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)

Outline: 1. Why Judgment? 2. Inverse Psychologism: General Issues 3. Inverse Psychologism in the Phenomeno-Logic of Judgment 4. Judgment and Language 5. [De-]stabilizing Kant ’s Inverse Psychologism.

Given an abstract logic L = L(Q i ) i ∈ I generated by a set of quantifiers Q i , one can construct for each type τ a topological space S τ exactly as one constructs the Stone space for τ in first-order logic. Letting T be an arbitrary directed set of types, the set $S_T = \{(S_\tau, \pi^\tau_\sigma)\mid\sigma, \tau \in T, \sigma \subset \tau\}$ is an inverse topological system whose bonding mappings π τ σ are naturally determined (...) by the reduct operation on structures. We relate the compactness of L to the topological properties of S T . For example, if I is countable then L is compact iff for every τ each clopen subset of S τ is of finite type and S τ is homeomorphic to $\underset{lim}S_T$ , where T is the set of finite subtypes of τ. We finally apply our results to concrete logics. (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)

The phenomenon of inverse linking, where a noun phrase embedded within another behaves with respect to binding as though it were structurally independent, has proven challenging for theories of the syntax–semantics interface. In this paper I show that, using an LF-movement style approach to the syntax–semantics interface, we can derive all and only the appropriate meanings for such constructions using no semantic operations other than function application and composition. The solution relies neither on a proliferation of lexical ambiguity nor (...) on abandoning the idea that pronouns denote variables, but rather on a straightforward (and standard) reification of assignment functions, which allows us to define abstraction operators within our models. (shrink)

Standpoint theory is an explicitly political as well as social epistemology. It’s distinctive features are commitment to understand the social locations that shape the epistemic capacities and resources of individuals in structural terms, and a recognition that those who are marginalized within hierarchically structured systems of social differentiation are often epistemically advantaged. In some crucial domains they know more and know better as a contingent function of their situated experience and knowledge. This “inversion thesis” counters the alignment of social (...) with epistemic privilege. (shrink)

Even if spectrum inversion of various sorts is possible, spectrum inversion without a difference in representation is not. So spectrum inversion does not pose a challenge for the intentionalist thesis that, necessarily, within a given sense modality, if two experiences are alike with respect to content, they are also alike with respect to their phenomenal character. On the contrary, reflection on variants of standard cases of spectrum inversion provides a strong argument for intentionalism. Depending on one’s views about the possibility (...) of spectrum inversion, the impossibility of spectrum inversion without a difference in representation can also be used as an argument against a variety of reductive theories of mental representation. (shrink)

In the last five years, a number of U.S. companies have either moved their locus of incorporation to countries with more favorable tax laws, or announced such moves. Given this trend toward “inversions”, and the polemics that have accompanied it, we offer two ways in which the ethics of such a move can be evaluated. We provide multinational executives with two applications of ethics to inversion: Kant’s deontological theory and the consequentialist perspective of utilitarianism.

According to the Contingency Theory of Laws, if there are possible worlds in which it is a law that all Fs are G, there are also possible F-containing worlds in which it is not. I argue here that the theory is forced to accept the possibility of nomic inversion: i.e. pairs of properties that have their actual nomic roles swapped in some possible world. Such inversions cannot be ruled out on grounds of logical or metaphysical inconsistency, and therefore (...) – since nomic inversion is counterintuitive – the Contingency Theory is undermined. (shrink)

The standard account of weakness of will identifies it with akrasia, that is, with action against one's best judgment. Elsewhere I have argued that weakness of will is better understood as over-readily giving up on one's resolutions. Many cases of weak willed action will not be akratic: in over-readily abandoning a resolution an agent may well do something that they judge at the time to be best. Indeed, in so far as temptation typically gives rise to judgment shift -- to (...) a tendency to change one's judgment so that one values the tempting option as the best -- weak willed action will typically be akratic. But conversely, strong willed action now looks as though it will be akratic. I argue though that it need not be, once we distinguish between actual judgment, and dispositions to judge. Within this framework, the issue of inverse akrasia looks rather different. I argue that whilst Huckleberry Finn plausibly does show weakness of will in abandoning his resolve to turn Jim in, it is far from clear that he is akratic: a point brought out well in Twain's later additions to the text. Whilst cases of inverse akrasia are clearly theoretically possible, I suggest that, given cognitive dissonance mechanisms, they are unlikely to be very common. (shrink)

