We extend the results of Laver on using inverse limits to reflect large cardinals of the form, there exists an elementary embedding Lα → Lα. Using these inverse limit reflection embeddings directly and by broadening the collection of U-representable sets, we prove structural results of L under the assumption that there exists an elementary embedding j : L → L. As a consequence we show the impossibility of a generalized inverse limit X-reflection result for X ⊆ (...) Vλ+1, thus focusing the study of L generalizations on L. (shrink)

We build a collection of topological Ramsey spaces of trees giving rise to universal inverse limit structures, extending Zheng’s work for the profinite graph to the setting of Fraïssé classes of finite ordered binary relational structures with the Ramsey property. This work is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. Based on these topological Ramsey spaces and the work of Huber-Geschke-Kojman on inverse limits of finite ordered graphs, we prove that (...) for each such Fraïssé class, its universal inverse limit structure has finite big Ramsey degrees under finite Baire-measurable colorings. For such Fraïssé classes satisfying free amalgamation as well as finite ordered tournaments and finite partial orders with a linear extension, we characterize the exact big Ramsey degrees. (shrink)

We show that there is a limit lemma for enumeration reducibility to 0 e ', analogous to the Shoenfield Limit Lemma in the Turing degrees, which relativises for total enumeration degrees. Using this and `good approximations' we prove a jump inversion result: for any set W with a good approximation and any set X< e W such that W≤ e X' there is a set A such that X≤ e A< e W and A'=W'. (All jumps are enumeration degree jumps.) (...) The degrees of sets with good approximations include the Σ0 2 degrees and the n-CEA degrees. (shrink)

We show that Sacks' and Shoenfield's analogs of jump inversion fail for both tt- and wtt-reducibilities in a strong way. In particular we show that there is a ${\mathrm{\Delta }}_{2}^{0}$ set B > tt ∅′ such that there is no c.e. set A with A′ ≡ wtt B. We also show that there is a ${\mathrm{\Sigma }}_{2}^{0}$ set C > tt ∅′ such that there is no ${\mathrm{\Delta }}_{2}^{0}$ set D with D′ ≡ wtt C.

Apart from positive priming effects, masked prime stimuli can impair responses to a subsequent target stimulus which shares response-critical features in contrast to a target assigned to the opposite response. This counterintuitive phenomenon is called inverse priming . Here we examine the generality of this phenomenon beyond priming of motor responses. We used a non-motor cue-priming paradigm to study the underlying mechanism of inverse priming for relevant features masks which include task-relevant stimulus features and for irrelevant masks which (...) omit task-relevant features. We found inverse cue-priming effects with both types of masks. With task-irrelevant masks inverse cue-priming was emphasized in those participants being unable to perceive the prime. The existence of inverse non-motor priming under conditions where simple perceptual interactions between the stimuli are ruled out as the source of inverse priming is at odds with the view that inverse priming reflects motor inhibition. Alternatives are discussed. (shrink)

Suppose $\lambda$ is a singular cardinal of uncountable cofinality $\kappa$. For a model $\mathscr{M}$ of cardinality $\lambda$, let No ($\mathscr{M}$) denote the number of isomorphism types of models $\mathscr{N}$ of cardinality $\lambda$ which are L$_{\infty\lambda}$- equivalent to $\mathscr{M}$. In [7] Shelah considered inverse $\kappa$- systems $\mathscr{A}$ of abelian groups and their certain kind of quotient limits Gr($\mathscr{A}$)/ Fact($\mathscr{A}$). In particular Shelah proved in [7, Fact 3.10] that for every cardinal $\mu$ there exists an inverse $\kappa$-system $\mathscr{A}$ such (...) that $\mathscr{A}$ consists of abelian groups having cardinality at most $\mu^\kappa$ and card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)) = $\mu$. Later in [8, Theorem 3.3] Shelah showed a strict connection between inverse $\kappa$-systems and possible values of No (under the assumption that $\theta^\kappa < \lambda$ for every $\theta < \lambda$): if $\mathscr{A}$ is an inverse $\kappa$- system of abelian groups having cardinality < $\lambda$, then there is a model $\mathscr{M}$ such that card $(\mathscr{M}) = \lambda$ and No($\mathscr{M}$) = card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)). The following was an immediate consequence (when $\theta^\kappa < \lambda$ for every $\theta < \lambda$): for every nonzero $\mu < \lambda$ or $\mu = \lambda^\kappa$ there is a model $\mathscr{M}_\mu$ of cardinality $\lambda$ with No$(\mathscr{M}_\mu) = \mu$. In this paper we show: for every nonzero $\mu \leq \lambda^\kappa$ there is an inverse $\kappa$-system $\mathscr{A}$ of abelian groups having cardinality < $\lambda$ such that card(Gr($\mathscr{A}$)/Fact($\mathscr{A}$)) = $\mu$ (under the assumptions $2^\kappa < \lambda$ and $\theta^{<\kappa} < \lambda$ for all $\theta < \lambda$ when $\mu > \lambda$), with the obvious new consequence concerning the possible value of No. Specifically, the case No($\mathscr{M}$) = $\lambda$ is possible when $\theta^\kappa < \lambda$ for every $\theta < \lambda$. (shrink)

