Suppose L = { <,...} is any countable first order language in which < is interpreted as a linear order. Let T be any complete first order theory in the language L such that T has a κ-like model where κ is an inaccessible cardinal. Such T proves the Inaccessibility Scheme. In this paper we study elementary end extensions of models of the inaccessibility scheme.

Some opponents of the incommensurability thesis, such as Davidson and Rorty, have argued that the very idea of incommensurability is incoherent and that the existence of alternative and incommensurable conceptual schemes is a conceptual impossibility. If true, this refutes Kuhnian relativism and Kantian scepticism in one fell swoop. For Kuhnian relativism depends on the possibility of alternative, humanly accessible conceptual schemes that are incommensurable with one another, and the Kantian notion of a realm of unknowable things-in-themselves gives rise to the (...) possibility of humanly inaccessible schemes that are incommensurable with even our best current or future science. In what follows we argue that the possibility of incommensurability of either the Kuhnian or the Kantian variety is inescapable and that this conclusion is forced upon us by a simple consideration of what is involved in acquiring a concept. It turns out that the threats from relativism and scepticism are real, and that anyone, including Davidson himself, who has ever defended an account of concept acquisition is committed to one or the other of these two possibilities.1. (shrink)

In this paper, following an idea of Christophe Chalons. I propose a new kind of forcing axiom, the Maximality Principle, which asserts that any sentence varphi holding in some forcing extension $V^P$ and all subsequent extensions $V^{P\ast Q}$ holds already in V. It follows, in fact, that such sentences must also hold in all forcing extensions of V. In modal terms, therefore, the Maximality Principle is expressed by the scheme $(\lozenge \square \varphi) \Rightarrow \square \varphi$ , and is equivalent (...) to the modal theory S5. In this article. I prove that the Maximality Principle is relatively consistent with ZFC. A boldface version of the Maximality Principle, obtained by allowing real parameters to appear in φ, is equiconsistent with the scheme asserting that $V_\delta \prec V$ for an inaccessible cardinal δ, which in turn is equiconsistent with the scheme asserting that ORD is Mahlo. The strongest principle along these lines is $\square MP\!_{\!\!\!\!\!\!_{\!\!_\sim}}$ , which asserts that $MP\!_{\!\!\!\!\!\!_{\!\!_\sim}}$ holds in V and all forcing extensions. From this, it follows that $0^\#$ exists, that $x^\#$ exists for every set x, that projective truth is invariant by forcing, that Woodin cardinals are consistent and much more. Many open questions remain. (shrink)

In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the “generalized positive” theory GPK∞+. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK∞+ interprets the Kelley Morse class theory. Here we prove that GPK∞+ + ACWF and the Kelley-Morse class theory with the axiom of global choice and the axiom “On is ramifiable” are mutually interpretable. This shows that GPK∞+ + ACWF is a “strong” theory since (...) “On is ramifiable” implies the existence of a proper class of inaccessible cardinals. (shrink)

