This article questions the prevailing opinion that Domitian's prohibition of castration was intended as a protective measure devised to check masters’ abuses on their slaves, as part of a larger trend towards more enlightened attitudes towards slavery among the Romans. While brutal, castration was the only type of mutilation which increased the monetary value of slaves. Banning it curtailed slaves’ chances of social climbing and narrowed their channels towards positions of power. The emasculation ban is, instead, better understood as one (...) of the many measures directed towards the control of the sexual behaviour and the sumptuary practices of the Roman elite. Introduced as a censorial decree, the ban gave Domitian the opportunity to act as the upholder of Republican traditions at the same time as he impinged on the private lives of his subjects and put senators and equestrians under his thumb. The article also argues that, contrary to what is usually argued, the constant re-enforcement of the prohibition to castrate by Domitian's successors is an indication of the effectiveness of the Roman legal machinery and its capacity to reach the most distant corners of the Roman empire. (shrink)

This book taps the best American thinkers to answer the essential American question: How do we sustain our experiment in government of, by, and for the people? Authored by an extraordinary and politically diverse roster of public officials, scholars, and educators, these chapters describe our nation's civic education problem, assess its causes, offer an agenda for reform, and explain the high stakes at risk if we fail.

We give examples of calculi that extend Gentzen’s sequent calculusLKby unsound quantifier inferences in such a way that derivations lead only to true sequents, and proofs therein are nonelementarily shorter thanLK-proofs.

We prove a number of results on the determinacy of σ-projective sets of reals, i.e., those belonging to the smallest pointclass containing the open sets and closed under complements, countable unions, and projections. We first prove the equivalence between σ-projective determinacy and the determinacy of certain classes of games of variable length <ω^2 (Theorem 2.4). We then give an elementary proof of the determinacy of σ-projective sets from optimal large-cardinal hypotheses (Theorem 4.4). Finally, we show how to generalize the proof (...) to obtain proofs of the determinacy of σ-projective games of a given countable length and of games with payoff in the smallest σ-algebra containing the projective sets, from corresponding assumptions (Theorem 5.1, Theorem 5.4). (shrink)

Summary A brief state of the art for Phlegon of Tralles’ De Mirabilia 3 anti-Roman prophecies is followed by a reassessment of four of its components: the historical identification of the Roman protagonist “Publius”, Naupaktos as the main stage for the prophecies, the multiple meanings of the Red Wolf as well as the Oak Tree, and the Roman military retreat. By analyzing these specific elements, it will be argued that these presages were not only associated with events during the Antiochean (...) and Mithridatic Wars, but were also related with historical experiences from the First Macedonian Conflict. (shrink)

We determine the consistency strength of determinacy for projective games of length ω^2. Our main theorem is that $\Pi _{n + 1}^1$-determinacy for games of length ω^2 implies the existence of a model of set theory with ω + n Woodin cardinals. In a first step, we show that this hypothesis implies that there is a countable set of reals A such that M_n(A), the canonical inner model for n Woodin cardinals constructed over A, satisfies $A = R$ and the (...) Axiom of Determinacy. Then we argue how to obtain a model with ω + n Woodin cardinal from this. We also show how the proof can be adapted to investigate the consistency strength of determinacy for games of length ω^2 with payoff in $R^R\Pi _1^1$ or with σ-projective payoff. (shrink)

The thesis is guided by the question: What is the subject matter of Heidegger’s philosophy in the period of Being and Time? I start by arguing that Heidegger’s formulation of the question of being is ambiguous because the term ‘being’ is open to at least two interpretations. I claim that this ambiguity has motivated two types of reading of Heidegger’s early work. On the first reading, Heidegger’s philosophy is understood as attempting to infer metaphysical claims (claims about what-is, or being (...) in a traditionally metaphysical sense) on the basis of claims about the structure of Dasein’s understanding. This reading typically renders Heidegger an idealist. On the second reading, Heidegger’s philosophy is taken to have no metaphysical ambitions, and thereby to be limited to elucidating the structure of Dasein’s understanding. I argue that both types of reading are inadequate and diagnose them as grounded in a Cartesian presupposition that Heidegger rejects. On the basis of direct textual evidence and a number of theoretical considerations I assert that although the second type of reading is right in that the primary object of Heidegger’s philosophy is the conditions of understanding and that the idealist reading is wrong, it is a mistake to deny that Heidegger’s philosophy has metaphysical implications. I claim that Heidegger’s exposition of the conditions of understanding involves a larger picture from the outset, a picture that delineates the relation between understanding and entities, and locates the objective in relation to Dasein. On this picture, 1) empirical entities are unqualifiedly independent of Dasein, 2) we have direct cognitive access to these entities as they are in themselves, and 3) there is no a priori unintelligible entities or aspects of entities. I address a number of potential objections to this way of interpreting Heidegger’s work. (shrink)

