Richard Peters argued for a general education based largely on the study of truth-seeking subjects for its own sake. His arguments have long been acknowledged as problematic. There are also difficulties with Paul Hirst's arguments for a liberal education, which in part overlap with Peters'. Where justification fails, can historical explanation illuminate? Peters was influenced by the prevailing idea that a secondary education should be based on traditional, largely knowledge-orientated subjects, pursued for intrinsic as well as practical ends. Does (...) history reveal good reasons for this view? The view itself has roots going back to the 16th century and the educational tradition of radical Protestantism. Religious arguments to do with restoring the image of an omniscient God in man made good sense, within their own terms, of an encyclopaedic approach to education. As these faded in prominence after 1800, old curricular patterns persisted in the drive for ‘middle-class schools’, and new, less plausible justifications grew in salience. These were based first on faculty psychology and later on the psychology of individual differences. The essay relates the views of Peters and Hirst to these historical arguments, asking how far their writings show traces of the religious argument mentioned, and how their views on education and the development of mind relate to the psychological arguments. (shrink)

Mancosu, P., Generalizing classical and effective model theory in theories of operations and classes, Annas of Pure and Applied Logic 52 249-308 . In this paper I propose a family of theories of operations and classes with the aim of developing abstract versions of model-theoretic results. The systems are closely related to those introduced and already used by Feferman for developing his program of ‘explicit mathematics’. The theories in question are two-sorted, with one kind of variable for individuals and the (...) other for classes. The individual variables range over a domain closed under pairing and containing, among other things, natural numbers and operations.All the theories used assume a common group of axioms that insure that the individuals in the domain satisfy the conditions for a partial combinatory algebra with pairing. We also assume a class of natural numbers and a class induction axiom on . Finally there are various class existence axioms. I work mainly with three theories, FMT0, FMT and FMTΩ, which differ from each other both in their class existence axioms as well as in some further applicative axioms.These theories have various interpretations in which every object is explicitly presented by some means of definition as well as classical, or ‘standard’, set-theoretical interpretation. The systems are formulated in a flexible general language which can be used to prove abstract theorems of mathematics , thereby generalizing recursive, hyperarithmetic and admissible versions of classical mathematics.The aim of my work is to give an abstract development of portions of model theory in the afore-mentioned theories, in a way to look as much as possible like classical mathematics. Thus, FMT0 generalizes portions of countable and recursive model theory; FMT further generalizes portions of countable and hyperarithmetical model theory and finally FMTΩ provides a generalization of the classical L-completeness theorem and of an admissible version of L-completeness due to Bruce and Keisler. This continues the development of the program mentioned above, originating with Feferman. (shrink)

Kripke convincingly argued that proper names in natural language are rigid designators, and observing that natural kind terms resemble proper names in important respects, he suggested that they are also rigid designators. But it is not immediately clear what exactly this means, for while rigidity as defined by Kripke is primarily a property of singular terms, some of the natural kind terms discussed by him are general terms functioning as predicates. In this paper, I propose a definition of rigidity (...) for predicative general terms, motivated by Putnam’s thesis that the rigidity of the term ‘water’ is a consequence of its indexicality. I argue that this definition satisfies the three desiderata put forward by Soames for an adequate notion of general term rigidity: (i) that it be a natural extension of the notion of singular term rigidity; (ii) that the class of rigid general terms roughly coincide with the class of natural kind terms; (iii) that it play the right role in explaining the necessity of true a posteriori theoretical identifications. I also compare this notion of rigidity with a certain notion proposed by Nimtz as an alternative to general term rigidity, explaining how they differ in crucial respects. On the conception of rigidity I advocate, rigid general terms can be characterized as terms that are semantically associated with what Locke called real essences. (shrink)

In this paper, I examine Hume’s account of an important class of causal belief, which he calls “general rules”. I argue that he understands general rules, like all causal beliefs, as lively ideas that are habitually associated with our impressions or memories. However, I argue that he believes they are unlike any reflectively produced causal beliefs in that they are produced quickly and automatically, such that they occur independently of any other processes of reasoning. Given this, I (...) argue that Hume appears to understand general rules as relatively simple beliefs, expressible only via generic sentences, like “fires cause heat”. (shrink)

