In this paper we present a general method of solving Smullyan’s puzzles. We do this by showing how a puzzle is translated into Classical Propositional Calculus.

In [4] R.Cowen considers a generalization of the resolution rule for hypergraphs and introduces a notion of satisfiability of families of sets of vertices via 2-colorings piercing elements of such families. He shows, for finite hypergraphs with no one-element edges that if the empty set is a consequence ofA by the resolution rule, thenA is not satisfiable. Alas the converse is true for a restricted class of hypergraphs only, and need not to be true in the general case. In this (...) paper we show that weakening slightly the notion of satisfiability, we get the equivalence of unsatisfiability and the derivability of the empty set for any hypergraph. Moreover, we show the compactness property of hypergraph satisfiability and state its equivalence to BPI, i.e. to the statement that in every Boolean algebra there exists an ultrafilter. (shrink)

Progress in the medical diagnostic is relentlessly pushing the measurement technology as well with its intertwined mathematical models and solutions. Mathematics has applications to many problems that are vital to human health but not for all. In this article we describe how the mathematics of acoustocerebrography has become one of the most important applications of mathematics to the problems of brain monitoring as well we will show some algebraic problems which still have to be solved. Acoustocerebrography is a set of (...) techniques of visualizing the state of brain tissue and its changes with use of ultrasounds, which mainly rely on a relation between the tissue density and speed of propagation for ultrasound waves in this medium. Propagation speed or, equivalently, times of arriving for an ultrasound pulse, can be inferred from phase relations for various frequencies. Since, due to Kramers-Kronig relations, the propagation speeds depend significantly on the frequency of investigated waves, we consider multispectral wave packages of the form W = ∑Hh=1 Ah · sin, n = 0,..., N – 1 with appropriately chosen frequencies fh, h = 1,...,H, amplifications Ah, h = 1,...,H, start phases ψh, h = 1,..., H and sampling frequency F. In this paper we show some problems of algebraic and, to some extend, algorithmic nature which raise up in this topic. Like, for instance, the influence of relations between the signal length and frequency values on the error on estimated phases or on neutralizing alien frequencies. Another problem is finding appropriate initial phases for avoiding improper distributions of peaks in the resulting signal or finding a stable algorithm of phase unwinding which is resistant to sudden random disruptions. (shrink)

We extend some results of Adam Kolany to show that large sets of satisfiable sentences generally contain equally large subsets of mutually consistent sentences. In particular, this is always true for sets of uncountable cofinality, and remains true for sets of denumerable cofinality if we put appropriate bounding conditions on the sentences. The results apply to both the propositional and the predicate calculus. To obtain these results, we use delta sets for regular cardinals, and, for singular cardinals, a generalization (...) of delta sets. All of our results are theorems in ZFC. (shrink)

In this essay, we suggest practical ways to shift the framing of crisis standards of care toward disability justice. We elaborate on the vision statement provided in the 2010 Institute of Medicine (National Academy of Medicine) “Summary of Guidance for Establishing Crisis Standards of Care for Use in Disaster Situations,” which emphasizes fairness; equitable processes; community and provider engagement, education, and communication; and the rule of law. We argue that interpreting these elements through disability justice entails a commitment to both (...) distributive and recognitive justice. The disability rights movement's demand “Nothing about us, without us” requires substantive inclusion of disabled people in decision‐making related to their interests, including in crisis planning before, during, and after a pandemic like Covid‐19. (shrink)

This third edition of The Infinite includes a new part 'Infinity Superseded' which contains two new chapters refining Moore's ideas through a re-examination of the ideas of Spinoza, Hegel, and Nietzsche. Much of this is heavily influenced by the work of Deleuze. There is also a new technical appendix on still unresolved issues about different infinite sizes.