[What It’s Like, or What It’s About? The Place of Consciousness in the Material World] Summary: The book is both a survey of the contemporary debate and a defense of a distinctive position. Most philosophers nowadays assume that the focus of the philosophy of consciousness, its shared explanandum, is a certain property of experience variously called “phenomenal character,” “qualitative character,” “qualia” or “phenomenology,” understood in terms of what it is like to undergo the experience in question. Consciousness as defined in (...) terms of its phenomenal aspect is often called “phenomenal consciousness.” The major issue that occupies most thinkers is whether this phenomenal character happens to be a physical property, or whether it is rather sui generis. Those who believe the former are materialists; those who conclude the latter are dualists. As the currently dominant metaphysic is materialism – also sometimes called physicalism – the challenge appears to be to slot phenomenal properties among the physical properties that ultimately make up the world. David Chalmers argued powerfully that we can go very far in situating many mental properties in the physical world – namely, the properties that can be understood in functional terms – but that phenomenal properties resist such a treatment. Chalmers calls this “the hard problem” of consciousness. But there are also some quite powerful positive arguments for dualism. The two most influential ones are the modal argument, also offered by Chalmers, and the knowledge argument invented by Frank Jackson. Chalmers invites us to conceive of creatures that are exactly like human beings – physically, functionally, behaviorally – only bereft of phenomenal consciousness. If such creatures are conceivable, says Chalmers, they are metaphysically possible. And if they are metaphysically possible, materialism is false. Jackson, for his part, suggests we imagine Mary who has spent her entire life inside a black-and-white room and has seen the world through a black-and-white TV screen. But she also happens to know everything there is to know about the physics of color. And yet, Jackson suggests that once Mary is finally released from her room and sees a lawn outside, she learns something new: that this is what it is like to experience green color. The current work on consciousness is by and large characterized by attempts to answer these two dualistic arguments. I try to make sense of the positions within the domain of philosophy of consciousness by means of two major distinctions that mutually intersect. First, there is a distinction between dualism and materialism. An apparent third alternative currently on offer, the so-called Russellian monism, is unstable, collapsing into either dualism (panpsychism) or materialism (Russellian physicalism). Materialism comes in two main flavors: either the a posteriori physicalism, which detects an epistemic gap between phenomenal and physical truths, hence denying that the former could be derived from the latter; or the a priori physicalism, which does not acknowledge any such obstacle. The second major distinction is between phenomenism and representationalism. It’s true that Ned Block, who introduced this contrast, meant to distinguish between two kinds of materialism. But I believe that the distinction actually intersects the one between materialism and dualism. We thus arrive at a table with six slots, representing six main positions in the philosophy of consciousness: (1) dualist phenomenism (Chalmers, the early Jackson, and Tyler Burge); (2) dualist representationalism (René Descartes); (3) aposteriori materialist phenomenism (Block); (4) a posteriori materialist representationalism (Michael Tye, Fred Dretske, David Rosenthal); (5) a priori materialist phenomenism (David Lewis); and (6) a priori materialist representationalism (Daniel Dennett, Derk Pereboom). However, this scheme is in fact somewhat misleading. It is true that Dennett is usually classified as an apriori materialist (or, more precisely an apriori materialist representationalist), but I believe that needs to be corrected. In order to understand why, I first analyze varieties of materialist representationalism in detail, in particular various construals of phenomenal character in terms of representation, or intentionality, which includes a discussion of the identity of its content (the issue of externalism). By contrast, Dennett rejects the concept of phenomenal character. Consciousness has no intrinsic, publicly inaccessible properties. On that ground, Dennett builds an empirical, fully functionalist theory of consciousness, which he also tries to integrate within a general Darwinian framework. From that point of view, one can contrast Dennettian and representationalist views on the issue of animal consciousness. In addition to his rejection of phenomenal character, Dennett also abstains from the regular metaphysical departure point of regular materialism. He does not so much ask how an enigmatic property of consciousness fits an antecedently characterized world, but rather how far we can investigate all aspects of the world, including consciousness, using the scientific method. He is thus a methodological naturalist, rather than a metaphysical materialist. While this approach removes obstacles to the science of consciousness, it does not solve what might be called “the hardest problem” – of intentionality, not phenomenal consciousness. The hardest problem consists in the fact that our intentional discourse involves conflicting commitments that prevent a coherent metaphysic of representational states. However, it does not follow that we should give up on this discourse as a theoretical means of reduction as well as a practical tool of explanation. But it might be that intentional discourse is a somewhat pseudo one. (shrink)

Always connect—that is the imperative of today’s media. But what about those moments when media cease to function properly, when messages go beyond the sender and receiver to become excluded from the world of communication itself—those messages that state: “There will be no more messages”? In this book, Alexander R. Galloway, Eugene Thacker, and McKenzie Wark turn our usual understanding of media and mediation on its head by arguing that these moments reveal the ways the impossibility of communication is integral (...) to communication itself—instances they call excommunication. In three linked essays, _Excommunication_ pursues this elusive topic by looking at mediation in the face of banishment, exclusion, and heresy, and by contemplating the possibilities of communication with the great beyond. First, Galloway proposes an original theory of mediation based on classical literature and philosophy, using Hermes, Iris, and the Furies to map out three of the most prevalent modes of mediation today—mediation as exchange, as illumination, and as network. Then, Thacker goes boldly beyond Galloway’s classification scheme by examining the concept of excommunication through the secret link between the modern horror genre and medieval mysticism. Charting a trajectory of examples from H. P. Lovecraft to Meister Eckhart, Thacker explores those instances when one communicates or connects with the inaccessible, dubbing such modes of mediation “haunted” or “weird” to underscore their inaccessibility. Finally, Wark evokes the poetics of the infuriated swarm as a queer politics of heresy that deviates from both media theory and the traditional left. He posits a critical theory that celebrates heresy and that is distinct from those that now venerate Saint Paul. Reexamining commonplace definitions of media, mediation, and communication, _Excommunication_ offers a glimpse into the realm of the nonhuman to find a theory of mediation adequate to our present condition. (shrink)

