We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a substitution and arrive at operation algebras that are not lattices what proves the claim. We devise algorithms and programs which write down any two-variable expression in an orthomodular lattice by means of classical and quantum operations in an identical form. Our results show that (...) lattice structure and classical operations uniquely determine quantum logic underlying Hilbert space. As a consequence of our result, recent proposals for a deduction theorem with quantum operations in an orthomodular lattice as well as a, substitution of quantum operations for the usual standard Hilbert space ones in quantum logic prove to be misleading. Quantum computer quantum logic is also discussed. (shrink)

Philologus, founded in 1846, is one of the oldest and most respected periodicals in the field of Classics. It publishes articles on Greek and Latin literature, historiography, philosophy, history of religion, linguistics, reception, and the history of scholarship. The journal aims to contribute to our understanding of Greco-Roman culture and its lasting influence on European civilization. The journal Philologus, conceived as a forum for discussion among different methodological approaches to the study of ancient texts and their reception, publishes original scholarly (...) contributions with a strong international focus. Publications languages are: German, English, Italian, French. As of 2014 the publication of supplementary volumes will be resumed. The series Philologus. Supplemente / Philologus. Supplementary Volumes will publish monographs and edited volumes pertaining to all aspects of the study of ancient literature and its reception, with a special focus on topics concerning literary theory, philosophy and the history of scholarship from an interdisciplinary perspective. (shrink)

Philologus, founded in 1846, is one of the oldest and most respected periodicals in the field of Classics. It publishes articles on Greek and Latin literature, historiography, philosophy, history of religion, linguistics, reception, and the history of scholarship. The journal aims to contribute to our understanding of Greco-Roman culture and its lasting influence on European civilization. The journal Philologus, conceived as a forum for discussion among different methodological approaches to the study of ancient texts and their reception, publishes original scholarly (...) contributions with a strong international focus. Publications languages are: German, English, Italian, French. As of 2014 the publication of supplementary volumes will be resumed. The series Philologus. Supplemente / Philologus. Supplementary Volumes will publish monographs and edited volumes pertaining to all aspects of the study of ancient literature and its reception, with a special focus on topics concerning literary theory, philosophy and the history of scholarship from an interdisciplinary perspective. (shrink)

In a text written during his stay in Paris, Leibniz, to deny ontological reality to relations, employs an argument well known to the medieval thinkers and which later would be revived by Francis H. Bradley. If one assumes that relations are real and that a relation links any property to a subject – so runs the argument – then one falls prey to an infinite regress. Leibniz seems to be well aware of the consequences that this argument has for his (...) own metaphysical views, where the relation of inherence plays such a central role. Thus, he attempts first to interpret the relation of inherence as something ‘metaphoric’, originating from our ‘spatial way’ of looking at the surrounding world; and then he tries to reduce it to the part-whole relation which clearly he considers weaker, from the ontological point of view, than that of ‘being in’. (shrink)

Objective Apeiron was founded in 1966 and has developed into one of the oldest and most distinguished journals dedicated to the study of ancient philosophy, ancient science, and, in particular, of problems that concern both fields. Apeiron is committed to publishing high-quality research papers in these areas of ancient Greco-Roman intellectual history; it also welcomes submission of articles dealing with the reception of ancient philosophical and scientific ideas in the later western tradition. The journal appears quarterly. Articles are peer-reviewed on (...) a double-blind basis. Topics ancient philosophy ancient science reception of ancient philosophical and scientific ideas in the later western tradition Article formats Original Articles. (shrink)

We discuss the content and significance of John von Neumann’s quantum ergodic theorem (QET) of 1929, a strong result arising from the mere mathematical structure of quantum mechanics. The QET is a precise formulation of what we call normal typicality, i.e., the statement that, for typical large systems, every initial wave function ψ0 from an energy shell is “normal”: it evolves in such a way that |ψt ψt| is, for most t, macroscopically equivalent to the micro-canonical density matrix. The QET (...) has been mostly forgotten after it was criticized as a dynamically vacuous statement in several papers in the 1950s. However, we point out that this criticism does not apply to the actual QET, a correct statement of which does not appear in these papers, but to a different (indeed weaker) statement. Furthermore, we formulate a stronger statement of normal typicality, based on the observation that the bound on the deviations from the average specified by von Neumann is unnecessarily coarse and a much tighter (and more relevant) bound actually follows from his proof. (shrink)