Let A be an admissible set. A sentence of the form ∀R̄φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence if φ ∈ A (φ is $\bigvee\Phi$ , where Φ is an A-r.e. set of sentences from A; φ ∈ Lω1ω). A sentence of the form ∃R̄φ is an ∃2(A) (∃s 2(A),∃2(Lω1ω)) sentence if φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence. A class of structures is, for example, a ∀1(A) class if it is the class of models of a (...) ∀1(A) sentence. Thus ∀1(A) is a class of classes of structures, and so forth. Let Mi be the structure $\langle i, 0$. Let Γ be a class of classes of structures. We say that a sequence $J_1,\ldots,J_i,\ldots, i < \omega$, of classes of structures is a Γ sequence if $J_i \in \Gamma, i < \omega$, and there is I ∈ Γ such that M ∈ Ji if and only if [M, Mi] ∈ I, where [,] is the disjoint sum. A class Γ of classes of structures has the easy uniformization property if for every Γ sequence $J_1,\ldots,J_i, \ldots, i < \omega$, there is a Γ sequence $J'_1,\ldots,J'_i,\ldots, i < \omega$, such that $J'_i \subseteq J_i, i < \omega, \bigcup J'_i = \bigcup J_i$, and the J'i are pairwise disjoint. The easy uniformization property is an effective version of Kuratowski's generalized reduction property that is closely related to Moschovakis's (topological) easy uniformization property. We show over countable structures that ∀1(A) and ∃2(A) have the easy uniformization property if A is a countable admissible set with an infinite member, that ∀s 1(Lα) and ∃s 2(Lα) have the easy uniformization property if α is countable, admissible, and not weakly stable, and that ∀1(Lω1ω) and ∃2(Lω1ω) have the easy uniformization property. The results proved are more general. The result for ∀s 1(Lα) answers a question of Vaught (1980). (shrink)

Phonological rules create alternations in the phonetic realizations of related words. These rules must be learned by infants in order to identify the phonological inventory, the morphological structure, and the lexicon of a language. Recent work proposes a computational model for the learning of one kind of phonological alternation, allophony. This paper extends the model to account for learning of a broader set of phonological alternations and the formalization of these alternations as general rules. In Experiment 1, we apply (...) the original model to new data in Dutch and demonstrate its limitations in learning nonallophonic rules. In Experiment 2, we extend the model to allow it to learn general rules for alternations that apply to a class of segments. In Experiment 3, the model is further extended to allow for generalization by context; we argue that this generalization must be constrained by linguistic principles. (shrink)

Recently, Brass and Dix showed 143–165) that the well founded semantics WFS can be defined as a confluent calculus of transformation rules. This led not only to a simple extension to disjunctive programs 167–213), but also to a new computation of the well-founded semantics which is linear for a broad class of programs. We take this approach as a starting point and generalize it considerably by developing a general theory of Confluent LP-systems CS. Such a system CS is (...) a rewriting system on the set of all logic programs over a fixed signature L and it induces in a natural way a canonical semantics. Moreover, we show four important applications of this theory: most of the well-known semantics are induced by confluent LP-systems, there are many more transformation rules that lead to confluent LP-systems, semantics induced by such systems can be used to model aggregation, the new systems can be used to construct interesting counterexamples to some conjectures about the space of well-behaved semantics. (shrink)

This chapter examines a lesser-known area of interest for Sartori: the theory of dictatorship. Political science literature on this subject has mostly focused on totalitarian and authoritarian regimes, to which Sartori also devoted some attention. What he was most interested in, however, was a theory of dictatorship in general, where dictatorship is a class that encompasses the traditional concepts of totalitarianism and authoritarianism. Sartori developed two typologies of dictatorships. The first is based on four basic distinct criteria: intensity, (...) objective, origin, and ideology. This results in up to ten types of dictatorship: simple, Caesarist, totalitarian, revolutionary, dictatorship of order, political, military, bureaucratic, non-ideological, and ideological. This broad typology, while highly original, is also somewhat convoluted and has not gained much traction (a role in this was also played, however, by the fact that it was not translated into English). Sartori, therefore, presented a much simpler typology of dictatorships in one of his later texts (in English), which was also more consistent with the more established typologies of other scholars: totalitarian, authoritarian, and simple. (shrink)

As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of a class of logical matrices. (...) In this way, any logic verified by an actual matrix in one of these classes has the property the class generally represents. Particular matrices (and so, logics) in each class are provided. (shrink)

