Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...) to other classes of algebras of logic, for example quasi-polyadic algebras and substitution-cylindrification algebras with and without equality, relation algebras, and special Boolean monoids. The results of op. cit. mentioned above are special cases of our general theorems. We point out an error in the proof of the Henkin-Monk-Tarski representation theorem for atomic, equality-free, quasi-polyadic algebras with rectangular atoms. The error consists in the implicit assumption of a property that does not, in general, hold. We then give a correct proof of their theorem. Henkin and Tarski also introduced the notion of a rich cylindric algebra and proved in op. cit. that every rich cylindric algebra of finite dimension satisfying certain special identities is representable. We introduce a modification of the notion of a rich algebra that, in our opinion, renders it more natural. In particular, under this modification richness becomes a density notion. Moreover, our notion of richness applies not only to algebras with equality, such as cylindric algebras, but also to algebras without equality. We show that a finite dimensional algebra is rich iff it is rectangularly dense and quasi-atomic; moreover, each of these conditions is also equivalent to a very natural condition of point density . As a consequence, every finite dimensional rich algebra of logic is representable. We do not have to assume the validity of any special identities to establish this representability. Not only does this give an improvement of the Henkin-Tarski representation theorem for rich cylindric algebras, it solves positively an open problem in op. cit. concerning the representability of finite dimensional rich quasi-polyadic algebras without equality. (shrink)

It is shown that for any cardinal $\kappa, \dbinom{(2^{ , and if κ is weakly compact $\dbinom{\kappa^+}{\kappa} \rightarrow \dbinom{\kappa}{\kappa}_{.

IntroductionMentalizing is a key aspect of social cognition. Several researchers assume that mentalization has two systems, an explicit one and an implicit one. In schizophrenia, several studies have confirmed the deficit of explicit mentalizing, but little data are available on non-explicit mentalizing. However, increasing research activity can be detected recently in implicit mentalizing. The aim of this systematic review and meta-analysis is to summarize the existing results of implicit mentalizing in schizophreniaMethodsA systematic search was performed in four major databases: MEDLINE, (...) EMBASE, Cochrane Central Register of Controlled Trials, Web of Science. Eleven publications were selected. Five studies were found to be eligible for quantitative synthesis, and 9 studies were included in qualitative synthesis.ResultsThe meta-analysis revealed significantly lower accuracy, slower reaction time during implicit mentalizing in patients with schizophrenia. The systematic review found different brain activation pattern, further alterations in visual scanning, cue fixation, face looking time, and difficulties in perspective taking.DiscussionOverall, in addition to the deficit of explicit mentalization, implicit mentalization performance is also affected in schizophrenia, if not to the same extent. It seems likely that some elements of implicit mentalization might be relatively unaffected, but the effectiveness is limited by certain neurocognitive deficits. These alterations in implicit mentalizing can also have potential therapeutic consequences.Systematic Review Registration:https://www.crd.york.ac.uk/prospero/, identifier: CRD42021231312. (shrink)

Whereas a growing bulk of work has demonstrated that both adults and children are sensitive to frequently occurring word sequences, little is known about the potential role of meaning in the processing of such multiword chunks. Here, we take a first step toward assessing the contribution of meaningfulness in the processing of multiword sequences, using items that varied in chunk meaningfulness. In a phrasal-decision study, we compared reaction times for triads of three-word sequences, corresponding to idiomatic expressions, compositional phrases, and (...) phrasal fragments, while controlling for phrase and substring frequencies. Chunk meaningfulness, as assessed by a separate subjective rating study, was found to speed up decision times for all three types of strings: The more meaningful a multiword sequence was judged to be, the faster it was processed, independently of whether it was idiomatic, compositional in nature, or a phrasal fragment. These results highlight the importance of taking meaning into account when considering the processing of multiword chunks, consistent with predictions of construction-based approaches to language. (shrink)