Process philosophy was on the periphery of academic thinking for much of the twentieth century. Whereas the focus of intellectual development was for the most part on scientific analysis, process philosophy argued for a more encompassing synthesis as well. Although the drive — the corpus delecti of formal research assessment funding exercises — for separate, discrete and latterly measurable bodies of knowledge arrived at from within increasingly autonomous academic disciplines has undoubtedly led to significant advance in many areas it has, (...) at the same time, rendered opaque the interconnectedness of all things and thereby diminished the perceived value of ideas developed in one field, in terms of their relevance to others. At its heart, this trend has arisen from a reliance upon a metaphysics of stasis; things are constant and can thus be analysed and re-analysed into ever finite and thoroughly separate elements. In contrast, a metaphysics of process suggests that change and interconnectedness are the predominant characteristics of nature. As such, it provides new directions for contemporary thought by enabling the development of ideas via an otherwise unavailable framework of coherence and comprehensiveness. One area in which process thought has proved helpful is organisation studies. This paper examines the role of interpersonal trust in organisations from a Whiteheadian perspective. As such, it aims to show how Whitehead’s thinking can be applied to complex human experiences in such a way as to reveal the nature of the processes that go toward their development. The paper begins with a theoretical explication of trust derived from the contemporary social scientific literature. The development of trust, a key component of human society, is argued to be a subjective and processual phenomenon. In the light of this discussion the paper uses appropriate elements of Whitehead’s Philosophy of Organism to provide a description of trust’s development in an individual for another individual, and its consequent impact on their cooperative behaviour. It thereby attempts to uncover the hitherto inaccessible micro-processes that go towards the development and continuation of interpersonal trust in organisational settings. In so doing, the paper seeks to demonstrate the explanatory power of an aspect of Whitehead’s work, his elucidation of human ‘emotional experience’, that is perhaps too often overlooked as a comparatively minor and non-technical use of his categoreal scheme. (shrink)

Based on the reception of Emmanuel Levinas philosophy in the English-speaking world, the paper highlights some tendencies in reading and commenting on classical philosophical works that have been the focus of attention for a long time. The author makes a suggestion that we can find persistent but nonetheless dynamic, patterns of commenting and interpreting. The first wave of Levinas studies was apologetic and laudatory. Its main task was to introduce new concepts, i.e. to paraphrase. The second wave was much more (...) appropriative and critical. In this period, the scholars tried to apply the philosophy of the Other to existing problems or they tried to resolve the paradoxes that were the products of apologetic readings. The today’s third wave recreates and readjusts interpretive strategies inherent to the first and second wave. To explain this dynamics of reading, the paper introduces a normative scheme that consists of three regulative principles – “faithfully”, “truthfully”, and “ethically”. Due to this tripartite opposition, in which “faithfully” refers to fidelity to an original, “truthfully” refers to the search for universal truth, and “ethically” refers to the inaccessibility for an ego to grab hold of a text of another person, commenting grows intensive. In addition, the opposition of “faithfully” and “truthfully” demonstrates some liberty in such, to some extent, involuntary practice as commenting. This reflexion helps identify the current phase of commenting on classical texts and the intentions of readers and commentators. What is more, it provides justifications for innovative readings of Levinas’ oeuvre as well as the texts of other great philosophers. (shrink)