“Normal science” is a concept introduced by Thomas Kuhn in The Structure of Scientific Revolutions. In Kuhn’s view, normal science means “puzzle solving”, solving problems within the paradigm—framework most successful in solving current major scientific problems—rather than producing major novelties. This paper examines Kuhnian and Popperian accounts of normal science and their criticisms to assess if normal science is good. The advantage of normal science according to Kuhn was “psychological”: subjective satisfaction from successful “puzzle solving”. Popper argues for an “intellectual” (...) science, one that consistently refutes conjectures and offers new ideas rather than focus on personal advantages. His account is criticized as too impersonal and idealistic. Feyerabend’s perspective seems more balanced; he argues for a community that would introduce new ideas, defend old ones, and enable scientists to develop in line with their subjective preferences. The paper concludes that normal science has no one clear-cut set of criteria encompassing its meaning and enabling clear assessment. (shrink)

Normality judgements are frequently used in everyday communication as well as in biological and social science. Moreover they became increasingly relevant to formal logic as part of defeasible reasoning. This paper distinguishes different kinds of normality statements. It is argued that normality laws like “Birds can normally fly” should be understood essentially in a statistical way. The argument has basically two parts: firstly, a statistical semantic core is mandatory for a descriptive reading of normality in order to explain the logical (...) features of normality laws. Secondly, a statistical justification of normality statements can be derived by game theoretic considerations if the normality law is understood as communication convention. (shrink)

Formal models of appearance and reality have proved fruitful for investigating structural properties of perceptual knowledge. This paper applies the same approach to epistemic justification. Our central goal is to give a simple account of The Preface, in which justified belief fails to agglomerate. Following recent work by a number of authors, we understand knowledge in terms of normality. An agent knows p iff p is true throughout all relevant normal worlds. To model The Preface, we appeal to the normality (...) of error. Sometimes, it is more normal for reality and appearance to diverge than to match. We show that this simple idea has dramatic consequences for the theory of knowledge and justification. Among other things, we argue that a proper treatment of The Preface requires a departure from the internalist idea that epistemic justification supervenes on the appearances and the widespread idea that one knows most when free from error. (shrink)

The "traditional" view of normative decision theory, as reported (for example) in chapter 2 of Luce and RaiÃa's [1957] classic work, Games and Decisions, proposes a reduction of sequential decisions problems to non-sequential decisions: a reduction of extensive forms to normal forms. Nonetheless, this reduction is not without its critics, both from inside and outside expected utility theory, It islay purpose in this essay to join with those critics by advocating the following thesis.

Different natural deduction proof systems for intuitionistic and classical logic —and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s natural deduction systems differ in fine structure. I also motivate directed proof nets as another natural deduction system which shares some of the design features of Genzen and Jaśkowski’s systems, but which differs again (...) in its treatment of the structural rules, and has a range of virtues absent from traditional natural deduction systems. (shrink)

This paper looks at the nature of normal-proper functions and the role they play in theories of representational content. More specifically: I lay down two desiderata for a theory which tries to capture what's distinctive of normal-proper functions and discuss two prominent theories which claim to satisfy them. I discuss the advantages of having normal-proper functions ground a theory of representational content. And, I look at both orthodox and heterodox versions of such theories.