In the pure powers ontology (PPO), basic physical properties have wholly dispositional essences. PPO has clear advantages over categoricalist ontologies, which suffer from familiar epistemological and metaphysical problems. However, opponents argue that because it contains no qualitative properties, PPO lacks the resources to individuate powers, and generates a regress. The challenge for those who take such arguments seriously is to introduce qualitative properties without reintroducing the problems that PPO was meant to solve. In this paper, I distinguish the core claim (...) of PPO: (i) basic physical properties have dispositional essences, from a hitherto unnoticed assumption: (ii) the dispositional essences of basic physical properties exclusively involve type-causal relations to other basic physical properties. I reject (ii), making room for a structuralist ontology in which all basic physical properties are pure powers, individuated by their places in a causal structure that includes not only other powers, but also physically realized qualitative properties such as shapes, patterns and structures. Such qualities individuate pure powers in the way that non-mental input and output properties individuate realized mental properties in functionalist theories of mind, except that here it is basic physical powers that are individuated by relations to realized non-powers. I distinguish one Platonic and two Aristotelian version of this theory, and argue that the Aristotelian versions require that grounding is not always a relative fundamentality relation, because the powers ground the qualities that individuate them. By considering ontic structural realism, I argue that symmetric grounding is the best way to make sense of relational individuation in structuralist ontologies, and is therefore no additional commitment of the one proposed here. (shrink)

The present paper introduces "ontomimetic simulation" and argues that this class of models has enabled the investigation of hypotheses about complex systems in new ways that have epistemological relevance. Ontomimetic simulation can be differentiated from other types of modeling by its reliance on causal similarity in addition to representation. Phenomena are modeled not directly but via mimesis of the ontology (i.e. the "underlying physics", microlevel etc.) of systems and a subsequent animation of the resulting model ontology as a dynamical system. (...) While the ontology is clearly used for computing system states, what is epistemologically important is that it is viewed as a hypothesis about the makeup of the studied system. This type of simulation, where model ontologies are used as hypotheses, is here called inverse ontomimetic simulation since it reverses the typical informational path from the target to the model system. It links experimental and analytical techniques in being explicitly dynamical while at the same time capable of abstraction. Inverse ontomimetic simulation is argued to have a great impact on science and to be the tool for hypothesis-testing that has made systematic theory development for complex systems possible. (shrink)

Darwin’s theory of evolution by natural selection unifies the world of physics with the world of meaning and purpose by proposing a deeply counterintuitive ‘‘inversion of reasoning’’ (according to a 19th century critic): ‘‘to make a perfect and beautiful machine, it is not requisite to know how to make it’’ [MacKenzie RB (1868) (Nisbet & Co., London)]. Turing proposed a similar inversion: to be a perfect and beautiful computing machine, it is not requisite to know what arithmetic is. Together, (...) these ideas help to explain how we human intelligences came to be able to discern the reasons for all of the adaptations of life, including our own. (shrink)

We point out a simple but hitherto ignored link between the theoryof updates, the theory of counterfactuals, and classical modal logic: update is a classicalexistential modality, counterfactual is a classical universalmodality, and the accessibility relations corresponding to these modalities are inverses. The Ramsey Rule (often thought esoteric) is simply an axiomatisation of this inverse relationship. We use this fact to translate between rules for updates andrules for counterfactuals. Thus, Katsuno and Mendelzons postulatesU1--U8 are translated into counterfactual rules C1--C8(Table (...) VII), and many of the familiar counterfactual rulesare translated into rules for updates (Table VIII). Ourconclusions are summarised in Table V. (shrink)

. The term inversion principle goes back to Lorenzen who coined it in the early 1950s. It was later used by Prawitz and others to describe the symmetric relationship between introduction and elimination inferences in natural deduction, sometimes also called harmony. In dealing with the invertibility of rules of an arbitrary atomic production system, Lorenzen’s inversion principle has a much wider range than Prawitz’s adaptation to natural deduction. It is closely related to definitional reflection, which is a principle for reasoning (...) on the basis of rule-based atomic definitions, proposed by Hallnäs and Schroeder-Heister. After presenting definitional reflection and the inversion principle, it is shown that the inversion principle can be formally derived from definitional reflection, when the latter is viewed as a principle to establish admissibility. Furthermore, the relationship between definitional reflection and the inversion principle is investigated on the background of a universalization principle, called the ω- principle, which allows one to pass from the set of all defined substitution instances of a sequent to the sequent itself. (shrink)

William Lane Craig has argued that there cannot be actual infinities because inverse operations are not well-defined for infinities. I point out that, in fact, there are mathematical systems in which inverse operations for infinities are well-defined. In particular, the theory introduced in John Conway's *On Numbers and Games* yields a well-defined field that includes all of Cantor's transfinite numbers.

