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)

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)

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)

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)

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)

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)

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)

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)

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)

Undoubtedly, democracy is in constant danger. The Athenian creation -later taken by the Latin American countries in the political-administrative figure of the Republic- has demonstrated not to be the best government model, but, the less evil, as expressed by an English politician when he saw that his empire era was coming to an end. And one of those defenders was the critical acid of the Vienna Circle and contemporary philosopher Karl Popper, who lived on his own flesh the mistakes of (...) democracy and the horrors of totalitarianism. Popper, defender of democracy to the limit, who even within his writings we can appreciate the paradoxes he sees in this, will not hesitate when the system of government of the people, for the people and the people, fall into the temptation to choose the dictatorship. For this, the philosopher tells us, democracy must create mechanisms so that this does not happen and we do not have a popular election that takes a demagogue and criminal to power, as was Hitler’s Germany. The thinking of the critical philosopher of historicism is liberal. An English liberalism and not as we understand it and we live in several States of America, where people is economic liberal and conservative in the ideas. No, Popper is liberal. A true liberal. (shrink)

This paper investigates the differences between ancient Greek and modern ethical naturalism, through the account of the whole classical tradition provided by Cicero in De finibus bonorum et malorum. Ever since Hume’s remarks on the topic, it is usually held that derivations of normative claims from factual claims require some kind of proper justification. It ́s a the presence of such justifications in the Epicurean, Stoic, and Academic-Peripatetic ethical theories (as portrayed in De finibus), and, after a negative conclusion, I (...) argue that we should conceive of this issue within a social-historical perspective: The radical difference between ancient and modern naturalistic ethics is due (in Weber’s terms) to the rationalization processes that generated the modern outlook on nature. (shrink)

Hubo pensadores que supieron leer en su tiempo signos de la catástrofe venidera. No eran profetas sino finos analistas. Nos referimos a Rosenzweig, Benjamin y Kafka. Rosenzweig denunció en el "idealismo" de la filosofía que viene desde Jonia y llega hasta Jena la tendencia a un totalitarismo que la convertía en potencialmente en una "ontología de la guerra". Benjamin dejó constancia de la ambigüedad radical del concepto de progreso, tan fundamental para el pensamiento ilustrado. La barbarie, en general, y el (...) fascismo, en particular, no son lo opuesto al progreso sino una de sus posibilidades. Esa fatal posibilidad es, para la víctima, la norma. Kafka capta anticipadamente la reducción fascista del hombre a nuda vida en la recurrente animalización de sus personajes, así como la negación del otro en sus personajes víctimas de la incomunicación. (shrink)

Hume presenta su teoría estética en el ensayo Sobre el criterio del gusto [On the Standard of Taste], en el que propone la existencia de un criterio [standard] capaz de zanjar discusiones de gusto. Ese criterio se basa en la existencia de ciertas formas y cualidades que complacen naturalmente a todo ser humano. Hume asevera que tal criterio corresponde a la opinión del crítico: un hombre que ha desplegado particularmente sus facultades cognoscitivas, lo cual le permite percibir esas finas cualidades (...) que suscitan naturalmente el placer de lo bello en el ser humano. Con respecto a en qué consisten esas formas y cualidades universalmente placenteras, Hume guarda silencio. Pretendo mostrar cómo la teoría de la emoción en la música desarrollada por Leonard Meyer en su texto Emoción y significado en la música (Emotion and Meaning in Music) puede aportar inmensidades en ese aspecto. (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)

The emergent Coronavirus Disease 2019 caused by the Severe Acute Respiratory Syndrome Coronavirus 2 could produce a maternal immune activation via the inflammatory response during gestation that may impair fetal neurodevelopment and lead to postnatal and adulthood mental illness and behavioral dysfunctions. However, so far, limited evidence exists regarding long-term physiological, immunological, and neurodevelopmental modifications produced by the SARS-CoV-2 in the human maternal-fetal binomial and, particularly, in the offspring. Relevant findings derived from epidemiological and preclinical models show that a MIA (...) is indeed linked to an increased risk of neurodevelopmental disorders in the offspring. We hypothesize that a gestational infection triggered by SARS-CoV-2 increases the risks leading to neurodevelopmental disorders of the newborn, which can affect childhood and the long-term quality of life. In particular, disruption of either the maternal or the fetal cholinergic anti-inflammatory pathway could cause or exacerbate the severity of COVID-19 in the maternal-fetal binomial. From a translational perspective, in this paper, we discuss the possible manifestation of a MIA by SARS-CoV-2 and the subsequent neurodevelopmental disorders considering the role of the fetal-maternal cytokine cross-talk and the CAP. Specifically, we highlight the urgent need of preclinical studies as well as multicenter and international databanks of maternal-fetal psychophysiological data obtained pre-, during, and post-infection by SARS-CoV-2 from pregnant women and their offspring. (shrink)

En este trabajo proponemos un análisis de los esquemas de argumento por signo que fueron identificados en las etiquetas interpretativas de las exposiciones permanentes de los museos de la región de la Araucanía. Se analizan cualitativa y críticamente tres casos de los veintiún esquemas por signo identificados. Las herramientas teóricas esgrimidas proceden de la pragma-dialéctica y la lógica informal. Nuestro objetivo es caracterizar los esquemas por signo identificados en las etiquetas de las exhibiciones de los museos de la Araucanía, en (...) la búsqueda de orientar su manejo en el diseño de exhibiciones museísticas significativas. Para ello, hemos desarrollado una matriz metodológica que adopta el levantamiento de una estructura argumental. Así, fue posible identificar los puntos de vista como las razones que lo justifican, además de identificar los esquemas argumentativos, a los cuales se les ha aplicado sus respectivas preguntas críticas. El análisis nos permitió concluir que en el empleo del esquema por signo siempre es necesario apoyarse en el entorno cercano donde se maneja el argumento, esto incluye la noción de lugar o de territorio en sus distintos niveles de significación. Asimismo, se ha comprobado como fundamental la incorporación de la tercera pregunta crítica al esquema por signo, la cual hace referencia al contexto donde se presenta el argumento. Por último, se ha detectado que los esquemas considerados complejos también realizan una referencia al lugar, pero con la utilización y combinación de variadas figuras retóricas, como la resignificación o sustitución. (shrink)

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)