Husserl and Foucault appear to have little in common when it comes to the question of normality. Husserl often discusses the emergence or constitution of norms from a subjective perspective whereas Foucault targets norms as a coercive problem. But if we recognize that the body is the locus of concern for both thinkers, then we can see that Husserl's interest in norm optimization is at home with Foucault's genealogical critique of bio-power . The essay draws a line of comparison between (...) Husserl and Foucault around the idea of an optimizing practice. (shrink)

In the face of increasing intervention in childbirth, ‘normal birth’ is currently being promoted by the World Health Organization, national governments, professional bodies and other organisations throughout the world. This paper takes a postmodernist stance and explores the idea of the ‘normal’ before going on to analyse normal childbirth, referring to concepts of the normal and the natural. It refers to historical developments in childbearing and lay organisations along with research relating to women’s views of childbirth, to question the appropriateness (...) of using ‘normal’ to describe the very individual experiences of childbirth. It laments the way in which women have been treated and arguably continue to be ‘cared for’ in maternity/obstetric services. It adds to the current discussion by recalling psychoanalytical theory and philosophical analysis to conclude with a call for future consideration of the ‘good‐enough’ birth instead of concentrating on promoting normal birth which is very difficult, if not impossible to define in retrospect, or to prospectively promote. (shrink)

In the following paper, I’ll try to summarize Husserl’s view on normality. I will claim that there is a contradiction between his early, transcendental conception, which claims the absolute normality of the transcendental consciousness, and his late genetic-generative analyzes that lead back the normality of experience to the normality of the psychophysical body. I will argue that his contradiction can be resolved from the perspective of the embodied consciousness which, according to Anthony Steinbock is also present in the late writings (...) of Husserl. (shrink)

. “Normal” Prisons in an “abnormal” society? A comparative perspective on South African prison law and practice. Criminal Justice Ethics: Vol. 6, No. 2, pp. 37-51. doi: 10.1080/0731129X.1987.9991816.

Normality Does Not Equal Mental Health: The Need to Look Elsewhere for Standards of Good Mental Health is the first book to question the equation of psychological normality and mental health. It is also the first book to take contemporary psychiatry and clinical psychology to task for deeply flawed thinking when they accept the diagnostic system propounded by the DSM, which reifies syndromes into alleged “mental disorders.” Where Thomas Szasz argued that “mental disorders” are myths, Bartlett makes the much more (...) damaging charge that reifying mental disorders involves a provable form of fallacious thinking, producing a variety of epistemological nonsense. /// -/- -/- The author weighs the evidence, and with strict logic, compelling evidence, and careful analysis, challenges the current paradigm of mental health theorists and practitioners. Never has the case against the standard of psychological normality and against the non-scientific creation of “mental disorders” been made with such boldness, multidisciplinary knowledge, solid scholarship, and clarity of language. /// -/- -/- Normality Does Not Equal Mental HealthAlthough the need to question psychological normality as a satisfactory standard of good mental health has been staring us in the face for a long time, no one, clinical professional or scholar, has had the courage or the intellectual willingness to face with unflinching honesty the shortcomings and disappointments of psychological normality and to propose that we should look elsewhere for standards of good psychological health. /// -/- -/- Contemporary psychiatry and clinical psychology, on the contrary, base their conception of mental health on the standard of psychological normality. This supposition has come to be accepted uncritically and without question, and yet it has become fundamental to current clinical theory and practice, and forms the core of the psychiatric classification system of the DSM, which has become today’s diagnostic authority. /// -/- -/- While touting today’s scientific gold standard of “evidence-based” research, DSM’s authoritative classification of “mental disorders” is itself hardly “evidence-based,” for it is recognized, but seldom emphasized, that the majority of DSM’s “mental disorders” have no known empirical, organic basis. /// -/- -/- Normality Does Not Equal Mental Health takes DSM to task not only for its failure to adhere to today’s evidence-based standard, but for its failure to rein in its highly speculative diagnostic labeling, in accordance with the modern paradigm of rigorous science, which repudiates metaphorical reifications whose alleged validity rests only on the voting preferences of a professional membership. /// -/- -/- The book is a carefully argued critique of the dominant assumption in current psychiatry and clinical psychology that psychological normality is fundamental to mental health and therefore good. In place of this unsatisfactory presumption, Normality Does Not Equal Mental Health proposes a positive and constructive revision in our understanding of mental health and of our conception of mental disorders. (shrink)

We characterize the situation of having at least $^{+}$-many normal ultrafilters on a measurable cardinal $\kappa$. We also show that if $\kappa$ is a compact cardinal, then $\kappa$ carries $^{+}$-many $\kappa$-complete ultrafilters, each of which extends the club filter on $\kappa$.