Universal Basic Income (UBI) is revolutionary and simple at the same time and elicits both attraction and aversion from the general public. This is one of the reasons why, despite its potential to contribute to some of the most pressing current challenges, UBI has not yet been implemented in any country in the world, at least at a system-wide scale. By drawing on innovation theories and adopting a mixed methods approach, this exploratory study investigates public acceptance of UBI in (...) Spain. This study contributes to the emerging literature on public opinion on a UBI as well as to the field of innovation of public policies. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Teaching General Music in Grades 4–8: A Musicianship ApproachKatherine StrandThomas Regelski, Teaching General Music in Grades 4–8: A Musicianship Approach ( Oxford: Oxford University Press 2004)In this recent addition to the world of texts for secondary methods classes, Teaching General Music in Grades 4–8: A Musicianship Approach, Thomas Regelski takes a new look at the challenging task of teaching the pre-adolescent and adolescent age group. (...) This text brings together many of Regelski's earlier writing on topics such as the professionalism of music teaching practice, music education as praxial education, and the operationalization of critical theory in music education. His thoughtful work offers insights and challenges to pre-service and in-service teachers.In the Introduction, Regelski provides a brief history of critical theory in education and describes how he applies critical theory to the profession of music teaching and the experience of musical learning. In this "new view" of education, teachers should seek to be transformative rather than simply transmitting a cultural status quo through status quo methods of teaching. Critical theory in teaching criticizes both the methods and the content in the light of context, student learning needs, praxis, and the situatedness of learning. He argues, as in earlier articles, against what he calls methodolotry: the tendency to adopt a method and follow that method unquestioningly. Rather, he proposes that teachers [End Page 121] should adopt a stance of reflective practitioner, becoming informal action researchers by questioning the value and effectiveness of instructional strategy and curricular content. (Sadly, once introduced, there is no more information about how to engage in action research, nor any encouragement to learn more about the subject.)Educational content should be based on critical theory which, as Regelski argues:... seeks to study the past, but in terms of its implications–positive or negative–for the present and, especially, as a basis for improving society and the individuals who constitute society.... [T]he past is evoked "critically" and selectively and new practices that will become traditions of the future will be initiated.1The job of the teacher is to help students make critical judgments regarding music and the "good time" the musical experience contributes to the students' lives.2 Music classrooms should be considered music laboratories in which children learn through thoughtful, investigatory experiences. Music education should promote life-skills relevant to the student's world, teach functional musical skills, incite interest in unfamiliar musical experiences, and address the pre-adolescent and adolescent student's "need to achieve."3In the first chapter, Regelski argues for "action learning," or learning in which the student is the principal actor. To support his argument, he cites findings in cognitive psychology, philosophical trends of pragmatism, utilitarianism, and humanism, transfer of learning theory, authentic learning and assessment, and constructivist learning theories. This myriad of ideas combine to form the essence of his argument: children in this age group need to develop intentionality in music-making to have a "good time" and instruction should always connect in-school musical learning with a student's real-world musical experiences. The value of action learning lies in the transfer of learning from the classroom to life after school:It advances the skills predictably useful to typical adults throughout life: for example, recreational singing, music reading sufficient to church and community choirs, "making sense" of music and enjoyment through listening, and the like. It is not a survey of disconnected musical generalities, a superficial sampling of music "in general"; boiled down theory, history, appreciation: or the introduction to the "discipline" of music as a "subject" of study for its own sake. Instead, it promotes the broad musicianship skills and positive attitudes for "breaking 100" [as in bowling, the level at which one calls oneself a "musician"] that enable students to be musically independent and active outside of class and after graduation, and to want to be musically active as part of the life well lived [italics added].4 [End Page 122]In the second chapter, Regelski provides an excellent summary of the physical, cognitive, and social development of children from age 9 to 14. Age categories are broken into upper elementary grades 4–6... (shrink)

In this study, an accurate convergence time of the supertwisting algorithm is proposed to build up a framework for nonaffine nonlinear systems’ finite-time control. The convergence time of the STA is provided by calculating the solution of a differential equation instead of constructing Lyapunov function. Therefore, precise convergence time is presented instead of estimation of the upper bound of the algorithm’s reaching time. Regardless of affine or nonaffine nonlinear systems, supertwisting control provides a general solution based on virtual control (...) law skill ensuring the output of the systems converges to the origin point at exact time. Benchmark tests are simulated to demonstrate the effectiveness and efficiency of the algorithm. (shrink)

