In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of type-2 theory of effectivity. This gives rise to a natural representation of the set of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. We show (...) that this canonical representation is admissible with respect to the weak topology on Borel probability measures. Moreover, we prove that for countably-based topological spaces the representation via probabilistic processes is equivalent to the canonical representation and thus admissible with respect to the weak topology. (shrink)

Forthcoming (2011) in K. Hawley and F. Macpherson (eds.) The Admissible Contents of Experience, Wiley‐Blackwell. The Admissible Contents of Experience Fiona Macpherson This essay provides an overview of the debate concerning the admissible contents of experience, together with an introduction to the papers in this volume. The debate is one that takes place among advocates of a certain way of thinking of perceptual experiences: that they are states that represent the world. For to say that a state (...) has content is to say that it represents; and its content is usually taken to be that which is represented. One should not be tempted to think that the debate is therefore marginal or esoteric, for this view of perceptual experience has been by far the dominant view of perceptual experience in recent years in philosophy (and in psychology and neuroscience). The debate is about what answer to give to a fundamental question about the nature of perceptual experience, namely: what objects and properties can it represent? (shrink)

The contraction-free sequent calculus G4 for intuitionistic logic is extended by rules following a general rule-scheme for nonlogical axioms. Admissibility of structural rules for these extensions is proved in a direct way by induction on derivations. This method permits the representation of various applied logics as complete, contraction- and cut-free sequent calculus systems with some restrictions on the nature of the derivations. As specific examples, intuitionistic theories of apartness and order are treated.

The property of admissibility of representations plays an important role in Type–2 Theory of Effectivity . TTE defines computability on sets with continuum cardinality via representations. Admissibility is known to be indispensable for guaranteeing reasonable effectivity properties of the used representations.The question arises whether every function that is computable with respect to arbritrary representations is also computable with respect to closely related admissible ones. We define three operators which transform representations into admissible ones in such a way that (...) relative computability of functions is preserved. Thus the use of admissible representations rather than of non–admissible ones does not decrease the class of relatively computable functions. (shrink)

This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman''s problem forGL andS. We also show that A. V. Kuznetsov''s problem of the existence of finite basis for admissible rules forGL andS has a negative solution. (...) Afterwards we give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions. (shrink)

The on-going debate over the ‘admissible contents of perceptual experience’ concerns the range of properties that human beings are directly acquainted with in perceptual experience. Regarding vision, it is relatively uncontroversial that the following properties can figure in the contents of visual experience: colour, shape, illumination, spatial relations, motion, and texture. The controversy begins when we ask whether any properties besides these figure in visual experience. We argue that ‘ensemble properties’ should be added to the list of visually (...) class='Hi'>admissible properties. Ensemble properties are features that belong to a set of perceptible objects as a whole as opposed to the individuals that constitute that set. They include such features as the mean size of an array of shapes or the average emotional expression of an array of faces. Recent work in vision science has yielded compelling evidence that the visual system routinely encodes such properties. We argue that epistemological considerations provide strong reasons to think that these properties figure in visual experience. Judgements about ensemble properties are immediately warranted by our perceptual experience, and the only plausible way that a perceptual experience could confer this warrant is if it confers awareness of ensemble properties. (shrink)

We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by (...) common reasoning about admissibility does not depend on how the strategic situation is represented. We further explore the links between iterated admissibility and backward and forward induction. (shrink)

In ordinal analysis of impredicative theories so-called collapsing functions are of central importance. Unfortunately, the definition procedure of these functions makes essential use of uncountable cardinals whereas the notation system that they call into being corresponds to a recursive ordinal. It has long been claimed that, instead, one should manage to develop such functions directly on the basis of admissible ordinals. This paper is meant to show how this can be done. Interpreting the collapsing functions as operating directly on (...) admissible sets also renders a new and perspicuous approach to well-ordering proofs possible. MSC: 03F15, 03F35. (shrink)

In this chapter, the author shows that the affinity between the two thinkers is far greater than interpreters like Farrell allow. He focuses on evaluating the argument that Richard Rorty is not able to get past the dichotomies ‐ although he will have cause to comment on the first one as well. In the context of a continued anti‐representationalism, Rorty comes to admit that there is a “truth in realism” and that our relations to the world are not just causal (...) but also normative. The author argues that with these admissions Rorty comes to articulate a view that can, with some plausibility, be said to have gotten beyond the dichotomies of scheme and content, subject and object, and realism and antirealism. D. Davidson agrees with Rorty that truth is not definable by simpler and more transparent concepts. Davidson has a pronged attack on the concept of representation. (shrink)

