ, then P can be split above Q. Both of these facts are then generalised to the embedding of arbitrary finite distributive lattices. A consequence of this is that both lattices have decidible (...) ∃-theories. (shrink)

A splitting of an r.e. set A is a pair A1, A2 of disjoint r.e. sets such that A1 A2 = A. Theorems about splittings have played an important role in recursion theory. One of the main reasons for this is that a splitting of A is a decomposition of A in both the lattice, , of recursively enumerable sets and in the uppersemilattice, R, of recursively enumerable degrees . Thus splitting theor ems have been used to (...) obtain results about the structure of , the structure of R, and the relationship between the two structures. Furthermore it is fair to say that questions about splittings have often generated important new technical developments in recursion theory. In this article we survey most of the results and techniques associated with splitting properties of r.e. sets in ordinary recursion theory. (shrink)

In this paper, I contend that there are at least two essential traits that commonly define being an I: self-identity and self-consciousness. I argue that they bear quite an odd relation to each other in the sense that self-consciousness seems to jeopardize self-identity. My main concern is to elucidate this issue within the range of the transcendental philosophies of Immanuel Kant and Edmund Husserl. In the first section, I shall briefly consider Kant’s own rendition of the problem of the Egosplitting. (...) My reading of the Kantian texts reveals that Kant himself was aware of this phenomenon but eventually deems it an unexplainable fact. The second part of the paper tackles the same problematic from the standpoint of Husserlian phenomenology. What Husserl’s extensive analyses on this topic bring to light is that the phenomenon of the Ego-splitting constitutes the bedrock not only of his thought but also of every philosophy that works within the framework of transcendental thinking. (shrink)

Is it time to take a break from feminism? In this pathbreaking book, Janet Halley reassesses the place of feminism in the law and politics of sexuality. She argues that sexuality involves deeply contested and clashing realities and interests, and that feminism helps us understand only some of them. To see crucial dimensions of sexuality that feminism does not reveal--the interests of gays and lesbians to be sure, but also those of men, and of constituencies and values beyond the realm (...) of sex and gender--we might need to take a break from feminism. Halley also invites feminism to abandon its uncritical relationship to its own power. Feminists are, in many areas of social and political life, partners in governance. To govern responsibly, even on behalf of women, Halley urges, feminists should try taking a break from their own presuppositions. Halley offers a genealogy of various feminisms and of gay, queer, and trans theories as they split from each other in the United States during the 1980s and 1990s. All these incommensurate theories, she argues, enrich thinking on the left not despite their break from each other but because of it. She concludes by examining legal cases to show how taking a break from feminism can change your very perceptions of what's at stake in a decision and liberate you to decide it anew. (shrink)

Reverse mathematics is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson and others. The aim of RM is to find the minimal axioms needed to prove a theorem of ordinary, that is, non-set-theoretic, mathematics. As suggested by the title, this paper deals with two RM-phenomena, namely, splittings and disjunctions. As to splittings, there are some examples in RM of theorems A, B, C such that A↔, that is, A can be split into two (...) independent parts B and C. As to disjunctions, there are examples in RM of theorems D, E, F such that D↔, that is, D can be written as the disjunction of two independent parts E and F. By contrast, we show in this paper that there is a plethora of splittings and disjunctions in Kohlenbach’s higher-order RM. (shrink)

In this paper, we first define the vector product in Minkowski space $\mathbb{R}_{4}^{7}$, which is identified with the space of spatial split-octonions. Next, we derive the $G_{2}-$ frame formulae for a seven dimensional Minkowski curve by using the spatial split-octonions and the vector product. We show that Frenet–Serret formulas are satisfied for a spatial split octonionic curve. We obtain the congruence of two spatial split octonionic curves and give relationship between the $G_{2}-$ frame and Frenet–Serret frame. Furthermore, we present the (...) Frenet–Serret frame with split octonions in $\mathbb{R}_{4}^{8}$. Finally, we give illustrative examples with Matlab codes. (shrink)

A common presupposition in the concepts literature is that concepts constitute a sin- gular natural kind. If, on the contrary, concepts split into more than one kind, this literature needs to be recast in terms of other kinds of mental representation. We offer two new arguments that concepts, in fact, divide into different kinds: (a) concepts split because different kinds of mental representation, processed independently, must be posited to explain different sets of relevant phenomena; (b) concepts split because different kinds (...) of mental representation, processed independently, must be posited to explain responses to different kinds of category. Whether these arguments are sound remains an open empirical question, to be resolved by future empirical and theoretical work. (shrink)