This thesis presents a proof theoretical investigation of some constructive set theories with restricted set induction. The set theories considered are various systems of Constructive Zermelo Fraenkel set theory, CZF ([1]), in which the schema of $\in$ - Induction is either removed or weakened. We shall examine the theories $CZF^\Sigma_\omega$ and $CZF_\omega$, in which the $\in$ - Induction scheme is replaced by a scheme of induction on the natural numbers (only for  formulas in the case of the (...) first theory, for arbitrary formulas in the second theory). Of particular interest is the system CZF− + INAC, which is obtained by removing $\in$ - Induction and by adding an axiom, INAC, for inaccessible sets. The main outcome is that CZF− + INAC is a predicative set theory with inaccessible sets, its proof theoretic ordinal being $\Gamma_0$. The proof theoretic strength of these theories, has been determined by means of proof theoretical reductions. The upper bounds have been obtained by interpreting the set theories in classical theories of (iterated) inductive definitions with ordinals. A significant feature of these interpretations is that they are realizability interpretations, which make an indirect use of Aczel’s interpretation of CZF in Martin Löf type theory, and, in the case of CZF− + INAC, also employ a maximum bisimulation relation to represent equality between sets. The lower bounds are obtained by interpreting appropriate subsystems of intuitionistic second order arithmetic in the set theories. At the conclusion of the thesis we present work unrelated to the previous chapters. It is a preliminary study of the constructible hierarchy in CZF. We begin by formalizing the notion of definability in constructive set theory and then introduce Gödel’s L in CZF. We prove that intuitionistic L is a model of a subsystem of CZF strong enough to include intuitionistic Kripke-Platek set theory, and also that L is a model of the axiom of constructibility, provably in CZF. (shrink)

We examine what happens if we replace ZFC with a localistic/relativistic system, LZFC, whose central new axiom, denoted by Loc(ZFC), says that every set belongs to a transitive model of ZFC. LZFC consists of Loc(ZFC) plus some elementary axioms forming Basic Set Theory (BST). Some theoretical reasons for this shift of view are given. All ${\Pi_2}$ consequences of ZFC are provable in LZFC. LZFC strongly extends Kripke-Platek (KP) set theory minus Δ0-Collection and minus ${\in}$ -induction scheme. ZFC+ “there is (...) an inaccessible cardinal” proves the consistency of LZFC. In LZFC we focus on models rather than cardinals, a transitive model being considered as the analogue of an inaccessible cardinal. Pushing this analogy further we define α-Mahlo models and ${\Pi_1^1}$ -indescribable models, the latter being the analogues of weakly compact cardinals. Also localization axioms of the form ${Loc({\rm ZFC}+\phi)}$ are considered and their global consequences are examined. Finally we introduce the concept of standard compact cardinal (in ZFC) and some standard compactness results are proved. (shrink)

The perception/planning–control conception has a direct predecessor in a cognitive/sensorimotor scheme, where the cognitive branch includes Glover's perception and planning functions. The sensorimotor branch corresponds to Glover's control function. The cognitive/sensorimotor scheme, like the perception/planning–control scheme, differentiates between motor planning and direct motor control, which is inaccessible to awareness or to long-term memory.

This paper explores two issues: (1) how our thought about nature could reflect natural processes, and (2) how our thoughts about nature are connected with each other. It argues, first, that the standard ways philosophers try to make sense of the notion that thought is separate from nature cannot be made intelligible and, second, that the conceptual schemes used to grasp nature fall broadly into two groups each of which presupposes the other, even though the two are incompatible. Although these (...) conclusions pose obstacles to the rationality of nature, the paper concludes by arguing for some significant degree of rationality of nature and explaining what this means for science. In brief, our ability to have an experience of nature and, especially, to connect disparate features of that experience with each other presupposes some intrinsic connections within nature itself, even if these are inaccessible to us. (shrink)

