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)

Closure-class formation involves two structurally distinct questions: the conditions under which closure of a specified class is admissible, and the contingent events through which any specific closure realizes. This paper develops the conditions side. Five structural obstruction modes — sparse-feedback, fragment-local, cost-imbalanced, energetically-starved, dimensionally-trapped — characterize seed-field incompetence: the conditions under which a substrate region is excluded from supporting closure-class formation across its accessible perturbation regimes. The admissibility theorem characterizes which closure classes a competent region admits as a (...) class='Hi'>function of a parameter family indexing the substrate's coupling structure, boundary exposure, energetic and temporal accessibility, and dimensional access. The theorem is stated spectrally — admissibility iff the linearized closure-formation operator possesses an unstable mode satisfying structural and dynamical conditions — and equivalently in variational form via the closure-potential functional. The four-stage architecture for closure-class formation (competence, admissibility, embryo formation, basin completion) entails a cascade structure in which closure-formation rates compose multiplicatively across stages, so that progressively more demanding closure classes are progressively rarer by structural composition rather than stipulation. The cascade is observable through four ensemble signatures — critical slowing, hysteresis, post-collapse renucleation, basin-deepening — that specialize the early-warning-signal apparatus independently developed in tipping-point ecology and regime-shift detection to closure-class transitions across substrate types. Consciousness-class closure is treated as a further-conditioned special case in which the cascade structure entails the framework's predicted rarity without further stipulation. (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)

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)

We propose two admissible closures \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{A}({\sf PTCA})}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{A}({\sf PHCA})}$$\end{document} 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) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{A}({\sf PTCA})}$$\end{document} is conservative over PTCA with respect to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall\exists\Sigma^b_1}$$\end{document} sentences, and (ii) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{A}({\sf PHCA})}$$\end{document} is conservative over full bounded arithmetic PHCA for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall\exists\Sigma^b_{\infty}}$$\end{document} sentences. This yields that (i) the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^b_1}$$\end{document} definable functions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{A}({\sf PTCA})}$$\end{document} are the polytime functions, and (ii) the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^b_{\infty}}$$\end{document} definable functions of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{A}({\sf PHCA})}$$\end{document} 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 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)

Data from college admissions tests can provide a valuable measure of student achievement, but the non-representativeness of test-takers is an important concern. We examine selectivity bias in both state-level and school-level SAT and ACT averages. The degree of selectivity may differ importantly across and within schools, and across and within states. To identify within-state selectivity, we use a control function approach that conditions on scores from a representative test. Estimates indicate strong selectivity of test-takers in "ACT states," where most (...) college-bound students take the ACT, and much less selectivity in SAT states. To identify within- and between-school selectivity, we take advantage of a policy reform in Illinois that made taking the ACT a graduation requirement. Estimates based on this policy change indicate substantial positive selection into test participation both across and within schools. Despite this, school-level averages of observed scores are extremely highly correlated with average latent scores, as across-school variation in sample selectivity is small relative to the underlying signal. As a result, in most contexts the use of observed school mean test scores in place of latent means understates the degree of between-school variation in achievement but is otherwise unlikely to lead to misleading conclusions. © 2008 Elsevier Ltd. (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)

Abstract We present a functional quantization scheme for a symmetric tensor field defined on a differentiable temporal base without metric structure. By replacing the Hilbert space formalism with a functional integral over admissible configurations of the field, we show that quantum phenomena (interference, decoherence, measurement) emerge as statistical effects of dynamically stabilized configurations. This framework offers a rigorous alternative to operator-based quantum mechanics, without invoking background geometry, and recovers classical structures in appropriate asymptotic limits.

We present a functional quantization scheme for a symmetric tensor field de- fined on a differentiable temporal base without metric structure. By replacing the Hilbert space formalism with a functional integral over admissible configurations of the field, we show that quantum phenomena (interference, decoherence, measure- ment) emerge as statistical effects of dynamically stabilized configurations. This framework offers a rigorous alternative to operator-based quantum mechanics, with- out invoking background geometry, and recovers classical structures in appropriate asymptotic limits.

