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

The Routley-Meyer relational semantics for relevant logics is extended to give a sound and complete model theory for many propositionally quantified relevant logics (and some non-relevant ones). This involves a restriction on which sets of worlds are admissible as propositions, and an interpretation of propositional quantification that makes ∀ pA true when there is some true admissible proposition that entails all p -instantiations of A . It is also shown that without the admissibility qualification many of the systems (...) considered are semantically incomplete, including all those that are sub-logics of the quantified version of Anderson and Belnap’s system E of entailment, extended by the mingle axiom and the Ackermann constant t . The incompleteness proof involves an algebraic semantics based on atomless complete Boolean algebras. (shrink)

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

We propose two admissible closures $${\mathbb{A}({\sf PTCA})}$$ and $${\mathbb{A}({\sf PHCA})}$$ of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i) $${\mathbb{A}({\sf PTCA})}$$ is conservative over PTCA with respect to $${\forall\exists\Sigma^b_1}$$ sentences, and (ii) $${\mathbb{A}({\sf PHCA})}$$ is conservative over full bounded arithmetic PHCA for $${\forall\exists\Sigma^b_{\infty}}$$ sentences. This yields that (i) the $${\Sigma^b_1}$$ definable functions of $${\mathbb{A}({\sf PTCA})}$$ are the polytime functions, and (ii) the $${\Sigma^b_{\infty}}$$ (...) definable functions of $${\mathbb{A}({\sf PHCA})}$$ are the functions in the polynomial time hierarchy. (shrink)

This study investigates the sampled-data admissibility problem for a singular system. The objective of this paper is to design a sampled-data controller to ensure the admissibility of a singular system and to construct an appropriate Lyapunov–Krasovskii functional to get less conservative results for the sampled-data singular system. To accomplish these objectives, the system is converted into a time-delay system by the input delay approach firstly, and both lower and upper bounds of the delay are considered. Secondly, by introducing a suitable (...) LKF, the admissibility criteria are obtained. Then, when estimating the derivative of the LKF, a relaxation variable is introduced by the method of reciprocally convex inequality, and it is proved that the conservatism is reduced. Finally, two numerical examples are given to prove that the designed sampled-data controller can ensure the states of the systems under the influence of external interference. (shrink)

Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis’s Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in (...) which these challenges may be addressed. (shrink)

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

The involuntary admission or treatment of a mentally ill individual is highly controversial, as it may be argued that such intervention infringes on individual autonomy and the right to choose a particular treatment. However, this argument must be balanced with the need to provide immediate healthcare services to a vulnerable person who cannot or will not make a choice in his or her own best interests at a particular time. A study carried out in Gauteng Province, South Africa, highlighted the (...) fact that the annual rate of involuntary admissions increased by almost double from 2007 to 2008. This could indicate that healthcare providers are not treating patients without their consent only when this is absolutely necessary. Alternatively, it could indicate that healthcare professionals are more aware of the provisions of the Mental Health Care Act and relevant national policy guidelines. Or it could suggest that more patients are presenting with mental illnesses or disorders that require their involuntary admission. It remains for strategies to be developed that change negative perceptions and inequities for individuals with mental illness. Above all, the strategies should be underpinned by inalienable respect for mentally ill individuals – a concept that was blatantly disregarded in the Life Esidimeni case. In this article, we highlight the functions of mental health review boards and their accountability where involuntary admissions are concerned, while emphasising the protections for mentally ill persons as a vulnerable population group, as set out in the SA Constitution. (shrink)

The system R## of "true" relevant arithmetic is got by adding the ω-rule "Infer VxAx from AO, A1, A2, ...." to the system R# of "relevant Peano arithmetic". The rule ⊃E (or "gamma") is admissible for R##. This contrasts with the counterexample to ⊃E for R# (Friedman & Meyer, "Whither Relevant Arithmetic"). There is a Way Up part of the proof, which selects an arbitrary non-theorem C of R## and which builds by generalizing Henkin and Belnap arguments a prime (...) theory T which still lacks C. (The key to the Way Up is a Witness Protection Program, using the ω-rule.) But T may be TOO BIG, whence there is a Way Down argument that produces a better theory TR, such that R## ⊆ TR ⊆ T. (The key to the Way Down is a Metavaluation, on which membership in T is combined with ordinary truth-functional conditions to determine TR.) The result is a theory that is Just Right, whence it never happens that A ⊃ C and A are theorems of R## but C is a non-theorem. (shrink)

