Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that each regular field is algebraically closed. Standard arguments show that a generically stable regular field is algebraically closed. LetKbe a regular field which is not generically stable and letpbe its global generic type. We observe that ifKhas a finite extensionLof degreen, thenPhas unbounded orbit (...) under the action of the multiplicative group ofL.Known to be true in the minimal context, it remains wide open whether regular, or even quasi-minimal, groups are abelian. We show that if it is not the case, then there is a counter-example with a unique nontrivial conjugacy class, and we notice that a classical group with one nontrivial conjugacy class is not quasi-minimal, because the centralizers of all elements are uncountable. Then, we construct a group of cardinality ω1with only one nontrivial conjugacy class and such that the centralizers of all nontrivial elements are countable. (shrink)

Extracting the regularities of our environment is one of our core cognitive abilities. To study the fine-grained dynamics of the extraction of embedded regularities, a method combining the advantages of the artificial language paradigm and the serial response time task was used with a group of Guinea baboons in a new automatic experimental device. After a series of random trials, monkeys were exposed to language-like patterns. We found that the extraction of embedded patterns positioned at the end of larger patterns (...) was faster than the extraction of initial embedded patterns. This result suggests that there is a learning advantage for the final element of a sequence that benefits from the contextual information provided by previous elements. (shrink)

Relatively congruence regular quasivarieties and quasivarieties of logic have noticeable similarities. The paper provides a unifying framework for them which extends the Blok-Pigozzi theory of elementarily algebraizable (and protoalgebraic) deductive systems. In this extension there are two parameters: a set of terms and a variable. When the former is empty or consists of theorems, the Blok-Pigozzi theory is recovered, and the variable is redundant. On the other hand, a class of membership logics is obtained when the variable is the (...) only element of the set of terms. For these systems the appropriate variant of equivalent algebraic semantics encompasses the relatively congruence regular quasivarieties. (shrink)

Relatively congruence regular quasivarieties and quasivarieties of logic have noticeable similarities. The paper provides a unifying framework for them which extends the Blok-Pigozzi theory of elementarily algebraizable (and protoalgebraic) deductive systems. In this extension there are two parameters: a set of terms and a variable. When the former is empty or consists of theorems, the Blok-Pigozzi theory is recovered, and the variable is redundant. On the other hand, a class of ‘membership logics’ is obtained when the variable is the (...) only element of the set of terms. For these systems the appropriate variant of equivalent algebraic semantics encompasses the relatively congruence regular quasivarieties. (shrink)

According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements in a (...) collection without counting them), or on the ability to approximate quantities (i.e., to assess anapproximatequantity of the elements in a collection without counting them), or both, fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm. In the final section, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics. (shrink)

Thomas Hobbes (1588-1679) was an English philosopher, remembered today for his work on political philosophy. His 1651 book Leviathan established the foundation for most of Western political philosophy from the perspective of social contract theory. He also contributed to a diverse array of fields, including history, geometry, physics of gases, theology, ethics, general philosophy, and political science. He was one of the main philosophers who founded materialism. He visited Florence in 1636 and later was a regular debater in philosophic (...) groups in Paris, held together by Marin Mersenne. Hobbes's first area of study was an interest in the physical doctrine of motion and physical momentum. Despite his interest in this phenomenon, he disdained experimental work as in physics. He built a good reputation in philosophic circles and in 1645, he was chosen with Descartes, Gilles de Roberval and others, to referee the controversy between John Pell and Longomontanus over the problem of squaring the circle. His other works include: The Elements of Law Natural and Politic (1640) and De Cive (The Citizen): Philosophical Rudiments Concerning Government and Society (1651). (shrink)

The de‐repression of transposable elements (TEs) in mammalian genomes is thought to contribute to genome instability, inflammation, and ageing, yet is viewed as a cell‐autonomous event. In contrast to mammalian cells, prokaryotes constantly exchange genetic material through TEs, crossing both cell and species barriers, contributing to rapid microbial evolution and diversity in complex communities such as the mammalian gut. Here, it is proposed that TEs released from prokaryotes in the microbiome or from pathogenic infections regularly cross the kingdom barrier to (...) the somatic cells of their eukaryotic hosts. It is proposed this horizontal transfer of TEs from microbe to host is a stochastic, ongoing catalyst of genome destabilization, resulting in structural and epigenetic variations, and activation of well‐evolved host defense mechanisms contributing to inflammation, senescence, and biological ageing. It is proposed that innate immunity pathways defend against the horizontal acquisition of microbial TEs, and that activation of this pathway during horizontal transposon transfer promotes chronic inflammation during ageing. Finally, it is suggested that horizontal acquisition of prokaryotic TEs into mammalian genomes has been masked and subsequently under‐reported due to flaws in current sequencing pipelines, and new strategies to uncover these events are proposed. (shrink)