Many believe that values are crucially dependent on emotions. This paper focuses on epistemic aspects of the putative link between emotions and value by asking two related questions. First, how exactly are emotions supposed to latch onto or track values? And second, how well suited are emotions to detecting or learning about values? To answer the first question, the paper develops the heuristics-model of emotions. This approach models emotions as sui generis heuristics of value. The empirical plausibility of the heuristics-model (...) is demonstrated using evidence from experimental psychology, evolutionary anthropology and neuroscience. The model is used then to answer the second question. If emotions are indeed heuristics of value, then it follows that emotions can be an important and useful source of information about value. However, emotions will not be epistemically superior in the sense of being the highest court of appeal for the justification of axiological beliefs (the latter view is referred to as the Epistemic Dependence Thesis, or EDT for short). The paper applies the heuristics-model to celebrated cases from the philosophy of emotions literature arguing that while the heuristics-model offers a good explanation of typical patterns of emotional reactions in such cases, advocates of EDT will have a hard time accounting for these patterns. The paper also shows that the conclusions drawn from special cases generalize. The paper ends by arguing that skepticism about the metaethical significance of emotions is compatible with a commitment to the importance of emotions in first-order normative ethics. (shrink)

People seem to differ in their visual search performance involving emotionally expressive faces when these expressions are seen on faces of others close to their age compared to faces of non-peers, known as the own-age bias. This study sought to compare search advantages in angry and happy faces detected on faces of adults and children on a pool of children and adults. The goals of this study were to examine the developmental trajectory of expression recognition and examine the development of (...) an OAB. Participants were asked to find a target face displaying an emotional expression among eight neutral faces. Results showed that children and adults found happy faces significantly faster than angry and fearful faces regardless of it being present on the faces of peers or non-peers. Adults responded faster to the faces of peers regardless of the expression. Furthermore, while children detected angry faces significantly faster compared to fearful ones, we found no such difference in adults. In contrast, adults detected all expressions significantly faster when they appeared on the faces of other adults compared to the faces of children. In sum, we found evidence for development in detecting facial expressions and also an age-dependent increase in OAB. We suggest that the happy face could have an advantage in visual processing due to its importance in social situations and its overall higher frequency compared to other emotional expressions. Although we only found some evidence on the OAB, using peer or non-peer faces should be a theoretical consideration of future research because the same emotion displayed on non-peers’ compared to peers’ faces may have different implications and meanings to the perceiver. (shrink)

What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...) As a counterproposal, then, we define a large fragment of predicate logic characterized by its use of only bounded quantification. This so-called guarded fragment enjoys the above nice properties, including decidability, through an effectively bounded finite model property. (These are new results, obtained by generalizing notions and techniques from modal logic.) Moreover, its own internal finite variable hierarchy turns out to work well. Finally, we shall make another move. The above analogy works both ways. Modal operators are like quantifiers, but quantifiers are also like modal operators. This observation inspires a generalized semantics for first-order predicate logic with accessibility constraints on available assignments (cf. N´emeti 1986, 1992) which moves the earlier quantifier restrictions into the semantics. This provides a fresh look at the landscape of possible predicate logics, including candidates sharing various desirable features with basic modal logic – in particular, its decidability. (shrink)

This article deals with some phenomena of the Hungarian legal language from a historical point of view, with special regard to the terminology of private law going back to Roman law tradition. The author aims, on the one hand, to present the historical background of the current terminology of Hungarian private law by means of some representative examples. On the other hand, it is attempted at demonstrating that “false friends” and some further misunderstandings in the current terminology of Hungarian private (...) law can be led back to the historical determination of the concepts/terms in question. A certain Hungarian legal language existed already in the 16th c., however it reached the common European level by the middle of the 19th c. This development took place mainly under the influence of the Austrian and German law and legal science. Due to the translation of foreign legal terms to Hungarian since the 19th c. there emerged some “global” difficulties of legal terminology also in the Hungarian legal language. As the most important example, the reception of bona fides can be mentioned. It was an amendment of the Hungarian Civil Code in 2006 which tried to eliminate the misunderstandings as regards the principle of good faith conceived formerly by many Hungarian jurists exclusively in subjective sense. The history of reception of the German notions of Gültigkeit and Wirksamkeit in Hungary is extremely intriguing, too. Hungarian jurists did not follow the pattern of the German BGB but developed this pair created by Windscheid by drawing a clear distinction between the validity and effectiveness of legal transactions, similar to the Italian terminology. Sometimes the reception of German notions happened in a less successful way. Despite the important foreign, especially German impacts, the Hungarian legal language is an autonomous one having several remarkable features which deserve attention also in comparison with terminology of the Western legal cultures. (shrink)

This essay discusses a less known period of Karl Mannheim's life, namely the period he spent in Hungary. I attempt to point out that the career of the young Mannheim, starting from a philosophical interest and continuing with a sociological one, is continuous. His first published works and letters prove that in the period preceding his emigration to Germany in 1919 he was concerned with questions that received their mature form in his sociology of knowledge. They include primarily the question (...) of culture, that of perspective-boundedness of cognition, interpretation and the problem of intellectuals. Despite changing disciplines from philosophy to sociology, the continuity of his oeuvre can be shown. (shrink)

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.