The system R## of "true" relevant arithmetic is got by adding the ω-rule "Infer VxAx from AO, A1, A2, ...." to the system R# of "relevant Peano arithmetic". The rule ⊃E (or "gamma") is admissible for R##. This contrasts with the counterexample to ⊃E for R# (Friedman & Meyer, "Whither Relevant Arithmetic"). There is a Way Up part of the proof, which selects an arbitrary non-theorem C of R## and which builds by generalizing Henkin and Belnap arguments a prime (...) theory T which still lacks C. (The key to the Way Up is a Witness Protection Program, using the ω-rule.) But T may be TOO BIG, whence there is a Way Down argument that produces a better theory TR, such that R## ⊆ TR ⊆ T. (The key to the Way Down is a Metavaluation, on which membership in T is combined with ordinary truth-functional conditions to determine TR.) The result is a theory that is Just Right, whence it never happens that A ⊃ C and A are theorems of R## but C is a non-theorem. (shrink)

An in-depth analysis of the recent reform in Italian psychiatry reveals that the relevance of these changes transcends national borders. However, these changes are, from the scientific point of view, worth much more than mere biased pragmatic interest. The reshaping of theory made possible by the transformation of Italian psychiatry in fact opens up new prospects for a scientifically founded form of psychiatric care. Thanks to the new Mental Health Act (No. 180 of 1978),2 it has been possible to set (...) up a type of administrative and institutional organization in which the psychiatric hospital no longer constitutes a functional part of the structures of psychiatric care. This reform thus provides the launching path for a real alternative where current psychiatric ideas and working methods can no longer be accepted as the gospel truth. This paper discusses how a correct problem-definition of psychiatric admission can provide a basis for a correct approach to psychopathological behaviour in a setting where the psychiatric hospital has no role to play and for the consolidation of this new practice. (shrink)

The notion of a function from ℕ to ℕ defined by recursion on ordinal notations is fundamental in proof theory. Here this notion is generalized to functions on the universe of sets, using notations for well orderings longer than the class of ordinals. The generalization is used to bound the rate of growth of any function on the universe of sets that is Σ1-definable in Kripke–Platek admissible set theory with an axiom of infinity. Formalizing the argument provides (...) an ordinal analysis. (shrink)

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of (...) probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility. (shrink)

The University of Tehran English Proficiency Test (UTEPT) is a high-stakes entrance examination taken by more than 10,000 master’s degree holders annually. The examinees’ scores have a significant influence on the final decisions concerning admission to the University of Tehran Ph.D. programs. As a test validation investigation, the present study, which is a bias detection research in nature, utilized multistep logistic regression (LR) procedure to examine the presence of gender differential item functioning (DIF) in the UTEPT with a sample of (...) 6,555 examinees who took the test in November 2006. Specifically, the LR DIF two-degree of freedom Chi-squared test of significance was employed to test the significance of DIF. Following what has been recently suggested in the literature, the test of significance for DIF was accompanied by a measure of magnitude, namely the R-squared effect size for LR DIF, for the interpretation of which the two widely accepted classification schemes were used comparatively. The results reveal that 39 of the 100 items in the test display significant gender differences. However, these group differences are viewed as “negligible” based on both of the schemes. Accordingly, it could be argued that the UTEPT is a gender DIF-free test, though the Reading Comprehension section of the test remains in need of further analysis as it seems that the general trend of DIF indices at the item level may hint at an inclination towards males. (shrink)

Few institutions have published reviews concerning the case consultation history of their ethics committees, and policies used by ethics committees to address inappropriate treatment are infrequently reviewed. We sought to characterize the operation of our institution’s ethics committee as a representative example of a volunteer ethics committee, and outline its use of a policy to address inappropriate treatment, the Conscientious Practice Policy. Patients were identified for retrospective review from the ethics consultation database. Patient demographics, medical admission information, and consultation information (...) were obtained from the medical record. Consultation notes were analyzed with directed content analysis. The use of the CPP was documented in each case. Groups of interest were compared via two-sample t-tests. There were 178 consultations between 2013 and 2018. The majority originated from medicine services. The most common consultation reasons were end-of-life balances of acute and palliative care, best interest standard, medical futility, and code status and intubation status. Average age was 65.5 years and average hospitalization before consultation was 51.4 days. 92 patients had a code status change that occurred after consultation. A policy to address inappropriate treatment was used in 42 of the consultations. Bivariate analysis demonstrated a reduction in policy use over time, with use in 32.1% of consultations from 2013 to 2016 and 11.4% of consultations 2017–2018, p = 0.002. End-of-life issues were the most common reason for consultation. Our consultation volume was lower than previously-published reports. A policy used to address inappropriate treatment was frequently used, although use decreased over time. (shrink)