This study evaluated the effects of an exergame program combined with traditional tennis training on autonomic regulation, tennis technique, gross motor skills, clinical reaction time, and cognitive inhibitory control in children. Sixty-three children were randomized into four groups and compared at baseline, 6-month immediately post intervention and at 1-year follow-up post intervention. At 6-month post intervention the combined exergame and regular training sessions revealed: higher breathing frequency, heart rate and lower skin conductance levels during exergaming; additional benefits in the (...) point of contact and kinetic chain elements of the tennis forehand and backhand technique ; negative impact on the shot preparation and the follow-through elements ; higher ball skills ; higher percentages of clinical reaction time improvement and cognitive inhibitory control improvement in both congruent and incongruent trials. The 1-year follow-up test showed no differences in the tennis technique, clinical reaction time and cognitive inhibitory control improvement between groups with the same number of trainings per week. The findings support exergaming as an additional training tool, aimed to improve important cognitive-motor tennis skills by adding dynamics to the standardized training process. Caution should be placed to planning this training, e.g., in a mesocycle, since exergaming might decrease the improvement of specific tennis technique parts of the trainees.. (shrink)

A regularity theory of causation analyses type-level causation in terms of Boolean difference-making. The essential ingredient that helps this theoretical framework overcome the problems of Hume’s and Mill’s classical accounts is a principle of non-redundancy: only Boolean dependency structures from which no elements can be eliminated track causation. The first part of this paper argues that the recent regularity theoretic literature has not consistently implemented this principle, for it disregarded an important type of redundancies: structural redundancies. Moreover, it is shown (...) that a regularity theory needs to be underwritten by a hitherto neglected metaphysical background assumption stipulating that the world's causal makeup is not ambiguous. Against that background, the second part then develops a new regularity theory that does justice to all types of redundancies and, thereby, provides the first all-inclusive notion of Boolean difference-making. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Notes and Fragments PLATONIC ELEMENTS IN KAFKA'S "INVESTIGATIONS OF A DOG" by Lewis W. Leadbeater Few critics of Kafka, and certainly few German critics of Kafka, have been willing to allow for much of any classical influence on his works. There are exceptions, but for the most part these commentators can bring themselves to admit only the fact Kafka endured with distaste his lengthy involvement with the classical languages (...) and literature and that, if in any way, he was influenced only in terms of syntax or style.1 Yet it is certain that Kafka read classical literature with interest and that he was well acquainted with classical epic, tragedy, philosophy, and mythology. The wandering Odysseus, the sea god Poseidon, tortured Prometheus —all these and other classical figures are to be found in his works. Indeed, a recent interpretation of The Trial involves a discussion of it in comparison with the trial of Socrates.2 The fact is that Kafka knew Plato's Apology and counted as one of his prized possessions a copy of Plato's Phaedrus. He and Brod read Plato together in high school.3 Are we really to assume, then, that, given Kafka's philosophical bent, he saw no relationship between Plato and the later philosophers, like Kierkegaard for instance, with whom he was quite taken, and that given his fertile mind and penchant for metaphor, Kafka reflects only Platonic syntax?4 Quite the contrary; we must, I think, cede his classicism to Kafka, and in the discussion which follows I should like to point out that in one of the short stories, "Investigations of a Dog," parable and metaphor blend as well as they do because of Platonic influence, and especially that of the Apology and the Phaedrus. Kafka's animals pervade his works in both metaphor and simile. Gregor Samsa awakes one morning to find himself transformed into a gigantic beetle; Joseph K dies, at the end of his trial, like a dog, and it is a questioning canine which investigates the meaning of dog104 Lewis W. Leadbeater105 ness in "Forschungen eines Hundes." Generally the animalistic metaphor involves removal, alienation, and isolation— a loss of kinship with humanity to be sure, but more important a loss of communication, an inability to communicate, and hence an emphasis on all-encompassing, frustrating silence. The natural result for these people turned animal is an involvement in a process of severe introspection frequently linked with the pursuit of some idea or ideal which will provide a hitherto unknown, transcendent nourishment for a famished, alienated soul. Such is certainly the case with Gregor Samsa and quite possibly the case with Joseph K; it is in fact such pursuits which lie at the heart of the researches of our investigating Dog. Though any attempt to pinpoint the source of Kafka's penchant for animalistic metaphors is quite certainly futile, one might well posit as paradigmatic the alienation plays of Aristophanes involving animals, and certainly the notion of a psychological link between man and beast is present in Plato's Phaedrus, a dialogue in which the soul metaphor itself involves horses, and one in which there is considerable discussion of the interchangeability of the souls of men and beasts.5 As noted above such interchangeability or transformation occurs regularly in Kafka; within the ugly form of beetle lay the psyche of Gregor Samsa. Perhaps within the not-so-ugly canine form of our investigating hound lies the soul of Socrates. Consider for a moment the character of our Dog in light of Plato's Socrates as he appears in the Apology. To begin with, the Dog, as he tells us, is a solitary creature, withdrawn and involved solely in his "investigations" (p. 278).6 In addition, he fully realizes that he is different from the rest of his species (p. 279) and that indeed at times he feels rejected by his kind, realizing as he does that his investigations run counter to the traditional values of his species, a species by which he had hoped at one time to be accepted with great honor (p. 308). What he has capitulated to is "questions" which, furthermore, have quite removed him from normal... (shrink)