La limite peut être entendue dans deux sens dont les implications sont différentes, voire opposées. Elle peut être considérée comme un horizon indépassable, un mur infranchissable qui borne très distinctement des domaines d'étude et des champs d'action. Dans une seconde acception, la limite est, au contraire, la ligne qui peut être franchie et par extension, la limite devient amovible : elle peut être déplacée, même légèrement, en fonction des événements. Le thème de ce colloque nous invite non pas à étudier (...) "la limite du droit", comme le suggèrerait le premier sens du mot limite. Cette idée n'aurait pas de sens, sauf à considérer un système pur de droit, isolé de tous les autres paramètres qui peuvent graviter autour de lui. Nous sommes, à l'inverse, amenés à nous rendre "Aux limites du droit", dans cette zone d'interférence, de superposition, d'interpénétration non seulement des disciplines théoriques mais aussi des circonstances ponctuelles dont l'enchevêtrement donne à la pratique de la science juridique toute son ampleur. Les limites du droit font donc référence à un lieu de communication et de négociation où la recherche d'un équilibre spontané est autant permanente qu'impossible à pérenniser. En effet, les divers facteurs qui entrent dans les limites du droit sont si riches et pourtant si mouvants qu'il paraît judicieux de tenter, tant que faire se peut, de cerner leur essence. D'autant que les limites sont souvent révélatrices de la nature profonde du droit. (shrink)

Kitarō Nishida introduces the concept of “inverse correlation‘ in his final work, The Logic of Place and the Religious Worldview, which he uses to illuminate the relation between finite and infinite, human and divine/buddha, such that the greater the realization of human limitation and finitude, the greater that of the limitless, infinite divine or buddhahood. This essay explores the applicability of the logic and rhetoric of inverse correlation in the cases of the early Daoist Zhuangzi, medieval Japanese Buddhist (...) Shinran, and modern Protestant Christian Kierkegaard, as well as broader ramifications for contemporary philosophy of religion. (shrink)

Introduction: Purpose of this essay is to draw attention to some points which are relevant to the underlying philosophy of modern statistics, but which the writer feels have been largely overlooked both by the defenders and the opponents of the classic conceptions of Laplace. There is no quarrel with methodologies as such which have found their introduction under the heads of “maximum likelihood”, “fiducial limits”, etc. But the writer cannot accept arguments ) which would make of such procedures an (...) absolute sine qua non for all decisions based on evidence, and which would relegate human judgment and all considerations of the intended use of a decision to the rubbish heap of outmoded conceptions. To assume that two rational minds, having different backgrounds and different objectives, must necessarily find themselves in agreement in their appraisal of a given objective situation, is simply absurd; yet this is the basis which underlies, so far as I can make out, all the “criticisms” of Laplace and Bayes which constitute the excuses put forward for attempting to displace those procedures in Statistics which involve “inverse probability”. Also the so-called “paradoxes” which have been invented by many writers in order to assail Laplace, contradict only this one assumption; without it they are not paradoxes. (shrink)