Previous studies have addressed many different kinds of confessions in police investigations – real, false, coerced, fabricated – and highlighted both psychological and social mechanisms that underlie them. Here, we focus on inadvertent confessions and admissions, which occur when a suspect appears to be confessing without being fully aware of doing so, or when police officers believe they have a confession or admission of guilt when in fact this is not the case. The goal of the study is to explain (...) when, how and why these confessions and admissions occur as well as how they are dealt with in two different jurisdictions, the United States and the United Kingdom. We use a discourse analysis approach because inadvertent confessions and admissions of guilt are the product of miscommunication – they happen because the speaker’s meaning and the hearer’s meaning are misaligned. The data consist of 50 interviews from the United Kingdom and 50 interrogations from the United States with both English-speaking and non-English speaking suspects. Our results demonstrate that inadvertent confessions can occur in both locales due to reliance on inference, which is inevitable since inference is the backbone of any human communication, as well as due to additional factors such as linguistic, cultural and procedural issues. We found that these phenomena are more frequent and less well controlled for in the United States context due to no systematic checking of understanding, adversarial questioning techniques and an absence of legal representation, and lack of professional, high-quality interpreting. We discuss the implications of our findings for current efforts to improve access to justice, custodial procedures and language services, and we make recommendations for the implementation of our research in professional practice. (shrink)

La judicialización de la política argentina abre un hiato entre el creciente activismo en materia política desarrollado por los tribunales de justicia y la tradicional legitimidad atribuida al judicial en tanto que poder conservador de la constitución. Este déficit de legitimidad del poder judicial ha intentado subsanarse mediante el recurso a instancias participativas, inspiradas en el modelo de la democracia deliberativa. Esto ha dado lugar a una serie de innovaciones institucionales en la corte suprema argentina, como la admisión de amigos (...) del tribunal y la celebración de audiencias públicas. La evaluación de estas experiencias permite, sin embargo, identificar una concepción de la participación ciudadana que apunta a la intervención de especialistas y que privilegia la intermediación de abogados y juristas. The judicialization of Argentine politics opens a gap between the activism in political matters developed by the judges and the legitimacy traditionally attributed to the judiciary, as the power in charge of the conservation of the constitution. Recent efforts to supersede this deficit in terms of legitimacy pointed to participatory processes, inspired by the model of deliberative democracy. In this sense, the Argentine supreme court has developed a series of institutional innovations, such as the admission of amici curiae and the holding of public hearings. The evaluation of these experiences allows nonetheless to identify an underlying conception of citizen participation focused on the intervention of specialists and the intermediation of lawyers and legal scholars. (shrink)

We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exists seem to be very rare. It is the main purpose of this paper to prove that, nevertheless, the (...) definition has a large number of important applications. Using the framework of TTE [40], we introduce computable metric spaces and computability on the compact subsets. We prove that every computable metric space has a c-proper c-admissible representation. We prove that Turing machine time complexity of a function computable relative to c-admissible c-proper representations has a computable bound on every computable compact subset. We prove that computably compact computable metric spaces have concise c-proper c-admissible representations and show by examples that many canonical representations are of this kind. Finally, we compare our definition with a similar one by Labhalla et al. [22]. Several examples illustrate the concepts. By these results natural and realistic definitions of computational complexity are now available for a variety of numerical problems such as image processing, integration, continuous Fourier transform or wave propagation. (shrink)

We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is Π20 source in the Borel hierarchy. Quasi-Polish spaces can be characterized within the framework of Type-2 Theory of Effectivity as precisely the countably based spaces (...) that have an admissible representation with a Polish domain. They can also be characterized domain theoretically as precisely the spaces that are homeomorphic to the subspace of all non-compact elements of an ω-continuous domain. Every countably based locally compact sober space is quasi-Polish, hence every ω-continuous domain is quasi-Polish. A metrizable space is quasi-Polish if and only if it is Polish. We show that the Borel hierarchy on an uncountable quasi-Polish space does not collapse, and that the Hausdorff–Kuratowski theorem generalizes to all quasi-Polish spaces. (shrink)

Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties (in logics) are exhibited. Consequently, RA and products of S5 as well as representable diagonal-free n-dimensional cylindric algebras, RDfn, are almost structurally complete but not structurally complete. In case of S5n a basis for admissible rules and the form of all passive rules are provided.

Consider a subjective expected utility preference relation. It is usually held that the representations which this relation admits differ only in one respect, namely, the possible scales for the measurement of utility. In this paper, I discuss the fact that there are, metaphorically speaking, two additional dimensions along which infinitely many more admissible representations can be found. The first additional dimension is that of state-dependence. The second—and, in this context, much lesser-known—additional dimension is that of act-dependence. The simplest implication (...) of their usually neglected existence is that the standard axiomatizations of subjective expected utility fail to provide the measurement of subjective probability with satisfactory behavioral foundations. (shrink)

We define a notion of reducibility for subsets of a second countable T 0 topological space based on relatively continuous relations and admissible representations. This notion of reducibility induces a hierarchy that refines the Baire classes and the Hausdorff–Kuratowski classes of differences. It coincides with Wadge reducibility on zero dimensional spaces. However in virtually every second countable T 0 space, it yields a hierarchy on Borel sets, namely it is well founded and antichains are of length at most 2. (...) It thus differs from the Wadge reducibility in many important cases, for example on the real line $${\mathbb{R}}$$ or the Scott Domain $${\mathcal{P}\omega}$$. (shrink)