A regularity theory of causation analyses type-level causation in terms of Boolean difference-making. The essential ingredient that helps this theoretical framework overcome the problems of Hume’s and Mill’s classical accounts is a principle of non-redundancy: only Boolean dependency structures from which no elements can be eliminated track causation. The first part of this article argues that the recent regularity-theoretic literature has not consistently implemented this principle, for it disregarded an important type of redundancies: structural redundancies. Moreover, it is shown that (...) a regularity theory needs to be underwritten by a hitherto neglected metaphysical background assumption stipulating that the world’s causal makeup is not ambiguous. Against that background, the second part then develops a new regularity theory that does justice to all types of redundancies and, thereby, provides the first all-inclusive notion of Boolean difference-making. (shrink)

This paper proposes a concept of creativity that stems from a semiotic and linguistic theoretical perspective, in which the formal frame of reference for variation and linguistic change considers and evaluates both the process of general interaction and the contact of languages as a global phenomenon. This method proposes an analysis of creativity that ranges from reflections of ancient philosophy to a contemporary linguistic perspective, incorporates international ideologies, and identifies, within the dimensions of use and social sharing, the principle capable (...) of guiding potentially unlimited forms of linguistic creativity that are self-expressive and communicative, far beyond the grammatical patterns of regularity and norm. Interpreting the paradigm of creativity according to this model means placing the semiotic property in a position of prima inter pares, entrusted not only with the “role” of forming signs (words, sentences, texts), but the function of arbitraire, as a phenomenon of language creation. The following reading references the semiotic contribution of Tullio De Mauro, an Italian linguist who has contributed to the systematization of creativity, overcoming and synthesizing both Saussurian structuralism and Chomskyan generativism. (shrink)

Previous chapter The period spanning between 1750 and 1900 has been marked, first of all, by a tremendous expansion of the Platonic metric paradigm. Poetry, dance and music continued their ancient numerical tradition, into which they tended to introduce, at least until the 1840s, strict regularity and pulsation. Life science witnessed the generalization by Wolff and his followers of the division of phenomena duration into time-sequences which had been initiated in Antiquity by the - Sur le concept de rythme – (...) Nouvel article. (shrink)

Originally published in 1951, this book contains the French text of six contes by Voltaire, including his famous Candide. The stories are prefaced with an introduction by Professor F. C. Green on why Voltaire chose to write short stories rather than long novels, and the philosophical themes the author employs most regularly in each work. This book will be of value to anyone with an interest in Voltaire's shorter prose works or in pre-Revolution French literature more generally.

The Oxford English Dictionary says that a rite is ‘a formal procedure or act in a religious or other solemn observance’. The word comes into English through the French rite from the Latin ritus . Its original meaning escapes etymologists; and this is a mixed blessing, for we neither can nor must attempt a retrieval of its hidden roots. We are told by respectable etymologists that the word is associated from earliest times with Latin religious usage, but that even in (...) the early Latin it was already extended to ‘custom, usage, manner or way’ of a non-religious sort. [Lewis and Short, A Latin Dictionary .] So, too, in modern languages the terms ‘rite’ and ‘ritual’ have specifically religious meaning, but they are also used in social and cultural settings that we would not call religious. What first strikes us about the terms ’ and ‘ritual’ is an emphasis upon a certain formality, upon a regular and stable way in which an action or set of actions is to be performed. A ritual is more than a formalism, however, since there are formalisms that are not rites, such as the logical rules for making a valid argument. Moreover, the term is frequently associated with the terms ‘myth’, ‘symbol’ and ‘faith’. These, too, are primarily religious, but are also extended to non-religious contexts. Indeed, there seems to be a network of such terms whose usage touches upon some extraordinary quality in things. Like them, the term ‘ritual’ shares both a wide variety of meanings and a certain hint of impropriety. The variety of ritual forms is notorious, ranging from the most sacred religious liturgies to the absurdities of a fraternity initiation; and the impropriety of the term breaks out whenever we brand a certain action ‘ritualistic’, just as we sometimes refer slightingly to an assertion, saying it is ‘mythical’, ‘merely symbolic’ or ‘credulous’. (shrink)

The account of causal regularities in the influential INUS theory of causation has been refined in the recent developments of the regularity approach to causation and of the Boolean methods for inference of deterministic causal structures. A key element in the refinement is to strengthen the minimality or non-redundancy condition in the original INUS account. In this paper, we argue that the Boolean framework warrants a further strengthening of the minimality condition. We motivate our stronger condition by showing, first, (...) that a rationale for strengthening the original minimality condition in the INUS theory is also applicable to our proposal to go further, and second, that the new element of the stronger condition is a counterpart to a well-established minimality condition for probabilistic causal models. We also compare the various minimality conditions in terms of the difference-making criteria they imply and argue for the criterion implied by our condition. Finally, we show that putative counterexamples to our proposal can be addressed in the same way that the Boolean theorists defend the current minimality conditions in their framework. (shrink)

