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)

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)

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 (‘inesse’) 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)

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)

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)

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)

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 (...) class='Hi'>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)

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)

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.

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.

Existing research suggests that people's judgments of actual causation can be influenced by the degree to which they regard certain events as normal. We develop an explanation for this phenomenon that draws on standard tools from the literature on graphical causal models and, in particular, on the idea of probabilistic sampling. Using these tools, we propose a new measure of actual causal strength. This measure accurately captures three effects of normality on causal judgment that have been observed in existing (...) studies. More importantly, the measure predicts a new effect ("abnormal deflation"). Two studies show that people's judgments do, in fact, show this new effect. Taken together, the patterns of people's causal judgments thereby provide support for the proposed explanation. (shrink)

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)

Alvin Goldman’s paper “What Is Justified Belief" and his book Epistemology and Cognition pioneered reliabilist theories of epistemic justifiedness. In light of counterexamples to necessity and counterexamples to sufficiency, Goldman has offered a number of refinements and modifications. This paper focuses on those refinements that relativize the justification conferring force of a belief-forming process to its reliably producing a high ratio of true beliefs over falsehoods in special circumstances: reliability in the actual world, in normal worlds, and in nonmanipulated (...) environments. This paper argues that Goldman’s refinements fall short and suggests instead the relativization to reliability in normal circumstances. Normal circumstances are those where the belief-forming process acquired the etiological function of reliably inducing true beliefs. This theory invites the Swampman objection. Two lines of response are pursued. (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)

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)

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 article draws attention to several common mistakes in thinking about biomedical enhancement, mistakes that are made even by some supporters of enhancement. We illustrate these mistakes by examining objections that John Harris has recently raised against the use of pharmacological interventions to directly modulate moral decision-making. We then apply these lessons to other influential figures in the debate about enhancement. One upshot of our argument is that many considerations presented as powerful objections to enhancement are really strong considerations in (...) favour of biomedical enhancement, just in a different direction. Another upshot is that it is unfortunate that much of the current debate focuses on interventions that will radically transform normal human capacities. Such interventions are unlikely to be available in the near future, and may not even be feasible. But our argument shows that the enhancement project can still have a radical impact on human life even if biomedical enhancement operated entirely within the normal human range. (shrink)

Consider how we evaluate how normal an object is. On the dual-nature hypothesis, a normality evaluation depends on the object’s goodness and frequency. On the single-nature hypothesis, the evaluation depends solely on either frequency or goodness. To assess these hypotheses, I ran four experiments. Study 1 shows that normality evaluations vary with both the goodness and the frequency assessment of the object. Study 2 shows that manipulating the goodness and the frequency dimension changes the normality evaluation. Yet, neither experiment (...) rules out that some people evaluate normality solely based on frequency, and the rest evaluate normality solely based on goodness. Whence two more experiments. Study 3 reveals that when scenarios are contrasted—presented one after another—only frequency matters. But, as study 4 shows, when scenarios are evaluated alone, both frequency and goodness influence normality evaluations in a single person, although the more a person is sensitive to one dimension, the less she’s sensitive to the other. The dual-nature hypothesis seems thus true of uncontrasted applications of the concept of normality, whereas the single-nature hypothesis seems true of contrasted applications. (shrink)

This paper shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.

The treatment-enhancement distinction draws a line between services or interventions meant to prevent or cure conditions that we view as diseases or disabilities and interventions that improve a condition that we view as a normal function or feature of members of our species. The line drawn here is widely appealed to in medical practice and medical insurance contexts, as well as in our everyday thinking about the medical services we do and should assist people in obtaining.

The Normal and the Pathological is one of the crucial contributions to the history of science in the last half century. It takes as its starting point the sudden appearance of biology as a science in the 19th-century and examines the conditions determining its particular makeup.Canguilhem analyzes the radically new way in which health and disease were defined in the early 19th-century, showing that the emerging categories of the normal and the pathological were far from being objective scientific (...) concepts. He demonstrates how the epistemological foundations of modern biology and medicine were intertwined with political, economic, and technological imperatives.Canguilhem was an important influence on the thought of Michel Foucault and Louis Althusser, in particular for the way in which he poses the problem of how new domains of knowledge come into being and how they are part of a discontinuous history of human thought. (shrink)

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)

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 shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.

People give surprising weight to others’ expectations about their behaviour. I argue the practice of conforming to others’ expectations is ethically well-grounded. A special class of ‘reasonable expectations’ can create prima facie obligations even in cases where the expectations arise from contingent pre-existing practices, and the duty-bearer has not created them, or directly benefited from them. The obligation arises because of the substantial goods that follow from such conformity—goods capable of being endorsed from many different ethical perspectives and implicating key (...) moral factors such as consent, fairness, respect, autonomy, and reciprocity. Given the innumerable situations where such expectations can arise, their ethical significance is critical both practically and philosophically. (shrink)

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)

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)

A notation for an ordinal using patterns of resemblance is based on choosing an isominimal set of ordinals containing the given ordinal. There are many choices for this set meaning that notations are far from unique. We establish that among all such isominimal sets there is one which is smallest under inclusion thus providing an appropriate notion of normal form notation in this context. In addition, we calculate the elements of this isominimal set using standard notations based on collapsing (...) functions. This provides a capstone to the results in [2, 6, 8, 9, 7], using further refinement of ordinal arithmetic developed in [8] which then both allows for a simple characterization of normal forms for patterns of order one and will play a key role in the arithmetical analysis of pure patterns of order two, [5]. (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.