ABSTRACT- In this paper my aim is to concentrate on the concepts like predicate, properties and classes; with an aim to understand the reason behind the re-applicability of general terms. It must also be noted that here general terms are supposed to be found in the predicate place of a proposition as properties and how they are ascribed to objects which may be mentioned in the subject place. This paper harps on the issue of; what acts as a (...) deciding factor behind such act of classification. A clear effort has been made as to the reason behind our grouping of objects and what we actually search for while choosing an object under a class. I have tried to make my point on the issue that at most we can call our act of classification as natural instead of calling a class as natural. For this I have particularly chosen an article of Anthony Quinton namely, ‘Properties and Classes’ (1958 vol-58, Issue 1, 1st June Proceedings of the Aristotelian Society). (shrink)

This paper addresses the significance of the general class of diffeomorphisms in the theory of general relativity as opposed to the Poincaré group in a special relativistic theory. Using Anderson's concept of an absolute object for a theory, with suitable revisions, it is shown that the general group of local diffeomorphisms is associated with the theory of general relativity as its local dynamical symmetry group, while the Poincaré group is associated with a special relativistic theory (...) as both its global dynamical symmetry group and its geometrical symmetry group. It is argued that the two groups are of equal significance as symmetry groups of their associated theories. (shrink)

"E. B. Pashukanis was the most significant contemporary to develop a fresh, new Marxist perspective in post-revolutionary Russia. In 1924 he wrote what is probably his most influential work, The General Theory of Law and Marxism. In the second edition, 1926, he stated that this work was not to be seen as a final product but more for ""self-clarification"" in hopes of adding ""stimulus and material for further discussion."" A third edition was printed in 1927. Pashukanis's ""commodity-exchange"" theory of (...) law spearheaded a perspective that traced the form of law, not to class interests, but to capital logic itself. Until his death, he continued to argue for the ideal of the withering away of the state, law, and the juridic subject. He eventually arrived at a position contrary to Stalin's who, at that time, was attempting to consolidate and strengthen the state apparatus under the name of the dictatorship of the proletariat. Inevitably, Pashukanis was branded an enemy of the revolution in January 1937. His works were subsequently removed from soviet libraries. In 1954, Pashukanis was ""rehabilitated"" by the Soviets and restored to an acceptable position in the historical development of marxist law. In Europe and North America, a number of legal theorists only rediscovered Pashukanis's work in the late 1970s. They subjected it to careful critical analysis, and realized that he offered an alternative to the traditional Marxist interpretations, which saw law simply and purely as tied to class interests of domination. By the mid-1980s the instrumental Marxist perspective in vogue in Marxist sociology, criminology, politics, and economics gave way, to a significant extent due to Pashukanis's insights, to a more structural Marxist accounting of the relationship of law to economics and other social spheres." --Descripción del editor. (shrink)

Working in constructive set theory we formulate notions of constructive topological space and set-generated locale so as to get a good constructive general version of the classical Galois adjunction between topological spaces and locales. Our notion of constructive topological space allows for the space to have a class of points that need not be a set. Also our notion of locale allows the locale to have a class of elements that need not be a set. Class (...) sized mathematical structures need to be allowed for in constructive set theory because the powerset axiom and the full separation scheme are necessarily missing from constructive set theory. We also consider the notion of a formal topology, usually treated in Intuitionistic type theory, and show that the category of set-generated locales is equivalent to the category of formal topologies. We exploit ideas of Palmgren and Curi to obtain versions of their results about when the class of formal points of a set-presentable formal topology form a set. (shrink)

Important examples of $\Pi^0_1$ classes of functions $f \in {}^\omega\omega$ are the classes of sets (elements of ω 2) which separate a given pair of disjoint r.e. sets: ${\mathsf S}_2(A_0, A_1) := \{f \in{}^\omega2 : (\forall i < 2)(\forall x \in A_i)f(x) \neq i\}$. A wider class consists of the classes of functions f ∈ ω k which in a generalized sense separate a k-tuple of r.e. sets (not necessarily pairwise disjoint) for each k ∈ ω: ${\mathsf S}_k(A_0,\ldots,A_k-1) := (...) \{f \in {}^\omega k : (\forall i < k) (\forall x \in A_i) f(x) \neq i\}$. We study the structure of the Medvedev degrees of such classes and show that the set of degrees realized depends strongly on both k and the extent to which the r.e. sets intersect. Let ${\mathcal S}^m_k$ denote the Medvedev degrees of those ${\mathsf S}_k(A_0,\ldots,A_{k-1})$ such that no m + 1 sets among A 0,...,A k-1 have a nonempty intersection. It is shown that each ${\mathcal S}^m_k$ is an upper semi-lattice but not a lattice. The degree of the set of k-ary diagonally nonrecursive functions $\mathsf{DNR}_k$ is the greatest element of ${\mathcal S}^1_k$. If 2 ≤ l < k, then 0 M is the only degree in ${\mathcal S}^1_l$ which is below a member of ${\mathcal S}^1_k$. Each ${\mathcal S}^m_k$ is densely ordered and has the splitting property and the same holds for the lattice ${\mathcal L}^m_k$ it generates. The elements of ${\mathcal S}^m_k$ are exactly the joins of elements of ${\mathcal S}^1_i$ for $\lceil{k \over m}\rceil \leq i \leq k$. (shrink)