Developments in the democratic theory of representation and deliberation enable renewed consideration of the ancient controversy over the proper place of rhetoric in politics. Rhetoric facilitates the making and hearing of representation claims spanning subjects and audiences divided in their commitments and dispositions. Deliberative democracy requires a deliberative system with multiple components whose linkage often needs rhetoric. Appreciation of these aspects of democracy exposes the limitations of categorical tests for the admissibility of particular sorts of rhetoric. Prioritization of (...) bridging over bonding rhetoric is a step in the right direction, while sometimes producing misleading results. A better systemic test asks whether or not rhetoric promotes an effective deliberative system linking competent and reflective actors. (shrink)

In searching for the origins of current conceptions of science in the history of physics, one encounters a remarkable phenomenon. A typical view today is that theoretical knowledge-claims have only relativized validity. Historically, however, this thesis was supported by proponents of a conception of nature that today is far from typical, a mechanistic conception within which natural phenomena were to be explained by the action of mechanically moved matter. Two of these proponents, Hermann von Helmholtz and his pupil Heinrich Hertz, (...) contributed significantly to the modernization of the conception of science. Paradigmatic for their common contribution to this development is the way in which they employed the concept of image. By considering the origin and the different meanings of this concept we may trace a line of development which begins with Helmholtz's original claim that a universally and forever valid theory provides a unique representation of nature. It continues with the realization that the status of scientific knowledge is capable of revision; and it arrives at Hertz's admission that a variety of theories over a domain of objects is possible, at least at times. (shrink)

In America today, the problem of achieving racial justice--whether through "color-blind" policies or through affirmative action--provokes more noisy name-calling than fruitful deliberation. In Color Conscious, K. Anthony Appiah and Amy Gutmann, two eminent moral and political philosophers, seek to clear the ground for a discussion of the place of race in politics and in our moral lives. Provocative and insightful, their essays tackle different aspects of the question of racial justice; together they provide a compelling response to our nation's most (...) vexing problem.Appiah begins by establishing the problematic nature of the idea of race. He draws on the scholarly consensus that "race" has no legitimate biological basis, exploring the history of its invention as a social category and showing how the concept has been used to explain differences among groups of people by mistakenly attributing various "essences" to them. Appiah argues that, while people of color may still need to gather together, in the face of racism, under the banner of race, they need also to balance carefully the calls of race against the many other dimensions of individual identity; and he suggests, finally, what this might mean for our political life.Gutmann examines alternative political responses to racial injustice. She argues that American politics cannot be fair to all citizens by being color blind because American society is not color blind. Fairness, not color blindness, is a fundamental principle of justice. Whether policies should be color-conscious, class conscious, or both in particular situations, depends on an open-minded assessment of their fairness. Exploring timely issues of university admissions, corporate hiring, and political representation, Gutmann develops a moral perspective that supports a commitment to constitutional democracy.Appiah and Gutmann write candidly and carefully, presenting many-faceted interpretations of a host of controversial issues. Rather than supplying simple answers to complex questions, they offer to citizens of every color principled starting points for the ongoing national discussions about race. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

This paper presents a theory of reasoning with evidence in order to determine the facts in a criminal case. The focus is on the process of proof, in which the facts of the case are determined, rather than on related legal issues, such as the admissibility of evidence. In the literature, two approaches to reasoning with evidence can be distinguished, one argument-based and one story-based. In an argument-based approach to reasoning with evidence, the reasons for and against the occurrence of (...) an event, e.g., based on witness testimony, are central. In a story-based approach, evidence is evaluated and interpreted from the perspective of the factual stories as they may have occurred in a case, e.g., as they are defended by the prosecution. In this paper, we argue that both arguments and narratives are relevant and useful in the reasoning with and interpretation of evidence. Therefore, a hybrid approach is proposed and formally developed, doing justice to both the argument-based and the narrative-based perspective. By the formalization of the theory and the associated graphical representations, our proposal is the basis for the design of software developed as a tool to make sense of the evidence in complex cases. (shrink)

Dès la simple annonce de la possibilité de cloner des humains, les moralistes ont formulé des argyuments contre l’introduction d’une telle pratique, la jugeant inadmissible. Or, un examen critique de ces arguments montre qu’il ne sont pas bien fondés, c’est-à-dire que, souvent, ils ne sont pas propres à être mis en avant en tant qu’arguments légitimes dans les débats sur ce qui est publiquement admissible, qu’ils reposent sur des prémisses erronées, ou qu’ils ne sont pas cohérents avec l’admissibilité d’autres (...) formes de reproduction humaine. Chacun des arguments en faveur de la proscription du clonage humain est analysé ici sous au moins l’un des aspects suivants : est-il en conformité avec les principes fondamentaux des démocraties modernes , est-il fondé sur les résultats incontestés et communément admis des recherches scientifiques, enfin, est-il cohérent avec l’attitude générale à l’égard d’autres formes de reproduction humaine. L’argument massue en faveur de la proscription du clonage humain est celui qui met en avant le devoir moral qui consiste à ne pas faire de tort à la future personne. Le résultat de cette réfutation des arguments éthiques traditionnels contre le clonage humain ne représentent pour autant pas une justification complète de ce dernier : elle montre tout simplement qu’il faudra trouver des arguments plus concluants si l’on veut faire interdire le clonage humain. (shrink)