In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially in formal argumentation, (...) (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. (shrink)

In this paper we argue that knowledge is characteristically safe true belief. We argue that an adequate approach to epistemic luck must not be indexed to methods of belief formation, but rather to explanations for belief. This shift is problematic for several prominent approaches to the theory of knowledge, including virtue reliabilism and proper functionalism (as normally conceived). The view that knowledge is characteristically safe true belief is better able to accommodate the shift in question.

Functions of type n are characteristic functions on n-ary relations. Keenan [5] established their importance for natural language semantics, by showing that natural language has many examples of irreducible type n functions, i.e., functions of type n that cannot be represented as compositions of unary functions. Keenan proposed some tests for reducibility, and Dekker [3] improved on these by proposing an invariance condition that characterizes the functions with a reducible counterpart with the same behaviour on product relations. The present paper (...) generalizes the notion of reducibility (a quantifier is reducible if it can be represented as a composition of quantifiers of lesser, but not necessarily unary, types), proposes a direct criterion for reducibility, and establishes a diamond theorem and a normal form theorem for reduction. These results are then used to show that every positive n function has a unique representation as a composition of positive irreducible functions, and to give an algorithm for finding this representation. With these formal tools it can be established that natural language has examples of n-ary quantificational expressions that cannot be reduced to any composition of quantifiers of lesser degree. (shrink)

There is little debate regarding the acceptability of providing medical care to restore physical or mental health that has deteriorated below what is considered typical due to disease or disorder (i.e., providing “treatment”—for example, administering psychostimulant medication to sustain attention in the case of attention deficit disorder). When asked whether a healthy individual may undergo the same intervention for the purpose of enhancing their capacities (i.e., “enhancement”—for example, use of a psychostimulant as a “study drug”), people often express greater hesitation. (...) Building on prior research in moral philosophy and cognitive science, in this work, we ask why people draw a moral distinction between treatment and enhancement. In two experiments, we provide evidence that the accessibility of health-related interventions determines their perceived descriptive or statistical normality (Experiment 1), and that gains in descriptive normality for such interventions weaken the moral distinction between treatment and enhancement (Experiment 2). In short, our findings suggest that the tendency to draw a moral distinction between treatment and enhancement is driven, in part, by assumptions about descriptive abnormality; and raise the possibility that normalizing novel biomedical interventions by promoting access could undermine people’s selective opposition toward enhancement, rendering it morally comparable to treatment. (shrink)

Given any oracle, A, we construct a basic sequence Q, computable in the jump of A, such that no A-computable real is Q-distribution-normal. A corollary to this is that there is a Δn+10 basic sequence with respect to which no Δn0 real is distribution-normal. As a special case, there is a limit computable sequence relative to which no computable real is distribution-normal.

The concept of normal is so familiar that it can be hard to imagine contemporary life without it. Yet the term entered everyday speech only in the mid-twentieth century. Before that, it was solely a scientific term used primarily in medicine to refer to a general state of health and the orderly function of organs. But beginning in the middle of the twentieth century, normal broke out of scientific usage, becoming less precise and coming to mean a balanced condition to (...) be maintained and an ideal to be achieved. In Normality, Peter Cryle and Elizabeth Stephens offer an intellectual and cultural history of what it means to be normal. They explore the history of how communities settle on any one definition of the norm, along the way analyzing a fascinating series of case studies in fields as remote as anatomy, statistics, criminal anthropology, sociology, and eugenics. Cryle and Stephens argue that since the idea of normality is so central to contemporary disability, gender, race, and sexuality studies, scholars in these fields must first have a better understanding of the context for normality. This pioneering book moves beyond binaries to explore for the first time what it does—and doesn’t—mean to be normal. (shrink)