(One) the general Hegelian and Schillerian ethics and aesthetics of Lukács’ concept of the realistic historical novel must be logically separated from (two) the contemporary political framework in which he wrote The Historical Novel, which is closely linked to the 1930s popular front movement against fascism. This is particularly important for understanding Lukács’ account of Heinrich Mann’s Young Henry of Navarre/Henry, King of France. It is also very important for understanding Lukács’ account of Walter Scott’s anti-tyranny novels, where only (...) a strong Hegelian emphasis can unlock their peculiar mix of political radicalism, liberalism, and conservatism. Lukács linked Hegelian Sittlichkeit ethics and aesthetic realism with popular front Marxism so closely in The Historical Novel that they often appear as logically inseparable. But at a deeper philosophical level they are logically separable, and must be seen as such in order to bring out the deepest elements in the political-historical imagination in the two novelists who dominate The Historical Novel, Scott and Mann. (shrink)

Being poor can influence how one makes ethical decisions in various fields. Nepotism is one such area, emerging as kinship-based favoritism in the job market. People can be poor on at least three levels: one can live in a poor country, be poor compared to others around them, or feel poor in their given situation. We assumed that these levels can simultaneously influence nepotistic hiring decisions among Hungarian and US participants. Prior cross-cultural, non-experimental studies demonstrated that nepotism is more prevalent (...) in poorer countries such as Hungary than in richer countries such as the United States. However, contrary to our expectations, in our non-representative, preliminary study, US participants showed stronger nepotistic behavioral tendencies than Hungarians. Furthermore, people with lower socioeconomic status had less nepotistic intentions than richer people. When participants were asked to imagine themselves as a poor person, they tended to be more nepotistic than had they imagined themselves to be rich. Finally, nepotistic hiring intentions were in general stronger than non-nepotistic hiring intentions. These seemingly paradoxical results were interpreted in the light of the COVID-19 job market context and were explained by the mechanisms described by research on wealth and immoral behaviors, as well as the presence of risk aversion. (shrink)

This study aims to provide a manageable symmetric two-players conflict model in which, defining measures for polarization and hostility, we investigate the effects of spillovers into the properties of the sets of equilibria, into the intensity of conflict, and into the endogenous changes in polarization and hostility. We show that, without spillovers, the equilibrium efforts’ intensity is uniquely connected to the ratio of the marginal productivity of effort to (ex ante) polarization. Conversely, we show that negative spillovers in conflict technology (...) can imply the non-existence of equilibria. Then, introducing spillovers in the possible outcomes of the conflict, we connect the existence of multiple symmetric and asymmetric equilibria to the intensity of growing polarization and hostility. We then investigate the different effects of marginal productivity of effort, (ex ante) polarization and rates of growth of polarization and hostility on the intensity of conflict as well as on polarization and hostility at equilibrium. The results show the crucial role played by hostility, a factor disregarded in many conflict models. Finally, we show how the results obtained by considering partial spillover effects are confirmed when the general case is taken into account. (shrink)

This article proposes a general taxonomy of artefacts, modeled on the Linnaean hierarchy of biological classification but grounded in criteria specific to material culture and technical kinds. It begins with a philosophical analysis of artefacts as material–intentional products of human design, emphasizing their decisive differences from living organisms and the consequent need for a distinct classificatory framework. Based on this foundation, the paper defines eight nested ranks (Domain, Kingdom, Phylum, Class, Order, Family, Genus, Species) intended to organize technodiversity (...) by progressively specifying (i) ontological constitution, (ii) large-scale structural form, (iii) operative mechanisms, and (iv) technical functions, down to concrete designs and models. The proposed system is guided by five methodological principles: ontological hierarchy, exclusivity and dominance, non-redundancy, universality and completeness, and dynamic revision. These principles constrain demarcation and facilitate cross-domain applicability. An illustrative example within the phylum of physical artefacts demonstrates the transition from broad categories to detailed identification of specific artefact types and models. The article concludes that a Linnaean-inspired taxonomy offers a unified conceptual framework for integrating diverse catalogues, enhancing artefact traceability, and establishing a foundation for future phylogenetic analyses of sociotechnical change in material culture. (shrink)

