This paper summarizes a theory of cognitive development and elaborates on its educational implications. The theory postulates that development occurs in cycles along multiple fronts. Cognitive competence in each cycle comprises a different profile of executive, inferential, and awareness processes, reflecting changes in developmental priorities in each cycle. Changes reflect varying needs in representing, understanding, and interacting with the world. Interaction control dominates episodic representation in infancy; attention control and perceptual awareness dominate in realistic representations in preschool; inferential control and (...) awareness dominate rule-based representation in primary school; truth and validity control and precise self-evaluation dominate in principle-based thought in adolescence. We demonstrate that the best predictors of school learning in each cycle are the cycle’s cognitive priorities. Also learning in different domains, e.g., language and mathematics, depends on an interaction between the general cognitive processes dominating in each cycle and the state of the representational systems associated with each domain. When a representational system is deficient, specific learning difficulties may emerge, e.g., dyslexia and dyscalculia. We also discuss the educational implications for evaluation and learning at school. (shrink)

In this chapter, we focus on the debate over publicly maintained racist monuments as it manifests in the mid-2010s Anglosphere, primarily in the United States and South Africa. After pointing to some representative examples of racist monuments, we discuss ways a monument can be thought racist and neutrally categorize removalist and preservationist arguments heard in the monument debate. We suggest that both extremist and moderate removalist goals are likely to be self-defeating and that when concerns of civic sustainability are put (...) on moral par with those of fairness and justice, something like a Mandela-era preservationist policy is best: one which removes the most offensive of the minor racist monuments, but which focuses on closing the monumentary gap between peoples and reframing existing racist monuments. (shrink)

Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the cases of (...) k-deductive systems and of consequence relations on associative, commutative, multiple conclusion sequents. Our main result subsumes all existing results in the literature and reveals their common character. The proofs are of order-theoretic and categorical nature. (shrink)

It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part (...) of the paper, we also discuss some extended forms of the Kolmogorov translation and we compare it to the Glivenko translation. (shrink)

This is also where we begin investigating lattices of logics and varieties, rather than particular examples.

Richard Nisbett and Dov Cohen’s (1996) influential account of “cultures of honor” speculates that honor norms are a socially-adaptive deterrence strategy. This theory has been appealed to by multiple empirically-minded philosophers, and plays an important role in John Doris and Alexandra Plakias’ (2008) antirealist argument from disagreement. In this essay, I raise four objections to the Nisbett-Cohen deterrence thesis, and offer another theory of honor in its place that sees honor as an agonistic normative system regulating prestige competitions. Since my (...) account portrays honor norms as radically different from liberal ones, it actually strengthens Doris and Plakias’ case in some respects: cultures of honor are not merely superficially different from Western liberal ones. Nonetheless, the persistent appeal of honor’s principles, and their moral plausibility in certain contexts, suggests not antirealism, but pluralism—a reply on behalf of realism that itself has considerable empirical support. (shrink)

Derk Pereboom's Four-Case Argument is among the most famous and resilient manipulation arguments against compatibilism. I contend that its resilience is not a function of the argument's soundness but, rather, the ill-gotten gain from an ambiguity in the description of the causal relations found in the argument's foundational case. I expose this crucial ambiguity and suggest that a dilemma faces anyone hoping to resolve it. After a thorough search for an interpretation which avoids both horns of this dilemma, I conclude (...) that none is available. Rather, every metaphysically coherent interpretation invites either a hard- or soft-line reply to Pereboom's argument. I then consider a recharacterization of the dilemma which seems to clear the way for the defence of a revised Four-Case Argument. I address this rejoinder by identifying a still more fundamental problem shared by all viable interpretations of the manipulation cases, showing that each involves a type of manipulation which undermines the victim's agency. Because this diagnosis supports a soft-line reply to every viable interpretation of the argument and can be endorsed by any compatibilist, I consider it the final piece of the Soft-line Solution to the Four-Case Argument. Finally, I suggest a new taxonomy of manipulation arguments, arguing that none that employs the suppressive variety of manipulation found in Pereboom's argument offers a threat to compatibilism. -/- (For direct download option, search Kristin M. Mickelson, Soft-line Solution). (shrink)