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)

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)

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)

The use of suicide risk assessments in individual psychiatric treatment is widespread and, in many countries, mandatory. However, these assessments exhibit poor predictive accuracy and offer limited clinical value. This raises the question of whether non-medical reasons underpin their continued use. In this paper, suicide risk assessments are interpreted as medical rituals—formalized, repetitive behaviours imbued with symbolic significance that fulfil social functions. Several such functions are proposed, including uniting care providers around shared values in suicide prevention, fostering a sense of (...) safety and control over suicidal behaviour, projecting accountability, and signalling to the public that action is being taken. However, this practice may inadvertently lead to an increase in non-beneficial compulsory admissions, flawed prioritization of patients, and the proliferation of defensive medicine. While the ritualistic use of suicide risk assessments may serve important societal purposes, their potential to harm individual patients renders them indefensible from a medico-ethical standpoint.Instead, evidence-based suicide preventive interventions are recommended. These include implementing general safety measures, equipping psychiatric patients with safety plans, and providing effective mental health treatment according to medical needs. (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)

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)

For twenty-five centuries the theory of inference has asked how warrant moves from evidence to conclusion, and its principal instruments, deduction, induction, abduction, Hegelian dialectic, consilience, and Bayesian credence, were each built to answer that question. What none of them answers is whether the evidence structure on which any such move runs is itself sound. Every mode in the tradition presupposes, and cannot certify, the independence and non-degeneracy of its evidence lines: a Bayesian posterior strengthens under a latent common cause (...) that should dissolve the convergence, consilience celebrates an independence it possesses no operational test for, and falsification cannot recognize a falsifier without a verification frame it does not supply. This paper presents Trisduction, a verification architecture operating at the certification layer beneath inference. Complete factual claims decompose, under a reproducible deletion test, into exactly three independent warrant lines, formal, empirical, and registrational; the three lines close geometrically on a fourth point into twelve directed verification conditions; and the verdict takes closed mathematical form, det(R) = (Re(q̂_F q̂_E q̂_ER))², a three-state output, sealed, broken, under-determined, whose admissible functional class is provably closed. The architecture's primary discriminator is provable and testable: on collinear evidence a Bayesian posterior strictly increases while the verdict determinant vanishes identically, and no weighted aggregation of positive inputs can vanish on collinear data, with the 2014 BICEP2 announcement and its Planck dust resolution supplying the worked historical case and an eight-check executable battery reproducing the verdict identities at machine precision on any floating-point substrate. If the analysis stands, the long search for epistemic certainty terminates the way genuine searches terminate, in a classification: indefeasibility is provably unattainable for finite verifiers, maximal warrant is attainable and its instrument is closed, and each historical mode survives, completed, at the one layer it actually occupies. (shrink)

This paper introduces a stratified non-normal modal logic, denoted R0, designed to formalize tran- sitions between epistemic regimes with partially ordered constraint structures. Unlike standard modal systems, R0 rejects normality and duality, allowing a finer articulation of local validity and inter-regime tension. The logic features regime-indexed modal operators, a stratified admissibility function, and a stability condition that governs modal transitions. We provide a formal Kripke-style semantics based on partial inclusion of constraint sets, and prove a completeness theorem relative to (...) this semantics. The system is self-sufficient within its minimal formal setting, yet explicitly avoids ontological or epistemic closure, making it suitable for applications in pluralist philosophy of science, model-theoretic relativism, and the formal analysis of conceptual change. This work lays the groundwork for a general theory of modal reasoning under heterogeneous and dynamically shifting regimes of validity. Open to feedback. (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)

This article provides a framework for comparing meritocratic and affirmative action admissions policies. The context of the analysis is admissions to public universities; admission rules are evaluated as part of the public investment problem faced by a state government. Meritocratic and affirmative admissions policies are compared in terms of their effects on the level and distribution of human capital. I argue that (a) meritocratic admissions are not necessarily efficient and (b) affirmative action policies may be efficiency enhancing relative to meritocratic (...) ones. Both these claims, as well as their negations, depend on features of individual behavior for which there is little empirical evidence. The implications of this absence of evidence are then explored, with a focus on policy evaluation when equality and efficiency are both desiderata. I argue that standard statistical decision theoretic approaches do not apply to the affirmative action case, even if equality and efficiency are rendered commensurable based on a scalar payoff function. In this context, I suggest that a presumption for equality-enhancing policies leads to support for affirmative action, but I emphasize the contingent nature of this conclusion. Key Words: affirmative action • meritocracy • college admissions • efficiency. (shrink)