In his book Objectivity, William Earle has attempted to give the phenomenologically intentional aspect of awareness its philosophical due. To sharpen the issues, it may be well to review some of the main points of his treatment. Earle combines a realist view of the object of awareness with a partially Hegelian conception of awareness. Awareness, according to Earle, involves three stages, recognizable as thesis, antithesis and synthesis. The thesis is made up of the subject and object intertwined, and not yet (...) distinguished from each other. The antithesis is constituted by a recoil of the subject from the object back upon itself. Earle terms this recoil a primary reflexivity of the subject, which, though ingredient in awareness, is not yet sufficient to constitute awareness. Whereas for Hegel the reflexive recoil of the subject back upon itself constitutes the object for the subject, for Earle this recoil of the subject in no way creates its object. The reflexive withdrawal of the subject from the object simply separates two metaphysically distinct entities. Hegel's separation of subject and object alienates the subject from himself; Earle's separation of subject and object alienates the subject from the world. But for both Earle and Hegel, knowledge of the object does not take place until a redemptive synthesis of subject and object occurs. In the Hegelian scheme the redemptive synthesis unifies the subject with himself. According to Earle, however, the redemptive synthesis achieves only knowledge of the object as other than the subject; that is, it is the object as distant from, therefore intended by, the subject that is known. The final stage in knowledge is thus constituted by a positive approach of the subject to a metaphysically distinct object. Earle must therefore insist, as he does, that immediate self-awareness is, in principle, impossible. He characterizes his own method as retrospectively reflexive, very different from the primary reflexivity involved in the constitution of awareness. To justify the validity and possibility of this retrospective reflexivity, he argues for the metaphysical identity of a subject forever outside of and beyond its own acts, and, of course, inaccessible to knowledge in a way that the world independent of the subject is not. (shrink)

ZusammenfassungDas Spektrum der dogmatischen Sündenlehre spannt sich zwischen zwei Polen auf: Auf der einen Seite wird bei der individuellen Sündenerfahrung angesetzt, um die verstörende Wirklichkeit des Schuldbewusstseins einzuholen. Exemplarisch dafür kann die Sündenlehre von Julius Müller gelten. Auf der anderen Seite wird der Ausgang bei der Selbstoffenbarung Gottes genommen, um der dem individuellen Sündenbewusstsein gerade unzugänglichen Radikalität der Sünde Rechnung zu tragen. Exemplarisch dafür kann die Sündenlehre von Karl Barth gelten. Bei näherer Betrachtung wird nun deutlich, dass beide Ansätze jeweils (...) ein elementares Grundanliegen der Sündenlehre zur Geltung bringen, das von der anderen Seite nicht eingeholt werden kann. Beide Ansätze sind insofern für sich allein defizitär und auf eine komplementäre Ergänzung angewiesen, ohne diese doch in den eigenen Entwurf integrieren zu können. Das irreduzible Gegenüber der Sündenlehren von Müller und Barth verweist damit auf die Notwendigkeit einer »doppelten Buchführung« in der Dogmatik.SummaryWhen approaching the doctrine of sin there are two standpoints from which one may proceed: the first begins with the individual experience of sin and highlights the unsettling reality of a guilty conscience. Here the conception of Julius Müller can be seen as an example for this approach. The other approach begins with the self-revelation of God; this revelation is understood to account for the radical nature of sin, for without this revelation the full understanding of sin would be inaccessible to the individual consciousness. Here the conception of Karl Barth can be seen as an example for this approach. On closer examination it appears that both conceptions assert an elementary concern of the doctrine of sin, which cannot be recovered by the other conception. Furthermore, when held in isolation from one another, both dispositions appear to be deficient for they depend on a complementary endorsement; however, they cannot integrate this complementary endorsement into their own scheme. The irreducible contrast between the doctrines of Müller and Barth thus implies the need of a »double accounting« in dogmatics. (shrink)

We introduce Broad Infinity, a new set-theoretic axiom scheme based on the slogan “Every time we construct a new element, we gain a new arity.” It says that three-dimensional trees whose growth is controlled by a specified class function form a set. Such trees are called broad numbers. Assuming AC (the axiom of choice) or at least the weak version known as WISC (weakly initial set of covers), we show that Broad Infinity is equivalent to Mahlo’s principle, which says (...) that the class of all regular limit ordinals is stationary. Assuming AC or WISC, Broad Infinity also yields a convenient principle for generating a subset of a class using a “rubric” (family of rules); this directly gives the existence of Grothendieck universes, without requiring a detour via ordinals. In the absence of choice, Broad Infinity implies that the derivations of elements from a rubric form a set; this yields the existence of Tarski-style universes. Additionally, we reveal a pattern of resemblance between “wide” principles, that are provable in ZFC, and “broad” principles, that go beyond ZFC. Note: this paper uses a base theory that is weaker than ZF but includes classical first-order logic and Replacement. (shrink)