Hospital admission and mortality statistics suggested that peptic ulcer reached a peak prevalence in the mid-1950s. During the Second World War, against this background of serious and common pathology, an epidemic of dyspepsia afflicted both service personnel and civilians alike. In the absence of reliable diagnostic techniques, physicians struggled to distinguish between life-threatening illness and mild, temporary disorders. This article explores the context in which non-ulcer stomach conditions flourished. At a time when fear was considered defeatist and overt psychological disorder (...) attracted stigma, both soldiers and civilians exposed to frightening events may have unconsciously translated their distress into gastrointestinal disorders. While the nature of army food was initially identified as the cause of duodenal ulcer in servicemen, the pre-war idea that conscientious and anxious individuals were at high risk gathered support and fed into post-war beliefs that this was a stress-related illness. Diet continued to be employed as a means of management at a time when the nation was preoccupied by food because of the constraints imposed by rationing. The peptic ulcer phenomenon set much of the medical agenda for the war years and conflicted with the commonly held view that the British people had never been healthier. (shrink)

Hospital admission and mortality statistics suggested that peptic ulcer reached a peak prevalence in the mid-1950s. During the Second World War, against this background of serious and common pathology, an epidemic of dyspepsia afflicted both service personnel and civilians alike. In the absence of reliable diagnostic techniques, physicians struggled to distinguish between life-threatening illness and mild, temporary disorders. This article explores the context in which non-ulcer stomach conditions flourished. At a time when fear was considered defeatist and overt psychological disorder (...) attracted stigma, both soldiers and civilians exposed to frightening events may have unconsciously translated their distress into gastrointestinal disorders. While the nature of army food was initially identified as the cause of duodenal ulcer in servicemen, the pre-war idea that conscientious and anxious individuals were at high risk gathered support and fed into post-war beliefs that this was a stress-related illness. Diet continued to be employed as a means of management at a time when the nation was preoccupied by food because of the constraints imposed by rationing. The peptic ulcer phenomenon set much of the medical agenda for the war years and conflicted with the commonly held view that the British people had never been healthier. (shrink)

Professor Imwinkelried is surely right: the propriety of bioethicists serving as expert witnesses in litigation is problematic, and, I would add, it should remain problematic. Such testimony most certainly does not belong everywhere it will be offered by lawyers and litigants in an effort to advance their interests. Yet in contrast to some commentators, Imwinkelried and I both see a place for bioethicists serving as expert witnesses, although we differ significantly on how to understand and justify this place. In any (...) event, serious questions regarding the proper place for expert bioethicist testimony in the courtroom do exist, not only for law but also bioethics as well.The threshold question regarding the prospect of bioethicists serving as expert witnesses would seemingly have to be: “could a bioethicist qualify as an expert witness under the controlling rules of evidence?” Imwinkelried, however, does not perceive any need to even entertain this question as he claims that “technical evidentiary standards are inapplicable when information is presented to a judge to permit the judge to perform… a legislative or law-making function.”. (shrink)

Professor Imwinkelried is surely right: the propriety of bioethicists serving as expert witnesses in litigation is problematic, and, I would add, it should remain problematic. Such testimony most certainly does not belong everywhere it will be offered by lawyers and litigants in an effort to advance their interests. Yet in contrast to some commentators, Imwinkelried and I both see a place for bioethicists serving as expert witnesses, although we differ significantly on how to understand and justify this place. In any (...) event, serious questions regarding the proper place for expert bioethicist testimony in the courtroom do exist, not only for law but also bioethics as well.The threshold question regarding the prospect of bioethicists serving as expert witnesses would seemingly have to be: “could a bioethicist qualify as an expert witness under the controlling rules of evidence?” Imwinkelried, however, does not perceive any need to even entertain this question as he claims that “technical evidentiary standards are inapplicable when information is presented to a judge to permit the judge to perform… a legislative or law-making function.”. (shrink)

In this paper two theories of defeasible reasoning, Pollock's account and my theory of ranking functions, are compared, on a strategic level, since a strictly formal comparison would have been unfeasible. A brief summary of the accounts shows their basic difference: Pollock's is a strictly computational one, whereas ranking functions provide a regulative theory. Consequently, I argue that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion of (...) class='Hi'>admissible rules. Conversely, I explain how quite a number of achievements of Pollock's account can be adequately duplicated within ranking theory. The main purpose of the paper, though, is not to settle a dispute with formal epistemology, but rather to emphasize the importance of formal methods to the whole of epistemology. (shrink)