For every countable wellordering $\alpha $ greater than $\omega $, it is shown that clopen determinacy for games of length $\alpha $ with moves in $\mathbb {N}$ is equivalent to determinacy for a class of shorter games, but with more complicated payoff. In particular, it is shown that clopen determinacy for games of length $\omega ^2$ is equivalent to $\sigma $ -projective determinacy for games of length $\omega $ and that clopen determinacy for games of length $\omega ^3$ is equivalent (...) to determinacy for games of length $\omega ^2$ in the smallest $\sigma $ -algebra on $\mathbb {R}$ containing all open sets and closed under the real game quantifier. (shrink)

Extending Aanderaa’s classical result that $\pi ^{1}_{1} < \sigma ^{1}_{1}$, we determine the order between any two patterns of iterated $\Sigma ^{1}_{1}$ - and $\Pi ^{1}_{1}$ -reflection on ordinals. We show that this order of linear reflection is a prewellordering of length $\omega ^{\omega }$. This requires considering the relationship between linear and some non-linear reflection patterns, such as $\sigma \wedge \pi $, the pattern of simultaneous $\Sigma ^{1}_{1}$ - and $\Pi ^{1}_{1}$ -reflection. The proofs involve linking the lengths of (...) $\alpha $ -recursive wellorderings to various forms of stability and reflection properties satisfied by ordinals $\alpha $ within standard and non-standard models of set theory. (shrink)

Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for L, (...) that is, the case n=0. As consequences of the proof, we see that determinacy of all projective games with moves in R is equivalent to the statement that Mn♯ exists for all n∈N, and that determinacy of all projective games of length ω2 with moves in N is equivalent to the statement that Mn♯ exists and satisfies AD for all n∈N. (shrink)

We prove a topological completeness theorem for the modal logic $$\textsf{GLP}$$ GLP containing operators $$\{\langle \xi \rangle :\xi \in \textsf{Ord}\}$$ { ⟨ ξ ⟩ : ξ ∈ Ord } intended to capture a wellordered sequence of consistency operators increasing in strength. More specifically, we prove that, given a tall-enough scattered space X, any sentence $$\phi $$ ϕ consistent with $$\textsf{GLP}$$ GLP can be satisfied on a polytopological space based on finitely many Icard topologies constructed over X and corresponding to the (...) finitely many modalities that occur in $$\phi $$ ϕ. (shrink)

Background: Heart rate variability (HRV) has been considered as a measure of heart-brain interaction and autonomic modulation, and it is modified by cognitive and attentional tasks. In cognitive tasks, HRV was reduced in participants who achieved worse results. This could indicate the possibility of HRV predicting cognitive performance, but this association is still unclear in a high cognitive load sport such as chess Objective: To analyse modifications on HRV and subjective perception of stress, difficulty and complexity in different chess problem (...) tasks. Design: HRV was assessed at baseline. During the chess problems, HRV was also monitored, and immediately after chess problems the subjective stress, difficulty and complexity were also registered. Method: A total of 16 male chess players, age: 35.19 (13.44) and ELO: 1927.69 (167.78) were analysed while six chess problem solving tasks with different level of difficulty were conducted (two low level, two medium level and two high level chess problems). Participants were classified according to their results into two groups: high performance or low performance. Results: Friedman test showed a significant effect of tasks in HRV indexes and perceived difficulty, stress and complexity in both high and low performance groups. A decrease in HRV was observed in both groups when chess problems difficulty increased. In addition, HRV was significantly higher in the high performance group than in the low performance group during chess problems. Conclusions: An increase in autonomic modulation was observed to meet the cognitive demands of the problems, being higher while the difficulty of the tasks increased. Non-linear HRV indexes seem to be more reactive to tasks difficulty, being an interesting and useful tool in chess training. (shrink)

Bhattacharyya, K. The Advaita concept of subjectivity.--Deutsch, E. Reflections on some aspects of the theory of rasa.--Nakamura, H. The dawn of modern thought in the East.--Organ, T. Causality, Indian and Greek.--Chatterjee, M. On types of classification.--Lacombe, O. Transcendental imagination.--Bahm, A. J. Standards for comparative philosophy.--Herring, H. Appearance, its significance and meaning in the history of philosophy.--Chang Chung-yuan. Pre-rational harmony in Heidegger's essential thinking and Chʼan thought.--Staal, J. F. Making sense of the Buddhist tetralemma.--Enomiya-Lassalle, H. M. The mysticism of Carl Albrecht (...) and Zen.--Parrinder, G. The nature of mysticism.--Cairns, G. E. Axiological contributions of East and West to the spiritual development of mankind.--Mayeda, S. Śaṇkara's view of ethics.--Mercier, A. On peace.--Barlingay, S. S. A discussion of some aspects of Gaudapāda's philosophy. (shrink)