Is there any link between the doctrine of logical fatalism and prime numbers? What do logic and prime numbers have in common? The book adopts truth-functional approach to examine functional properties of finite-valued Łukasiewicz logics Łn+1. Prime numbers are defined in algebraic-logical terms and represented as rooted trees. The author designs an algorithm which for every prime number n constructs a rooted tree where nodes are natural numbers and n is a root. Finite-valued logics Kn+1 are specified that they have (...) tautologies if and only if n is a prime number. It is discovered that Kn+1 have the same functional properties as Łn+1 whenever n is a prime number. Thus, Kn+1 are 'logics' of prime numbers. Amazingly, combination of logics of prime numbers led to uncovering a law of generation of classes of prime numbers. Along with characterization of prime numbers author also gives characterization, in terms of Łukasiewicz logical matrices, of powers of primes, odd numbers, and even numbers. (shrink)

The paper builds on the postulate of “myths we live by,” which shape our imaginative life (and hence our social expectations), but which are also open to reflective study and reinvention. It applies this principle, in particular, to the concepts of love and vulnerability. We are accustomed to think of the condition of vulnerability in an objectifying and distancing way, as something that affects the bearers of specific (disadvantaged) social identities. Against this picture, which can serve as a pretext for (...) paternalist and controlling attitudes to the groups in question – notably to women – Anderson urges us to reimagine our vulnerability as a condition not merely of exposure to violence but of openness to mutual affection, love, and friendship. Hegel’s celebrated image of the owl of Minerva, which takes wing only with the coming of dusk, suggests an association of (philosophical) wisdom with negativity – with the experience of death or loss. Anderson, by contrast, proposes an alternative and more hopeful image of the dawn of enlightenment, in the guise of new ethical dispositions shaped by an emancipatory (and so, no longer an oppressive or sexist) conception of our capacity for love. Her main interlocutors or influences in this piece are Judith Butler (who contributes the idea of a “relational ontology”), Michèle Le Doeuff, and Mary Midgley. (shrink)

In this paper, we present an expansion of one of the well-known classical inventory management models, which is the static model of inventory management without a deficit and for a single substance, based on the neutrosophic logic, where we provide through this study a basis for dealing with all data, whether specific or undefined in the field of inventory management, as it provides safe environment to manage inventory without running into deficit , and give us an approximate ideal volume of (...) inventory. Since the ideal size is affected by the rate of demand for inventory, we present in this paper a study of the rate of demand for inventory when it is not precisely refined, and we find that the indeterminate values of the demand rate cannot be ignored, because they actually affect determining the ideal size of inventory and calculating its costs, thus affecting on the efficiency of the facility and achieve great profits for it. (shrink)

The star-nosed mole is aptly named. Its distinctive snout consists of 22 tendrils ringing a pair of nostrils and, from some angles, the entire setup resembles a misshapen star. The tendrils are fleshy and look a bit like fingers, and, like fingers, they have a certain dexterity. But why? Why does the mole have such a singular appendage as opposed to something more ordinary? What is the function or purpose of this bizarre structure? From the dedicated work of Ken Catania, (...) of Vanderbilt University, and colleagues, it appears that the appendage facilitates rapid handling of small prey items, making it advantageous for an organism whose diet consists of tiny invertebrates. We might therefore hazard that this feature arose evolutionarily because it conferred this benefit. But the matter is difficult to resolve, because current utility does not permit a straightforward inference of a reason for existence. -/- A correction has been published: BioScience, Volume 72, Issue 7, July 2022, Page 708. (shrink)

Political and social thoughts of Muḥammad Ḥusayn Ṭabāṭabāʼī and Thomas Hobbes,1588-1679.