Suppose λ is a singular cardinal of uncountable cofinality κ. For a model M of cardinality λ, let No (M) denote the number of isomorphism types of models N of cardinality λ which are L ∞λ - equivalent to M. In [7] Shelah considered inverse κ- systems A of abelian groups and their certain kind of quotient limits Gr(A)/ Fact(A). In particular Shelah proved in [7, Fact 3.10] that for every cardinal μ there exists an inverse κ-system (...) A such that A consists of abelian groups having cardinality at most μ κ and card(Gr(A)/Fact(A)) = μ. Later in [8, Theorem 3.3] Shelah showed a strict connection between inverse κ-systems and possible values of No (under the assumption that $\theta^\kappa for every $\theta ): if A is an inverse κ- system of abelian groups having cardinality $\theta^\kappa for every $\theta ): for every nonzero $\mu or μ = λ κ there is a model M μ of cardinality λ with No(M μ ) = μ. In this paper we show: for every nonzero μ ≤ λ κ there is an inverse κ-system A of abelian groups having cardinality $2^\kappa and $\theta^{ for all $\theta when $\mu > \lambda$ ), with the obvious new consequence concerning the possible value of No. Specifically, the case No(M) = λ is possible when $\theta^\kappa for every $\theta. (shrink)

It is proved that for every countable structure and a computable successor ordinal α there is a countable structure which is ‐least among all countable structures such that is Σ‐definable in the αth jump. We also show that this result does not hold for the limit ordinal. Moreover, we prove that there is no countable structure with the degree spectrum for.

Signal transduction pathways are largely conserved throughout the animal kingdom. The repertoire of pathways is limited and each pathway is used in different intercellular signaling events during the development of a given animal. For example, Wnt signaling is recruited, sometimes redundantly with other molecular pathways, in four cell specification events during Caenorhabditis elegans vulva development, including the activation of vulval differentiation. Strikingly,a recent study finds that Wnts act to repress vulval differentiation in the nematode Pristionchus pacificus,1 demonstrating evolutionary flexibility in (...) the use of intercellular signaling pathways. BioEssays 27:765–769, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

Issues about the nature and ontology of works of art play a central part in contemporary aesthetics. But such issues are complicated by the fact that there seem to be two fundamentally different kinds of artworks. First, a visual artwork such as a picture or drawing seems to be closely identified with a particular physical object, in that even an exact copy of it does not count as being genuinely the same work of art. Nelson Goodman describes such works as (...) being “autographic.” Second, other artworks such as musical or literary works seem to be copyable without any such limitations: for example, two identical copies of a novel could each equally be a genuine instance of that novel; such works are “allographic,” in Goodman’s terminology. Nevertheless, it seems clear enough that a deeper understanding of both kinds of artworks requires the pursuit of analogies or similarities between them, in spite of their differences. Any such analogies that may be found will provide critical tests for more general theories about the nature of artworks. I show how to resolve such analogies for the orientational concept of inversion. (shrink)

In Minkowski flat space-time, it is perceived that time inversion is unitary rather than antiunitary, with energy being a time vector changing sign under time inversion. The Dirac equation, in the case of electromagnetic interaction, is not invariant under unitary time inversion, giving rise to a “Klein paradox.” To render unitary time inversion invariance, a nonlinear wave equation is constructed, in which the “Klein paradox” disappears. In the case of Coulomb interaction, the revised nonlinear equation can be linearized to give (...) energy solutions for Hydrogen-like ions without singularity when nuclear number Z>137, showing a reversed energy order pending for experimental tests such as Zeeman effects. In non-relativistic limit, this nonlinear equation reduces to nonlinear Schrödinger equation with soliton-like solutions. Moreover, particle conjugation and electron-proton scattering with a nonsingular current-potential interaction are discussed. Finally the explicit form of gauge function is found, the uniqueness of Lorentz gauge is proven and the Lagrangian density of quantum electrodynamics (QED) is revised as well. The implementation of unitary time inversion leads to the ultimate derivation of nonlinear QED. (shrink)

Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle’s state as it approaches the origin when the attractive coupling parameter is greater than the critical value of 1/4. Due to this unphysical divergence in oscillations, we are proposing that the interaction gets screened at short distances making the coupling parameter acquire an effective (renormalized) value that falls within the weak range 0–1/4. This prevents the (...) oscillations form growing without limit giving a lower bound to the energy spectrum and forcing the Hamiltonian of the system to be self-adjoint. Technically, this translates into a regularization scheme whereby the inverse square potential is replaced near the origin by another that has the same singularity but with a weak coupling strength. Here, we take the Eckart as the regularizing potential and obtain the corresponding solutions (discrete bound states and continuum scattering states). (shrink)

Cet article montre que l’anthropologie religieuse est le point aveugle du marxisme. Il renvoie dos-à-dos l’athéisme communiste et les théologies de la révolution en les saisissant comme deux faces d’une même hégémonie biblique s’exerçant sur le langage des luttes d’émancipation. Il analyse ensuite la façon dont la construction croisée des concepts de religion et d’aliénation limite la critique du capitalisme et de l’État. La critique terrestre devrait donc être refondée si l’anthropologie qui la soutenait s’écroule.

