Hastings Center Report, Volume 51, Issue 5, Page 53-55, September‐October 2021.

Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| for c|$\vee (...) $|cHas are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce’s logic and Vakarelov’s logic MIN. With a focus on properties of the two negations, relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$| are obtained with respect to four classes of frames, and inter-translations between the classes preserving truth and validity are provided. ILM and |${\textrm {ILM}}$|-|${\vee }$| are shown to have the finite model property with respect to these classes of frames and proved to be decidable. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn’s logical framework for the purpose, two logics |$K_{im}$| and |$K_{im-{\vee }}$| are discussed, where the language does not include implication. The |$K_{im}$|-algebras are reducts of ccHas and are different from relevant algebraic structures having two negations. The negations in the |$K_{im}$|-algebras and |$K_{im-{\vee }}$|-algebras are shown to occupy distinct positions in an enhanced form of Dunn’s kite of negations. Relational semantics for |$K_{im}$| and |$K_{im-{\vee }}$| is provided by a class of frames that are based on Dunn’s compatibility frames. It is observed that this class coincides with one of the four classes giving the relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$|⁠. (shrink)

We investigate model theoretic characterisations of the expressive power of modal logics in terms of bisimulation invariance. The paradigmatic result of this kind is van Benthem’s theorem, which says that a first-order formula is invariant under bisimulation if, and only if, it is equivalent to a formula of basic modal logic. The present investigation primarily concerns ramifications for specific classes of structures. We study in particular model classes defined through conditions on the underlying frames, with a focus on frame classes (...) that play a major role in modal correspondence theory and often correspond to typical application domains of modal logics. Classical model theoretic arguments do not apply to many of the most interesting classes–for instance, rooted frames, finite rooted frames, finite transitive frames, well-founded transitive frames, finite equivalence frames–as these are not elementary. Instead we develop and extend the game-based analysis over such classes and provide bisimulation preserving model constructions within these classes. Over most of the classes considered, we obtain finite model theory analogues of the classically expected characterisations, with new proofs also for the classical setting. The class of transitive frames is a notable exception, with a marked difference between the classical and the finite model theory of bisimulation invariant first-order properties. Over the class of all finite transitive frames in particular, we find that monadic second-order logic is no more expressive than first-order as far as bisimulation invariant properties are concerned — though both are more expressive here than basic modal logic. We obtain ramifications of the de Jongh–Sambin theorem and a new and specific analogue of the Janin–Walukiewicz characterisation of bisimulation invariant monadic second-order for finite transitive frames. (shrink)

We consider fixed point logics, i.e., extensions of first order predicate logic with operators defining fixed points. A number of such operators, generalizing inductive definitions, have been studied in the context of finite model theory, including nondeterministic and alternating operators. We review results established in finite model theory, and also consider the expressive power of the resulting logics on infinite structures. In particular, we establish the relationship between inflationary and nondeterministic fixed point logics and second order logic, and we consider (...) questions related to the determinacy of games associated with alternating fixed points. (shrink)

We consider Choiceless Polynomial Time , a language introduced by Blass, Gurevich and Shelah, and show that it can express a query originally constructed by Cai, Fürer and Immerman to separate fixed-point logic with counting from image. This settles a question posed by Blass et al. The program we present uses sets of unbounded finite rank: we demonstrate that this is necessary by showing that the query cannot be computed by any program that has a constant bound on the rank (...) of sets used, even in image, an extension of image with counting. (shrink)

We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence ϕ in the language (...) of set theory that is in one of the following forms: ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns distinct values to all of the variables y1,…,yl, ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns the same value to all of the variables y1,…,yl. (shrink)

This important and comprehensive work of 18th-century Islamic religious thought written in Arabic by a pre-eminent South Asian scholar provides an extensive and detailed picture of Muslim theology and interpretive strategies on the eve of the modern period.

A Theory of Magnitude suggests that space, time, and quantities are processed through a generalized magnitude system. ATOM posits that task-irrelevant magnitudes interfere with the processing of task-relevant magnitudes as all the magnitudes are processed by a common system. Many behavioral and neuroimaging studies have found support in favor of a common magnitude processing system. However, it is largely unknown whether such cross-domain monotonic mapping arises from a change in the accuracy of the magnitude judgments or results from changes in (...) precision of the processing of magnitude. Therefore, in the present study, we examined whether large numerical magnitude affects temporal accuracy or temporal precision, or both. In other words, whether numerical magnitudes change our temporal experience or simply bias duration judgments. The temporal discrimination paradigm was used to present numerical magnitudes across varied durations. We estimated temporal accuracy and precision for each numerical magnitude. The results revealed that temporal accuracy for large numerical magnitude was significantly lower than that of small and identical magnitudes. This implies that the temporal duration was overestimated for large numerical magnitude compared to small and identical numerical magnitude, in line with ATOM’s prediction. However, no influence of numerical magnitude was observed on temporal precision. The findings of the present study suggest that task-irrelevant numerical magnitude selectively affects the accuracy of processing of duration but not duration discrimination itself. Further, we argue that numerical magnitude may not directly affect temporal processing but could influence via attentional mechanisms. (shrink)

This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first-order definable over the class of finite directed graphs and that this class admits a first-order definable global linear order. We apply this last result to show that FO = FO.