Within the polemic work which was developed by Eastern Christians it is necessary to underline the transmission of the whole of the religious conceptions, the kinds of argumentation and defence of the dogma, the elaboration of the discourse, the debate techniques used, the vocabulary which was adapted and generated, the rewriting developed from the Biblical material and Quranic criticism, as well as the refutations of the Muslim ideas, and the huge information which is inside the intrachristian polemics. Theology is the (...) most important element to describe the abridged knowledge which is in all of the treatises which make whole the polemic typology. This element allows us to rebuild the rich and involved tram which forms the 'theological knowledge' of the different Ch1istian churches and the several Muslim trends too. This, polemics help to clarify the processes which shape the ideology of the different human groups in conflict. (shrink)

One of the modern features in Maimonides’ exegesis is the interpretation of the figurative and symbolic concepts which can be found in the Biblical text. To this respect, the task developed by the Cordovan writer place the texts before new hermeneutic possibilities of analysis which offer original readings from his interpretation.

ABSTRACTThe social content of affective stimuli has been proposed as having an influence on cognitive processing and behaviour. This research was aimed, therefore, at studying whether automatic exogenous attention demanded by affective pictures was related to their social value. We hypothesised that affective social pictures would capture attention to a greater extent than non-social affective stimuli. For this purpose, we recorded event-related potentials in a sample of 24 participants engaged in a digit categorisation task. Distracters were affective pictures varying in (...) social content, in addition to affective valence and arousal, which appeared in the background during the task. Our data revealed that pictures depicting high social content captured greater automatic attention than other pictures, as reflected by the greater amplitude and shorter latency of anterior P2, and anterior and posterior N2 components of the ERPs. In addition, social content also provoked greater allocation of processing resour... (shrink)

Mindfulness and compassion meditation are thought to cultivate prosocial behavior. However, the lack of diverse representation within both scientific and participant populations in contemplative neuroscience may limit generalizability and translation of prior findings. To address these issues, we propose a research framework calledIntersectional Neurosciencewhich adapts research procedures to be more inclusive of under-represented groups. Intersectional Neuroscience builds inclusive processes into research design using two main approaches: 1) community engagement with diverse participants, and 2) individualized multivariate neuroscience methods to accommodate neural (...) diversity. We tested the feasibility of this framework in partnership with a diverse U.S. meditation center (East Bay Meditation Center, Oakland, CA). Using focus group and community feedback, we adapted functional magnetic resonance imaging (fMRI) screening and recruitment procedures to be inclusive of participants from various under-represented groups, including racial and ethnic minorities, gender and sexual minorities, people with disabilities, neuropsychiatric disorders, and/or lower income. Using person-centered screening and study materials, we recruited and scanned 15 diverse meditators (80% racial/ethnic minorities, 53% gender and sexual minorities). The participants completed the EMBODY task – which applies individualized machine learning algorithms to fMRI data – to identify mental states during breath-focused meditation, a basic skill that stabilizes attention to support interoception and compassion. All 15 meditators’ unique brain patterns were recognized by machine learning algorithms significantly above chance levels. These individualized brain patterns were used to decode the internal focus of attention throughout a 10-min breath-focused meditation period, specific to each meditator. These data were used to compile individual-level attention profiles during meditation, such as the percentage time attending to the breath, mind wandering, or engaging in self-referential processing. This study provides feasibility of employing an intersectional neuroscience approach to include diverse participants and develop individualized neural metrics of meditation practice. Through inclusion of more under-represented groups while developing reciprocal partnerships, intersectional neuroscience turns the research process into an embodied form of social action. (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 multidisciplinary volume documents the resurrection of the importance of narrative to the study of individuals and groups and argues that narrative may become a lingua franca of future debates in the human sciences.

We determine the number of non‐isomorphic semi‐Heyting algebras on an n‐element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non‐isomorphic semi‐Heyting chains of a given size in some important subvarieties of the variety of semi‐Heyting algebras that were introduced in [5]. We further exploit this recursive method to calculate the numbers of non‐isomorphic semi‐Heyting chains with (...) n elements such that removing the mth element () we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi‐Heyting chain with elements can be extended to a n element semi‐Heyting chain by adding a new element in the mth place. Finally we combine these results by finding a second way to calculate the numbers that provides some extra information. (shrink)

An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ ≈ x ∧ y, x ∧ ≈ x ∧ [ → ], and x → x ≈ 1.