It is important to have an adequate model of uncertainty, since decisions must be made before the uncertainty can be resolved. For instance, flood defenses must be designed before we know the future distribution of flood events. It is standardly assumed that probability theory offers the best model of uncertain information. I think there are reasons to be sceptical of this claim. I criticise some arguments for the claim that probability theory is the only adequate model of uncertainty. In particular (...) I critique Dutch book arguments, representation theorems, and accuracy based arguments. Then I put forward my preferred model: imprecise probabilities. These are sets of probability measures. I offer several motivations for this model of uncertain belief, and suggest a number of interpretations of the framework. I also defend the model against some criticisms, including the so-called problem of dilation. I apply this framework to decision problems in the abstract. I discuss some decision rules from the literature including Levi’s E-admissibility and the more permissive rule favoured by Walley, among others. I then point towards some applications to climate decisions. My conclusions are largely negative: decision making under such severe uncertainty is inevitably difficult. I finish with a case study of scientific uncertainty. Climate modellers attempt to offer probabilistic forecasts of future climate change. There is reason to be sceptical that the model probabilities offered really do reflect the chances of future climate change, at least at regional scales and long lead times. Indeed, scientific uncertainty is multi-dimensional, and difficult to quantify. I argue that probability theory is not an adequate representation of the kinds of severe uncertainty that arise in some areas in science. I claim that this requires that we look for a better framework for modelling uncertainty. (shrink)

The article takes as its starting point the work of Tomas Kulka on Kitsch and Art to further a philosophical move aiming at the very logical core of the question of art. In conclusion, the idea of Singular Rule is offered as capturing the defining logic of art. In so doing, the logical structure of a singular rule is uncovered and in that also the sense in which the idea of singular rule both explains and justifies the role that art (...) plays in our life. In his Kitsch and Art Tomas Kulka extends Karl Popper's refutation principle in science to the arts. He asks of a true work of art to be open to “refutation” by way of evaluating it against its own admissible alterations or variations. An admissible alteration according to Kulka is a change or a modification of the work that does not “shatter its basic perceptual gestalt”. In considering alterations that are aesthetically better, worse or neutral with respect to the original picture, Kulka offers us a rational reconstruction of key aesthetics concepts such as unity, complexity and intensity. His reconstruction will show that a work of kitsch does not qualify as art in direct analogy to a proposition that cannot qualify as scientific if it is not refutable. Kitsch cannot be “refuted” by any of its possible alterations as they are all of equal aesthetic value. This explains the aura of empty perfectionism that accompanies the experience of kitsch since the work of kitsch does not carry any promise for improvement nor does it show itself superior to any of its possible alterations. Notwithstanding Kulka’s novel analysis, its premise we must note is grounded in the work of art impressing on us a single basic perceptual gestalt with respect to which an alteration can qualify as admissible. But in acknowledging the possibility of a gestalt-switch or the fact that the work of art can impress on us a variety of mutually-exclusive perceptual gestalts, Kulka's analysis loses the logical anchor necessary for it to work. However, in what might look at first sight as an unrecoverable logical deficiency, we find an anchor to a novel analysis to the question of art. This is our analysis to the idea of art as a singular rule. Indeed, the concept of a singular rule - a rule onto itself which has exclusively itself as its own argument - must strike us as paradoxical. But in offering to reconstruct the work of art through the complementary concepts of background and figure - to match respectively the how and the what of the work - we are able to provide a structural resolution to the idea of singular rule as what defines art. In this we believe we deliver a definitive answer to the question of art. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

This article presents an approach to the semantics of non-distributive propositional logics that is based on a lattice representation theorem that delivers a canonical extension of the lattice. Our approach supports both a plain Kripke-style semantics and, by restriction, a general frame semantics. Unlike the framework of generalized Kripke frames, the semantic approach presented in this article is suitable for modeling applied logics, as it respects the intended interpretation of the logical operators. This is made possible by restricting (...) class='Hi'>admissible interpretations. (shrink)

Cet article nous met en garde contre une représentation biaisée, largement véhiculée, du débat actuel qui associe la défense d’une intégration du privé dans le système public à un désaveu du principe de l’égalité d’accès pour tous et comme une admission sans réserve d’un système injuste à « deux vitesses ». Or, il nous faut constater les conséquences négatives perverses de notre régime public limitant, dans les faits, l’utilisation optimale des ressources disponibles et l’accès aux soins, et reconnaître les avantages (...) d’une coexistence positive du privé et du public qui, outre les solutions pratiques qu’elle comporte, se conforme au droit fondamental de la liberté de choix des individus. Bien comprise et intelligemment orchestrée, l’intégration des sources privées de financement en amont ne remet pas en cause l’égalité d’accès aux soins en aval mais nous permettra, bien plutôt, de résorber la crise systémique qui paralyse le système de santé. (shrink)