A splitting A1A2 = A of an r.e. set A is called a Friedberg splitting if for any r.e. set W with W — A not r.e., W — Ai≠0 for I = 1,2. In an earlier paper, the authors investigated Friedberg splittings of maximal sets and showed that they formed an orbit with very interesting degree-theoretical properties. In the present paper we continue our investigations, this time analyzing Friedberg splittings and in particular their orbits and degrees for (...) various classes of r.e. sets. (shrink)

After the first callosotomy surgeries were performed, the general consensus among the medical community was that severing the corpus callosum had relatively little, if any, effect on an individual's behavior. Nearly twenty years later, researchers discovered that, under experimental conditions, the two hemispheres could simultaneously maintain very different interpretations of the same stimulus. These findings immediately called into question the unity of subjective experience, a fundamental characteristic of human consciousness. How could the split‐brain patient not experience any disruption in his (...) experience as a unified self when the two hemispheres are physically and functionally disconnected? In this chapter, we review the research that has led to a conceptualization of the split brain as two minds within one body and the implications of this research for the scientific study of consciousness. We argue that consciousness is a neural function that emerges from the integration of information across available functional modules. (shrink)

The traditional scope theory of intensionality (STI) (see Russell 1905; Montague 1973; Ladusaw 1977; Ogihara 1992, 1996; Stowell 1993) is simple, elegant, and, for the most part, empirically adequate. However, a few quite troubling counterexamples to this theory have lead researchers to propose alternatives, such as positing null situation pronouns (Percus 2000) or actuality operators (Kamp 1971; Cresswell 1990) in the syntax of natural language. These innovative theories do correct the undergeneration of the original scope theory, but at a cost: (...) the situation pronoun and operator theories overgenerate, as argued extensively by Percus (2000) and Keshet (2008). This paper presents new data that supports the STI over other analyses, such as structures where DPs lose their de re readings in positions where syntactic movement is blocked. These data point the way to a new theory of intensionality. This new theory, called split intensionality, is a modification of the STI which aims to solve the problems raised for the original scope theory without overgenerating. The proposal calls for an additional intensional abstraction operator that creates an expression denoting an intension from an expression denoting an extension. When a DP moves to a position above this operator, it is interpreted de re; otherwise it is de dicto. The crucial part of the new proposal is that a DP may move above this operator and yet remain, for instance, below an intentional verb or inside an if-clause. Therefore, a DP within an island for syntactic movement may be de re and yet not move out of the island when the intensional abstraction operator is also within the island. (shrink)

In this paper I argue that split-brain syndrome is best understood within an extended mind framework and, therefore, that its very existence provides support for an externalist account of conscious perception. I begin by outlining the experimental aberration model of split-brain syndrome and explain both: why this model provides the best account of split-brain syndrome; and, why it is commonly rejected. Then, I summarise Susan Hurley’s argument that split-brain subjects could unify their conscious perceptual field by using external factors to (...) stand-in for the missing corpus callosum. I next provide an argument that split-brain subjects do unify their perceptual fields via external factors. Finally, I explain why my account provides one with an experimental aberration model which avoids the problems typically levelled at such views, and highlight some empirical predictions made by the account. The nature of split-brain syndrome has long been considered mysterious by proponents of internalist accounts of consciousness. However, in this paper I argue that externalist theories can provide a straightforward explanation of the condition. I therefore conclude that the ability of externalist accounts to explain split-brain syndrome gives us strong reason to prefer them over internalist rivals. (shrink)

Elizabeth Schechter explores the implications of the experience of people who have had the pathway between the two hemispheres of their brain severed, and argues that there are in fact two minds, subjects of experience, and intentional agents inside each split-brain human being: right and left. But each split-brain subject is still one of us.