The paper investigates inaccessible set axioms and their consistency strength in constructive set theory. In ZFC inaccessible sets are of the form Vκ where κ is a strongly inaccessible cardinal and Vκ denotes the κth level of the von Neumann hierarchy. Inaccessible sets figure prominently in category theory as Grothendieck universes and are related to universes in type theory. The objective of this paper is to show that the consistency strength of inaccessible set axioms heavily depend on the context in (...) which they are embedded. The context here will be the theory CZF− of constructive Zermelo–Fraenkel set theory but without -Induction . Let INAC be the statement that for every set there is an inaccessible set containing it. CZF−+INAC is a mathematically rich theory in which one can easily formalize Bishop style constructive mathematics and a great deal of category theory. CZF−+INAC also has a realizability interpretation in type theory which gives its theorems a direct computational meaning. The main result presented here is that the proof theoretic ordinal of CZF−+INAC is a small ordinal known as the Feferman–Schütte ordinal Γ0. (shrink)

We construct models for the level-by-level equivalence between strong compactness and supercompactness containing failures of the Generalized Continuum Hypothesis at inaccessible cardinals. In one of these models, no cardinal is supercompact up to an inaccessible cardinal, and for every inaccessible cardinal $\delta $, $2^{\delta }\gt \delta ^{++}$. In another of these models, no cardinal is supercompact up to an inaccessible cardinal, and the only inaccessible cardinals at which GCH holds are also measurable. These results extend and generalize earlier work of (...) the author. (shrink)

We show that a coding principle introduced by J. Moore with respect to all ladder systems is equiconsistent with the existence of a strongly inaccessible cardinal. We also show that a coding principle introduced by S. Todorcevic has consistency strength at least of a strongly inaccessible cardinal.

This paper is the first in a series whose objective is to study notions of large sets in the context of formal theories of constructivity. The two theories considered are Aczel's constructive set theory and Martin-Löf's intuitionistic theory of types. This paper treats Mahlo's π-numbers which give rise classically to the enumerations of inaccessibles of all transfinite orders. We extend the axioms of CZF and show that the resulting theory, when augmented by the tertium non-datur, is equivalent to ZF plus (...) the assertion that there are inaccessibles of all transfinite orders. Finally, the theorems of that extension of CZF are interpreted in an extension of Martin-Löf's intuitionistic theory of types by a universe. (shrink)

In Türkiye, although induced abortion (I/A) is legal and recognized as a free public health service within the first ten weeks of pregnancy, reports and qualitative studies indicate that women encounter difficulties accessing I/A services in public health institutions. This paper suggests, based on various local reports and studies, that the denial of I/A in the last decade is, in part, attributable to various reproductive governance mechanisms that create a chilling effect on clinicians and institutions, making them unwilling to perform (...) or provide abortions. Finally, based on a socio‐political analysis of the status quo, this paper emphasizes that when discussing the inaccessibility of I/A or any topic related to reproductive ethics, it is essential that bioethical discussions must recognize and consider the role of politics and the reproductive governance mechanisms at play in reproductive healthcare, as they have significant ethical implications for the access and provision of these services. This approach allows for a deeper exploration of the less visible ethical implications of restrictive policies on legal reproductive services. (shrink)

Throughout history philosophers have relentlessly pursued what may be called "inaccessible domains." This book explores how the traditions of existential phenomenology relate to Freudian psychoanalysis. A clear, succinct, and systematic account of the philosophical presuppositions of psychoanalytic theory and practice, this work offers a deeper and richer understanding and appreciation of Freudian thought, as well as its antecedents and influences. With its unique perspective on Freud's work, Apprehending the Inaccessible puts readers in a better position to appreciate his contributions and (...) evaluate the relationship between his and other philosophical world views. The authors, both of whom have extensive backgrounds in philosophy and psychology, present balanced critical analyses of crucial developments in, for example, the evolution of the Freudian notion of the unconscious, and the engagement of existential phenomenology with Freudian psychoanalysis. Askay and Farquhar then consider-often for the first time-individual thinkers' reflections on and interpretations of Freud, ranging from the primary figures in existential phenomenology to the most prominent figures in the existential psychoanalytic movement. Even as their work offers a new approach to Freudian thought, it reasserts the importance of alternative views found in existential phenomenology as those views pertain to psychoanalysis and the question of apprehending the inaccessible. (shrink)