It is shown that the Schrödinger equation can be solved by means of spectrum-generating algebra techniques for the most general class of Natanzon potentials based on the SO(2, 1) algebra. This paper describes in detail thelinear spectrum generating algebra method which is then applied to solve the Natanzon confluent potentials, and it is extended to one example with spin-orbit coupling. Further, the method is used to explain in detail how to find the energy spectrum for the Dirac equation (...) with a Coulomb potential. Afterwards thequadratic spectrum generation algebra method is presented, and it is used to solve the most general hypergeometric Natanzon potential: The bound state problem and the corresponding wave functions are given. A simple example further illustrates the use of the quadratic method. (shrink)

The main aim of our paper is to show that interpretative issues belonging to classical General Relativity (GR) might be preliminary to a deeper understanding of conceptual problems stemming from on-going attempts at constructing a quantum theory of gravity. Among such interpretative issues, we focus on the meaning of general covariance and the related question of the identity of points, by basing our investigation on the Hamiltonian formulation of GR. In particular, we argue that the adoption of a (...) peculiar gauge-fixing within the canonical reduction of ADM metric gravity may yield a new solution to the debate between substantivalists and relationists, by suggesting a \emph{tertium quid} between these two age-old positions. Such a third position enables us to evaluate the controversial relationship between entity realism and structural realism in a well-defined case study. After having indicated the possible developments of this approach in Quantum Gravity, we discuss the structuralist and holistic features of the class of spacetime models that are used in the above mentioned canonical reduction. (shrink)

There are several known Lindström-style characterization results for basic modal logic. This paper proves a generic Lindström theorem that covers any normal modal logic corresponding to a class of Kripke frames definable by a set of formulas called strict universal Horn formulas. The result is a generalization of a recent characterization of modal logic with the global modality. A negative result is also proved in an appendix showing that the result cannot be strengthened to cover every first-order elementary (...) class='Hi'>class of frames. This is shown by constructing an explicit counterexample. (shrink)

The text presented contains an interview conducted with Domenico Losurdo about "La lotta di classe. Una storia politica e filosofica" (Laterza: Rome 2016) [Class Struggle: A Political and Philosophical History (Palgrave: New York 2018)] and "La sinistra assente. Crisi, società dello spettacolo, guerra" (Carocci: Rome 2014).

The history of political philosophy is certainly not without its share of morally objectionable ideas. Aristotle’s notion of natural slavery, the subordination of women in Rousseau, and Kant’s hierarchy of the races are just a few examples from a long list of morally problematic concepts encountered in the study of political thought. In this article, I argue that our moral discomfort is a pedagogically valuable starting point for critically engaging with political theories that contain controversial ideas. By developing a “critical-hermeneutical” (...) framework that fosters a nuanced understanding of theories as both enablers of emancipation and solidifiers of domination, I aim to demonstrate how philosophy educators can design their courses in a socially responsible manner by transforming adverse or affirmative reactions to morally objectionable ideas into opportunities for engaging critically with a text. (shrink)

Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during (...) the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. This book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones. (shrink)