Understanding academic gender gaps is difficult because gender-imbalanced fields differ across many features, limiting researchers’ ability to systematically study candidate causes. In the present preregistered research, we isolate two potential explanations—brilliance beliefs and fixed versus growth intelligence mindsets—by comparing two fields that have inverse gender gaps and historic and topical overlap: philosophy and psychology. Many more men than women study philosophy and vice versa in psychology, with disparities emerging during undergraduate studies. No prior work has examined the contributions of (...) both self-perceptions of brilliance and fixed versus growth mindsets on choice of major among undergraduate students. We assessed field-specific brilliance beliefs, brilliance beliefs about self, and mindsets, cross-sectionally in 467 undergraduates enrolled in philosophy and psychology classes at universities in the United States and Canada via both in-person and online questionnaires. We found support for the brilliance beliefs about the self, but not mindset, explanation. Brilliance beliefs about oneself predicted women’s but not men’s choice of major. Women who believed they were less brilliant were more likely to study psychology (perceived to require low brilliance) over philosophy (perceived to require high brilliance). Findings further indicated that fixed versus growth mindsets did not differ by gender and were not associated with major. Together, these results suggest that internalized essentialist beliefs about the gendered nature of brilliance are uniquely important to understanding why men and women pursue training in different academic fields. (shrink)

Given a program of a linear bounded and bijective operator T, does there exist a program for the inverse operator T−1? And if this is the case, does there exist a general algorithm to transfer a program of T into a program of T−1? This is the inversion problem for computable linear operators on Banach spaces in its non-uniform and uniform formulation, respectively. We study this problem from the point of view of computable analysis which is the Turing machine (...) based theory of computability on Euclidean space and other topological spaces. Using a computable version of Banach’s Inverse Mapping Theorem we can answer the first question positively. Hence, the non-uniform version of the inversion problem is solvable, while a topological argument shows that the uniform version is not. Thus, we are in the striking situation that any computable linear operator has a computable inverse while there exists no general algorithmic procedure to transfer a program of the operator into a program of its inverse. As a consequence, the computable version of Banach’s Inverse Mapping Theorem is a powerful tool which can be used to produce highly non-constructive existence proofs of algorithms. We apply this method to prove that a certain initial value problem admits a computable solution. As a preparation of Banach’s Inverse Mapping Theorem we also study the Open Mapping Theorem and we show that the uniform versions of both theorems are limit computable, which means that they are effectively -measurable with respect to the effective Borel hierarchy. (shrink)

The translation of Newton’s geometrical Propositions in the Principia into the language of the differential calculus in the form developed by Leibniz and his followers has been the subject of many scholarly articles and books. One of the most vexing problems in this translation concerns the transition from the discrete polygonal orbits and force impulses in Prop. 1 to the continuous orbits and forces in Prop. 6. Newton justified this transition by lemma 1 on prime and ultimate ratios which was (...) a concrete formulation of a limit, but it took another century before this concept was established on a rigorous mathematical basis. This difficulty was mirrored in the newly developed calculus which dealt with differentials that vanish in this limit, and therefore were considered to be fictional quantities by some mathematicians. Despite these problems, early practitioners of the differential calculus like Jacob Hermann, Pierre Varignon, and Johann Bernoulli succeeded without apparent difficulties in applying the differential calculus to the solution of the fundamental problem of orbital motion under the action of inverse square central forces. By following their calculations and describing some essential details that have been ignored in the past, I clarify the reason why the lack of rigor in establishing the continuum limit was not a practical problem. (shrink)