Let U be an initial segment of $^*{\mathbb N}$ closed under addition (such U is called a cut) with uncountable cofinality and A be a subset of U, which is the intersection of U and an internal subset of $^*{\mathbb N}$ . Suppose A has lower U-density α strictly between 0 and 3/5. We show that either there exists a standard real $\epsilon$ > 0 and there are sufficiently large x in A such that | (A+A) ∩ [0, 2x]| > (...) (10/3+ $\epsilon$ ) | A ∩ [0, x]| or A is a large subset of an arithmetic progression of difference greater than 1 or A is a large subset of the union of two arithmetic progressions with the same difference greater than 2 or A is a large subset of the union of three arithmetic progressions with the same difference greater than 4. (shrink)

A class of probability functions is studied. This class contains the probability functions of half-spin particles and spinning classical objects. A notion of realisability for these functions is defined. In terms of this notion two versions of Bell's theorem and their inverses are stated and proved.

Christopher Peacocke has recently made an important and insightful effort to fashion a non-verificationist method for distinguishing sense from nonsense. The argument is subtle and complex, and varies somewhat with each of his three target ‘spurious hypotheses’: that if a perfect fission of one person into two were to occur, one and only one of the resulting persons would be identical with the original; that another person’s visual experience can be qualitatively different from your own when you are both seeing (...) the same object, even though your relevant brain states are physically identical and so are your environmental conditions; and that the entire material universe is moving undetectably at a particular uniform velocity with respect to absolute space. My own assessment of his efforts is that they are most successful against the third of these hypotheses, and that this is a function of the fact that of the three, it alone clearly employs a problematic concept- that of absolute location. However, my purpose here is not to engage in a comprehensive evaluation of Peacocke’s project; it is rather to defend the extreme inverted spectrum hypothesis against his attack. I shall argue not only that his argument against EISH fails, but that he is himself independently committed to its intelligibility. Beyond that, I shall point out some striking and, to my mind, welcome consequences of his plausible claims concerning the relations between his own proposal and certain other views concerning content theory; the consequences in question depend both on his positive proposal and on my reasons for rejecting his argument against the extreme inversion hypothesis. (shrink)

Christopher Peacocke has recently made an important and insightful effort to fashion a non-verificationist method for distinguishing sense from nonsense. The argument is subtle and complex, and varies somewhat with each of his three target ‘spurious hypotheses’: that if a perfect fission of one person into two were to occur, one and only one of the resulting persons would be identical with the original; that another person’s visual experience can be qualitatively different from your own when you are both seeing (...) the same object, even though your relevant brain states are physically identical and so are your environmental conditions; and that the entire material universe is moving undetectably at a particular uniform velocity with respect to absolute space. My own assessment of his efforts is that they are most successful against the third of these hypotheses, and that this is a function of the fact that of the three, it alone clearly employs a problematic concept- that of absolute location. However, my purpose here is not to engage in a comprehensive evaluation of Peacocke’s project; it is rather to defend the extreme inverted spectrum hypothesis against his attack. I shall argue not only that his argument against EISH fails, but that he is himself independently committed to its intelligibility. Beyond that, I shall point out some striking and, to my mind, welcome consequences of his plausible claims concerning the relations between his own proposal and certain other views concerning content theory; the consequences in question depend both on his positive proposal and on my reasons for rejecting his argument against the extreme inversion hypothesis. (shrink)

An inverse akratic act is one who believes X, all things considered, is the correct act, and yet performs ~X, where ~X is the correct act. A famous example of such a person is Huck Finn. He believes that he is wrong in helping Jim, and yet continues to do so. In this paper I investigate Huck’s nature to see why he performs such acts contrary to his beliefs. In doing so, I explore the nature of empathy and show (...) how powerful Huck’s empathic feelings are. Drawing from Martin L. Hoffman, I show the relationship between empathy and a principle of justice. This relationship leads to Huck acting virtuously, as Rosalind Hursthouse maintains. (shrink)