Continuum physics represents states as real- or complex-valued fields and dynamics as operators on infinite-dimensional function spaces. Under an ontic interpretation, however, fundamental evolution must be semantically total: it must take every admissible state specification to a successor state specification in which all admitted magnitudes remain denoting. We make this requirement explicit using standard admissible representations, in which denotation is characterized by bounded finite-precision input dependence on state descriptions. We show that standard continuum dynamics can violate this (...) semantic closure requirement even when the underlying PDE is linear, well posed, and uniquely solvable. The obstruction is forced extensional totalization: a regional readout can require joint control over countably many individually well-behaved contributions in a way that destroys bounded input dependence and hence denotation. Because locality commits a field ontology to treating spatial restrictions on compact regions as single physical magnitudes, this failure mode cannot be avoided by appealing to pointwise readouts or sequential access. Reanalyzed in these terms, the Pour-El and Richards Theorem 2 construction for the three-dimensional wave equation provides a concrete witness: admissible finite energy initial data evolve to states whose regional field restrictions do not admit admissible names in the required function space topology. The obstruction is semantic rather than epistemic: it does not concern what can be computed or observed, but the failure of continuum evolution to preserve denotation under realist locality commitments. The conclusion is eliminative: unrestricted continuum field ontology cannot serve as the basis of a semantically closed fundamental dynamics. (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)

Bearers track closure classes; closure classes do not track bearers. This inversion is the substantive claim the present paper defends, and its grounds are structural: the framework operates at the admissibility stratum, characterizing what closure formation can produce; bearers are realization-stratum products of closure formation; the partition between class members and non-members is a consequence of closure rather than a feature of the framework's structural commitments. The seed-field framework (Thomas 2026a) characterizes closure-class formation through structural conditions on admissibility analysis, but (...) the relation between class C and the conditions characterizing it is left underspecified in that paper alone; the present paper specifies the relation by establishing where the framework's apparatus operates and what it characterizes. The structural conditions S_C are specified through five formal families — eigenstructure conditions on the linearized closure-formation operator, rank conditions on the eigenmode's projection across maintenance-cost surfaces, graph-theoretic support conditions on the correction graph, scaling conditions on the cost functional, and bound conditions on the temporal ratios — each statable on the admissibility analysis without reference to bearer-types. Closure classes are equivalence classes of closures whose admissible modes satisfy a given S_C, with class identity attaching to constraint-preserving dynamical possibility structure rather than to recognized bearer-type. The apparatus is read correctly across five common questions through the bearers-track-classes inversion, the distinction among definitional, discovery, and naming dependence, the Platonism disclaimer, the demonstration that the apparatus extends to hypothetical and uninstantiated classes, and the labels-versus-apparatus distinction. The methodological precedent is the universality-class apparatus in critical phenomena, which operates at the class stratum upstream of where phase boundaries are realized. The consequence framing licenses cross-substrate predictions: substrates satisfying S_C in basin completion produce closure with the structural features S_C characterizes, regardless of substrate type. The framework's empirical commitments are preserved with this addition; the architectural foundation is clarified. (shrink)

Standard accuracy arguments for Probabilism require acceptable scoring rules to be strictly proper. This requirement makes these arguments question-begging. In this paper, I offer an alternative, better argument for a version of Probabilism. It avoids the strict propriety requirement, hence, my argument is not question-begging. Moreover, dropping strict propriety enables agents to use a wider variety of scoring rules, giving them more freedom in how to represent their uncertainty. My argument utilizes and improves upon an old argument by Dennis Lindley (...) for the conclusion that representations of uncertainty are rationally admissible if and only if they are probabilistic through a transform. This means that these representations must be implicitly probabilistic through a transform function that is uniquely determined by the agent's scoring rule. This conclusion is preferable to Probabilism, as it is both more permissive in how agents can represent their uncertainty and relies on weaker and less questionable premises. (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)

In contrast to Kant’s metatheoretical (“transcendental”) approach grounded in the operations of an abstract logical subject, Herbart and Bolzano aimed to avoid subject-dependent foundations of logic. They instead proposed formal logics founded, respectively, on the form of conceptual content (Herbart) and on the extensions of logical forms (Bolzano). Among the traditions originating from Herbart and Bolzano, we consider the role of Bolzano’s informal disciple Robert Zimmermann, who subsequently adopted Herbartianism, and Zimmermann’s own disciple, the mathematical logician and philosopher Albino Nagy. (...) Special attention is given to Nagy’s analysis of expressive completeness and his treatment of the Jevons-Clifford problem: how many and which types and representatives of types there are of Boolean propositional functions. We transform this latter problem into the question of types of sequent refutations and examine the corresponding admissibility of the cut rule. (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)