R. M. Friedberg demonstrated the existence of a recursive functional that agrees with no Banach-Mazur functional on the class of recursive functions. In this paper Friedberg's result is generalized to both α-recursive functionals and weak α-recursive functionals for all admissible ordinals α such that $\lambda , where α * is the Σ 1 -projectum of α and λ is the Σ 2 -cofinality of α. The theorem is also established for the metarecursive case, α = ω 1 , where (...) α * = λ = ω. (shrink)

In this paper two theories of defeasible reasoning, Pollock's account and my theory of ranking functions, are compared, on a strategic level, since a strictly formal comparison would have been unfeasible. A brief summary of the accounts shows their basic difference: Pollock's is a strictly computational one, whereas ranking functions provide a regulative theory. Consequently, I argue that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion of (...) class='Hi'>admissible rules. Conversely, I explain how quite a number of achievements of Pollock's account can be adequately duplicated within ranking theory. The main purpose of the paper, though, is not to settle a dispute with formal epistemology, but rather to emphasize the importance of formal methods to the whole of epistemology. (shrink)

In this paper we work in an arbitrary o-minimal structure with definable Skolem functions and prove that definably connected, locally definable manifolds are uniformly definably path connected, have an admissible cover by definably simply connected, open definable subsets and, definable paths and definable homotopies on such locally definable manifolds can be lifted to locally definable covering maps. These properties allow us to obtain the main properties of the general o-minimal fundamental group, including: invariance and comparison results; existence of universal (...) locally definable covering maps; monodromy equivalence for locally constant o-minimal sheaves – from which one obtains, as in algebraic topology, classification results for locally definable covering maps, o-minimal Hurewicz and Seifert–van Kampen theorems. (shrink)

BackgroundCognitive dysfunctions, both subjective and detectable at psychometric testing, may follow SARS-CoV-2 infection. However, the ecological-functional relevance of such objective deficits is currently under-investigated. This study thus aimed at investigating the association between objective cognitive measures and both physical and cognitive, ecological-functional outcomes in post-COVID-19.MethodsForty-two COVID-19-recovered individuals were administered the Mini-Mental State Examination and the Montreal Cognitive Assessment. The Functional Independence Measure was adopted to assess functional-ecological, motor/physical and cognitive outcomes at admission and discharge.ResultsWhen predicting both T0/T1 FIM-total and-Motor scores (...) based on MMSE/MoCA scores, premorbid risk for cognitive decline and disease-related features, no model yielded a significant fit. However, the MoCA - but not the MMSE significantly predicted T0/T1 FIM-Cognitive scores. The MoCA was significantly related only to T0/T1 FIM-Cognitive Memory items.DiscussionCognitive measures are not associated with physical/motor everyday-life outcomes in post-COVID-19 patients. The MoCA may provide an ecological estimate of cognitive functioning in this population. (shrink)

In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product (or, more generally, from any strict Frank t-norm) all measurable logical functions can be derived, provided that also operations with countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all strict t-norms possess this property. We give a full solution to this problem (in the case of strict t-norms), together with convenient (...) sufficient conditions. We list several families of strict t-norms having this property and provide also counterexamples (the Hamacher product is one of them). Finally, we discuss the consequences of these results for the characterization of tribes based on strict t-norms. (shrink)

Neuroimaging showing brain abnormalities is increasingly being introduced in criminal court proceedings to argue that a defendant could not control his behavior and should not be held responsible for it. But imaging has questionable probative value because it does not directly capture brain function or a defendant’s mental states at the time of a criminal act. Advanced techniques could transform imaging from a coarse-grained measure of correlations between brain states and behavior to a fine-grained measure of causal connections between (...) them. Even if this occurs, bias and other attitudes may unduly influence jurors’ interpretation of the data. Moreover, judges’ decisions about whether neuroimaging data is legally relevant and admissible are normative decisions based on more than empirical evidence. Advanced neuroimaging will better inform assessments of criminal responsibility but will not supplant or explain away the psychological and normative foundation of the criminal law. (shrink)