Does the claimed fine-tuning of the constants of nature for life give reason to think that there are many other universes in which the constants have different values? Or does the inference from fine-tuning to a multiverse commit what Hacking calls the inverse gambler’s fallacy? The present paper considers two fine-tuning problems that seem promising to consider because they are in many respects analogous to the problem of the fine-tuned constants. Reasoning that parallels the inference from fine-tuning to a (...) multiverse seems prima facie adequate in these problems. However, it turns out that in both cases there are independent empirical reasons to believe the hypotheses that are analogous to the multiverse hypothesis. In the absence of such evidence, it would be coherent to raise the inverse gambler’s fallacy charge against the inference from fine-tuning to these multiverse-type hypotheses. In response to this finding, I suggest taking the possibility seriously that established standards of rationality may not allow us to decide whether the inference from fine-tuning to a multiverse is fallacious or not. The paper concludes by sceptically assessing the prospects for obtaining independent empirical evidence for concrete multiverse theories. (shrink)

Charles S. Peirce introduced in the late 19th century the notion of abduction as inference from effects to causes, or from observational data to explanatory theories. Abductive reasoning has become a major theme in contemporary logic, philosophy of science, and artificial intelligence. This paper argues that the new growing branch of applied mathematics called inverse problems deals successfully with various kinds of abductive inference within a variety of scientific disciplines. The fundamental theorem about the inverse reconstruction of plane (...) functions from their line integrals was proved by Johann Radon already in 1917. The practical applications of Radon’s theorem and its generalizations include computerized tomography which became a routine imaging technique of diagnostic medicine in the 1970s.Keywords: Abduction; Inference to the best explanation; Inverse problems; Peirce; Radon’s theorem; Tomography. (shrink)

D. M. Armstrong has objected that the Dispositionalist theory of laws and properties is modally inverted, for it entails that properties are constituted by relations to non-actual possibilia. I contend that, if this objection succeeds against Dispositionalism, then Armstrong's nomic necessitation relation is also modally inverted. This shows that at least one of Armstrong's reasons for preferring a nomic necessitation theory is specious.

Two-stage voting is prone to majority inversions, a situation in which the outcome of an election is not backed by a majority of popular votes. We study the probability of majority inversion in a model with two candidates, three states and uniformly distributed fractions of supporters for each candidate. The model encompasses equal or distinct population sizes, with equal, population-based or arbitrary voting weights in the second stage. We prove that, when no state can dictate the outcome of the election (...) by commanding a voting weight in excess of one half, the probability of majority inversion increases with the size disparity among the states. (shrink)

The possibility of spectrum inversion has been debated since it was raised by Locke and is still discussed because of its implications for functionalist theories of conscious experience . This paper provides a mathematical formulation of the question of spectrum inversion and proves that such inversions, and indeed bijective scramblings of color in general, are logically possible. Symmetries in the structure of color space are, for purposes of the proof, irrelevant. The proof entails that conscious experiences are not identical with (...) functional relations. It leaves open the empirical possibility that functional relations might, at least in part, be causally responsible for generating conscious experiences. Functionalists can propose causal accounts that meet the normal standards for scientific theories, including numerical precision and novel prediction; they cannot, however, claim that, because functional relationships and conscious experiences are identical, any attempt to construct such causal theories entails a category error. (shrink)

Over _Principles_ 42-43, Berkeley worried that we might "in truth" see things existing at a distance from us, in which case they could not plausibly be supposed to exist independently of being perceived. He went on to say that he had developed his new theory of vision to address this worry. This paper argues that the worry is serious and that Berkeley was right to think that it would take nothing less than a theory of vision to address (...) it. The paper further argues that Berkeley's theory of vision fails to adequately address the worry. The locus of the failure is Berkeley's account of what he called "situation." The term has an ambiguity that Berkeley exploited. It can refer to how coloured points are localized on a two dimensional visual field or it can mean how the visual field is oriented with respect to the direction of gravity. Berkeley focused on the second when he needed to explain how the first is possible without granting that we originally experience objects as disposed over at least two spatial dimensions. (shrink)