In liberal democracies it is now a commonplace that public debates in the institutionalized political sphere should involve only arguments and reasons that are in principle intelligible, accessible and acceptable to all citizens. Many political theorists take the view that religious arguments and reasons do not meet these requirements. My article interrogates this widely held position, considering each of the three requirements in turn. Motivating my discussion is the view that religious beliefs and practices should not be regarded as essentially (...) private matters, with discussion of their validity confined to some antecedently demarcated sphere. Rather, claims made for the validity of religious beliefs and practices should be thematized and evaluated in public processes of deliberation, opening them to possible challenges from other citizens, irrespective of whether these other citizens are religious believers. My article offers a freedom-based argument for this position. (shrink)

In this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of 2κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^\kappa$$\end{document}, κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa$$\end{document} inaccessible, and study its associated ideal of null sets and notion of measurability. This issue was addressed by Shelah ), arXiv:0904.0817, Problem 0.5) and concerns the definition of a forcing which is κκ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa ^\kappa$$\end{document}-bounding, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,>\,$$\end{document}cov_λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\_\lambda$$\end{document}), arXiv:0904.0817, Problem 0.5), and in this paper we independently reprove this result by using a different type of construction. This also contributes to a line of research adressed in the survey paper :439–456, 2016). (shrink)

The religious inquirer is, however, in a tough spot, for she is subject to norms that it appears she cannot jointly satisfy. On the one hand, there are norms for the conduct of one's doxastic life, which do not emanate from any particular religious tradition, that enjoin us to be conscientious in our believings. In her view, conforming to these norms does not license having religious beliefs: there are simply too many evidential impediments to having such beliefs, ranging from deep (...) theoretical challenges to the fundamental religious claims to questions about the reliability of the fundamental religious texts and traditions. Call these norms, which the religious inquirer holds that religious belief does not satisfy, external epistemic norms. On the other hand, there are norms that emanate from within the religious traditions themselves that speak against engaging in a religious way of life in order to enjoy its considerable goods by doing such things as playing the role of a believer or going through the ritualistic motions. Instead, these norms seem to call for genuine faith, which is understood to be something approximating what the true believer has. Call these norms, which place restrictions on how one could legitimately engage in a religious way of life, the internal religious norms. (shrink)

Abstract:In this article, Kundakunda's theory of omniscience is defended using formal principles derived from set theory. More precisely, analogous features in the work of Jain mystic Kundakunda and the German mathematician Georg Cantor are described, demonstrating that both thinkers demanded an independently existent, transcendental Absolute to render consistent their own systems of thought. Both of their projects entailed resolving the formal quandary of inaccessibility, or the inability for any sequential, determinate objectifications to ever mereologically sum up to a genuine (...) 'Absolute'—that is, a 'gestalt' that is 'more than the sum of its parts'. (shrink)

In this paper it is shown that the meet-inaccessible degrees are dense in R. The construction uses an 0''-priority argument. As a consequence, the meet-inaccessible degrees and the meet-accessible degrees give a partition of R into two sets, either of which is a nontrivial dense subset of R and generates R - {0} under joins (thus an automorphism base of R).

We prove optimal lower bounds on the computation time for several well-known test problems on a quite realistic computational model: the random access machine. These lower bound arguments may be of special interest for logicians because they rely on finitary analogues of two important concepts from mathematical logic: inaccessible numbers and order indiscernibles.

The usual problems of measurement and its meaning are complicated and magnified when the object of study is in principle and in fact inaccessible. When a phenomenon occurs in a place where our instruments cannot reach, what can the relation between the instrument, its reading, and the phenomenon be? This essay asks how researchers have addressed questions about inaccessible processes of Earth's magnetic field on the surface, at the edge of space and under its surface. This case takes us beyond (...) simple contrasts of inductive and deductive methods, or field sciences versus basic sciences, to a messier, more nuanced view of inherently complex sciences. The article focuses on investigations of Earth's magnetism and electricity, but its perspectives are applicable to many areas of recent science. (shrink)

Argues, contra Dummett, that the platonist need not be any more committed than the intuitionist to the notion that there are arithmetical truths in principle inaccessible to any finite intelligence.