This paper argues that group attitudes can be assessed in terms of standards of rationality and that group-level rationality need not be due to individual-level rationality. But it also argues that groups cannot be collective epistemic agents and are not collectively responsible for collective irrationality. I show that we do not need the concept of collective epistemic agency to explain how group-level irrationality can arise. Group-level irrationality arises because even rational individuals can fail to reason about how their attitudes will (...) combine with those of others. In some cases they are morally responsible for this failure, in others they are not. Moreover, the argument for collective epistemic agency is incoherent because reasons-for-groups are ipso facto reasons-for-individual. Instead of talking about reasons-for-groups, we should therefore distinguish between self-regarding reasons and group-regarding reasons. Both kinds of reasons are reasons-for-individuals. These conceptual considerations in favour of moderate individualism are strengthened by an analysis of our moral practice of responding to collective shortfalls of rationality and by the unpalatable moral implications of collectivism about epistemic agency. There is no need to change the subject. Groups can be rational or irrational, but they do not reason. (shrink)

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

Mutually beneficial exchanges in markets can be exploitative because one party takes advantage of an underlying injustice. For instance, employers of sweatshop workers are often accused of exploiting the desperate conditions of their employees, although the latter accept the terms of their employment voluntarily. A weakness of this account of exploitation is its tendency for over-inclusiveness. Certainly, given the prevalence of global and domestic socioeconomic inequalities, not all exchanges that take place against background injustices should be considered exploitative. This paper (...) offers a framework to identify exploitation in mutually beneficial exchange, focusing on the case of sweatshop labor. It argues that an employer can be viewed as taking unfair advantage of an underlying injustice if and only if the employer’s surplus from the exchange in the unjust state of affairs exceeds the surplus it could maximally obtain in a just state of affairs. The paper illustrates the applicability of this framework using three different conceptions of justice and argues that it is superior to microlevel accounts of exploitation that regard background justice as irrelevant. The paper concludes by describing some normative implications that follow from judging an exchange exploitative. (shrink)

This article discusses how everyday speech was mediated in early modern England: how speech was registered and remediated through various cultural techniques making it recognizable as a distinct linguistic medium and how these processes intersected with literary writing. A contribution to the study of the early modern English mediascape and its literary ramifications, this essay is also an effort to think historically about media change and literary transformation both as they happen and as they become visible over time. In what (...) follows, I trace the relationship between speech and the cultural techniques that engage with speech as the medium of everyday face-to-face interaction. Although my question is ultimately about speech, not poetry, and although the larger question I am interested in is not about artistic production but about media and cultural techniques more broadly, literary—poetic and especially dramatic—writing is nevertheless central to my essay. My argument grows out of the insights of twentieth-century literary criticism, whose observations about the relationship between speech and writing in 1600 were recognizably informed by the discourse network of their own moment and by their own concerns with modernity and its origins. So even as I am making an argument about the media constellation of a particular moment (an argument that could perhaps be described as crudely historicist), I am also curious about how the features of that moment became visible under different historical conditions or were imprinted by different media constellations and also how the defamiliarizing effect of the new may have made the past look familiar. (shrink)

We give two theories, Th1 and Th2, which are explicitly definable over each other , but are not definitionally equivalent. The languages of the two theories are disjoint.

Filosofía antigua -- Filosofía medieval : heavy metal y religión -- Filosofía moderna y contemporánea.