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

Philosophers typically rely on intuitions when providing a semantics for counterfactual conditionals. However, intuitions regarding counterfactual conditionals are notoriously shaky. The aim of this paper is to provide a principled account of the semantics of counterfactual conditionals. This principled account is provided by what I dub the Royal Rule, a deterministic analogue of the Principal Principle relating chance and credence. The Royal Rule says that an ideal doxastic agent’s initial grade of disbelief in a proposition \(A\) , given that the (...) counterfactual distance in a given context to the closest \(A\) -worlds equals \(n\) , and no further information that is not admissible in this context, should equal \(n\) . Under the two assumptions that the presuppositions of a given context are admissible in this context, and that the theory of deterministic alethic or metaphysical modality is admissible in any context, it follows that the counterfactual distance distribution in a given context has the structure of a ranking function. The basic conditional logic V is shown to be sound and complete with respect to the resulting rank-theoretic semantics of counterfactuals. (shrink)

Patients’ admission to modern substance use disorder treatment comes with the attendant risk of being discharged from treatment— a widespread practice. This article describes the three mainstream theories of addiction that operate as a reference point for clinicians in reasoning about a decision to discharge a patient from treatment. The extant literature is reviewed to highlight the pathways that patients follow after administrative discharge. Little scientific research has been done to investigate claims and hypotheses about the therapeutic function of (...) AD, which points to the need for empirical ethics to inform clinical addictions practice. (shrink)

This paper examines the ethical conundrum between a hospital's ethos of relieving distress, investigation and treatment, and its concurrent duties under English law to administer tests of decision-making capacity and safeguarding protection where it believes the patient may lack this capacity. Delirium, characterised by a precipitous decline in mental functioning exhibiting the shared symptomology of recoverable depressive disorders and terminal dementia, is not uncommon after emergency admission of elderly patients into acute medical hospital wards. The use of functional capacity testing (...) as a benchmark for decision-making capacity for post-discharge residence has been criticised as outdated, conceptually floored, subjective, lacking central guidance, transparent process, and accountability. A study of patient experience demonstrates the potential for hospital misuse of capacity testing, the failure of functional testing to differentiate decision making capacity from the disability of partial cognitive impairment, and how hospital capacity processes can interact and amplify patient pathology thereby decreasing recovery prospects. Prioritisation of mental capacity obligations above thorough investigation of emergent mental pathology and relief of patient anguish, results in extended detention in medical wards lacking bespoke facilities. Further understanding of patient experience is needed to inform policy with interventions tailored to avoid harm and increase wellbeing. (shrink)

In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all other sentences to be equally interpreted as true. Paraconsistent logics are exactly those logics that escape this explosive effect of the presence of inconsistencies and allow for sensible reasoning still to take effect. To provide reasonably intuitive semantics for paraconsistent logics has traditionally proven to be a challenge. Possible-translations (...) semantics can meet that challenge by allowing for each interpretation to be composed of multiple scenarios. Using that idea, a logic with a complex semantic behavior can be understood as an appropriate combination of ingredient logics with simpler semantic behaviors into which the original logic is given a collection of translations preserving its soundness. Completeness is then achieved through the judicious choice of the admissible translating mappings. The present note provides interpretation by way of possible-translations semantics for a group of fundamental paraconsistent logics extending the positive fragment of classical propositional logic. The logics PI, Cmin, mbC, bC, mCi and Ci, among others, are all initially presented through their non-truth-functional bivaluation semantics and sequent versions and then split by way of possible-translations semantics based on 3-valued ingredients. (shrink)

This article provides unified axiomatic foundations for the most common optimality criteria in statistical decision theory. It considers a decision maker who faces a number of possible models of the world (possibly corresponding to true parameter values). Every model generates objective probabilities, and von Neumann–Morgenstern expected utility applies where these obtain, but no probabilities of models are given. This is the classic problem captured by Wald’s (Statistical decision functions, 1950) device of risk functions. In an Anscombe–Aumann environment, I characterize Bayesianism (...) (as a backdrop), the statistical minimax principle, the Hurwicz criterion, minimax regret, and the “Pareto” preference ordering that rationalizes admissibility. Two interesting findings are that c-independence is not crucial in characterizing the minimax principle and that the axiom which picks minimax regret over maximin utility is von Neumann–Morgenstern independence. (shrink)

On Sartre's own admission, his account of the emotions discloses them as functional. As such, the emotions aim to serve a particular purpose for which he provides the phenomenology. Sartre's phenomenology discloses consciousness as being-in-the-world in two ways, actually as having two worlds. One is a deterministic world, the other magical. Emotion is the drop from the deterministic world to the magical. In order for emotion to perform the function Sartre has in mind it performs, it is crucial there (...) be a certain tension between the deterministic world and the magical world. I argue that given what Sartre himself says about the magical world, the necessary tension can never arise; hence, no functional thesis of emotion is possible if it is formed along Sartre's lines. (shrink)