Cancer biologists ascribe normal functions to parts of cancer. Normal functions are activities that parts of systems are in some minimal sense supposed to perform. Cancer biologists’ finding normality within the abnormality of cancer pose difficulties for two main approaches to normal function. One approach claims that normal functions are activities that parts are selected for. However, some parts of cancers that have normal functions aren’t selected to perform them. The other approach claims that normal functions are part-activities typical for (...) the system and that contribute to survival/reproduction. However, cancers are too heterogeneous to establish what’s typical across a type. (shrink)

Petrovich provides an insightful study on analytic philosophy (AP) with the intention of determining whether this sub-field of philosophy has been operating within what Kuhn calls a normal science framework. Through a citation analysis, Petrovich concludes that AP does not exhibit the sort of pattern that we would expect of a field operating in a normal science phase. I take issue with Petrovich’s way of measuring normal science. I provide some insight into how we might better measure normal science in (...) future studies. (shrink)

Normal narcissistic functioning has to do with the regulation of a coherent set of metarepresentations of the acting agent. That set of meta-representations has its own interior architecture and dynamics. Normal narcissistic functioning is an adaptive form of interpsychic processing which can be given a general account by integrating views of it drawn from the clinical traditions of psychoanalysis, empirical psychology, and contemporary cognitive and neurosciences. This is not to be confused with any form of organized psychopathology, though pathological forms (...) of narcissism are relevant to understanding normal narcissism. Neural correlates of normal narcissism, as also the characteristic emotions and pleasures/displeasures that accompany its operations, are also explored. It is proposed that this allostatic regulatory system plays a prominent role in a wide range of human behaviors. It also closes the gap between social norms governing such behaviors and the minds of the agents performing them. This integrative interpretation of the scientific material is offered as an exercise in “philosophy in cognitive science” and belongs to the tradition of naturalistic philosophical accounts of the human mind. (shrink)

Taking the visual appeal of the ‘bell curve’ as an example, this paper discusses in how far the availability of quantitative approaches (here: statistics) that comes along with representational standards immediately affects qualitative concepts of scientific reasoning (here: normality). Within the realm of this paper I shall focus on the relationship between normality, as defined by scientific enterprise, and normativity, that result out of the very processes of standardisation itself. Two hypotheses are guiding this analysis: (1) normality, as it is (...) defined by the natural and the life sciences, must be regarded as an ontological, but epistemological important fiction and (2) standardised, canonical visualisations (such as the ‘bell curve’) impact on scientific thinking and reasoning to a significant degree. I restrict my analysis to the epistemological function of scientific representations of data: This means identifying key strategies of producing graphs and images in scientific practice. As a starting point, it is crucial to evaluate to what degree graphs and images could be seen as guiding scientific reasoning itself, for instance in attributing to them a certain epistemological function within a given field of research. (shrink)

The technique of the normal ordering of non-commuting operators is an important tool in the solution of problems involving creation and annihilation operators in quantum physics, such as in many-body theory or quantum optics. We point out the inconsistencies in previous definitions of the two standard normal ordering procedures for such operators, and show how consistent definitions may be made.

It is well known that Nash equilibria may not be Pareto-optimal; worse, a unique Nash equilibrium may be Pareto-dominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: every finite normal-form game of complete information and common knowledge has at least one Pareto-optimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, may or may not coincide with that given by a Nash equilibrium. We use (...) some simple examples to illustrate properties of NMEs—for instance, that NME outcomes are usually, though not always, maximin—and seem likely to foster cooperation in many games. Other approaches for analyzing farsighted strategic behavior in games are compared with the NME analysis. (shrink)

