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)

ABOUT THE BOOK:Sri Aurobindo has developed an original system of the Vedanta called Integral Advaitism. This book gives a systematic, thorough and authentic exposition of his thought. The fundamental and living issues, namely, the concept of the Absol.

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)

With the end of the Cold War, political and ideological competition has decreased as a stated reason for space exploration. The possibility of establishing a settlement on Mars is being seriously evaluated by state and commercial space agencies, which includes objectives to expand human civilization and ensure the continuity of the human species. The technological challenges associated with space settlement continue to receive significant attention, but the success of space settlement will also depend on other human factors. This study presents (...) a high-level overview of some potential issues that could arise with the development of a permanent populationand a space economyon Mars. This study highlights some of the anticipated problems of overnance, trade, production, and proliferation that will need pragmatic solutions to ensure the sustainability of a martian settlement. This paper is intended to instigate further discussion and research regarding human and economic factors that could enable or constrain future settlements on Mars. (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)

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)

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)

Immanuel Kant, with his “brilliantly dry style” (Schopenhauer), expounds the notable theory that “objects are approaching to the mind” via the spectacle metaphor by addressing transcendental idealism in support of the mind as an active knower (mind-making nature), not passive in a realistic sense, while objects of knowledge conform to the mind begotten in categories of understanding. On Kant’s view, James Conant writes, “Kant’s term for this unity, considered at this level of abstraction, is the original synthetic unity of the (...) understanding. This admits of forms of further determination, one sensible and one intellectual. This form of unity – categorial unity – characterizes both the manner in which objects are given to us in intuition and the manner in which concepts are combined in judgments” (Conant 2016: 114). -/- Insofar the same pioneering stance is reflected in the Groundwork of Metaphysics of Morals (Kant 1972) and the Critique of Practical Reason (Kant 1996), where Kant underscores the accessible account of reason and freedom as the content of fundamental moral principle toward a kind of universalizable moral duty attuned with the formulation of categorical imperative. The justification and groundwork of these moral laws cannot be liaison in sensory experience but on pure reason, which Kant calls “a priori,” a conviction stems from the understanding of rational necessitation of moral obligation and free autonomous agency. This interpretation absorbs the practical principle that underlies the subjective maxim to justify the necessary and sufficient conditions for a universal moral law. Kant starts out saying that an act is morally right if it is performed for the sake of broadening the vista of maxim infused by goodwill consisting of the categorical imperative that sounds an exceptionless command, abstract law, and universally applicable normative principle as well. For Kant, the categorical imperative has many-sided structures: a. Ethical requirements are rational requirements of the moral agent. b. The rational requirement goes toward universal laws. c. These moral requirements must be followed by equality, freedom, and goodwill. (shrink)

Over the past decade, Convergence Research has increasingly gained prominence as a research, development, and innovation (RDI) strategy to address grand societal challenges. However, a dearth of research-based evidence is available to aid researchers, research teams, and institutions with navigating the complexities attendant to the specifics of Convergence Research. This paper presents a multilevel research agenda that accounts for an integral understanding of Convergence Research as a complex adaptive system. Furthermore, by developing a framework that accounts for ancillary, yet essential, (...) systems associated with Convergence Research, we enrich the agenda with a literature-steeped discussion that considers how systems-based practices of collaboration, inquiry, and context interact with the processes and products of Convergence Research. Finally, we synthesize and apply insights from the reviewed literature by providing paths for empirical exploration emphasizing systems-based practices. In so doing, we delineate an extended boundary for a research stream that both clarifies and enlarges our understanding of Convergence Research as a ‘system-of-systems’. (shrink)

Anthropogenic climate change poses some difficult ethical quandaries for non-anthropocentrists. While it is hard to deny that climate change is a substantial moral ill, many types of non-human organisms stand to benefit from climate change. Modelling studies provide evidence that net primary productivity (NPP) could be substantially boosted, both regionally and globally, as a result of warming from increased concentrations of greenhouse gases. The same holds for deployment of certain types of climate engineering, or large-scale, technological modifications of the global (...) environment in order to prevent or slow anthropogenic climate change. For example, solar radiation management with stratospheric aerosol injections could benefit plant life by promoting enhanced photosynthesis, increasing diffuse radiation, and reducing heat stress. This has a surprising implication: from some non-anthropocentric perspectives, certain scenarios of climate change and climate engineering might bring about morally better states of affairs when compared to emission-mitigation baselines. (shrink)

There is a growing need to identify what really can converge classroom learning to the real-life practising of ethical principles. We examine if the effectiveness of ethics education can be improved through meditation-based mindfulness intervention. Our baseline experiment is a procedurally modified version of the anagram exercise (Ruedy and Schweitzer 2010) for measuring unethical behaviour. We introduce a brief meditation intervention to induce instant mindfulness. Our findings indicate substantive evidence confirming the positive effect of the state of mindfulness on ethical (...) behaviour. Subjects in the meditation group engage in more low-level cheating compared to the control group who cheated more severely. Gender and academic grade do not influence ethical behaviour. Mindfulness fosters composure, mental poise, and a conducive environment for upholding ethical values, as indicated by a lower incidence of cheating in our study. We propose to promote a learning environment with mindfulness intervention in educational programmes. (shrink)

This article explored the role of personality disposition and value preference as predictors of social well-being in the context of ecological setting. Ecological contexts like rural and urban are critical, particularly in a developing country like India, because they represent significant disparities and variations in the lived experiences of the people. The participants from the age range of 15–65 years were drawn from two ecological settings, that is, rural and urban and from both the genders. They completed the measures of (...) social well-being, value preference and personality dispositions. The results showed that the different facets of social well-being were differentially related to the aspects of personality and value preference. Ecological setting had significant influence on the measures of personality disposition, value preference and social well-being. Regression analysis showed that except neuroticism, all other factors of personality had consistent positive contribution as the predictors of social well-being. It was also observed that social value and growth factors of value preference had significant contribution, whereas personal value and protection—factors of value preference—had negative contribution as the predictors of social well-being. (shrink)

Commentary on Judith Shklar's skepticism has ranged from the claim that it was not the central characteristic of her thought to the argument that it seriously hobbled her thinking about justice. In fact Shklar's uniqueness as a thinker resides precisely in the fact that she combined a sweeping skepticism with a strong commitment to liberal justice. Skepticism interacted with her liberal moral commitments to inspire her account of injustice, without which her views about justice are impossible to grasp. Shklar's skepticism (...) produced her laser-like focus on sources of injustice and oppression for the individual, whom she perceived to be potentially threatened no less by tribe, nation, family, or a democratic citizens' community than by the state itself. It produced not only her highly original insights into the inadequacy of all existing models of justice, but also her subtle yet concerted effort to render democracy safe for liberalism in political theory while at the same make liberalism more egalitarian. (shrink)

In a recent editorial, Raymond Spier expresses skepticism over claims that climate change is driven by human actions and that humanity should act to avoid climate change. This paper responds to this skepticism as part of a broader review of the science and ethics of climate change. While much remains uncertain about the climate, research indicates that observed temperature increases are human-driven. Although opinions vary regarding what should be done, prominent arguments against action are based on dubious factual and ethical (...) positions. Thus, the skepticisms in the recent editorial are unwarranted. This does not diminish the general merits of skeptical intellectual inquiry. (shrink)