The standard treatment of fundamental constants rests on two separate domains: physical constants such as α⁻¹ = 137.036 are measured experimentally and classified by CODATA, while mathematical constants such as π and e are defined through analytic or geometric necessity. No structural criterion distinguishes derivable constants from contingent ones, and the total number of fundamental constants has no theoretical bound. -/- This separation creates a deep asymmetry. Physicists treat α⁻¹ as a contingent empirical fact with no known reason for its (...) specific value; mathematicians treat π as logically necessary. Yet both are dimensionless, scale-invariant, and protocol-independent. The question of why they belong to different ontological categories has no answer within the standard paradigm. -/- The present paper resolves this within Operatiology by introducing Operational Invariants (操作遍数, Sousa Hensuu), dimensionless constants derivable from the common foundation C⁽³⁾_Πd realised as M₃(ℂ). An ontological trichotomy partitions all quantities into Class I (Operational Invariants), Class II (dimensional constants encoding unit system choice), and Class III (running coupling constants). A Class I Completeness Theorem is proved without circularity. -/- The Euler-Mascheroni constant γ_E is established as M₃(ℂ)-grounded as the unique structural invariant measuring the discrepancy between the discrete factorial structure of U(n) (Tier 2) and its continuous analytic extension (Tier 3), and as the compression residue of the relational closure of M₃(ℂ) into finite algebraic invariants. This enables identification of the BCS gap ratio κ_BCS = 2π/e^γ_E = 3.52775... as a new Operational Invariant. -/- Version 2 extended the framework by defining the set S of Operational Invariants without restriction to the candidate space F_ext: S = {κ | M₃(ℂ)-grounded and A4-irreducible}. S properly contains F_ext; confirmed elements of S \ F_ext include e, ln 2, α⁻¹, μ, and ξ². Each element of S is assigned a structural category: (A) M₁-algebraic; (B) M₁-condition/M₃-value (πᵏ, e); (C) projection-connection invariant (γ_E); (D) M₃-operation on M₁-element (ln 2); (E) composite. The constants √2 = γ⁻¹/² and √3 = K = √2·δ satisfy Class I observational conditions but are A4-redundant and excluded from S. The finiteness of S was proved in full, covering both S ∩ F_ext and S \ F_ext. -/- Version 3 completes the grounding structure. M₃(ℂ)-groundedness is now established via three structurally independent and jointly exhaustive conditions: (G1) volumetric grounding, governing πᵏ; (G2) normalization grounding, governing γ_E; and (G3) exponential unit grounding, newly introduced, governing the natural logarithm base e as the value of the Lie algebra exponential map at the multiplicative unit of the A2-selected field ℝ. The uniqueness of this evaluation point and the exhaustiveness of the three conditions are each proved as independent results. A new section establishes, paper by paper, the citation integrity of the companion derivations of e, μ, π, and α⁻¹ against the present version, resolving a prior citation gap with the companion paper on e and confirming the absence of impact elsewhere. -/- The distinction between physical and mathematical constants is dissolved: π, e, √2, √3, γ_E, and α⁻¹ are ontologically equivalent Class I Operational Invariants, all projectives of the common foundation C⁽³⁾_Πd. This Version 3 supersedes Version 2 (DOI: 10.5281/zenodo.20647095) in all respects. -/- Published on June 18, 2026 DOI: 10.5281/zenodo.20747691. (shrink)

Procedures were designed to test for the effects of working-memory training on children at risk of fluency difficulty that apply to English and to many of the languages spoken by children with English as an Additional Language (EAL) in UK schools. Working-memory training should: (1) improve speech fluency in high-risk children; (2) enhance non-word repetition (NWR) (phonological) skills for all children; (3) not affect word-finding abilities. Children starting general education (N = 232) were screened to identify those at risk (...) of fluency difficulty. Children were selected who were at high-risk (12), or low-risk (27) of fluency difficulty. For the low-risk children 10 received, and 17 did not receive, the working-memory training. All children in the treatment groups received working-memory training over a 2-week period. For the high-risk group, fluency improved and lasted for at least a week after the end of the study. Phonological skills improved in this group and in the low-risk group who received the training and the improvements continued for at least a week. The low-risk group who did not receive working-memory training showed no improvements, and no group improved word-finding ability. (shrink)

During spring of 2020, environmental ethics students at a medium sized metropolitan university in the Southeastern United States were asked to read and comment on classic essays from Robert Heilbroner and Garrett Hardin, essays regarding our responsibilities towards future generations. In general, students seemed to hold more with Heilbroner’s stance, which left room for compassion, while condemning Hardin’s harshness. Students were then asked to provide written responses stating whether they would personally sacrifice their eventual retirement in order to stop (...) COVID-19 and the reasons for their views. Responses were analyzed and categorized to detect inconsistencies between students’ described views and their willingness to personally sacrifice for the sake of others. Almost 72% of respondents asserted that they would be willing to intervene to stop the novel coronavirus by sacrificing their retirement. A fair number of respondents that stated they would sacrifice said that they would do so because they would benefit personally from the avoidance of guilt and/or from the opportunity to feel good about themselves, suggesting that even seemingly selfless behaviors are sometimes driven by egoistic motivations. Forty percent of all respondents held inconsistent views. Most notably, a number of students condemned Hardin for his lack of compassion, yet were not willing to act compassionately themselves. (shrink)