A down-to-earth admission of abstract objects can be based on detailed explanation of where the objectivity of mathematics comes from, and how a ‘thin’ notion of object emerges from objective mathematical discourse or practices. We offer a sketch of arguments concerning both points, as a basis for critical scrutiny of the idea that mathematical and social objects are essentially of the same kind—which is criticized. Some authors have proposed that mathematical entities are indeed institutional objects, a product of our collective (...) imposition of function onto reality (the phrase comes from Searle) and of surrogation or hypostasis. Yet there are significant disanalogies between the typical social objects and mathemata, on which basis I argue that one should make a clear distinction between both. The comparison of mathematical with social objects helps understanding how non-physical objects can figure prominently in our explanations of reality. Yet mathematical objects have a different kind of cognitive grounding, and the more elementary of them emerge under relatively very simple sociocultural conditions. The differences are also reflected in the wide scope of use of mathematical concepts, and the much higher degree of variation found among social objects. On the basis of all of these features, I defend the thesis that one can significantly distinguish degrees of objectivity, and I use the distinction to articulate a graded ontology where one can locate the different kinds of mathematical and social objects. (shrink)

This paper describes the admissible classes of parametric distribution functions of return portfolios and analyzes their consistency with the maximization of the expected utility. In particular, we present a general theory and a unifying framework with the following aims: (1) studying the implications of the classical market restrictions on the portfolio distributions; (2) establishing general rules of ordering, when the uncertain prospect depends by a finite number of parameters; (3) understanding how a dispersion measure has to be used, in (...) order to obtain the investors' optimal portfolios. (shrink)

Given an admissible indexing φ of the countable atomless Boolean algebra B, an automorphism F of B is said to be recursively presented (relative to φ) if there exists a recursive function $p \in \operatorname{Sym}(\omega)$ such that F ⚬ φ = φ ⚬ p. Our key result on recursiveness: Both the subset of $\operatorname{Aut}(\mathscr{B})$ consisting of all those automorphisms which are recursively presented relative to some indexing, and its complement, the set of all "totally nonrecursive" automorphisms, are uncountable. (...) This arises as a consequence of the following combinatorial investigations: (1) A comparison of the cycle structures of f and f̄, where f is a permutation of some free basis of B and f̄ is the automorphism of B induced by f. (2) An explicit description of the permutations of ω whose conjugacy classes in $\operatorname{Sym}(\omega)$ are (a) uncountable, (b) countably infinite, and (c) finite. (shrink)

This monograph contributes to the scientific misconduct debate from an oblique perspective, by analysing seven novels devoted to this issue, namely: Arrowsmith by Sinclair Lewis (1925), The affair by C.P. Snow (1960), Cantor’s Dilemma by Carl Djerassi (1989), Perlmann’s Silence by Pascal Mercier (1995), Intuition by Allegra Goodman (2006), Solar by Ian McEwan (2010) and Derailment by Diederik Stapel (2012). Scientific misconduct, i.e. fabrication, falsification, plagiarism, but also other questionable research practices, have become a focus of concern for academic communities (...) worldwide, but also for managers, funders and publishers of research. The aforementioned novels offer intriguing windows into integrity challenges emerging in contemporary research practices. They are analysed from a continental philosophical perspective, providing a stage where various voices, positions and modes of discourse are mutually exposed to one another, so that they critically address and question one another. They force us to start from the admission that we do not really know what misconduct is. Subsequently, by providing case histories of misconduct, they address integrity challenges not only in terms of individual deviance but also in terms of systemic crisis, due to current transformations in the ways in which knowledge is produced. Rather than functioning as moral vignettes, the author argues that misconduct novels challenge us to reconsider some of the basic conceptual building blocks of integrity discourse. (shrink)

The best accuracy arguments for probabilism apply only to credence functions with finite domains, that is, credence functions that assign credence to at most finitely many propositions. This is a significant limitation. It reveals that the support for the accuracy-first program in epistemology is a lot weaker than it seems at first glance, and it means that accuracy arguments cannot yet accomplish everything that their competitors, the pragmatic (Dutch book) arguments, can. In this paper, I investigate the extent to which (...) this limitation can be overcome. Building on the best arguments in finite domains, I present two accuracy arguments for probabilism that are perfectly general—they apply to credence functions with arbitrary domains. I then discuss how the arguments’ premises can be challenged. We will see that it is particularly difficult to characterize admissible accuracy measures in infinite domains. (shrink)