I argue that Greene’s research, although fascinating for many reasons, doesn’t undermine deontological moral philosophy. This is because both sentimentalist and rationalist moral epistemologies, applied to deontological value, predict exactly the data Greene has found. My discussion proceeds in three steps. In the first section I summarize Greene’s brief against deontology. In the second section I draw on standard accounts of moral emotions to suggest that there are ‘deontological emotions’ made rational by appearances of ‘deontological value.’ Finally, I outline a (...) modest but realist intuitionist account of moral intuitions that connects deontological emotion to putative deontological value in a way that predicts Greene’s findings. (shrink)

Writing a history of ancient Greece, in periods of political turbulence and transition, involved the construction of an edifying platform for civil conduct. Britain, 1770-1850, was one such period. In examining Athenian democracy the British historians of the late eighteenth century, like William Mitford and John Gillies, found a convenient channel to articulate their private political preferences and antipathies, thereby accentuating the ideological antagonism of the post-revolutionary age. Athenian liberalism was deliberately drawn from oblivion only to be set as a (...) constitutional example to avoid, whereas the merits of the mixed British constitution were distinctly exposed. The British Utilitarians, by contrast, produced a case on behalf of representative government that included the basic characteristics of democracy and which witnessed its minimum prototype in ancient Athens. George Grote assumed the task of upsetting the conventional idea of Athens, thus perpetuating the typical association of Greek historiography with contemporary political discussion. (shrink)

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.

Two constructions for adding an involution operator to residuated ordered monoids are investigated. One preserves integrality and the mingle axiom x 2x but fails to preserve the contraction property xx 2. The other has the opposite preservation properties. Both constructions preserve commutativity as well as existent nonempty meets and joins and self-dual order properties. Used in conjunction with either construction, a result of R.T. Brady can be seen to show that the equational theory of commutative distributive residuated lattices (without involution) (...) is decidable, settling a question implicitly posed by P. Jipsen and C. Tsinakis. The corresponding logical result is the (theorem-) decidability of the negation-free axioms and rules of the logic RW, formulated with fusion and the Ackermann constant t. This completes a result of S. Giambrone whose proof relied on the absence of t. (shrink)

We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...) with and is algebraizable, with the variety of residuated lattice-ordered groupoids with unit serving as its equivalent algebraic semantics. Overcoming technical complications arising from the lack of associativity, we introduce a generalized version of a logical matrix and apply the method of quasicompletions to obtain an algebra and a quasiembedding from the matrix to the algebra. By applying the general result to specific cases, we obtain important logical and algebraic properties, including the cut elimination of and various extensions, the strong separation of , and the finite generation of the variety of residuated lattice-ordered groupoids with unit. (shrink)

We provide an alternative proof of the decidability of the equational theory of lattices. The proof presented here is quite short and elementary.

Given a positive universal formula in the language of residuated lattices, we construct a recursive basis of equations for a variety, such that a subdirectly irreducible residuated lattice is in the variety exactly when it satisfies the positive universal formula. We use this correspondence to prove, among other things, that the join of two finitely based varieties of commutative residuated lattices is also finitely based. This implies that the intersection of two finitely axiomatized substructural logics over FL + is also (...) finitely axiomatized. Finally, we give examples of cases where the join of two varieties is their Cartesian product. (shrink)