Cet article cherche à montrer qu’en comprenant la protention comme fonctionnant comme la rétention mais en sens inverse, on ne rend pas correctement compte de la conscience interne du temps. L’auteur commence par explorer plus largement la place de la rétention dans la théorie husserlienne de la conscience interne du temps, puis par montrer qu’on ne peut faire l’expérience phénoménologique de la protention de cette manière. A travers une analyse approfondie du concept de remplissement, l’article montre ensuite comment au (...) cœur de l’analyse husserlienne de la conscience interne du temps, en fait même au cœur de son analyse de la rétention, nous voyons la protention fonctionner d’une façon unique et distinctive. En dégageant dans l’analyse du remplissement de Husserl l’importance de la directionalité inhérente de la protention et sa capacité à distinguer entre les modes clarifiant et confirmant de l’intuition, l’avant-dernière section de cet article montre une fois pour toutes ce qui distingue la protention de la rétention. La différence n’est pas simplement une différence de direction, mais aussi de fonction essentielle. Enfin, l’auteur avance pour terminer qu’en échouant à reconnaître le rôle unique de la protention, on prend le risque non seulement de comprendre incorrectement la protention, mais aussi de rendre compte de la rétention elle-même de manière erronée, qui empêche d’apprécier avec exactitude ce qui est innovant dans l’analyse husserlienne de la conscience interne du temps. (shrink)

Cet article, qui fait suite à une publication précédente (« Les apories du concept de redondance logique chez Bolzano »), poursuit un double objectif : (I) démontrer que les apories que nous avions relevées peuvent être surmontées par l’analyse des rapports extensionnels entre représentations ; (II) évaluer la contribution de Bolzano à la question classique des rapports intension/extension telle qu’elle a été posée par Port-Royal. La logique des classes, dont Bolzano pose les fondements ( Théorie de la science, 2 e (...) partie, 3 e section), permet en effet de dégager les lois de la redondance logique — auxquelles Bolzano ne cesse de faire implicitement référence sans en donner la formule — et de délimiter le champ d’application du principe classique de proportionnalité inverse entre intension et extension auquel déroge précisé­ment la redondance. La critique bolzanienne de la logique de Port-Royal prend alors tout son sens. (shrink)

Este artigo tematiza o apóstolo Pedro como personagem no evangelho de Mateus. O objetivo é identificar as nuances e transformações do personagem Pedro no evangelho. Para tanto, tomo como ponto de partida a pertença do evangelho ao gênero literário biografia greco-romana, que apresenta Jesus Cristo como protagonista. Os demais personagens são desenvolvidos em relação com ele. O mesmo se dá com o apóstolo Pedro. O texto se desenvolve a partir da teoria narrativa, de modo particular a caracterização de personagens. Identifico, (...) a partir de Erich Auerbach e Robert Alter, as características de personagens bíblicos, tecendo comparações com teorias do personagem no romance moderno. A análise de textos do evangelho de Mateus que retratam o personagem Pedro leva à conclusão que suas principais características são a complexidade e a inversão. Elas produzem uma visão geral da involução do personagem na narrativa do evangelho de Mateus. Palavras-chave: Pedro. Evangelho de Mateus. Teoria narrativa. Complexidade. Inversão.This article focuses on the apostle Peter as a character in the Gospel of Matthew. It aims at identifying the nuances and changes of the character Peter in the Gospel. For this purpose, I take as a starting point that the gospel belongs to the literary genre of ancient Greco-Roman Biography, which presents Jesus Christ as the protagonist. The other characters are developed in relationship with him. The same is true with the Apostle Peter. The article unfolds from narrative theory, in particular the categorization of characters. I categorize, based on Erich Auerbach and Robert Alter, the features of biblical characters, developing comparisons with theories of the character in the modern novel. The analysis of the main texts from the Gospel of Matthew that portray the character Peter leads to the conclusion that its main features are complexity and inversion. They produce an overview of the involution of the character in the narrative of the Gospel of Matthew. Key words: Peter. Gospel of Matthew. Narrative theory. Complexity. Inversion. (shrink)