In the context of modal logics one standardly considers two modal operators: possibility ) and necessity ) [see for example Chellas ]. If the classical negation is present these operators can be treated as inter-definable. However, negative modalities ) and ) are also considered in the literature [see for example Béziau ; Došen :3–14, 1984); Gödel, in: Feferman, Collected works, vol 1, Publications 1929–1936, Oxford University Press, New York, 1986, p. 300; Lewis and Langford ]. Both of them can be (...) treated as negations. In Béziau a logic \ has been defined on the basis of the modal logic \. \ is proposed as a solution of so-called Jaśkowski’s problem [see also Jaśkowski ]. The only negation considered in the language of \ is ‘it is not necessary’. It appears that logic \ and \ inter-definable. This initial correspondence result between \ and \ has been generalised for the case of normal logics, in particular soundness-completeness results were obtained [see Marcos :279–300, 2005); Mruczek-Nasieniewska and Nasieniewski :229–248, 2005)]. In Mruczek-Nasieniewska and Nasieniewski it has been proved that there is a correspondence between \-like logics and regular extensions of the smallest deontic logic. To obtain this result both negative modalities were used. This result has been strengthened in Mruczek-Nasieniewska and Nasieniewski :261–280, 2017) since on the basis of classical positive logic it is enough to solely use \ to equivalently express both positive modalities and negation. Here we strengthen results given in Mruczek-Nasieniewska and Nasieniewski by showing correspondence for the smallest regular logic. In particular we give a syntactic formulation of a logic that corresponds to the smallest regular logic. As a result we characterise all logics that arise from regular logics. From this follows via respective translations a characterisation of a class of logics corresponding to some quasi-regular logics where \ is the smallest element. Moreover, if a given quasi-regular logic is characterised by some class of models, the same class can be used to semantically characterise the logic obtained by our translation. (shrink)

This essay is an introduction to a lecture course "Elements of Descriptive Psychology" delivered by Anton Marty in around 1903/04. Marty offered courses on descriptive psychology at regular intervals in the course of his career at the University of Prague. The content of these courses follows closely the ideas of Marty’s teacher Franz Brentano, though with some interesting divergences and extrapolations. The present work is a historical and systematic introduction to an extract from notes taken of Marty’s lecture, with (...) some discussion of the work of Dilthey on similar topics, and of Marty’s influence on Franz Kafka and on the Gestalt psychologist Max Wertheimer. (shrink)

The spiral form of the Periodic Law is proposed as its fundamental graphic representation. This idea is based on the fact that the spiral is the most appropriate form in description transitions from simple to complicated. The spiral is easily obtained from the linear succession of the elements when they are ranged by growing nuclear charge. The spiral can be simply transformed into many other graphic representations, including tables. This paper suggests the conception of the autonomy of blocks. This autonomy (...) is clearly seen in the variation of the outer electronic shells, in the width and the height of the blocks, as well as the number and properties of elements included therein. The regularities in the changes of element properties are pronounced in certain blocks but actually absent in others. The blocks can be permuted to obtain full-fledged versions of Periodic Table. The new stage of the verification of the blocks autonomy is the use of the total number of the differentiating electrons as an independent variable in describing the properties of the elements and their compounds. Consideration of individual blocks made it possible to deduce the periodic equations valid for all the elements within each block. Formulation of the Periodic Law is advanced: while describing characteristic determining the properties of the elements, the nuclear charge is replaced by the total number of differentiating electrons. Two modifications of the conventional Periodic Table are obtained by minimal changes. The first one shows the secondary and the additional periodicites. Another table shows the total number of differentiating electrons for each element. (shrink)

Timaeus after assigning four regular solids – tetrahedra, octahedra, icosahedra and cubes – to fire, air, water and earth, respectively, submits at 57d–e that different kinds of gaseous, liquid or solid materials, and their interactions and intertransformations require that the four solids occur in different sizes. The paper discusses two different strategies for the generation of these differences in size: the traditional one, which allows that the triangles that are the fundamental building blocks of these solids do occur in (...) different sizes, and the one proposed by Cornford, which suggests that triangles of exactly the same size may form different structures, and these can give rise to solids of different sizes. Considerations are drawn from descriptions of some specific interactions , from the account of sight , and physiology . All in all, these considerations seem to favour the traditional account. After this, in a final section I suggest that the specific claims Timaeus makes about the status of his account about the elements – certainty for the assignment of tetrahedra to fire, octahedra to air, and icosahedra to water, whereas the half-equilateral triangle as the fundamental building block of these solids is introduced in a tentative manner, explicitely stressing that this detail is revisable – makes it unsurprising that he does not discuss in detail how solids – and triangles and squares – of different sizes are constructed. (shrink)

This paper investigates the affiliation of Book I of the Latin translation of Euclid's Elements attributed to Hermann of Carinthia with the Arabic transmission of the Greek mathematical work. It argues that it is a translation of a text of the Arabic secondary transmission, that is, of an Arabic edition mixed with comments. Two methodological claims are made in the paper. The first insists that the determination of a text whose transmission was as multifaceted and complex as the Euclidean Elements (...) needs to be based on a systematic investigation of entire books rather than on selected theorems or diagrams of global, mostly structural relevance. The second claim starts from the experience that almost all results regarding the place of a particular document in a chain of transmission are conjectural. It acknowledges that individual results are more or less persuasive, depending upon the qualitative status of the argument. It suggests that the quantitative accumulation of similarities, differences, errors, regularities, or peculiarities allows one to recognize patterns and thus improves the reliability of judgment. (shrink)