Although most cultures have held honorableness to be a virtue of the first importance, contemporary analytic ethicists have just begun to consider honor’s nature and ethical worth. In this essay, I provide an analysis of the honor ethos and apply it to business ethics. Applying honor to business may appear to be a particularly challenging task, since (for reasons I discuss) honor has traditionally been seen as incompatible with commerce. Nonetheless, I argue here that two of the central virtues of (...) the honor ethos—competiveness and magnificence—are perfectly apt ones for rich business executives, who plausibly can be expected to work more for prestige and the thrill of competition than for wealth itself. In addition to making top executives more honorable people, the virtues of competitiveness and magnificence would have positive social effects: honorable competitiveness would intrinsically dispose executives to shun anti-competitive practices, and magnificence would encourage tycoons to redistribute their fortunes voluntarily through philanthropy. (shrink)

In The Problem of Punishment, David Boonin offers an analysis of punishment and an account of what he sees as ethically problematic about it. In this essay I make three points. First, pace Boonin's analysis, everyday examples of punishment show that it sometimes isn't harmful, but merely "discomforting." Second, intentionally discomforting offenders isn't uniquely problematic, given that we have cases of non-punitive intentional discomforture---and perhaps even harmful discomforture---that seem unobjectionable. Third, a notable fact about both non-harmful punishment and non-punitive intentional (...) discomforture is that they aim at improving the subject. This suggests that, if the prima facie wrongness of intentionally harming another person is the fundamental challenge for punishment, the "educative defense" is the royal road to justifying the practice. I conclude by outlining one version of the educative defense that exploits this advantage while avoiding some traditional objections to the approach. (shrink)

This essay distinguishes between honor-typical and authoritarian behavior in humans and animals. Whereas authoritarianism concerns hierarchies coordinated by control and obedience, honor concerns rankings of prestige determined by fair contests. Honor-typical behavior is identifiable in non-human species, and is to be expected in polygynous species with non-resource-based mating systems. This picture lends further support to an increasingly popular psychological theory that sees morality as constituted by a variety of moral systems. If moral cognition is pluralistic in this way, then the (...) question of moral agency is better considered in terms of particular moral modes, one of which will be “honor-agency.” The universal principles of honorable conduct suggest a handful of criteria for counting as an honorable agent (human or otherwise), and these criteria can be specified without commitment to any particular account of what it takes to be an agent in general. (shrink)

All known structural extensions of the substructural logic $\textbf{FL}_{\textbf{e}}$, the Full Lambek calculus with exchange/commutativity (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$ -equations), have decidable theoremhood; in particular all the ones defined by knotted axioms enjoy strong decidability properties (such as the finite embeddability property). We provide infinitely many such extensions that have undecidable theoremhood, by encoding machines with undecidable halting problem. An even bigger class of extensions is shown to have undecidable deducibility problem (the (...) corresponding varieties of residuated lattices have undecidable word problem); actually with very few exceptions, such as the knotted axioms and the other prespinal axioms, we prove that undecidability is ubiquitous. Known undecidability results for non-commutative extensions use an encoding that fails in the presence of commutativity, so and-branching counter machines are employed. Even these machines provide encodings that fail to capture proper extensions of commutativity, therefore we introduce a new variant that works on an exponential scale. The correctness of the encoding is established by employing the theory of residuated frames. (shrink)

In this chapter we focus on the debate over publicly-maintained racist monuments as it manifests in the mid-2010s Anglosphere, primarily in the US (chiefly regarding the over 700 monuments devoted to the Confederacy), but to some degree also in Britain and Commonwealth countries, especially South Africa (chiefly regarding monuments devoted to figures and events associated with colonialism and apartheid). After pointing to some representative examples of racist monuments, we discuss ways a monument can be thought racist, and neutrally categorize removalist (...) and preservationist arguments heard in the monument debate. We suggest that both extremist and moderate removalist goals are likely to be self-defeating, and that when concerns of civic sustainability are put on moral par with those of fairness and justice, something like a Mandela-era preservationist policy is best: one which removes the most offensive of the minor racist monuments, but which focuses on closing the monumentary gap between peoples and reframing existing racist monuments. (shrink)

This commentary compares the P-FIT model with psychometric and developmental models of intelligence and shows that there are isomorphisms and divergences between them. All three models involve some common dimensions, but the P-FIT model lacks many of the dimensions of the other models. Then we point to research that can lead to the integration of brain models with cognitive-developmental models.