The admissions cheating scandal illustrated how colleges and universities in the US depend upon and reinforce socio-economic privilege. The first part of this paper uses a Reformed Christian approach to moral virtue to analyze privilege in higher education as an ethical problem. Understanding privilege as moral vice clarifies the relationships between practices, attitudes, and intentions we associate with privilege. The second part of this paper contrasts ethical frameworks prominent in the discourse on higher education with a commitment to the common (...) good. Within an ethics of the common good, privilege’s function as vice becomes clear, as does its deleterious effect on US higher education’s “original intent.” Ultimately, cultivation of a “character of inclusion” is the necessary antidote to the vice of privilege, to realign higher education with its historic responsibility to the common good of a just society. (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 develops a categorical distinction between two kinds of informational object: compressed descriptions, which specify a full admissible configuration space without selecting any particular element, and resolved descriptions, which contain selection information identifying one particular element as actual in a structural sense. -/- The distinction is anchored in the Kolmogorov structure function decomposition, which independently identifies model and selection components as formally separable individual-level facts in individual strings, and motivates the extension to descriptions in general by analogy. (...) On this basis, the paper develops and argues for the Compression--Resolution Duality: no single informational object can simultaneously be compressed and resolved with respect to the same admissible configuration space. This is the paper's central formal result. -/- The paper then develops two structural consequences. The Hierarchical Asymmetry argues that elimination across levels is local while resolution is perspectivally global: from the perspective of any resolved description, the containing descriptions are presupposed as resolved from within that description, whereas compressed descriptions generate no such chain. -/- The Boundedness interpretation, motivated by the Hierarchical Asymmetry, proposes that resolved descriptions are self-limiting---unable to represent the containing structure without access to compressed information they lack. -/- These structural claims are explored in application to the relationship between the universal wavefunction and any particular experienced quantum outcome: from within a resolved description of an outcome, other outcomes are not absent from what the wavefunction encodes---they are inaccessible from within that descriptive environment. -/- The paper does not adjudicate between interpretations of quantum mechanics. The analysis is structural and informational throughout, making no claims about physical dynamics, temporal processes, or empirical matters. (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)

Causal–Continuity Stabilization Theory (CCST) characterizes macroscopic causal persistence as a physical stability property of finite substrates rather than as an ontological feature of the universal wavefunction. In its original formulation, CCST formalized descriptive admissibility: a coarse–grained macroscopic causal history remains well–posed only when thermodynamic dissipation stays below a substrate–dependent bound and when coarse–grained dynamical sensitivity preserves closure. This work develops an extension of CCST that targets a logically distinct stability question in Everettian dynamics: not only whether a macroscopic description remains (...) admissible within a branch, but whether a branch structure itself can remain dynamically coherent as an organized physical entity under sustained environmental coupling. Although unitary quantum mechanics preserves all components of the global quantum state [1, 2], organized branch structure may dynamically disperse into microscopic degrees of freedom under open–system dynamics, thereby losing the correlation patterns required for macroscopic organization [3, 4]. We distinguish structural dispersion (loss of branch–level organizational coherence) from Causal Exit (loss of description–level definability on a finite physical substrate), emphasizing that these correspond to stability failures at distinct physical layers and should not be conflated. We derive a dynamical weighting over coarse–grained path ensembles from open–system effective action and influence functional formalisms [5–7], showing how microscopic dynamics inducesanon–uniformstabilitygeometryinpathspacethroughirreversibledynamicalsuppression rather than probabilistic selection, without introducing collapse, selection rules, or inter–branch transport. Finally, a minimal toy model is introduced to visualize the qualitative sensitivity of branch structural persistence under controlled stability thresholds. The model is strictly illustrative and is accompanied by transparent parameter definitions and a reproducible numerical implementation in the appendix. (shrink)

In this paper the classical topic of “conventionality” in defining the simultaneity (or synchrony) of distant events is tackled again, and the validity of Reichenbach's view is carefully circumscribed. In particular, the role of “one-way” assumptions in the foundations of special relativity is emphasized. The restriction by the round-trip isotropy condition on the admissible distance functions in inertial frames is studied, and its relevance to several issues (absolute simultaneity, the interpretation of Michelson–Morley type experiments, the self-measured speed of a (...) clock) is shown. Two “clock transport” synchronizations in an inertial frame, using self-measured speed and “proper distance,” are presented in detail, and the agreement of the synchronies so established with standard synchrony is proven to be non- circular. By assuming a reasonable concept of “convention” this result is shown to dissolve several objections by supporters of a strong version of conventionalism. Throughout, a number of common misapprehensions in the literature are pointed out. (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)

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)

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)

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 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)

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)