Demarcation of elements for two subsets appears to be the most fundamental approach to their classification. If one draws a vertical straight line through the middle of each block of elements in the Periodic table, all the elements are divided into two subsets: “early” and “later”. For example, in the d-block, the early ones are Sc–Mn, and the late ones, respectively, are Fe–Zn. Later elements partially repeat the properties of the early ones, and this is defined as the internal periodicity. (...) Another criterion for dividing the elements into two subsets is the evenness and oddness of the sum of n + l, where n is the principal quantum number, and l is the orbital quantum number for the outer electron subshells. Properties of the odd elements are closer to each other than to properties of even elements, and vice versa. This regularity is manifested as the secondary periodicity. The history of concepts, which considered the existence of subsets as well as of inner and secondary periodicities, is discussed. The features of the electronic structure, which underlie the existence of subsets, are considered. The existence of subsets was depicted earlier by dividing the periodic table into two tables or by applying a mirror-symmetric table. Small changes are proposed in the conventional Periodic table, allowing to reflect the existence of the considered subsets. (shrink)

Demarcation of elements for two subsets appears to be the most fundamental approach to their classification. If one draws a vertical straight line through the middle of each block of elements in the Periodic table, all the elements are divided into two subsets: “early” and “later”. For example, in the d-block, the early ones are Sc–Mn, and the late ones, respectively, are Fe–Zn. Later elements partially repeat the properties of the early ones, and this is defined as the internal periodicity. (...) Another criterion for dividing the elements into two subsets is the evenness and oddness of the sum of n + l, where n is the principal quantum number, and l is the orbital quantum number for the outer electron subshells. Properties of the odd elements are closer to each other than to properties of even elements, and vice versa. This regularity is manifested as the secondary periodicity. The history of concepts, which considered the existence of subsets as well as of inner and secondary periodicities, is discussed. The features of the electronic structure, which underlie the existence of subsets, are considered. The existence of subsets was depicted earlier by dividing the periodic table into two tables or by applying a mirror-symmetric table. Small changes are proposed in the conventional Periodic table, allowing to reflect the existence of the considered subsets. (shrink)

The book provides a deep account of the use of computational thinking (CT) skills in education, with a focus on individual, social and cultural elements, and dives into issues foregrounding CT skills. Although the chapters of the book provide important educational and practical implications for the reader, methodological choices and the lack of theoretical connections of CT concepts curtail the use of CT skills in education, from a constructionist view.

Selon l'étude européenne translinguistique Neurodys (Becker et al., 2013), la prévalence de la dyslexie touche entre 5 et 10% des enfants âgés de 8 à 12 ans. L’apprentissage du langage écrit revient à maîtriser conjointement ses deux versants : lecture et écriture. La présente étude vise l’analyse des processus d'écriture utilisés par des scripteurs dyslexiques (DL) et dysorthographiques (DO). Afin de favoriser les collaborations chercheurs-praticiens, comme le proposent Hayes et Berninger (2014), nous étudions les données chronométriques relatives à un corpus (...) de textes recueillis auprès de 7 adolescents dyslexiques et dysorthographiques, recrutés dans le cadre de situations de soin courant orthophonique, afin de décrire les opérations de traitement cognitif du langage écrit en contexte d’activité rédactionnelle. Les corpus de productions écrites d’adolescents DL/DO suivis en orthophonie apportent par le biais du relevé chronométrique (vitesses d’écriture, durées des pauses en fonction de leur localisation dans le texte, longueur des passages d’écriture sans pause longue) des éléments sur l’activité de rédaction et les modalités de révision du texte. Ce travail ouvre des perspectives quant au recueil de données en contexte professionnel, de manière à interroger les données cliniques par des outils de recherche développés en linguistique de corpus. (shrink)

Abstract. Let REL(O*E) be the relation algebra of binary relations defined on the Boolean algebra O*E of regular open regions of the Euclidean plane E. The aim of this paper is to prove that the canonical contact relation C of O*E generates a subalgebra REL(O*E, C) of REL(O*E) that has infinitely many elements. More precisely, REL(O*,C) contains an infinite family {SPPn, n ≥ 1} of relations generated by the relation SPP (Separable Proper Part). This relation can be used to (...) define point-free concept of connectedness that for the regular open regions of E coincides with the standard topological notion of connectedness, i.e., a region of the plane E is connected in the sense of topology if and only if it has no separable proper part. Moreover, it is shown that the contact relation algebra REL(O*E, C) and the relation algebra REL(O*E, NTPP) generated by the non-tangential proper parthood relation NTPP, coincide. This entails that the allegedly purely topological notion of connectedness can be defined in mereological terms. (shrink)

Continuing the earlier research in [1] and [4] we work out a class of interstices in countable arithmetically saturated models of PA in which selective types are realized and a class of interstices in which 2-indiscernible types are realized.