Two studies substantiating Blair's main postulates are summarized. The first study showed that fluid cognition, reasoning, and perceived competence about reasoning are separate and equipotent partners in g. The second study showed that reasoning, understanding of emotions, and perceived competence about reasoning and emotions partake in the formation of g, substantiating Blair's claim that cognition and emotion are linked in the brain.

The British utilitarians are not generally considered explorers of classical Greek thought. This paper examines the contribution of James Mill, John Stuart Mill, and George Grote to the development of Platonic studies in nineteenth-century Britain. Their understanding of Platonic philosophy challenged prevalent interpretations, and caused a fruitful debate over long neglected aspects of Plato's thought. Grote's Platonic analysis, which comes last in order of time, cannot, of course, be considered in isolation from the relevant debates in Germany. Grote, the erudite (...) historian of ancient Greece, paid considerable attention to the arguments of the German classicists, put forward in many cases a new point of view, and prompted a radical revaluation of Platonic political thought. (shrink)

Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed. A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional support for this approach. In our work, a geometric approach to quantum indistinguishability is introduced which allows the treatment of singlevaluedness of wave functions in a global, model independent way.

If X is a locally compact Polish space, then LSC denotes the compact Polish space of lower semi-continuous real-valued functions on X equipped with the topology of epi-convergence.Our purpose in this article is to prove the following: if –∞ < α < β < ∞ and –∞ < a < b < ∞, while r ∈ ℕ \ {0}, then the set CV of all f ∈ LSC for which there is u ∈ Cr such that for any v ∈ (...) Cr we have that ∫αβf , v ′)dx ≥ ∫αβf , v )dx is not Borel. (shrink)

The purpose of this paper is first to show that if X is any locally compact but not compact perfect Polish space and stands for the one-point compactification of X, while E X is the equivalence relation which is defined on the Polish group C(X,R +*) by where f, g are in C(X,R +*), then E X is induced by a turbulent Polish group action. Second we show that given any if we identify the n-dimensional unit sphere S n with (...) the one-point compactification of R n via the stereographic projection, while E n , r is the equivalence relation which is defined on the Polish group C r (R n ,R +*) by where f, g are in C r (R n ,R +*), then E n , r is also induced by a turbulent Polish group action. (shrink)

Με αφορμή ένα γεωμετρικό αμφορέα του επιγάστριου αττικο-κυκλαδικού τύπου από το νεκροταφείο της Ελεύθερνας, διακοσμημένο με τρεις μετόπες ομόκεντρων κύκλων στη ζώνη της κοιλιάς, συζητούνται τα προβλήματα τυπολογίας και προέλευσης αυτής της χαρακτηριστικής κατηγορίας αγγείων στο φως της νεότερης έρευνας. Η τεχνοτροπία όλων των αμφορέων αυτού του τύπου, δηλ. με δύο ή με τρεις μετόπες ομοκέντρων κύκλων, ακολουθεί πάντοτε τον αττικό ρυθμό, αλλά ενώ η αττική καταγωγή των διμετο- πικών αμφορέων του τύπου ουδέποτε αμφισβητήθηκε, η καταγωγή των τριμετοπικών αμφορέων, που (...) παρουσιάζουν ευρύτατη διάδοση στο Αιγαίο και κυρίως στις Κυκλάδες, άλλοτε αποδίδεται στην Αττική και άλλοτε στις Κυκλάδες. Στη μελέτη αυτή επιχειρείται ένας επαναπροσδιορισμός της τυπολογίας του επιγάστριου ομοκεντρικού αμφορέα και συζητείται διεξοδικά η κατηγορία των αμφορέων με τρεις μετόπες. (shrink)