We show the following results on Wainer's notation for a minimal subrecursive inaccessible ordinal τ: First, we give a constructive proof of the collapsing theorem. Secondly, we prove that the slow-growing hierarchy and the fast-growing hierarchy up to τ have elementary properties on increase and domination, which completes Wainer's proof that τ is a minimal subrecursive inaccessible. Our results are obtained by showing a strong normalization theorem for the term structure of the notation. MSC: 03D20, 03F15.

Let T be the standard Veblen 1908 ordinal notation system for Γ0 as defined, for example, in Schütte's 1977 textbook [13] on Proof Theory. We define a slight modification of the standard assignment of fundamental sequences for the limit ordinals in T and prove that Γ0 is subrecursively inaccessible for this assignment, i.e. the induced slow and fast growing hierarchy match up at Γ0 for the first time.The results of this paper also indicate that φε00 may be considered as a (...) new slow growing ordinal of PA in the sense that the induced slow growing hierarchy up to φε00 classifies the PA-provablyrecursive functions.We show how the results of this paper can be used to bui d a subrecursive hierarchyover the predicative ordinals in the spirit of Wainer's 1970 abstract [16 ]. (shrink)

The claim that language is in principle inaccessible to consciousness may look counterintuitive but is not as challenging as finding an answer to the subsequent question of why that must be the case -- if language is a function that is in the service of consciousness and we cannot imagine why language would have existed at all without the existence of consciousness. On the one hand, language is the cognitive capacity that seems best fit to support consciousness in its monitoring (...) and control functions; on the other hand, language learning (learning the rules of one's own language), language structure and language processing turn out upon closer scrutiny to be in principle inaccessible to consciousness. I present a set of arguments in favour of the thesis that language is in principle inaccessible to consciousness on the basis of a set of asymmetries between sentence structure and the structure of consciousness. If the thesis in question is on the right track, we have to face two basic problems. The first deals with linguistics method(s), namely how can we study a very complex mental phenomenon like language if it is not available to introspection? The second problem is related to the question put in the title of this article. The suggested answer is along the lines that inaccessibility of language to consciousness enables a cognitive architecture that can run a Cartesian theatre. (shrink)

This paper offers a critical phenomenological view of the concept of access intimacy, a term coined by disability justice advocate Mia Mingus. Access intimacy refers to a mode of relation between disabled people or between disabled and non-disabled people that can be born of concerted cultivation or instantly intimated and centrally concerns the feeling of someone genuinely understanding and anticipating another’s access needs. Putting in conversation this notion of intimacy with Kym Maclaren’s critical phenomenological account of intimacy, I show how (...) accessibility is not about what one person or institution can do for another but involves an ongoing, interpersonal process of relating and taking responsibility for our inevitable encroachment on one another in ways that enhance one another’s freedom. (shrink)

The distinction between uninformed learning (type-1) and learning based on recoding using prior information (type-2) helps to clarify some long-standing psychological problems, including misunderstanding of mathematics by children, the need for active construction of concepts in cognitive development, and the difficulty of configural learning tasks. However, an alternative to recoding some type-2 tasks is to represent the input as separate dimensions, which are processed jointly. This preserves the original structure, but is subject to processing capacity limitations.

Este artigo visa compreender como os filtros embelezadores do Instagram Stories influenciam a percepção de beleza de seus usuários. Estudos informam que a prática de selfies tem orientado jovens em busca de cirurgias e procedimentos estéticos. Frente a isso, a questão de pesquisa é: de que forma os filtros embelezadores do Instagram Stories interferem na percepção de beleza dos seus usuários? Para tanto, recorre-se à bibliografia sobre plataformas digitais, Instagram Stories e selfies, além de um estudo empírico sobre os filtros (...) embelezadores nessa plataforma e aplicação de questionário. Como resultado, percebe-se, no Instagram, uma dinâmica de performance com selfies que se ajusta com a emergência de uma percepção beleza (pele lisa, nariz fino, lábios volumosos) reconhecida pelas usuárias e desejada como resultado de intervenções cirúrgicas e de procedimentos estéticos. (shrink)