Late ancient Platonists discuss two theories in which geometric entities xplain natural phenomena : the regular polyhedra of geometric atomism and the ccentrics and epicycles of astronomy. Simplicius explicitly compares the status of the first to the hypotheses of the astronomers. The point of omparison is the fallibility of both theories, not the reality of the entities postulated. Simplicius has strong realist commitments as far as astronomy is concerned. Syrianus and Proclus, too, do not consider the polyhedra as devoid (...) of physical reality. Proclus rejects epicycles and eccentrics, but accepts the reality of material homocentric spheres, moved by their own souls. The spheres move the astral objects contained in them, which, however, add motions caused by their own souls. The epicyclical and eccentric hypotheses are useful, as they help us to understand the complex motions resulting from the interplay of spherical motions and volitional motions of the planets. Yet astral souls do not think in accordance with human theoretical constructs, but rather grasp the complex patterns of their motions directly. Our understanding of astronomy depends upon our own cognition of intelligible patterns and their mathematical images. (shrink)

Investigation of the factors in natural history which conditioned the appearance of consciousness, that specifically human form of mental activity, necessarily presumes, in particular, a study of its functional preconditions or, in other words, of the higher forms of animal activity involving objects and of the corresponding mental processes. It is not enough to know the general psychological qualities of animals, the general principles by which their behavior is shaped, principles and properties offering evidence of a type of vital activity (...) qualitatively different from that of man. The traits of psychology and behavior, characteristic of the preponderance of the animal world, could not have become the immediate functional foundation capable of providing the real opportunity for the onset of the shaping of new regularities of mental activity. (shrink)

"In Realms of Legal Interpretation, Kent Greenawalt focuses on how courts decide what is legally forbidden or authorized, and how context shapes their decisions. The problem, he argues, is that we do not, and never have, agreed on all the details of the standards United States judges should employ - like everyone else, judges have different ideas of what constitutes good common sense. Moreover, circumstance regularly throws up hurdles... Different judges react in different ways. Acknowledging that courts will never agree (...) upon a uniform approach to applying norms and interpreting the law, Greenawalt's aim is to provide a capacious, user-friendly model for approaching hard cases sensibly in both public and private law. Just as importantly, the book serves as a pithy guide to the major forms of legal interpretation for nonlawyers" --. (shrink)

Disjunctivism, as a theory of visual experience, claims that the mental states involved in a “good case” experience of veridical perception and a “bad case” experience of hallucination differ, even in those cases in which the two experiences are indistinguishable for their subject. Consider the veridical perception of a bar stool and an indistinguishable hallucination; both of these experiences might be classed together as experiences (as) of a bar stool or experiences of seeming to see a bar stool. This might (...) lead us to think that the experiences we undergo in the two cases must be of the same kind, the difference being that the former, but not the latter, is connected to the world in the right kind of way. Such a conjecture has been called a “highest common factor” or “common kind” assumption. At heart, disjunctivism consists in the rejection of this assumption. According the disjunctivist, veridical experiences and hallucinations do not share a common component. There are a host of interesting questions surrounding disjunctivism including: What is involved in the claims that good case and bad case experiences differ? Why might one might want to be a disjunctivist? What kinds of claims can the disjunctivist make about hallucination and illusion? These questions, and problems for the thesis, will be discussed as we proceed. (shrink)

Using the theory of BL-algebras, it is shown that a propositional formula ϕ is derivable in Łukasiewicz infinite valued Logic if and only if its double negation ˜˜ϕ is derivable in Hájek Basic Fuzzy logic. If SBL is the extension of Basic Logic by the axiom (φ & (φ→˜φ)) → ψ, then ϕ is derivable in in classical logic if and only if ˜˜ ϕ is derivable in SBL. Axiomatic extensions of Basic Logic are in correspondence with subvarieties of the (...) variety of BL-algebras. It is shown that the MV-algebra of regular elements of a free algebra in a subvariety of BL-algebras is free in the corresponding subvariety of MV-algebras, with the same number of free generators. Similar results are obtained for the generalized BL-algebras of dense elements of free BL-algebras. (shrink)

In this paper, I outline a grammar of lifting (i.e., resistance training) and compare it to that of language. I approach lifting as a system of generating complex meaning–form correspondences from regularized elements and describe the levels of mental representations and relationships between them that are involved in full command of this system. To be able to do so, I adopt a goal-based conception of meaning, which allows us to talk about mappings from complex goals to complex surface outputs in (...) systems of intentional action, signaling and non-signaling, interactive and non-interactive, in a unified way, and show how it applies in lifting. I then proceed to argue that the grammar of lifting is architecturally very similar to that of language. First, I show that both involve stable (idiomatized/lexicalized) pairings of regularized forms with regularized meanings. Second, I argue that in both lifting and language, meaning–form mapping is mediated by syntax, which, crucially, operates on non-linearized hierarchical structures of abstract objects that include both content morphemes and functional morphemes. I conclude, following and expanding on some insights from prior literature and offering further evidence for them, that neither of these architectural phenomena (idiomatized meaning–form pairings and abstract syntax) is specific to language, with both of them likely emerging in skilled action that does not necessarily involve social interaction, due to considerations of repeatability and reusability of elements in new contexts. (shrink)