In a recent article in this journal, Mona Simion argues that Sally Haslanger’s “engineering” approach to gender concepts such as ‘woman’ faces an epistemic objection. The primary function of all concepts—gender concepts included—is to represent the world, but Haslanger’s engineering account of ‘woman’ fails to adequately represent the world because, by her own admission, it doesn’t include all women in the extension of the concept ‘woman.’ I argue that this objection fails because the primary function of gender concepts—and (...) social kind concepts in general—is not (merely) to represent the world, but rather to shape it. I finish by considering the consequences for “conceptual engineering” in philosophy more generally. While Haslanger’s account may escape Simion’s objection, other appeals to conceptual engineering might not fair so well. (shrink)

I follow Hájek (Synthese 137:273–323, 2003c) by taking objective probability to be a function of two propositional arguments—that is, I take conditional probability as primitive. Writing the objective probability of q given r as P(q, r), I argue that r may be chosen to provide less than a complete and exact description of the world’s history or of its state at any time. It follows that nontrivial objective probabilities are possible in deterministic worlds and about the past. A very (...) simple chance–credence relation is also then natural, namely that reasonable credence equals objective probability. In other words, we should set our actual credence in a proposition equal to the proposition’s objective probability conditional on available background information. One advantage of that approach is that the background information is not subject to an admissibility requirement, as it is in standard formulations of the Principal Principle. Another advantage is that the “undermining” usually thought to follow from Humean supervenience can be avoided. Taking objective probability to be a two-argument function is not merely a technical matter, but provides us with vital flexibility in addressing significant philosophical issues. (shrink)

Multidimensional adjectives are ubiquitous in natural language. An adjective F is multidimensional just in case whether F applies to an object or pair of objects depends on how those objects stand with respect to multiple underlying dimensions of F-ness. Developing a semantics for multidimensional adjectives requires us to address the problem of dimensional aggregation: how do the application conditions of an adjective F in its positive and comparative forms depend on its underlying dimensions? Here we develop a semantics for multidimensional (...) adjectives that incorporates aggregation functions. We then explore an analogy between dimensional aggregation and preference aggregation, bringing results from social choice theory to bear on the number and kind of aggregation functions that are admissible in a context. These results suggest that, for any given adjective, there will often be multiple aggregation functions admissible, meaning that multidimensional comparatives are often vague. (shrink)

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

The paper characterizes the second order arithmetic theorems of a set theory that features a recursively Mahlo universe; thereby complementing prior proof-theoretic investigations on this notion. It is shown that the property of being recursively Mahlo corresponds to a certain kind of β-model reflection in second order arithmetic. Further, this leads to a characterization of the reals recursively computable in the superjump functional.

In a recent discussion article in this journal, Gila Sher responds to some of my criticisms of her work on what she calls the formal-structural account of logical consequence. In the present paper I reply and attempt to advance the discussion in a constructive way. Unfortunately, Sher seems to have not fully understood my 1997. Several of the defenses she mounts in her 2001 are aimed at views I do not hold and did not advance in my 1997. Most prominent (...) among these are her claims that I reject the formal-structural account, because it licenses “unnatural” logical constants, and that I consider the “truth-functional criterion” for connectives “a paradigm of a successful criterion of logicality”. Both of these claims are simply false, as even a moderately careful reading of my 1997 will show. Other charges she makes have some basis in fact but are inaccurate. For example, she says that I claim that FS is “neutral with regard to the apriority of logic,” and that this neutrality “renders it inconsistent”. What I actually say is that Sher’s acceptance of the neutrality in question is “inconsistent with part of the legacy of Tarski, a legacy that she finds very congenial”, not that FS itself is inconsistent. More interestingly, she misunderstands my claim about the apriority of logic, and clarification of this misunderstanding suggests two distinct ways in which logic might be held to be free of empirical influence. It is also noteworthy that Sher’s statements about the apriority of logic constitute both a change in the position she took in her 1991 and, although she seems not to realize it, an admission that she does not take issue with one of my major criticisms. (shrink)