This paper analyzes the ‘Theory of Inverse Numbers’ that appears in Chapter 3 of the “Shuogua zhuan” 說卦傳 in the I Ching and seeks to apply the findings to the Yi studies of Cheng Yi. The Yi studies of Shao Yong, Zhu Xi, and Cheng Yi are generally explained in the categories of Xiangshu(Image-Number) Yi studies and Yili(Meaning-Principle) Yi studies. However, upon analyzing the ‘Theory of Inverse Numbers’ as a theory representing numbers of principles, it is evident that (...) the framework of this theory is also reflected in Cheng Yi’s Yi studies. The analysis of the ‘Theory of Inverse Numbers’ was conducted through the interpretations of Shao Yong and Zhu Xi, proposing the concept of the ‘Theory of Inverse Numbers’ as a Yi interpretation framework that accounts for what has already occurred [yisheng 已生] and what has not yet occurred [weisheng 未生]. By applying the Yi interpretation framework of what has arisen and what has not, which was developed through the explanations of Shao Yong and Zhu Xi, to Cheng Yi’s Yi studies, it is revealed that even though Cheng Yi does not directly mention Chapter 3 of the “Shuogua zhuan,” the narrative framework of Yichuan Yizhuan 伊川易傳 can be well elucidated by the ‘Theory of Inverse Numbers.’ Accordingly, it suggests that viewing Cheng Yi’s Yi studies merely as a dichotomy of meaning-principle and image-number is limited, and that the concept of Xiangshu Yi is inherent in Cheng Yi’s Yi studies. In other words, the ‘Theory of Inverse Numbers’ as a theory of principle-representing numbers originating from Shao Yong is inherent throughout Cheng Yi’s interpretation of the I Ching as a framework of Yi interpretation for what has arisen and what has not, and this was systematized as the ‘Theory of Inverse Numbers’ by Zhu Xi. (shrink)

It is proved that for any k, the class of classical categorial grammars that assign at most k types to each symbol in the alphabet is learnable, in the Gold (1967) sense of identification in the limit from positive data. The proof crucially relies on the fact that the concept known as finite elasticity in the inductive inference literature is preserved under the inverse image of a finite-valued relation. The learning algorithm presented here incorporates Buszkowski and Penn's (1990) algorithm (...) for determining categorial grammars from input consisting of functor-argument structures. (shrink)

A question dating to Mardešić and Prasolov’s 1988 work [S. Mardešić and A. V. Prasolov, Strong homology is not additive, Trans. Amer. Math. Soc. 307(2) (1988) 725–744], and motivating a considerable amount of set theoretic work in the years since, is that of whether it is consistent with the ZFC axioms for the higher derived limits [Formula: see text] [Formula: see text] of a certain inverse system [Formula: see text] indexed by [Formula: see text] to simultaneously vanish. An (...) equivalent formulation of this question is that of whether it is consistent for all [Formula: see text]-coherent families of functions indexed by [Formula: see text] to be trivial. In this paper, we prove that, in any forcing extension given by adjoining [Formula: see text]-many Cohen reals, [Formula: see text] vanishes for all [Formula: see text]. Our proof involves a detailed combinatorial analysis of the forcing extension and repeated applications of higher-dimensional [Formula: see text]-system lemmas. This work removes all large cardinal hypotheses from the main result of [J. Bergfalk and C. Lambie-Hanson, Simultaneously vanishing higher derived limits, Forum Math. Pi 9 (2021) e4] and substantially reduces the least value of the continuum known to be compatible with the simultaneous vanishing of [Formula: see text] for all [Formula: see text]. (shrink)

This interdisciplinary volume questions one of the most fundamental tenets of social theory by focusing on detachment, an important but neglected aspect of social life. Going against the grain of recent theoretical celebrations of engagement, this book challenges us to re-think the relational basis of social theory. In so, doing it brings to light the productive aspects of disconnection, distance and detachment. Rather than treating detachment simply as the moral inversion of compassion and engagement, the volume brings together empirical studies (...) and theoretical comments by leading anthropologists, sociologists and science studies scholars. Taken together, these illustrate the range of contexts within which distance and disconnection can offer meaningful frameworks for action. Positioned at the cutting edge of social theory, this landmark volume will be of great interest to students and academics across the social sciences and humanities. (shrink)

The article shows the “Appendix” to Søren Kierkegaard’s Philosophical Fragments to be a response to Ludwig Feuerbach’s critique of Christianity. While previous studies have detected some influence by Feuerbach on Kierkegaard, they have so far discovered little in the way of specific responses to Feuerbach’s ideas in Kierkegaard’s published works. The article first makes the historical argument that Kierkegaard was very likely reading Feuerbach’s Essence of Christianity while he was writing Philosophical Fragments, as several of Kierkegaard’s journal entries from that (...) period discuss Feuerbach in relation to central ideas in Fragments. The article then shows how Kierkegaard’s pseudonym Johannes Climacus inverts Feuerbach’s projection theory, turning it against critics like Feuerbach. At the heart of Feuerbach’s critique of Christianity is the claim that religion is a conceptual illusion, whereby the individual projects his or her personal limits onto the species and then projects the unlimited onto a supposed divine being. Furthermore, Feuerbach sees Christianity as rife with absurdities that tell against its reasonableness. In exploring a hypothetical transcendent avenue toward the truth, Climacus inverts both of these philosophical moves. He argues that on the transcendent hypothesis, the immanentist critic is himself a victim of an “acoustical illusion”: the absolute paradox of the appearance of the god in time is in fact not judged by, but rather judges, the critic as absurd. In inverting and not repudiating Feuerbach’s critique, Climacus reveals the critic as a Socratic figure who displays the heights—and ultimately, the limits—of secular philosophy’s capabilities. (shrink)