In this paper we shall introduce the variety WQS of weak-quasi-Stone algebras as a generalization of the variety QS of quasi-Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬-lattices to give a duality for WQS. We prove that a weak-quasi-Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice congruences. We will also determine the simple and (...) subdirectly irreducible algebras. (shrink)

In this paper, we mainly investigate the existence of states based on the Glivenko theorem in bounded semihoops, which are building blocks for the algebraic semantics for relevant fuzzy logics. First, we extend algebraic formulations of the Glivenko theorem to bounded semihoops and give some characterizations of Glivenko semihoops and regular semihoops. The category of regular semihoops is a reflective subcategory of the category of Glivenko semihoops. Moreover, by means of the negative translation term, we characterize the Glivenko (...) variety. Then we show that the regular semihoop of regular elements of a free algebra in the variety of Glivenko semihoops is free in the corresponding variety of regular semihoops. Similar results are derived for the semihoop of dense elements of free Glivenko semihoops. Finally, we give a purely algebraic method to check the existence of states on Glivenko semihoops. In particular, we prove that a bounded semihoop has Bosbach states if and only if it has a divisible filter, and a bounded semihoop has Riečan states if and only if it has a semi-divisible filter. (shrink)

BackgroundPublic involvement activities are promoted as measures for ensuring good governance in challenging fields, such as biomedical research and innovation. Proponents of public involvement activities include individual researchers as well as non-governmental and governmental organizations. However, the concept of ‘public’ in public involvement deserves more attention by researchers because it is not purely theoretical: it has important practical functions in the guidance, evaluation and translation of public involvement activities.DiscussionThis article focuses on collective agency as one property a public as a (...) small group of participants in a public involvement activity could exhibit. It introduces a prominent theoretical approach to collective agents as one specific kind of social entities and demonstrates how this approach can be applied to current practice in public involvement activities. A brief discussion of different types of representation as they are used in the existing literature on this topic is also included because representation and collective agency can be closely related to each other. Suggestions and ideas that are derived from this reasoning include the proposal to use a ‘validity check’ for the generation of collective agents as a regular element of certain types of public involvement activities, the consequences of combining collective agency and representativeness as a further property a public could exhibit, and standards for reporting the content of public involvement activities in scientific publications.SummaryThis article discusses the importance of the concept of ‘public’ in public involvement activities, with a focus on biomedical research and innovation. It introduces various practically relevant ideas that are based on a theoretical analysis of collective agency as an important property a public can possess. (shrink)

The classical Glivenko theorem asserts that a propositional formula admits a classical proof if and only if its double negation admits an intuitionistic proof. By a natural expansion of the BCK-logic with negation we understand an algebraizable logic whose language is an expansion of the language of BCK-logic with negation by a family of connectives implicitly defined by equations and compatible with BCK-congruences. Many of the logics in the current literature are natural expansions of BCK-logic with negation. The validity of (...) the analogous of Glivenko theorem in these logics is equivalent to the validity of a simple one-variable formula in the language of BCK-logic with negation. (shrink)

In this paper we shall introduce the variety WQS of weak-quasi-Stone algebras as a generalization of the variety QS of quasi-Stone algebras introduced in [9]. We shall apply the Priestley duality developed in [4] for the variety N of ¬-lattices to give a duality for WQS. We prove that a weak-quasi-Stone algebra is characterized by a property of the set of its regular elements, as well by mean of some principal lattice congruences. We will also determine the simple and (...) subdirectly irreducible algebras. (shrink)

In a classical paper [15] V. Glivenko showed that a proposition is classically demonstrable if and only if its double negation is intuitionistically demonstrable. This result has an algebraic formulation: the double negation is a homomorphism from each Heyting algebra onto the Boolean algebra of its regular elements. Versions of both the logical and algebraic formulations of Glivenko’s theorem, adapted to other systems of logics and to algebras not necessarily related to logic can be found in the literature (see (...) [2, 9, 8, 14] and [13, 7, 14]). The aim of this paper is to offer a general frame for studying both logical and algebraic generalizations of Glivenko’s theorem. We give abstract formulations for quasivarieties of algebras and for equivalential and algebraizable deductive systems and both formulations are compared when the quasivariety and the deductive system are related. We also analyse Glivenko’s theorem for compatible expansions of both cases. (shrink)

Perceptual neuroscience has identified mechanisms of perceptual grouping which account for the ways in which visual sensitivity to ordered structure and regularities expresses itself, in behavior and in the brain. The need to actively construct order, notably representations of objects in depth, is mandated as soon as visual signals reach the retina, given the occlusion of retinal signals by retinal veins and other retinal elements or blur. Multiple stages of neural processing transform fragmented signals into visual key representations of 3D (...) scenes that can be used to control effective behaviors. Since our survival depends on our ability to pick up order in the physical world, and since we conceive the physical world as an ordered one, our perception must somehow be sensitive to order. The articles from this collection illustrate how texture dissimilarity, boundary completion, surface filling-in, and figure-ground segregation generate perceptual order. (shrink)