Les philosophies et les sciences humaines sont des fabriques de l'homme, selon le double sens du génitif. Elles sont fabriquées par des hommes, mais elles fabriquent aussi l'homme, en tant qu'elles véhiculent une représentation de ce qui le constitue et (ou) du rapport qu'il entretient avec ce qui n'est pas lui (nature, société). La construction d'un discours impose en effet une grille de lecture, un découpage et une articulation du réel. Aussi, en dépit de l'effort que l'on rencontre parfois pour (...) élaborer des discours sans présupposé ontologique sur la nature humaine, une prise de position au sujet de l'homme semble en fait inévitable. Prendre par exemple pour point de vue celui de l'individu ou, au contraire, celui du tout social n'est pas neutre mais il s'agit déjà d'une façon de régler le rapport de l'un à l'autre. Et partir d'un homme ramené au statut d'agent rationnel visant à maximiser son profit est un choix massif qu'il convient d'analyser. Mais, s'il y a toujours, en philosophie morale et politique, ou dans les sciences humaines, des présupposés anthropologiques, on ne trouve pas forcément dans, ou à l'arrière-plan de tout discours sur les hommes, l'admission d'une essence générique de l'homme; autrement dit, le présupposé peut être aussi de contestation. Quoi qu'il en soit, il faut mettre en évidence un personnage abstrait, parfois assumé, parfois caché et parfois contesté donc, mais toujours là à sa façon, à défaut d'être à chaque fois opératoire. (shrink)

The article takes as its starting point the work of Tomas Kulka on Kitsch and Art to further a philosophical move aiming at the very logical core of the question of art. In conclusion, the idea of Singular Rule is offered as capturing the defining logic of art. In so doing, the logical structure of a singular rule is uncovered and in that also the sense in which the idea of singular rule both explains and justifies the role that art (...) plays in our life. In his Kitsch and Art Tomas Kulka extends Karl Popper's refutation principle in science to the arts. He asks of a true work of art to be open to “refutation” by way of evaluating it against its own admissible alterations or variations. An admissible alteration according to Kulka is a change or a modification of the work that does not “shatter its basic perceptual gestalt”. In considering alterations that are aesthetically better, worse or neutral with respect to the original picture, Kulka offers us a rational reconstruction of key aesthetics concepts such as unity, complexity and intensity. His reconstruction will show that a work of kitsch does not qualify as art in direct analogy to a proposition that cannot qualify as scientific if it is not refutable. Kitsch cannot be “refuted” by any of its possible alterations as they are all of equal aesthetic value. This explains the aura of empty perfectionism that accompanies the experience of kitsch since the work of kitsch does not carry any promise for improvement nor does it show itself superior to any of its possible alterations. Notwithstanding Kulka’s novel analysis, its premise we must note is grounded in the work of art impressing on us a single basic perceptual gestalt with respect to which an alteration can qualify as admissible. But in acknowledging the possibility of a gestalt-switch or the fact that the work of art can impress on us a variety of mutually-exclusive perceptual gestalts, Kulka's analysis loses the logical anchor necessary for it to work. However, in what might look at first sight as an unrecoverable logical deficiency, we find an anchor to a novel analysis to the question of art. This is our analysis to the idea of art as a singular rule. Indeed, the concept of a singular rule - a rule onto itself which has exclusively itself as its own argument - must strike us as paradoxical. But in offering to reconstruct the work of art through the complementary concepts of background and figure - to match respectively the how and the what of the work - we are able to provide a structural resolution to the idea of singular rule as what defines art. In this we believe we deliver a definitive answer to the question of art. (shrink)

This paper presents a sound and complete five-sided sequent calculus for first-order weak Kleene valuations which permits not only elegant representations of four logics definable on first-order weak Kleene valuations, but also admissibility of five cut rules by proof analysis.

Abstract.This paper is the first in a series of three which culminates in an ordinal analysis of Π12-comprehension. On the set-theoretic side Π12-comprehension corresponds to Kripke-Platek set theory, KP, plus Σ1-separation. The strength of the latter theory is encapsulated in the fact that it proves the existence of ordinals π such that, for all β>π, π is β-stable, i.e. Lπ is a Σ1-elementary substructure of Lβ. The objective of this paper is to give an ordinal analysis of a scenario of (...) not too complicated stability relations as experience has shown that the understanding of the ordinal analysis of Π12-comprehension is greatly facilitated by explicating certain simpler cases first.This paper introduces an ordinal representation system based on ν-indescribable cardinals which is then employed for determining an upper bound for the proof–theoretic strength of the theory KPi+ ∀ρ ∃ππ is π+ρ-stable, where KPi is KP augmented by the axiom saying that every set is contained in an admissible set. (shrink)