Cet article analyse le risque de corruption que les arrêts Citizens United de 2010 et l’apparition des Super-PACs font peser sur le système électoral états-unien. Lors de la dernière campagne présidentielle, plus de 730 millions de dollars ont été investis dans des publicités électorales par de riches contributeurs et des entreprises privées regroupés en Super-PACs. Nous montrons que cet afflux d’argent consacré à des publicités politiques expose la démocratie américaine à trois formes de « corruption grise », en favorisant la (...) banalisation de pratiques contestables et en troublant la frontière entre ce qui est licite et ce qui ne l’est pas. (1) Déplafonné, le soutien financier aux candidats risque de s’apparenter à de la subornation; (2) certaines des techniques publicitaires employées semblent réduire l’exercice de conviction démocratique à une tentative de corruption de l’électeur; (3) enfin les immenses inégalités d’influence politique que ce système de financement induit participent de la corruption des affaires démocratiques en favorisant leur captation par un petit nombre d’individus fortunés. Nous mettons en évidence que le refus systématique de la Cour Suprême d’envisager ces phénomènes comme des vecteurs de corruption se fonde sur une conception discutable de la démocratie comme système de libre concurrence pour le pouvoir politique. Comprendre la démocratie à partir de son impératif d’égalité permet à l’inverse de rendre visible la corruption à laquelle son système de financement électoral expose la démocratie américaine. (shrink)

The article shows the "Appendix" to Søren Kierkegaard's "Philosophical Fragments" to be a response to Ludwig Feuerbach's critique of Christianity. While previous studies have detected some influence by Feuerbach on Kierkegaard, they have so far discovered little in the way of specific responses to Feuerbach's ideas in Kierkegaard's published works. The article first makes the historical argument that Kierkegaard was very likely reading Feuerbach's "Essence of Christianity" while he was writing "Philosophical Fragments", as several of Kierkegaard's journal entries from that (...) period discuss Feuerbach in relation to central ideas in "Fragments". The article then shows how Kierkegaard's pseudonym Johannes Climacus inverts Feuerbach's projection theory, turning it against critics like Feuerbach. At the heart of Feuerbach's critique of Christianity is the claim that religion is a conceptual illusion, whereby the individual projects his or her personal limits onto the species and then projects the unlimited onto a supposed divine being. Furthermore, Feuerbach sees Christianity as rife with absurdities that tell against its reasonableness. In exploring a hypothetical transcendent avenue toward the truth, Climacus inverts both of these philosophical moves. He argues that on the transcendent hypothesis, the immanentist critic is himself a victim of an "acoustical illusion": the absolute paradox of the appearance of the god in time is in fact not judged by, but rather judges, the critic as absurd. In inverting and not repudiating Feuerbach's critique, Climacus reveals the critic as a Socratic figure who displays the heights—and ultimately, the limits—of secular philosophy's capabilities. (shrink)

The study aims to help characterize the sort of structures about which people can acquire unconscious knowledge. It is already well established that people can implicitly learn n-grams and also repetition patterns. We explore the acquisition of unconscious structural knowledge of symmetry. Chinese Tang poetry uses a specific sort of mirror symmetry, an inversion rule with respect to the tones of characters in successive lines of verse. We show, using artificial poetry to control both n-gram structure and repetition patterns, that (...) people can implicitly learn to discriminate inversions from non-inversions, presenting a challenge to existing models of implicit learning. (shrink)