It has been nearly a decade and a half since Fred Dretske, David Armstrong and Michael Tooley, having each rejected the Regularity theory, independently proposed that natural laws are grounded in a second-order relation that somehow binds together universals.' (l shall call this the ‘DTA theory’). In this way they sought to overcome the major - and notorious — shortcomings of every version of the Regularity theory: how to provide truth conditions for laws that lack instances; how to distinguish laws (...) from accidental generalizations; how to provide truth conditions for the counterfactuals and disposition statements that laws apparently ‘support’; how to justify inductive inferences from past events to laws and future events. For each of these puzzles, an apparently key element in the solution seems to be missing from Regularity theories. That missing element is a genuine connection, a relation with more than merely spatial and/or temporal content, linking the antecedent of a law to its consequent. Once such an additional objective element - however understood — is admitted to be essential to the analysis of laws, one is forced to give up the idea that the logical form of laws can be given in terms of quantifiers ranging over events or states of alfairs, and truth-functions. (shrink)

The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety \(\mathbb{DHMSH}\) from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal algebraic study of their corresponding algebraic semantics. Firstly, we present a (...) Hilbert-style axiomatization of a new logic called "Dually hemimorphic semi-Heyting logic" (\(\mathcal{DHMSH}\), for short), as an expansion of semi-intuitionistic logic \(\mathcal{SI}\) (also called \(\mathcal{SH}\)) introduced by the first author by adding a weak negation (to be interpreted as a dual hemimorphism). We then prove that it is implicative in the sense of Rasiowa and that it is complete with respect to the variety \(\mathbb{DHMSH}\). It is deduced that the logic \(\mathcal{DHMSH}\) is algebraizable in the sense of Blok and Pigozzi, with the variety \(\mathbb{DHMSH}\) as its equivalent algebraic semantics and that the lattice of axiomatic extensions of \(\mathcal{DHMSH}\) is dually isomorphic to the lattice of subvarieties of \(\mathbb{DHMSH}\). A new axiomatization for Moisil's logic is also obtained. Secondly, we characterize the axiomatic extensions of \(\mathcal{DHMSH}\) in which the "Deduction Theorem" holds. Thirdly, we present several new logics, extending the logic \(\mathcal{DHMSH}\), corresponding to several important subvarieties of the variety \(\mathbb{DHMSH}\). These include logics corresponding to the varieties generated by two-element, three-element and some four-element dually quasi-De Morgan semi-Heyting algebras, as well as a new axiomatization for the 3-valued Łukasiewicz logic. Surprisingly, many of these logics turn out to be connexive logics, only a few of which are presented in this paper. Fourthly, we present axiomatizations for two infinite sequences of logics namely, De Morgan Gödel logics and dually pseudocomplemented Gödel logics. Fifthly, axiomatizations are also provided for logics corresponding to many subvarieties of regular dually quasi-De Morgan Stone semi-Heyting algebras, of regular De Morgan semi-Heyting algebras of level 1, and of JI-distributive semi-Heyting algebras of level 1. We conclude the paper with some open problems. Most of the logics considered in this paper are discriminator logics in the sense that they correspond to discriminator varieties. Some of them, just like the classical logic, are even primal in the sense that their corresponding varieties are generated by primal algebras. (shrink)

This Element is a philosophical history of Social Darwinism. It begins by discussing the meaning of the term, moving then to its origins, paying particular attention to whether it is Charles Darwin or Herbert Spencer who is the true father of the idea. It gives an exposition of early thinking on the subject, covering Darwin and Spencer themselves and then on to Social Darwinism as found in American thought, with special emphasis on Andrew Carnegie, and Germany with special emphasis (...) on Friedrich von Bernhardi. Attention is also paid to outliers, notably the Englishman Alfred Russel Wallace, the Russian Peter Kropotkin, and the German Friedrich Nietzsche. From here we move into the twentieth century looking at Adolf Hitler - hardly a regular Social Darwinian given he did not believe in evolution - and in the Anglophone world, Julian Huxley and Edward O. Wilson, who reflected the concerns of their society. (shrink)

Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR)‐based “active genetic” elements developed in 2015 bypassed the fundamental rules of traditional genetics. Inherited in a super‐Mendelian fashion, such selfish genetic entities offered a variety of potential applications including: gene‐drives to disseminate gene cassettes carrying desired traits throughout insect populations to control disease vectors or pest species, allelic drives biasing inheritance of preferred allelic variants, neutralizing genetic elements to delete and replace or to halt the spread of gene‐drives, split‐drives with the core constituent (...) Cas9 endonuclease and guide RNA (gRNA) components inserted at separate genomic locations to accelerate assembly of complex arrays of genetic traits or to gain genetic entry into novel organisms (vertebrates, plants, bacteria), and interhomolog based copying systems in somatic cells to develop tools for treating inherited or infectious diseases. Here, we summarize the substantial advances that have been made on all of these fronts and look forward to the next phase of this rapidly expanding and impactful field. (shrink)