We investigate splitting number and reaping number for the structure (ω) ω of infinite partitions of ω. We prove that ${\mathfrak{r}_{d}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N}),\mathfrak{d}}$ and ${\mathfrak{s}_{d}\geq\mathfrak{b}}$ . We also show the consistency results ${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}$ and ${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})}$ . To prove the consistency ${\mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}$ and ${\mathfrak{s}_{d} < \mathsf{cof}(\mathcal{M})}$ we introduce new cardinal invariants ${\mathfrak{r}_{pair}}$ and ${\mathfrak{s}_{pair}}$ . We also study the relation between ${\mathfrak{r}_{pair}, \mathfrak{s}_{pair}}$ and other cardinal invariants. We (...) show that ${\mathsf{cov}(\mathcal{M}),\mathsf{cov}(\mathcal{N})\leq\mathfrak{r}_{pair}\leq\mathfrak{s}_{d},\ma thfrak{r}}$ and ${\mathfrak{s}\leq\mathfrak{s}_{pair}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N})}$. (shrink)

Many have claimed that split-brain patients are actually two persons. I maintain that both the traditional separation argument and the more recent sophistication argument for the two persons interpretation are inadequate on conceptual grounds. An autonomy argument is inadequate on empirical grounds. Overall, theoretical and practical consequences weigh heavily in favor of adopting a one person interpretation.

Neither the George Washington University embryo splitting experiment nor the technique of embryo splitting itself has ethical flaws. The experiment harmed or wronged no one, and the investigators followed intramural review procedures for the experiment, although some might fault them for failing to seek extramural consultation or for not waiting until national guidelines for research on preembryos were developed. Ethical objections to such cloning on the basis of possible loss of individuality, possible lessening of individual worth, and concern (...) about potential harm to the resulting children are discussed and challenged, as are objections to the creation of embryos for the purpose of genetic diagnosis. Many of the ethical questions raised by the George Washington experiment are similar to those posed by existing reproductive technologies that allow the simultaneous production of several embryos. A multidisciplinary group should consider whether regulation of cloning is needed, and laws should be enacted to prohibit a commercial market for all frozen embryos. (shrink)

We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, the splitting number, and the existence of certain kinds of splitting families.

In this paper, I contend that there are at least two essential traits that commonly define being an I: self-identity and self-consciousness. I argue that they bear quite an odd relation to each other in the sense that self-consciousness seems to jeopardize self-identity. My main concern is to elucidate this issue within the range of the transcendental philosophies of Immanuel Kant and Edmund Husserl. In the first section, I shall briefly consider Kant’s own rendition of the problem of the Ego- (...) class='Hi'>splitting. My reading of the Kantian texts reveals that Kant himself was aware of this phenomenon but eventually deems it an unexplainable fact. The second part of the paper tackles the same problematic from the standpoint of Husserlian phenomenology. What Husserl’s extensive analyses on this topic bring to light is that the phenomenon of the Ego-splitting constitutes the bedrock not only of his thought but also of every philosophy that works within the framework of transcendental thinking. (shrink)

The goal of this paper is to propose a unified approach to the split scope readings of negative indefinites, comparative quantifiers, and numerals. There are two main observations that justify this approach. First, split scope shows the same kinds of restrictions across these different quantifiers. Second, split scope always involves low existential force. In our approach, following Sauerland, natural language determiner quantifiers are quantifiers over choice functions, of type <<,t>,t>. In split readings, the quantifier over choice functions scopes above other (...) operators (such as intensional verbs like must or can). Determiner quantifiers leave a choice-function trace when they move and this trace combines with the noun restriction, which is interpreted low. That split scope always involves low existential force is derived, without stipulation, from Kratzer’s idea that low existential force can be achieved via binding (into the noun restriction). (shrink)

Keywords: Recursively Enumerable; Computably Enumerable; Friedberg Splitting; Congruence Relation; Ideal; Quotient; Lattice.

Splitting livers allows two people (usually an adult and a child) to receive a liver transplant from one donated adult liver, but the risks to the adult recipient are greater than if they had received the equivalent whole liver. It has been suggested, therefore, that splitting livers harms adult recipients. Without liver splitting, however, there would be few livers available for children, and paediatric waiting time and waiting list mortality would significantly increase. In this paper, we argue (...) that although splitting livers makes adults worse off, this should be considered sub-optimal benefit rather than harm. We explore justifications for sub-optimally benefitting adults in this way and consider alternatives to the current approach. We argue that splitting livers masks the more fundamental problem of low paediatric donation rates and that increasing the number of paediatric donations would improve the situation for both adult and paediatric liver patients. (shrink)

By splitting idempotent morphisms in the total and base categories of fibrations we provide an explicit elementary description of the Cauchy completion of objects in the categories Fib) of fibrations with a fixed base category \ and Fib of fibrations with any base category. Two universal constructions are at issue, corresponding to two fibered reflections involving the fibration of fibrations \.