In formal theories of measurement meaningfulness is usually formulated in terms of numerical statements that are invariant under admissible transformations of the numerical representation. This is equivalent to qualitative relations that are invariant under automorphisms of the measurement structure. This concept of meaningfulness, appropriately generalized, is studied in spaces constructed from a number of conjoint and extensive structures some of which are suitably interrelated by distribution laws. Such spaces model the dimensional structures of classical physics. It is shown (...) that this qualitative concept corresponds exactly with the numerical concept of dimensionally invariant laws of physics. (shrink)

I would like to introduce the problematic to be addressed in this short article simply as follows. According to the majority of the modern interpreters of the Nyāya philosophy, the Naiyāyika-s are ontologically committed to an uncompromising direct realist theory of perception and to externalism both in epistemology and philosophy of mind. Computationalists, on the other hand, in their ontology, are frank or secret supporters of the view that what we cognize, even what we perceive, is representational. These two claims (...) appear to be opposed to each other. Naturally, the question arises: Is a computational account of intentional mental state, as proposed by Matilal, in his magnum opus Perception, admissible in the Navya-Nyāya framework? Though Matilal has not restricted the conundrum to Navya-Nyāya, the way he has analyzed the cognitive states are available only in the Navya-Nyāya literature. The main objective of this article is to strengthen Matilal’s position further with the help of some additional arguments from the Navya-Nyāya treatises. (shrink)

One might think that a healthy respect for the deliverances of experience would require us to give up any claim to nontrivial a priori knowledge. One way it might not would be if the very admission of something as an episode of experience required the use of substantive a priori knowledge -- if there were certain a priori standards that a representation had to meet in order to count as an experience, rather than as, say, a memory or daydream. (...) This paper argues that, surprisingly enough, we can find elements of this essentially Kantian line about experience even in the work of empiricists, such as John Locke and Bas van Fraassen. (shrink)

The ‘content view’, in slogan form, is ‘Perceptual experiences have representational content’. I explain why the content view should be reformulated to remove any reference to ‘experiences’. I then argue, against Bill Brewer, Charles Travis and others, that the content view is true. One corollary of the discussion is that the content of perception is relatively thin (confined, in the visual case, to roughly the output of ‘mid‐level’ vision). Finally, I argue (briefly) that the opponents of the content view are (...) partially vindicated, because perceptual error is due to false belief. (shrink)

Arthur Danto was an original thinker, and like all creative readers of the history of philosophy he invariably heard in those who caught his attention echoes, faint or raucous, of his own thoughts. Danto rejects the transparency theory as inadequate to how we talk about art and to artistic practice. For Danto, an artwork is not a mere representation, with a particular kind of content. Echoing a familiar theme from traditional aesthetic theory, Danto reminds us that “it is crucial (...) to distinguish the form of a representation from the content of the representation”. Sartre and Danto agree that artistic style and expression differ essentially from mundane character and meaning. By his own admission, Sartre's favored argumentative technique was to invest heavily in sharp categorical distinctions where common sense and philosophical refinement are inclined to see complexity and ambiguity. (shrink)

The nontechnical ability to identify or match argumentative structure seems to be an important reasoning skill. Instruments that have questions designed to measure this skill include major standardized tests for graduate school admission, for example, the United States-Canadian Law School Admission Test (LSAT), the Graduate Record Examinations (GRE), and the Graduate Management Admission Test (GMAT). Writers and reviewers of such tests need an appropriate foundation for developing such questions--they need a proper representation of phenomenological argumentative structure--for legitimacy, and because (...) these tests affect people's lives. This paper attempts to construct an adequate and appropriate representation of such structure, that is, the logical structure that an argument is perceived to have by mature reasoners, albeit ones who are untrained in logic. (shrink)

If we take the indexical, “I”, to be epistemologically identical across different contexts, as in, for example, it is the same “I” that at one moment observes, “I see a puddle of water on the floor”, and then, subsequently, exclaims, “I detect a leaking tap”, and, furthermore, we attribute not only self reference but self awareness in the use of the indexical, “I”, then a question arises as to how the “I” finds itself to be in reference to the speaker (...) in one context and not another. We cannot look to the ingredients of the context that the “I” inhabits for the answer because, based upon the above assumptions, the identity, or character, of the “I” stands independently of the context of the speaker. The answer, I argue, requires both the admission of the unreality of space and time, as well as an explanation as to why we have a sense of the here and now despite space and time being unreal. To this end, I turn to the juxtaposition of Kant’s a priori forms of inner sense and outer sense to explain how the cognitive faculty arrives at a sense of time and place despite the declared unreality of time and space. To sustain this explanation in the face of the problem of localisation, I draw on the full implications of Kant’s transcendental idealism in which the properties of time and space are not only withdrawn from things as they exist externally to the mind but also from mental representations insofar as mental representations can be said to exist in themselves. (shrink)