Dans cet ouvrage, Franck Varenne pose la question du réalisme scientifique, essentiellement dans sa forme contemporaine, et ce jusqu’aux années 1980. Il s’est donné pour cela la contrainte de focaliser l’attention sur ce que devenaient sa formulation et les réponses diverses qu’on a pu lui apporter en réaction spécifique à l’évolution parallèle qu’ont subie les notions de théories et surtout de modèles dans les sciences, à la même époque. Même si, bien sûr, on ne peut pas attribuer le considérable essor (...) des modèles au XXe siècle au projet qu’auraient eu les scientifiques de régler cette question, en grande partie philosophique, du réalisme – car les modèles scientifiques ont bien d’autres fonctions et ils proviennent de bien d’autres demandes techniques, cognitives et sociales –, son choix épistémologique a consisté à suivre la littérature contemporaine désormais classique, tant scientifique que philosophique, sur les théories puis sur les modèles afin d’une part, d’en rapporter l’évolution générale, mais, d’autre part aussi, afin de l’interroger de proche en proche, et systématiquement, sur ce qu’elle entend à chaque fois réévaluer ou remettre en débat au moyen de cette question persistante du réalisme et de la réalité en science. Au-delà de l’enquête historique, cette étude se révèle donc également comparative. Elle présente l’intérêt de mettre en évidence des similitudes de forme remarquables (identités, symétries, inversions, déplacements) entre des séquences argumentatives produites par des auteurs différents, dans des contextes distincts, au sujet de cette capacité qu’aurait – ou non – la science à rendre véritablement compte de la réalité. -/- Ainsi, via l’analyse épistémologique historique et comparative qu’en propose Franck Varenne, la question cruciale de la médiation du réel par nos outils conceptuels ou expérientiels reçoit dans ce livre l’éclairage d’auteurs dont les conceptions sont, pour certaines encore, méconnues du lecteur non anglophone : Peter Achinstein, Max Black, Ludwig Boltzmann, Nancy Cartwright, Pierre Duhem, Ian Hacking, Mary Hesse, Evelyn Fox Keller, Imre Lakatos, Ernst Mach, Ernest Nagel, Henri Poincaré, Willard V.O. Quine, Bas van Fraassen, etc. (shrink)

This chapter offers a close reading of a passage from the literary and philosophical work Minima Moralia that enacts Theodor W. Adorno's radical concept of nonpropositional truth content in philosophical aesthetics after Auschwitz. Readers of Adorno's texts, especially those devoted to philosophical aesthetics, can hardly fail to be struck by their chiastic structure. The aesthetic theory that Adorno develops constitutes not only a theory of the aesthetic but also a theory that is itself aesthetic, hence a (...) class='Hi'>theory of literature that exhibits qualities associated with literary texts, and a theory of music that harbors within itself traces of musical composition. The rhetorically self-conscious tropes of his posthumous Aesthetic Theory, the stylized literary studies of his Notes to Literature, his musically inflected meditations on musicological questions from Ludwig van Beethoven to Arnold Schönberg, and so many of his other texts perform this provocative inversion in a variety of registers and conceptual modulations. (shrink)

The extraordinary parallel between the psychological theory of reversals (Apter, 1982) and the anthropological theory of anti-structure (Turner, 1982)-- both derived independently and almost simultaneously from entirely different kinds of evidence and research-- would seem to point to something profound and universal in human experience which has been curiously neglected in the behavioural sciences and entirely ignored in consciousness studies. What I will do here is to introduce reversal theory, show how it applies to ritual, and then (...) compare it with Victor Turner's well-known approach to the very same topic. Reversal theory has in fact been used to elucidate many diverse social phenomena, for example criminal violence, military combat, sexual behaviour, family relationships, soccer hooliganism, organizational culture, leadership, team sports, social advocacy and classroom management (see review in Apter, 2001a). The present paper extends these ideas to ritual for the first time, and makes reference especially to the work of Turner and his idea of cultural inversions (Turner, 1969). Reversal theory is also about inversions, but the inversions in this case (i.e. reversals) occur at the level of individual psychology and are identified initially as experiential rather than behavioural or social. This paper will explore the relationship between these two kinds of reversal, psychological and anthropological. (shrink)

We present a survey of proof theory in the USSR beginning with the paper by Kolmogorov [1925] and ending (mostly) in 1969; the last two sections deal with work done by A. A. Markov and N. A. Shanin in the early seventies, providing a kind of effective interpretation of negative arithmetic formulas. The material is arranged in chronological order and subdivided according to topics of investigation. The exposition is more detailed when the work is little known in the West (...) or the original presentation can be improved using notions or results which appeared later. This includes such topics as Novikov's cut-elimination method (regular formulas) and Maslov's inverse method for the predicate logic. (shrink)