The way of thinking of mathematicians and chemists in their respective disciplines seems to have very different levels of abstractions. While the firsts are involved in the most abstract of all sciences, the seconds are engaged in a practical, mainly experimental discipline. Therefore, it is surprising that many luminaries of the mathematics universe have studied chemistry as their main subject. Others have started studying chemistry before swapping to mathematics or have declared some admiration and even love for this discipline. Here (...) I reveal some of these mathematicians who were involved in chemistry from a biographical perspective. Then, I analyze what these remarkable mathematicians and statisticians could have learned while studying chemical subjects. I found analogies between code-breaking and molecular structure elucidation, inspiration for statistics in quantitative analytical chemistry, and on the role of topology in the study of some organic molecules. I also analyze some parallelisms between the way of thinking of organic chemists and mathematicians in terms of the use of backward analysis, search for patterns, and use of pictures in their respective researches. (shrink)

Professor James R. Flynn is renowned for his belief that the IQ gap between black and white Americans is not genetic, but environmental in origin. Flynn's controversial new book offers an alternative to the vision of American society popularized by Herrnstein and Murray in The Bell Curve and is a must-read for all those wanting to keep up to date with the IQ debate. It traces the history of American idealism from Jefferson to the followers of Leo Strauss; analyses the (...) black marriage market, the case for affirmative action, the folly of Iraq, and the liberal failure of will; and concludes with a powerful defence of humane ideals and human autonomy. With its clear and attractive prose, social scientists, philosophers and the general public will find this a unique and exciting book that will rearm American idealism with new ideas. (shrink)

GEORGE BOOLE died one hundred years ago. This essay from Cork is intended as commemorative of a great man, for too long forgotten in the College he served so well.

This article explores the value of teaching Environmental Ethics as an introductory-level general education course for non-majors. It focuses on how philosophy can help students discern multiple voices within discourses, texts and thinking, and by doing so disrupt several untenable mental paradigms that new and underprepared students often bring with them to college: fixed and dualistic notions of truth, relativistic conceptions of difference, and decontextualized approaches to issues and ideas. This article also presents examples of class activities that (...) are designed to foster multivocal thinking and that are also manageable for faculty with high teaching loads. (shrink)

Causal sets are a particular class of partially ordered sets, which are proposed as basic models of discrete space-time, specially in the field of quantum gravity. In this context, we show the existence of temporal foliations for any causal set, or more generally, for a causal space. Moreover, we show that automorphisms of a large class of infinite causal sets fall into two classes 1) Automorphisms of spacelike hypersurfaces in some given foliation, or 2) Translations in time. More (...) generally, we show that for any automorphism \ of a generic causal set \, there exists a partition of \ into finitely many subcausets, on each of which or above hold. These subcausets can be assumed connected if, in addition, there are enough distinct orbits under \. (shrink)

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339-1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174: 1339-1368, 2010) (...) to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases. (shrink)

examine Nathan Salmon’s solution to the problem of trivialization, as it arises for conceptions of general term rigidity that construe it as identity of designation across possible worlds. I argue that he does not succeed in showing that some alleged general terms, such as “the colour of the sky” are non-rigid, but also that a small class of different examples that he presents, which can be construed as second order descriptions, are indeed non-rigid general terms, although (...) for reasons different from those he thought. (shrink)

We consider a class of Lindström extensions of first-order logic which are susceptible to a natural Skolemization procedure. In these logics Ehrenfeucht Mostowski (EM) functors for theories with arbitrarily large models can be obtained under suitable restrictions. Characteristic dependencies between algebraic properties of the quantifiers and the maximal domains of EM functors are investigated.Results are applied to Magidor Malitz logic,L(Q <ω), showing e.g. its Hanf number to be equal to ℶω(ℵ1) in the countably compact case. Using results of Baumgartner, (...) the maximal number of isomorphism types of linearly ordered models of regular cardinality is shown to be achieved for theories that admit an EM functor on a typically restricted domain. (shrink)

Over the past two decades, work relations have changed dramatically. New phenomena like “gig-economy” or “crowd work” not only constitute precarious working conditions but also contradict with our social esteem of work resulting from the social theories of the classical economy of the eighteenth and nineteenth centuries. The central focus of classical economists on building an educated and disciplined workforce provided not only the base for the upcoming industrial society but also resulted in a work-based society where “being employed” became (...) the precondition for social security and social participation. It is the aim of this contribution to show how our positive attitudes towards work, established by the political economic theories of the eighteenth and nineteenth centuries, are jeopardized by the social changes in post-industrialized societies, due to the effects of globalized economies, digitalization and changed industrial relations. This has also far-reaching consequences for managerial theories based on conceptions like meaningful work or discussions about social responsibilities vis-à-vis employees as primary stakeholder groups. (shrink)