This article takes issue with the practical and the cognitive roles of normality within political life and its relevance to the constitution of the groups that comprise a political community. From a practical viewpoint, normality fosters standards of correctness; from a cognitive viewpoint, these standards are what allows individuals to perceive themselves, and to be recognized, as group members. To achieve this aim, the article delves into Carl Schmitt’s and Pierre Bourdieu’s accounts of how politics is a field where semantic (...) struggles take place that are meant to impose alternative visions of the social world. Different types of connections and relationships among individuals and groups (which rule out alternative connections and relationships) shore up a specific vision of the social world (which rules out alternative visions). The article concludes by saying that awareness of the normalizing effects of politics is key to producing a counter-politics meant to defy the naturalization and de-historicization that every political representation furthers. (shrink)

Let ℳ be a countable, recursively saturated model of Peano Arithmetic, and let Aut be its automorphism group considered as a topological group with the pointwise stabilizers of finite sets being the basic open subgroups. Kaye proved that the closed normal subgroups are precisely the obvious ones, namely the stabilizers of invariant cuts. A proof of Kaye's theorem is given here which, although based on his proof, is different enough to yield consequences not obtainable from Kaye's proof.

This paper considers the relevance of a class of hermeneutic concepts to the philosophical reading of normal scientific research. The author opposes the view that the notion of "normal science" can only be read in socio-psychological, sociological or ethnomethodological terms. By drawing parallels between Kuhn's original reading of puzzle-solving enterprise and Gadamer's philosophical hermeneutics, a context of "Continental theories" for interpreting the dynamics of research practices is delineated. The rereading of normal science provides the opportunity for developing a hermeneutic alternative (...) to the analytic philosophy of science. /// Este trabajo examina la relevancia de cierta clase de conceptos hermenéuticos para la lectura filosófica de la investigación cientifica normal. El autor se opone a la idea de que la noción de "ciencia normal" sólo se puede entender en términos socio-psicológicos, sociológicos o etnometodológicos. Trazando paralelos entre la lectura original kuhniana de la empresa de solutión de enigmas y la hermenéutica filosófica de Gadamer, se delinea un contexto de "teorias de Europa continental" para interpreter la dinámica de las prácticas de investigación. La relectura de la ciencia normal da la oportunidad de desarrollar una alternativa hermenéutica a la filosofia analitica de la ciencia. (shrink)

(2013). NORMAL MONSTERS AND MONSTROUS MONSTROSITIES: a response to cary wolfe. Angelaki: Vol. 18, No. 2, pp. 191-196.

The biological sciences employ a concept of normality that must be distinguished from statistical or value concepts. The concept of normality is presupposed in the standard explications of biological functions, and it is crucial to the strategy of explanation by approximations in, for example, physiology. Nevertheless, this concept of normality does not seem to be captured in the language of physics. Thus attempts at explaining the methodological relationship between the biological sciences and the physical sciences by concentrating only on the (...) concept of biological function cannot go very far. An analysis of the concept of normality is also necessary. (shrink)

People’s beliefs about normality play an important role in many aspects of cognition and life (e.g., causal cognition, linguistic semantics, cooperative behavior). But how do people determine what sorts of things are normal in the first place? Past research has studied both people’s representations of statistical norms (e.g., the average) and their representations of prescriptive norms (e.g., the ideal). Four studies suggest that people’s notion of normality incorporates both of these types of norms. In particular, people’s representations of what is (...) normal were found to be influenced both by what they believed to be descriptively average and by what they believed to be prescriptively ideal. This is shown across three domains: people’s use of the word ‘‘normal” (Study 1), their use of gradable adjectives (Study 2), and their judgments of concept prototypicality (Study 3). A final study investigated the learning of normality for a novel category, showing that people actively combine statistical and prescriptive information they have learned into an undifferentiated notion of what is normal (Study 4). Taken together, these findings may help to explain how moral norms impact the acquisition of normality and, conversely, how normality impacts the acquisition of moral norms. (shrink)