Marx’s critical theory of slavery is the operational subtext throughout his critique of political economy. For Marx, the movement from modern slavery to capital represents a historical transition of significance, not only (or foremost) as an empirical transition but also as a transformation of social substance. Marx reveals why, in retrospect, production based on slavery, as logical configuration, must give way to the generalising logic of wage labour. Marx’s critical theory of slavery historicises wage labour (qua category) as (...) the dissolution and inversion of enslaved labour (qua category). Plantation slavery production in the colonised territories initiates a qualitative development that constitutes the historical condition for the emergence of a mode of sociality that we can call ‘value’. Marx’s theoretical account of modern slavery is a lever in his broader critique of capital and is fundamentally distinct from empirical, historical accounts. (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)

This paper examines an annotation in Newton’s hand found by H. W. Turnbull in David Gregory’s papers in the Library of the Royal Society. It will be shown that Gregory asked Newton to explain to him how the trajectories of a body accelerated by an inverse-cube force are determined in a corollary in the Principia: an important topic for gravitation theory, since tidal forces are inverse cube. This annotation opens a window on the more hidden mathematical methods (...) which Newton deployed in his magnum opus. The received view according to which the Principia are written in a geometric style with no help from calculus techniques must be revised. (shrink)

No one before Platter and Kepler proposed retinal reception of an inverted visual image. The dominant tradition in visual theory, especially that of Alhazen and his Western followers, subordinated the intra-ocular geometry of visual rays to the requirement for an upright image and to preconceptions about the precise nature of the visual spirit and its part in vision. Henry of Langenstein and an anonymous glossator in the late Middle Ages proposed alternatives to Alhazen, including the suggestion of double inversion (...) of the image. Leonardo da Vinci was aware of both Alhazen's theory and Henry's contradiction, but perhaps not of the anonymous hypothesis of double inversion. Leonardo's visual ‘theory’ has more the character of a critique than of a theoretical alternative, and he did not transcend the medieval concept of visual spirit. (shrink)

This commentary extends arousal theory to suggest an explanation for the well-established inverse correlation between church attendance and involvement in crime. In addition, the results of two surveys of social scientists are reviewed to reveal just how little impact the biosocial/sociobiological perspective has had thus far on social science.

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 inverse compressibility, i.e., the change in the chemical potential as the number of particles in the sample is changed, is studied for a small quantum dot. It is found that the inverse compressibility behaves differently for different values of disorder and electron-electron interactions. For weak interactions or strong disorder one may understand this behavior in the framework of a random matrix theory.

We prove some results about the model theory of fields with a derivation of the Frobenius map, especially that the model companion of this theory is axiomatizable by axioms used by Wood in the case of the theory $\operatorname {DCF}_p$ and that it eliminates quantifiers after adding the inverse of the Frobenius map to the language. This strengthens the results from [4]. As a by-product, we get a new geometric axiomatization of this model companion. Along the (...) way we also prove a quantifier elimination result, which holds in a much more general context and we suggest a way of giving “one-dimensional” axiomatizations for model companions of some theories of fields with operators. (shrink)

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian ℒ, from which the field equations as well as, e.g., (...) the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed. (shrink)

We investigate the theories of linear algebra, which were originally defined to study the question of whether commutativity of matrix inverses has polysize Frege proofs. We give sentences separating quantified versions of these theories, and define a fragment in which we can interpret a weak theory V 1 of bounded arithmetic and carry out polynomial time reasoning about matrices - for example, we can formalize the Gaussian elimination algorithm. We show that, even if we restrict our language, proves the (...) commutativity of inverses. (shrink)

Dynamics of complex systems is often hierarchically organized on different time scales. To understand the physics of such hierarchy, here Brownian motion of a particle moving through a fluctuating medium with slowly varying temperature is studied as an analytically tractable example, and a kinetic theory is formulated for describing the states of the particle. What is peculiar here is that the (inverse) temperature is treated as a dynamical variable. Dynamical hierarchy is introduced in conformity with the adiabatic scheme. (...) Then, a new analytical method is developed to show how the Fokker–Planck equation admits as a stationary solution the Maxwellian distribution modulated by the temperature fluctuations, the distribution of which turns out to be determined by the drift term. A careful comment is also made on so-called superstatistics. (shrink)