We sketch out two basic paradigms informing banking practice: the economistic paradigm focusing on profit maximization and the humanistic one, serving the common good. We then highlight paradigmatic cases to explore how each of these business models fared during the quasi-natural experiment of the financial crisis. We find that many humanistic banks outperformed traditional economistic banks. Despite the uneven playing field humanistic banks fared remarkably well with regard to traditional financial performance judgements, muting criticisms of competitiveness. We find that overall (...) both paradigms can provide a basis for successful banking as long as social and financial value generation are blended. We conclude by providing lessons learned for better banking. (shrink)

This experiment investigated the effect of format (line vs. bar), viewers’ familiarity with variables, and viewers’ graphicacy (graphical literacy) skills on the comprehension of multivariate (three variable) data presented in graphs. Fifty-five undergraduates provided written descriptions of data for a set of 14 line or bar graphs, half of which depicted variables familiar to the population and half of which depicted variables unfamiliar to the population. Participants then took a test of graphicacy skills. As predicted, the format influenced viewers’ interpretations (...) of data. Specifically, viewers were more likely to describe x–y interactions when viewing line graphs than when viewing bar graphs, and they were more likely to describe main effects and “z–y” (the variable in the legend) interactions when viewing bar graphs than when viewing line graphs. Familiarity of data presented and individuals’ graphicacy skills interacted with the influence of graph format. Specifically, viewers were most likely to generate inferences only when they had high graphicacy skills, the data were familiar and thus the information inferred was expected, and the format supported those inferences. Implications for multivariate data display are discussed. (shrink)

We consider the problem of obtaining logical characterisations of oracle complexity classes. In particular, we consider the complexity classes LOGSPACENP and PTIMENP. For these classes, characterisations are known in terms of NP computable Lindström quantifiers which hold on ordered structures. We show that these characterisations are unlikely to extend to arbitrary structures, since this would imply the collapse of certain exponential complexity hierarchies. We also observe, however, that PTIMENP can be characterised in terms of Lindström quantifers , though it remains (...) open whether this can be done for LOGSPACENP. (shrink)

Contemporary Kantianism is often regarded as both a position within normative ethics and as an alternative to metaethical moral realism. We argue that it is not clear how contemporary Kantianism can distinguish itself from moral realism. There are many Kantian positions. For reasons of space we focus on the position of one of the most prominent, contemporary Kantians, Christine Korsgaard. Our claim is that she fails to show either that Kantianism is different or that it is better than realism. Our (...) strategy is to argue that what are supposed to be claims that conflict with realism in fact do not. (shrink)

The U.S. Federal regulations allow institutional review boards (IRBs) to approve non-beneficial pediatric research when the risks are a minor increase over minimal, provided that the research is likely to develop generalizable knowledge about the subjects' disorder or condition. This “subjects' condition” requirement is quite controversial; commentators have argued for a variety of interpretations. Despite this considerable disagreement in the literature, there have not been any attempts to apply principles of legal interpretation to determine how the subjects' condition requirement should (...) be understood. (shrink)

Current formal dialectical models postulate normative rules that enable discussants to conduct dialogical interactions without committing fallacies. Though the rules for conducting a dialogue are supposed to apply to interactions between actual arguers, they are without exception theoretically motivated. This creates a gap between model and reality, because dialogue participants typically leave important content-related elements implicit. Therefore, analysts cannot readily relate normative rules to actual debates in ways that will be empirically confirmable. This paper details a new, data-driven method for (...) describing discussants’ actual reply structures, wherein corpus studies serve to acknowledge the complexity of natural argumentation. Rather than refer exclusively to propositional content as an indicator of arguing pro/contra a given claim, the proposed approach to dialogue structure tracks the sequence of dialogical moves itself. This arguably improves the applicability of theoretical dialectical models to empirical data, and thus advances the study of dialogue systems. (shrink)