IntroductionScientific pluralism is generally understood in the backdrop of scientific monism. So is mathematical pluralism. Though there are many culture-dependent mathematical practices, mathematical concepts and theories are generally taken to be culture invariant. We would like to explore in this paper whether mathematical pluralism is admissible or not.Materials and methodsMathematical pluralism may be approached at least from five different perspectives. 1. Foundational: The view would claim that different issues within mathematics need support of different foundations, apparently incompatible with one (...) another. 2. Ontological: The world itself is dappled—the mathematical counterpart of which can be traced to the admission of non-Euclidean spaces and also in simultaneous acceptance of set-theoretic and category theoretic entities in the ontology of mathematics. 3. The third route is epistemological. It follows from the view that the nature of reality is so complex that different aspects of it require alternative modes of representation and explanation sometimes severally, sometimes simultaneously, e.g., classical, constructivist, computer-aided and different finitist mathematics can be used depending on the knowledge situation. 4. The fourth route is semantic. Fuzzy mathematics, we know, gives up bivalence in theory of truth, and ascribes truth to mathematical propositions in degrees. 5. The last one is Programmatic: for some, mathematical pluralism is a stance, a programme. It provides a framework which strikes at the root of cultural hegemony and nourishes a climate of intellectual humility and tolerance. It is not my intention to hold the brief of any of these versions. I just want to present to the readers a more or less complete picture of the scenario, though not an exhaustive one. ConclusionUnlike monism, mathematical pluralism does not rule out any possibility—even the possibility of having a unitary over-arching framework of interpretation remains as an open option. This paper highlights the fact that motivations for upholding pluralism in mathematics have been many and one can be a pluralist just by subscribing to any of the views listed above. (shrink)

The paper is devoted to the concise description of some Natural Deduction System (ND for short) for Linear Temporal Logic. The system's distinctive feature is that it is labelled and analytical. Labels convey necessary semantic information connected with the rules for temporal functors while the analytical character of the rules lets the system work as a decision procedure. It makes it more similar to Labelled Tableau Systems than to standard Natural Deduction. In fact, our solution of linearity representation is (...) rather independent of the underlying proof method, provided that some form of (analytic) cut is admissible. We will also discuss some generalisations of the system and compare it with other formalizations of linearity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 40.2 (2002) 273-274 [Access article in PDF] Book Review Aspects of Reason Paul Grice. Aspects of Reason. New York: Oxford University Press, 2001. Pp. xxxviii + 136. Cloth, $29.95. H. P. Grice made it clear in some of his best works that he was a friend of reason. In "Logic and Conversation," he suggested that it was plausible that the general principles regulating (...) conversation are instantiations of principles of reason. His friendship with reason is central to Aspects of Reason, a revision of the John Locke Lectures given at Harvard. Unfortunately, not far into reading Aspects of Reason, Wittgenstein's quip, "A philosophical problem has the form: 'I don't know my way about'" (Philosophical Investigations, paragraph 123) came to mind and it did not leave me for the rest of the book. (See Grice's own admission on page 4.)As best I can tell, Grice has two main goals. The first is to show that theoretical (or alethic) reasoning and practical reasoning are at bottom the same. Aristotle and Kant held the same thing, as Grice notes more than once. Pace many philosophers who hold that 'ought' does not mean the same thing in the sentences 'She ought to repay the loan' and 'He ought to be home by this time,' Grice holds that it does. That is, the practical 'ought' and the alethic 'ought' have the same sense or senses. While the thesis is clear enough, Grice's path to proving it is not sufficiently clear. He claims that the same general sense of 'rational acceptability' is involved in each sentence. This claim is not informative because the idea of acceptability is no clearer than the claim roughly that 'ought' has the same sense in both its alethic and practical uses. (The editor Richard Warner recognizes this, and tries to shore up Grice's view; see xvi-xvii.)The second of Grice's main goals is to prove that modals in both alethic and practical sentences are conditional. In effect, sentences that say something ought to be the case or ought to be done are conditioned on some premises from which the sentence is or may be logically derived. (Nonetheless, he thinks some sentences with modals are a priori and underived.)There are too many promissory and subjunctive gestures like this: "I suspect that such a reply could be constructed, but I do not have it at my fingertips (or tongue-tip), so I shall not try to produce it." And too many prepositional phrases, under the shared command of abstract nouns and verbs in the passive voice, march single file through the pages, e.g.: "a brief consideration of what modifications might be required or convenient for the employment of mode-markers in the representation of the content of thought (or acceptance)" (70). Some of the few substantive results seem to me to be prolix: Let us suppose it to be a fundamental psychological law that, ceteris paribus, for a creature x (of a sufficiently developed kind), no matter what A and B are, if x wills A and judges that if A, A only as a result of B, then x wills B. This I take to be a proper representation of "he who wills the end, wills the indispensable means"; and in calling it a fundamental law I mean that it is the law, or one of the laws, from which 'willing'... (94-5) and so on.A large part of the problem, I think, is that Grice does not pay much attention to the ordinary uses in which 'reason' or some cognate might be used nor to the ordinary circumstances [End Page 273] in which people are reasoning even if none of them uses the word 'reason' or its cognates. His brief excursion into uses of 'reason' are dominated by such stilted expressions as 'The fact that p was reason for thinking that q,' 'That p was reason to think that q," and 'He had reason to think that p but he seemed unaware of the fact' (39).The editor Richard... (shrink)