On Roger Bacon's life and works, by A. G. Little.--Der einfluss des Robert Grosseteste auf die wissenschaftliche richtung des Roger Bacon, von Ludwig Baur.--La place de Roger Bacon parmi les philosophes du XIIIe siècle, par François Picavet.--Roger Bacon and the Latin vulgate, by Francis Aidan, cardinal Gasquet.--Roger Bacon and philology, by S. A. Hirsch.--The place of Roger Bacon in the history of mathematics, by David Eugene Smith.--Roger Bacon und seine verdienste um die optik, von Eilhard Wiedemann.--Roger Bacons lehre von der (...) sinnlichen spezies und vom seḣvorgange, von Sebastian Vogl.--Roger Bacons art des wissenschaftlichen arbeitens dargestellt nach seiner schrift De speculis, von J. Würschmidt.--Roger Bacon et l'horreur du vide, par Pierre Duhem.--Roger Bacon, his relations to alchemy and chemistry, by M. M. Pattison Muir.--Roger Bacon and gunpowder, by H. W. L. Hime.--Roger Bacon and medicine, by E. Withington. (shrink)

The article proposes a new approach to understanding gamification. Its feature lies in taking into account the criticism expressed against gamifi­cation to date. The article examines in detail the history of gamification, it is shown that at its first stage (before 2015) approaches oriented towards extrinsic motivation prevailed, while at the second stage (after 2015) ap­proaches oriented towards intrinsic motivation began to prevail. Ignoring this point just leads to the fact that the criticism expressed in the early 2010s (its main (...) idea was that gamification is a new form of exploitation and manipulation) seems relevant today, although in fact it is no longer so. But it’s not just about rethinking criticism, it’s also about taking a fresh look at gamification itself, which has continued (since 2011) to be defined as «the use of game design elements in non-game contexts”. And this is even despite the fact that such a definition no longer corresponds to the current situation. First, it is confusing by mixing gamification with seri­ous games. Second, it is confusing by limiting gamification to non-game contexts. Third, it is silent about why gamification is used. Fourth, it does not explain exactly which elements are being implemented. Alternatively, we propose our own definition: gamification is a methodology for using metagame elements and mechanics to correct human behavior by creating a favorable emotional background. (shrink)

ObjectivesTo describe reporting of informed consent in pragmatic trials, justifications for waivers of consent and reporting of alternative approaches to standard written consent. To identify factors associated with (1) not reporting and (2) not obtaining consent.MethodsSurvey of primary trial reports, published 2014–2019, identified using an electronic search filter for pragmatic trials implemented in MEDLINE, and registered in ClinicalTrials.gov.ResultsAmong 1988 trials, 132 (6.6%) did not include a statement about participant consent, 1691 (85.0%) reported consent had been obtained, 139 (7.0%) reported a (...) waiver and 26 (1.3%) reported consent for one aspect (eg, data collection) but a waiver for another (eg, intervention). Of the 165 trials reporting a waiver, 76 (46.1%) provided a justification. Few (53, 2.9%) explicitly reported use of alternative approaches to consent. In multivariable logistic regression analyses, lower journal impact factor (p=0.001) and cluster randomisation (p<0.0001) were significantly associated with not reporting on consent, while trial recency, cluster randomisation, higher-income country settings, health services research and explicit labelling as pragmatic were significantly associated with not obtaining consent (all p<0.0001).DiscussionNot obtaining consent seems to be increasing and is associated with the use of cluster randomisation and pragmatic aims, but neither cluster randomisation nor pragmatism are currently accepted justifications for waivers of consent. Rather than considering either standard written informed consent or waivers of consent, researchers and research ethics committees could consider alternative consent approaches that may facilitate the conduct of pragmatic trials while preserving patient autonomy and the public’s trust in research. (shrink)

The authors attempt to speculatively reconstruct the concept of the “So­viet computer game”. They propose to consider gaming practices associ­ated with computers as a derivative of the accepted ideological guidelines that accompany the Soviet project of machine modernization. Within this framework, the concept of the Soviet computer game appears as an unre­alized historical alternative to the normative game design that has devel­oped in countries with market economies. Despite the industry — or the electronic entertainment market — not having had the (...) time to be properly established in the USSR, there were a number of discursive attitudes re­garding the game as such, and the gaming function of computing devices in particular. Even early Soviet pedagogical theories assumed that “playing like a Soviet” involves performing activities structurally similar to labor, where the player becomes part of production. Later, cybernetic discourse, through game theory, indicated the possibility of formalizing any prag­matic activity as a game model; with the advancement of programming, the pragmatics of digital gaming as a way of educating and solving utili­tarian tasks was developed. Based on the memoir archive of Soviet cyber­netics, and publications in the late-Soviet press, the authors demonstrate that the Soviet computer game was not seen an entertainment product, but a representative model for solving problems in an algorithmic form. Thus, the article is not about specific games that could be called Soviet, but about the logic that guided and set the tone for the interpretation of certain computer-game phenomena in the USSR. (shrink)