The riddle of the Cleitophon is a creature of nineteenth-century German scholarship which premised that Plato had developed a profound philosophical system. Thus, having no intrinsic purpose to serve in the context of the development of Plato's philosophy, Cleitophon was disallowed as spurious. Documenting the reception of this minor dialogue provides insights into the pluralism and the perplexities of modern Platonic exegesis. The more recent idea of a genre of literary fiction helps to restore cleitophon to its place in the (...) Platonic corpus. S.R. Slings's edition of this dialogue, with introduction, translation and commentary reconsiders both Plato's dialogical engagements and intellectual commitments, utilizes a two-dimensional approach to the text that avoids exaggerated conjectures, and effectively defends the authenticity of Cleitophon. (shrink)

Background:Withdrawal of treatment is a common practice in intensive care units when treatment is considered futile. Compassion is an important aspect of care; however, it has not been explored much within the context of treatment withdrawal in intensive care units.Objectives:The aim was to examine how concepts of compassion are framed, utilised and communicated by intensive care nurses in the context of treatment withdrawal.Design:The study employed a qualitative approach conducting secondary analysis of an original data set. In the primary study, 13 (...) nurses were recruited from three intensive care units within a large hospital in United Kingdom. Deductive framework analysis was used to analyse the data in relation to compassionate care.Ethical considerations:The primary study was approved by the local Research Ethics Committee and the hospital’s Research and Development services.Findings:Compassionate care was mostly directed to the patient’s family and was demonstrated through care and emotional support to the family. It was predominantly expressed through attempts to maintain the patient’s dignity by controlling symptoms, maintaining patient cleanliness and removing technical apparatus.Conclusion:This study’s findings provide insight about compassionate care during treatment withdrawal which could help to understand and develop further clinicians’ roles. Prioritising the family over the patient raised concerns among nurses, who motivated by compassion, may feel justified in taking measures that are in the interests of the family rather than the patient. Further work is needed to explore the ethics of this. (shrink)

From the early 1930s to the early 1960s many scholars, whether liberal-minded or socialist ideologues, Marxist or scientific positivists, classical scholars or political theorists and historians, have shown a widespread consensus in discrediting and assailing the man and political philosopher Plato. Such an extensive assault led the 'Platonic Legend' to an unprecedented crisis. Philosophically, it was a reaction to the undisguised Platonolatry coming from Oxford and the school of the British Idealists. Ideologically, the appropriation of Plato by Nazi apologists fostered (...) further this vehement indictment. But a lot of other causes worked to the same effect. The general anguish and humanistic anxiety on the eve of World War II and the postwar traumas led scholars to reconsider the meaning of history and historicism, the psychology of the masses and the ethical responsibility of the citizen, the role of propaganda and state education. Such complementary elements converged in sustained anti-Platonic polemics, which in turn provoked a vigorous defence. Here an attempt is made to offer a preliminary survey of this complex debate and to provide a general intellectual framework in terms of which that controversy can be further explored. (shrink)

Cet article présente une série d’épigrammes hellénistiques généralement peu étudiées et quelques témoignages littéraires et épigraphiques attestant le culte d’Aphrodite en tant que protectrice de la navigation. Les temples de la déesse occupaient souvent une position littorale, non parce qu’ils étaient des lieux où la « prostitution sacrée » était pratiquée, mais plutôt en raison de l’association d’Aphrodite avec la mer et de son rôle de patronne des marins. La protection qu’elle accordait était destinée à tous les navigateurs, y compris (...) la marine et les commerçants, et est attestée dans toute la Méditerranée, depuis la période archaïque jusqu’à la période hellénistique. De plus, les textes examinés révèlent un lien métaphorique entre les rôles d’Aphrodite comme protectrice de la navigation d’une part et comme déesse de la sexualité d’autre part. (shrink)