It is a commonplace in the foundations of physics, attributed to Kretschmann, that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics and mathematics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and (...) Polubarinov constructed spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, OP spinors resemble the orthonormal basis or tetrad formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is thus de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. As developed nonperturbatively by Bilyalov, OP spinors admit any coordinates at a point, but `time' must be listed first; `time' is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object. Important results on Lie and covariant differentiation are recalled and applied. The rather mild consequences of the coordinate order restriction are explored in two examples: the question of the conventionality of simultaneity in Special Relativity, and the Schwarzschild solution in General Relativity. (shrink)

Le monde se révèle à l'homme, comme matière, temps et esprit. L'on sait à présent que considérés dans l'espace et le temps, la terre est d'une extrême petitesse et l'homme un être éphémère. Une conception du monde qui prendrait l'homme pour centre et partirait de lui ne donnerait donc aucune garantie de probabilité. Pourtant elle est assez générale, accoutumés comme nous sommes à juger d'après les perceptions grossières des sens, qui trop souvent nous induisent en erreur. Selon les physiciens, la (...) formule mathématique réunissant les coördonnées du temps et de l'espace, serait la plus conforme à la représentation du monde matériel. Nous avançons ici l'hypothèse que le monde matériel répond effectivement à cette conception, et qu'il est donc un monde plongé dans un repos éternel, dans lequel nous voyageons, pour ainsi dire, avec notre temps. Grâce à cette hypothèse, la causalité, le miracle, la prévoyance de l'avenir, s'expliquent plausiblement. Manifestement le troisième principe, l'esprit, est à la fois en interaction avec la matière et indépendante d'elle (p.e. la télépathie). Cette action réciproque suppose une parenté partielle entre l'esprit et la matière. C'est pourquoi nous proposons une seconde hypothèse: l'esprit est une "facies" de la matière qui reste en dehors de la rigidité du monde considéré comme espace et temps. On a toujours considéré ces éléments spirituels comme étant des êtres spirituels, mais leur aspect anthropomorphique nous empêche de croire à leur existence réelle. Si nous identifions la partie spirituelle du corps humain avec l'homme spirituel, le problème du libre arbitre s'explique avec clarté. Seul le procès spirituel du libre arbitre est vraiment libre, mais la volonté ne peut réaliser aucun changement dans la substance purement matérielle. La conception d'une àme se logeant dans le corps matériel comme dans une maison, et qui par ses actions détermine sa demeure future ne s'accorde pas avec l'hypothèse du monde matériel-et-temporel-en-repos. Suivant nos conceptions humaines, nous avons imaginé des êtres spirituels animés d'une volonté libre. Mais alors il faut supposer une unité spirituelle supérieure, qui considère et qui décide. Or, cette conception étant anthropomorphique il est admissible qu'elle soit la véritable figuration du monde. La solution de ce problème pourrait être trouvée par une troisième hypothèse" selon laquelle il existerait un monde supérieur, dans lequel le monde-du-temps-et-de-l'espace fusionne avec un temps supérieur, auquel le nom de "temps spirituel" serait approprié. Seul, ce monde supérieur plongé dans un repos éternel peut nous expliquer d'une façon convaincante l'univers. Un monde d'une essence et d'une invariabilité éternelles, dans lequel le temps, capable d'agir pas des voies infiniment variées, introduit des événements innombrables, les processus spirituels étant effectués par le temps spirituel, les événements matériels par ce que nous sommes habitués à appeler "le temps". (shrink)

In a recent paper on Truth, Knowability and Neutrality Timothy Kenyon sets out to defend the coherence of a putative anti-realist truth-predicate, superassertibility, due to Wright (1992, 1999), against a number of Wright’s critics. By his own admission, the success of Kenyon’s defensive strategies turns out to hinge upon a realist conception of absolute warrant which conflicts with the anti-realist character of the original proposal, based, as it was, on a notion of defeasible warrant. Kenyon’s potential success in resisting Wright’s (...) critics brings a pyrrhic victory: either way, realism wins. Here I argue that the link between superassertibility and defeasible warrant can be restored in a way which clarifies the consistency of the pair, provided that the notion of inference to superassertibility is properly understood in logical terms. As one might expect, the requisite notion is not classical in character. As one might not expect, the notion cannot be properly construed in intuitionist terms either. Hence, I propose an alternative logical framework which, I believe, is at least formally adequate to the representation of superassertibility on the basis of defeasible warrant. The price to be paid for rejecting the ‘third way’ proposed here in favour of either of the two more traditional logical options is precisely that indicated by Kenyon’s discussion. (shrink)