This book distinguishes itself in its integrated approach towards scientific research, and studies the basics of the methodology of scientific research and the organization of scientific activity from the viewpoint of systems science and system analysis. The book discusses the basics of the methodology including philosophical, psychological, epistemological and ethical/aesthetical foundations, the characteristics of scientific activity, including principles of scientific cognition, the means and methods of scientific research, the organization of a research implementation process and its chronological structure and finally, (...) the organization of a collective scientific research design. (shrink)

This paper aims to contribute to the goal of finding influential legal precedents by quantitative methods. A lot of work has been made in this direction worldwide, especially in the context of common law jurisdictions. However, this type of work is extremely scarce in the Brazilian literature. In addition, our work also contributes to the research of network analysis and the law by applying these methods to unprecedented amount of data and narrowing our inquiry to a single law area, corporate (...) law. Furthermore, whereas most of the literature applying network analysis to judicial decisions had access to readily available data on the citations to precedent within each ruling, our raw data was nothing but the full text of decisions. We focus on data produced by the Superior Court of Justice, the highest court in Brazil for matters of federal law, including statutory interpretation of civil, criminal and corporate law. The Court issued an astonishing 282040 opinions tagged as related to corporate law between 2008 and 2018. This amount of cases is unparalleled internationally for superior courts and for studies in network analysis and law. In our results, we rank precedents quantitatively based on the citations they receive and make. We also qualitatively analyze some of the results, especially related to groups identified in the network with the Modularity algorithm. Our findings also reveal that corporate law jurisprudence in the STJ is quantitatively dominated by a few legal issues around one single theme that is only tangentially related to corporate law. That is, a type of contract used for the expansion of telephone landlines, which also allowed the consumer to become a shareholder of the telecommunication company. This comparison is especially pertinent because the utter lack of data on the quantitative weight of STJ precedents means the national literature has been operating in a void of objective measurements, one which has been filled with cherry-picked rulings and subjective ranking criteria. (shrink)

This is the first study to compare the philosophical systems of secular scientific philosopher Mario Bunge (1919-2020), and Moroccan Islamic philosopher Taha Abd al-Rahman (b.1945). In their efforts to establish the philosophical underpinnings of an ideal modernity these two great thinkers speak to the same elements of the human condition, despite their opposing secular and religious worldviews. While the differences between Bunge’s critical-realist epistemology and materialist ontology on the one hand, and Taha’s spiritualist ontology and revelational-mystical epistemology on the other, (...) are fundamental, there is remarkable common ground between their scientific and Islamic versions of humanism. Both call for an ethics of prosperity combined with social justice, and both criticize postmodernism and religious conservatism. The aspiration of this book is to serve as a model for future dialogue between holders of Western and Islamic worldviews, in mutual pursuit of modernity’s best-case scenario. (shrink)

Individuals exposed to dieting-related environmental cues have been repeatedly shown to be better able to resist tempting food. This especially applies to restrained eaters who hold a chronic dieting goal. Thus far, mainly short-term effects of environmental dieting cues have been examined and the individuals were typically unaware of being influenced. Yet, it is unclear whether individuals can deliberately apply environmental dieting cues for themselves to facilitate the pursuit of the longer-term goal of losing weight. The present longitudinal study applied (...) a 2 × 2 between-subjects design for 6 months. Our results provide preliminary indications that cue, awareness, and restrained eating interact. The results suggest that high restrained eaters could deliberately apply environmental dieting cues for themselves to facilitate losing weight. However, further studies are needed to explore the effects of environmental dieting cues over a longer period of time. (shrink)