« L’histoire de la “pensée clinique” – prise en son sens le plus large – peut être dite vectorisée par une dé-singularisation toujours plus nette des situations de soin. Que ce soit en médecine somatique, en psychiatrie ou en psychologie, le colloque soignant/soigné s’est progressivement standardisé, par l’opérationnalisation d’un ensemble de procédures thérapeutiques jugées efficaces. La psychanalyse, dernière-née des sous-disciplines cliniques, occupe à ce titre une position “à la limite”. Soucieuse comme les autres de connaître pour mieux soigne r, elle (...) monte en généralité ( cf. ses étiologies, ses diagnostics et le modèle métapsychologique). Mais elle adopte simultanément – suivant cette même exigence d’efficacité – une démarche inverse qu’on peut à bon droit nommer “descente en singularité”. De fait, Freud met en évidence que certaines représentations uniques verbalisées au cas par cas de ses patients (non reproductibles par d’autres, et non utilisables pour d’autres) constituent le principal levier thérapeutique pour une série de troubles et souffrances psychiques. Son legs scientifique consiste ainsi en une reproblématisation de la question des niveaux logiques opérants dans le champ clinique : est-ce avant tout au niveau du générique (comme en médecine) qu’il faut situer l’effort de vérité pour bien soigner, à l’échelle du typique (comme en psychologie), ou, au contraire, dans l’ordre de l’ unique (proposition originale de la psychanalyse)? Une relecture du fameux cas freudien de Lucy R., tiré des Études sur l’hystérie (1895) – permet de préciser ces enjeux épistémo-cliniques, toujours d’actualité. Est alors discutée la proposition de l’extension de l’usage de l’adjectif “clinique” pour désigner toute pensée du singulier – même hors cadre thérapeutique –, dans l’art, en littérature ou en sciences humaines. ». (shrink)

Our contention is that while what may be termed woke capitalism is the result of real changes in both the material structure of capitalism and its ideological superstructure, those are not changes pulling in the same direction. The main material development is the consolidation of the shift from a quasi-deterministic to a more pronouncedly probabilistic nexus of class and race. But it is unclear that this makes much difference to the material prospects of the vast majority of people of color (...) or indeed of people in general. Indeed, the racial permeability of the upper classes is accompanied by an increased and inverse racial permeability of the underclass. Diversification is so elite-driven that it is unlikely to proceed beyond the cosmetic, and for that reason it seems that diversification does not necessarily correspond to any major structural changes in the relations between groups of people, whether we consider them as arranged by class, race, or the intersection of the two. It follows that the politics of representation should not be regarded as a vehicle for the agenda of the materialist left. We propose instead a responsive universalist approach—responsive to racism and all other forms of marginalization and different from the homogenizing universalism of class-only politics. (shrink)

The languages of finitary and infinitary logic over the alphabet of bounded lattices have proven to be of considerable use in the study of compacta. Significant among the sentences of these languages are the ones that are base free, those whose truth is unchanged when we move among the lattice bases of a compactum. In this paper we define syntactically the expansive sentences, and show each of them to be base free. We also show that many well-known properties of compacta (...) may be expressed using expansive sentences; and that any property so expressible is closed under inverse limits and co-existential images. As a byproduct, we conclude that co-existential images of pseudo-arcs are pseudo-arcs. This is of interest because the corresponding statement for confluent maps is still open, and co-existential maps are often—but not always—confluent. (shrink)

Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint (...) pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general­ ized monoid. Chapters VI and VII explore this notion and its generaliza­ tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure lead inter alia to the study of more convenient categories of topological spaces. (shrink)

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than (...) or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes. (shrink)

A well-known polymodal provability logic inlMMLBox due to Japaridze is complete w.r.t. the arithmetical semantics where modalities correspond to reflection principles of restricted logical complexity in arithmetic. This system plays an important role in some recent applications of provability algebras in proof theory. However, an obstacle in the study of inlMMLBox is that it is incomplete w.r.t. any class of Kripke frames. In this paper we provide a complete Kripke semantics for inlMMLBox . First, we isolate a certain subsystem inlMMLBox (...) of inlMMLBox that is sound and complete w.r.t. a nice class of finite frames. Second, appropriate models for inlMMLBox are defined as the limits of chains of finite expansions of models for inlMMLBox . The techniques involves unions of n -elementary chains and inverse limits of Kripke models. All the results are obtained by purely modal-logical methods formalizable in elementary arithmetic. (shrink)

AssumeGis a group definable in a modelMof a stable theoryT. We prove that the semigroupSG of completeG-types overMis an inverse limit of some semigroups type-definable inMeq. We prove that the maximal subgroups ofSG are inverse limits of some definable quotients of subgroups ofG. We consider the powers of types in the semigroupSG and prove that in a way every type inSG is profinitely many steps away from a type in a subgroup ofSG.