In this paper, we extend the expressive power of the logics K3, LP and FDE with anormality operator, which is able to express whether a for-mula is assigned a classical truth value or not. We then establish classical recapture theorems for the resulting logics. Finally, we compare the approach via normality operator with the classical collapse approach devisedby Jc Beall.

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)

According to human enhancement advocates, it is morally permissible (and sometimes obligatory) to use biomedical means to modulate or select certain biological traits in order to increase people’s welfare, even when there is no pathology to be treated or prevented. Some authors have recently proposed to extend the use of biomedical means to modulate lust, attraction, and attachment. I focus on some conceptual implications of this proposal, particularly with regard to bioconservatives’ understanding of the notions of therapy and enhancement I (...) first explain what makes the proposal of medicalizing love interesting and unique, compared to the other forms of bioenhancement usually advocated. I then discuss how the medicalization of love bears on the more general debate on human enhancement, particularly with regard to the key notion of “normality” that is commonly used to define the therapy–enhancement distinction. This analysis suggests that the medicalization of love, in virtue of its peculiarity, requires bioconservatives to reconsider their way of understanding and applying the notions of “therapy” and “enhancement.” More in particular, I show that, because a non-arbitrary and value-free notion of “therapy” cannot be applied to the case of love, bioconservatives have the burden of either providing some new criterion that could be used for drawing a line between permissible and impermissible medicalization, or demonstrating that under no circumstances—including the cases in which love is already acknowledged to require medical intervention—can love fall within the domain of medicine. (shrink)

The vagueness or imprecision of ‘the normal’ allows it to be exploited for various purposes and political ends. It is conspicuous in both medicine and athletics; I am going to try to say something about the normal in each of these areas. In medicine the idea of the normal is often deployed in understanding what constitutes disease and hence, as some see it, in determining the role of physicians, in determining what is or ought to be covered (...) by insurance, and in underwriting certain views on social justice. In athletics the use of performance enhancing substances raises different sorts of questions about the normal, especially when it comes to deciding what constitutes an enhancement and which enhancements, if any, are acceptable. (shrink)

In this article, I argue that many women lack the epistemic resources that would allow them to recognise the practice of vaginal examinations during childbirth as violent or as unnecessary and potentially declinable. I address vaginal examinations during childbirth as a special case of obstetric violence, in which women frequently lack the epistemic resources necessary to recognise the practice as violent not only because of the inherent difficulty of recognising violence that happens in an ‘essentially benevolent’ setting such as the (...) medical one, but also, and mainly, due to the pervasive sexual reification of women under patriarchy and the pervasive shame to which women are subjected. My argument is that the practice of vaginal examinations is indeed experienced – bodily apprehended – as violent by many women, but that full epistemic recognition of this violence is frequently obstructed because the experience perfectly coincides with the normal phenomenological situation of women within patriarchy and thus cannot really be framed as violent. A phenomenological analysis presenting the embodied experience of women under patriarchy as always already essentially tied to sexual availability and commodification, and to shame, will explain this epistemological impairment. A phenomenological take on Judith Butler’s distinction between ‘recognition’ and ‘apprehension’ informs my analysis: I deploy it to provide a richer, more nuanced response to the question of why vaginal examinations are not fully recognised and expressed as violent – even when they are, frequently, apprehended as such. Furthermore, Butler’s ideas about the epistemic ‘framings’ through which we make sense of different kinds of lives (grievable versus ungrievable) will help me to explain how the patriarchal sexual reification of women in fact already frames sexual violence as not-violence – which ultimately also prevents labouring women (and obstetrics staff) from recognising vaginal examinations during labour as violence. (shrink)

Charles Perrow used the term normal accidents to characterize a type of catastrophic failure that resulted when complex, tightly coupled production systems encountered a certain kind of anomalous event. These were events in which systems failures interacted with one another in a way that could not be anticipated, and could not be easily understood and corrected. Systems of the production of expert knowledge are increasingly becoming tightly coupled. Unlike classical science, which operated with a long time horizon, many current (...) forms of expert knowledge are directed at immediate solutions to complex problems. These are prone to breakdowns like the kind discussed by Perrow. The example of the Homestake mine experiment shows that even in modern physics complex systems can produce knowledge failures that last for decades. The concept of knowledge risk is introduced, and used to characterize the risk of failure in such systems of knowledge production. (shrink)

Akama et al. [1] systematically studied an arithmetical hierarchy of the law of excluded middle and related principles in the context of first-order arithmetic. In that paper, they first provide a prenex normal form theorem as a justification of their semi-classical principles restricted to prenex formulas. However, there are some errors in their proof. In this paper, we provide a simple counterexample of their prenex normal form theorem [1, Theorem 2.7], then modify it in an appropriate way which (...) still serves to largely justify the arithmetical hierarchy. In addition, we characterize a variety of prenex normal form theorems by logical principles in the arithmetical hierarchy. The characterization results reveal that our prenex normal form theorems are optimal. For the characterization results, we establish a new conservation theorem on semi-classical arithmetic. The theorem generalizes a well-known fact that classical arithmetic is $\Pi _2$ -conservative over intuitionistic arithmetic. (shrink)