This essay intends to reveal the contribution of some Aristotelian concepts – such as “just measure” (metron, meson) and “lack of measure” (alloiosis) as well as some other connected pathological affections (pathe) of the human volitive part of the soul (thymos), caused by certain changes of the humoral mixtures, especially the ones of the black bile, a humoral substance that was considered largely responsible for the severe alterations of the normal rational activity of the human soul (logismos). – to the (...) definition of melancholy as a natural/pathological condition. This type of analysis could be useful for wider cultural studies in which certain medical traditions would have a significant contribution and would help us understand better the holistic thought of the ancient and medievalEuropean culture. (shrink)

There is much to like about the idea that justification should be understood in terms of normality or normic support (Smith 2016, Goodman and Salow 2018). The view does a nice job explaining why we should think that lottery beliefs differ in justificatory status from mundane perceptual or testimonial beliefs. And it seems to do that in a way that is friendly to a broadly internalist approach to justification. In spite of its attractions, we think that the normic support view (...) faces two serious challenges. The first is that it delivers the wrong result in preface cases. These cases suggest that the view is either too sceptical or too externalist. The second is that the view struggles with certain kinds of Moorean absurdities. It turns out that these problems can easily be avoided. If we think of normality as a condition on *knowledge*, we can characterise justification in terms of its connection to knowledge and thereby avoid the difficulties discussed here. The resulting view does an equally good job explaining why we should think that our perceptual and testimonial beliefs are justified when lottery beliefs cannot be. Thus, it seems that little could be lost and much could be gained by revising the proposal and adopting a view on which it is knowledge, not justification, that depends directly upon normality. (shrink)

Formulas of n variables of Łukasiewicz sentential calculus can be represented, via McNaughton’s theorem, by piecewise linear functions, with integer coefficients, from hypercube [0,1] n to [0,1], called McNaughton functions. As a consequence of the McNaughton representation of a formula it is obtained a canonical form of a formula. Indeed, up to logical equivalence, any formula can be written as an infimum of finite suprema of formulas associated to McNaughton functions which are truncated functions to $[0,1]$ of the restriction to (...) [0,1] n of single hyperplanes, for short, called simple McNaughton functions. In the present paper we will concern with the problem of presenting formulas of Lukasiewicz sentential calculus in normal form. Here we list the main results we obtained: a) we give an axiomatic description of some classes of formulas having the property to be canonically mapped one-to-one onto the class of simple Mc Naughton functions; b) we provide normal forms for Lukasiewicz sentential calculus, making use of formulas defined in a); c) we prove the polynomial complexity of formulas, in normal form, coming from a certain class described as in a); d) we extend the results described in a), b) and c) to Rational Lukasiewicz logic. (shrink)

Using representations of nonflat Scott domains to model type systems, it is natural to wish that they be “linear”, in which case the complexity of the fundamental test for entailment of information drops from exponential to linear, the corresponding mathematical theory becomes much simpler, and moreover has ties to models of computation arising in the study of sequentiality, concurrency, and linear logic. Earlier attempts to develop a fully nonflat semantics based on linear domain representations for a rich enough type system (...) allowing inductive types, were designed in a way that felt rather artificial, as it featured certain awkward and counter‐intuitive properties; eventually, the focus turned on general, nonlinear representations. Here we try to turn this situation around, by showing that we can work linearly in a systematic way within the nonlinear model, and that we may even restrict to a fully linear model whose objects are in a bijective correspondence with the ones of the nonlinear and are easily seen to form a prime algebraic domain. To obtain our results we study mappings of finite approximations of objects that can be used to turn approximations into normal and linear forms. (shrink)

A concise description of, and a detailed coding guidance to the electronic text format for Søren Kierkegaards Skrifter. Kierkegaard Normal Format 1 obeys the rules of the XML standard.

This paper proves the finite model property and the finite axiomatizability of a class of normal modal logics extending K4.3. The frames for these logics are those for K4.3, in each of which every point has a bounded number of irreflexive successors if it is after an infinite ascending chain of (not necessarily distinct) points.