تشخيص فكري ومعرفي لمفهوم الأسرة ومكانتها في الفكر الإسلامي، وتفحّصٌ علمي ومنهجي لأسس البناء الأسري ومقاصده، وكشفٌ عن تأثير التحوّلات الاجتماعية في الأسرة والتحديات التي تواجهها، وتتبعٌ لانعكاسات الفكر الغربي في المنظومة القيمية للأسرة، وتبيّنٌ لبعض التجارب والخبرات في مجال المحافظة على دور الأسرة، لا سيما بعد هيمنة النموذج المعرفي الغربي، ومحاولة طمسه للخصوصيات الثقافية والمجتمعية. حاولت بحوث هذا الكتاب أن تجيب عن تساؤلات معرفية ومجتمعية مهمة مثل: ما أهم التحديات التي تواجه الأسرة المسلمة في الراهن المعاصر وكيفية مواجهتها، وما (...) التغيرات التي طرأت على الأسرة المسلمة في ظل التطورات والتسارعات المجتمعية والاقتصادية والتقنية إلخ، وما التصوّر الإسلامي لدور الأسرة في بناء المجتمع، وما دور مؤسسات المجتمع المدني في الحد من تأثير الاستلاب الثقافي، وما الإسهام الذي قدمته حركات الإصلاح الإسلامية في مجال المحافظة على الدور المحوري للأسرة في تشكيل الشخصية الإسلامية القادرة على تفعيل النهوض الحضاري؟ وقد أسهم المشاركون في هذا العمل الجماعي، الذين بلغ عددهم واحداً وعشرين باحثاً، في محاورة هذه الأسئلة المعرفية، وفي التأسيس لمنظومة معرفية مجتمعية قادرة على الإسهام في البناء الحضاري، وفي توجيه دفة الأسرة بما ينسجم مع التوجيهات الربانية والفطرة الإنسانية. (shrink)

This essay begins by focusing on four cultural characters that signify different but associated aspects of the changing destiny of the human figure at the end of the twentieth century and beyond. These characters embody the human figure, in the double sense of form and metaphor, at work, at leisure and at war, and as gendered cultural and philosophical ideal. It is our suggestion that they provide excellent images of a general economy of the future present. Their significance as indices (...) of the destiny of the human resides in the way that they disclose the effects of a restricted economy that overflows its boundaries to incorporate, utilise and restrict every element of its generalised expenditure, to use the categories of Georges Bataille: its sumptuary excess, its sacred forms, its abjected waste, its modes of eroticism, its violence. The essay continues by discussing the implications of, and consequences for, human life in the face of the corporate or techno‐bureaucratic drive to incorporate the ‘impossible‐real’. For Paul Virilio, the technological desire to overwrite the temporal and spatial dimensions of ‘the actual’ discloses something of the ‘divine’ in this new technology. In conclusion, then, the essay questions what resistance there might be to the law of the machine‐God who lies, impossibly, as the immanent being of machinic efficiency, operativity and becoming excellence. (shrink)

Research teams have made considerable progress in treating absolute uterine factor infertility through uterus transplantation, though studies have differed on the choice of either deceased or living donors. While researchers continue to analyze the medical feasibility of both approaches, little attention has been paid to the ethics of using deceased versus living donors as well as the protections that must be in place for each. Both types of uterus donation also pose unique regulatory challenges, including how to allocate donated organs; (...) whether the donor / donor's family has any rights to the uterus and resulting child; how to manage contact between the donor / donor's family, recipient, and resulting child; and how to track outcomes moving forward. (shrink)

This study aims to draw a gender based analysis of social and economic conditions of child labourers living in Karachi. Globally the issue of child labour is growing constantly and children are engaged in all sorts of hazardous forms of work, like adults, which deprives them from education, healthy life, child hood activities and balanced diet. In Pakistan the child labour is very common in all economic sectors, but it is mainly found in the informal sector and the household sector. (...) Purposive and convenience sampling techniques of non-probability sampling are used to collect data through structured questionnaire from 900 respondents from eighteen administrative districts of Karachi, which is based upon primarily quantitative and narrowly focused qualitative research methods. The findings of the study reveal that mostly children between the ages of 12 to 14 years are commonly inducted in different economic sectors. This clear violation of child rights makes them vulnerable to health and safety threats and putting them forcefully in hazardous occupations to earn bread and butter for their family by compromising their education. (shrink)

Writing the Mughal World: Studies on Culture and Politics. Muzzafar Alam and Sanjay Subrahmanyam. New York: Columbia University Press, 2011. Pp. xviii + 516. $89.50, £62 ; $29.50, £20.50.

Visual masking of primes lowers prime visibility but spares processing of primes as reflected in prime–target congruence and prime–response compatibility effects. However, the question is how to appropriately measure prime visibility. Here, we tested the influence of three procedural variables on prime visibility measures: prime–target similarity, prime–response similarity, and the variability of prime–response mappings. Our results show that a low prime–target similarity is a favorable condition for a prime visibility measure because it increases the sensitivity of this measure in comparison (...) to a high prime–target similarity. (shrink)

Believing that p, assuming that p, and imagining that p involve regarding p as true—or, as we shall call it, accepting p. What distinguishes belief from the other modes of acceptance? We claim that conceiving of an attitude as a belief, rather than an assumption or an instance of imagining, entails conceiving of it as an acceptance that is regulated for truth, while also applying to it the standard of being correct if and only if it is true. We argue (...) that the second half of this claim, according to which the concept of belief includes a standard of correctness, is required to explain the fact that the deliberative question whether to believe that p is transparent to the question whether p. This argument raises various questions. Is there such a thing as deliberating whether to believe? Is the transparency of the deliberative question whether to believe that p the same as the transparency of the factual question whether I do believe that p? We will begin by answering these questions and then turn to a series of possible objections to our argument. (shrink)