There is a considerable effort in current theorizing about psychological phenomena to eliminate minds and selves as a vestige of folk theories. The pertinent strategies are quite varied and may focus on experience, cognition, interests, responsibility, behavior and the scientific explanation of these phenomena or what they purport to identify. The minimal function of the notion of self is to assign experience to a suitable entity and to fix such ascription in a possessive as well as a predicative way. (...) It is usually argued that Hume formulated an empiricist account of experience that obviated the need for reference to selves; and recent arguments mustered by Derek Parfit claim to show how to preserve experience, interest, responsibility usually assigned selves and persons without invoking any such entities. The argument here advanced demonstrates that Hume actually concedes the minimal use of the notion of self, that there appear to be no convincing grounds for eliminating it, that there are critical uses for the notion that render it ineliminable, that admission is neutral regarding the nature of selves, and that Parfit''s arguments in particular fail. There appear, therefore, to be no empiricist or materialist grounds for the eliminative move. A large recent literature that favors various eliminative strategies is canvassed and shown to be inadequate to its task and unlikely (for principled reasons) to be able to achieve its eliminative objective. (shrink)

OBJECTIVES: To study the resuscitation preferences, choice of decision-maker, views on the seeking of patients' wishes and determinants of these of elderly hospital in-patients. DESIGN: Questionnaire administered on admission and prior to discharge. SETTING: Two acute geriatric medicine units (Southampton and Poole). PARTICIPANTS: Two hundred and fourteen consecutive consenting mentally competent patients admitted to hospital as emergencies. RESULTS: Resuscitation was wanted by 60%, particularly married and functionally independent patients and those who had not already considered it. Not wanted resuscitation was (...) associated with lack of social contacts. Sixty-seven per cent welcomed enquiry about their preferences and 78% wanted participation in decision, 43% as sole decision-maker. Wishing to choose oneself was associated with not wanting resuscitation, prior knowledge of it, and lack of a spouse. Patients' opinions remained stable during their admission. CONCLUSIONS: Discussion of resuscitation is practical on hospital admission without causing distress and the views expressed endure through the period of hospitalisation. Elderly patients' attitudes depend partly on personal health and social circumstances. This may assist doctors when patients are unable to participate themselves. (shrink)

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

In late February and early March 2020, Italy became the European epicenter of the COVID-19 pandemic. Despite increasingly stringent containment measures enforced by the government, the health system faced an enormous pressure, and extraordinary efforts were made in order to increase overall hospital beds’ availability and especially ICU capacity. Nevertheless, the hardest-hit hospitals in Northern Italy experienced a shortage of ICU beds and resources that led to hard allocating choices. At the beginning of March 2020, the Italian Society of Anesthesia, (...) Analgesia, Resuscitation, and Intensive Care issued recommendations aimed at supporting physicians in prioritizing patients when the number of critically ill patients overwhelm the capacity of ICUs. One motivating concern for the SIAARTI guidance was that, if no balanced and consistent allocation procedures were applied to prioritize patients, there would be a concrete risk for unfair choices, and that the prevalent “first come, first served” principle would lead to many avoidable deaths. Among the drivers of decision for admission to ICUs, age, comorbidities, and preexisting functional status were included. The recommendations were criticized as ageist and potentially discriminatory against elderly patients. Looking forward to the next steps, the Italian experience can be relevant to other parts of the world that are yet to see a significant surge of COVID-19: the need for transparent triage criteria and commonly shared values give the Italian recommendations even greater legitimacy. (shrink)

Hexa-Sabbath. Foreign Matter and Vital Substances, Experts and the Critical Consumer in the FRG during the 1950s and 1960sIn the late Fifties and early Sixties the regulation of food additives represented a remarkable turning point in German consumer politics, establishing a debate about decision making and policy advice, altering the discourse of purity and contamination, and inaugurating a new political actor, the organized critical consumer. The amendment of the Food Law in December 1958 functioned as a negotiation process between representatives (...) of science, industry and the state, which was institutionalized in the Senate Commissions of the German Research Foundation. While these Commissions for preservatives, foreign matter and colorants worked behind closed doors, a public discourse about the “toxic condition” of modern life and the negative role of the pharmaceutical and chemical industry gained strength.The debate about the admission of hexamethylenetetramine (hexa) took part at a crucial moment. Hexa was used as a preservative in the fish industry. But its anti microbial effectiveness was caused by the decomposition of hexa to formaldehyde. Despite the commission’s verdict against hexa, the lobbying activities of the industry granted it a reprieve. In the media, the case of hexa was seen as a touchstone for the capacity of negotiated decision making and the ability of rational scientists to resist the demands of industry. Finally, in 1963 it was the new political actor of the organized critical consumer, heir and successor to the housewife federations as well as to “purists” advocating life reform, who, supported by the media, enforced the prohibition of hexa as a preservative. (shrink)