Profinite groups are Galois groups. The effective study of infinite Galois groups was initiated by Metakides and Nerode [8] and further developed by LaRoche [5]. In this paper we study profinite groups without considering Galois extensions of fields. The Artin method of representing a finite group as a Galois group has been generalized by Waterhouse [14] to profinite groups. Thus, there is no loss of relevance in our approach.The fundamental notions of a co-r.e. profinite group, recursively profinite group, and the (...) degree of a co-r.e. profinite group are defined in §1. In this section we prove that every co-r.e. profinite group can be effectively represented as an inverse limit of finite groups. The degree invariant is shown to behave very well with respect to open subgroups and quotients. The work done in this section is basic to the rest of the paper.The commutator subgroup, the Frattini subgroup, thep-Sylow subgroups, and the center of a profinite group are essential in the study of profinite groups. It is only natural to ask if these subgroups are effective. The following question exemplifies our approach to this problem: Is the center a co-r.e. profinite group? Theorem 2 provides a general method for answering this type of question negatively. Examples 3,4 and 5 are all applications of this theorem. (shrink)

This essay attempts to develop a psychologically informed semantics of perception reports, whose predictions match with the linguistic data. As suggested by the quotation from Miller and Johnson-Laird, we take a hallmark of perception to be its fallible nature; the resulting semantics thus necessarily differs from situation semantics. On the psychological side, our main inspiration is Marr's (1982) theory of vision, which can easily accomodate fallible perception. In Marr's theory, vision is a multi-layered process. The different layers have filters of (...) different gradation, which makes vision at each of them approximate. On the logical side, our task is therefore twofold • to formalise the layers and the ways in which they may refine each other, and • to develop logical means to let description vary with such degrees of refinement. The first task is formalised by means of an inverse systems of first order models, with reality appearing as its inverse limit. The second task is formalised by means of so-called conditional quantifiers, a new form of generalised quantification which can best be described as resource bounded quantification. We show that the logic provides for a semantics and pragmatics of direct perception reports. In particular, direct perception reports have a possibly nonveridical, approximative semantics, which becomes veridical only by virtue of our pragmatic expectation that what is perceived would continue to be the case, were we to perceive more accurately. It is a general feature of resource bounded logics that the underlying logics are weak, but that stronger principles can be obtained pragmatically, by strengthening the resource. For the logic of vision this feature is clarified by showing how changes in the resource capture different notions of partiality, and by studying how the perception verb interacts with connectives and quantifiers in different visual contexts. The inference Veridicality, which is now viewed rather as a nonmonotonic inference, is also studied in depth. We end with an attempt to buttress the proposed model by comparing it with suggestions put forward in Cognitive or Conceptual Semantics, in the literature on evidentials, and in Husserl's philosophy of perception. (shrink)

The concept of elementary epimorphism is introduced. Inverse systems of such maps are considered, and a dual of the elementary chain lemma is found (Cor. 4.2). The same is done for pure epimorphisms (Cor. 4.3 and 4.4). Finally, this is applied to certain inverse limits of flat modules (Thm. 6.4) and certain inverse limits of absolutely pure modules (Cor. 6.3).

We study the embedding property in the category of sorted profinite groups. We introduce a notion of the sorted embedding property (SEP), analogous to the embedding property for profinite groups. We show that any sorted profinite group has a universal SEP-cover. Our proof gives an alternative proof for the existence of a universal embedding cover of a profinite group. Also our proof works for any full subcategory of the sorted profinite groups, which is closed under taking finite quotients, fibre products, (...) and inverse limits. We also show that any sorted profinite group having SEP has a sorted complete system whose theory is $\omega $ -categorical and $\omega $ -stable under the assumption that the set of sorts is countable. (shrink)

Let equation image denote the inverse limit of all finite cyclic groups. Let F, G and H be abelian groups with H ≤ G. Let FβH denote the abelian group , where +βis defined by +β = + β — β) for a certain β : F → G linear mod H meaning that β = 0 and β + β — β ∈ H for all a, b in F. In this paper we show that the following hold: (...) The additive group of any nonstandard model ℤ* of the ring ℤ is isomorphic to βH for a certain β : ℤ*+/H → equation image linear mod H. equation image is isomorphic to βH for some β : equation image/H →ℚ linear mod H, though equation image is not the additive group of any model of Th and the exact sequence H → equation image → equation image/H is not splitting. (shrink)