We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...) for every natural number k there is an equation in E containing more than k distinct variables and all the operation symbols, if 2 < n < ω. Completely analogous statement holds for the case n ω. This improves Monk's famous non-finitizability theorem for which we give here a simple proof. We prove analogous nonfinitizability properties of the larger varieties SNrnCAn + k. We prove that the complementation-free subreducts of RCAn do not form a variety. We also investigate the reason for the above “non-finite axiomatizability” behaviour of RCAn. We look at all the possible reducts of RCAn and investigate which are finitely axiomatizable. We obtain several positive results in this direction. Finally, we summarize the results and remaining questions in a figure. We carry through the same programme for RPEAn and for RRA. By looking into the reducts we also investigate what other kinds of natural algebras of relations are possible with more positive behaviour than that of the well known ones. Our investigations have direct consequences for the logical properties of the n-variable fragment Ln of first order logic. The reason for this is that RCAn and RPEAn are the natural algebraic counterparts of Ln while the varieties SNrnCAn + k are in connection with the proof theory of Ln. This paper appears in two parts. The first part contains the non-finite axiomatizability results. The present second part contains finite axiomatizations of some fragments together with a figure summarizing the finite and non-finite axiomatizability results in this area and the problems left open. (shrink)

Neanderthal extinction is a matter of intense debate. It has been suggested that demography (as opposed to environment or competition) could alone provide a sufficient explanation for the phenomenon. We argue that demography cannot be a ‘stand-alone’ or ‘alternative’ explanation of token extinctions as demographic features are entangled with competitive and environmental factors, and further because demography should not be conflated with neutrality.

This paper develops an account of how economic and political institutions can limit the applicability of principles of justice even in non-relational cosmopolitan conceptions. It shows that fundamental principles of justice underdetermine fair distributive shares as well as justice -based requirements. It argues that institutions partially constitute the content of justice by determining distributive shares and by resolving indeterminacies about justice -based requirements resulting from strategic interaction and disagreement. In the absence of existing institutions principles of justice might not be (...) applicable for assessing distributions or guiding individual action and institutional design. Hence, accepting a specific cosmopolitan conception of justice is insufficient to settle global distributive questions. (shrink)

There are several reasons to explore the role theater played in the life of Søren Kierkegaard and in the inspiration for his works. There are probably more reasons to analyze the role Kierkegaard played for theater, both as a source of inspiration and as a thinker reflecting on different facets of drama, performance, and acting. In the present study I focus on the diversity and complexity of Kierkegaard’s views on theater to elaborate on the possible connections and types of influence (...) he exercised on stage artists and theorists, shaping our contemporary theater theories. Approaches include literature, philosophy, theology, staging, acting, audience, and the history of theater, both in Kierkegaard’s times and later. (shrink)

The article analyzes ethnic data collection pertaining to criminal justice in Hungary. With such a sensitive and delicate issue at hand, Hungary has decided on an evasive approach, resisting ethnic data collection by law enforcement authorities. The author argues that this approach has become one of the obstacles in fighting discrimination and ethnic profiling. Moreover, Hungary’s restrictive approach to ethno-national data classification also causes severe constitutional problems in other, noncriminal legal circumstances, where ethnic data is used in the context of (...) additional rights and affirmative protection provided for ethno-national minorities. The first part of the article describes general problems relating to ethnic data collection and analyses of the Hungarian minority protection framework, in particular, the minority self-government structure (a unique constitutional institution). The second part focuses on the criminal justice system; the author’s aim is to show that prohibiting the official recognition and collection of data on ethnicity by criminal justice authorities has potentially ethnically discriminatory consequences. (shrink)

We give a novel application of algebraic logic to first order logic. A new, flexible construction is presented for representable but not completely representable atomic relation and cylindric algebras of dimension n (for finite n > 2) with the additional property that they are one-generated and the set of all n by n atomic matrices forms a cylindric basis. We use this construction to show that the classical Henkin-Orey omitting types theorem fails for the finite variable fragments of first order (...) logic as long as the number of variables available is > 2 and we have a binary relation symbol in our language. We also prove a stronger result to the effect that there is no finite upper bound for the extra variables needed in the witness formulas. This result further emphasizes the ongoing interplay between algebraic logic and first order logic. (shrink)

We shall show that certain natural and interesting intervals in the lattice of varieties of representable relation algebras embed the lattice of all subsets of the natural numbers, and therefore must have a very complicated lattice-theoretic structure.

The thirty year long friendship between Imre Lakatos and the classic scholar and historian of mathematics Árpád Szabó had a considerable influence on the ideas, scholarly career and personal life of both scholars. After recalling some relevant facts from their lives, this paper will investigate Szabó's works about the history of pre-Euclidean mathematics and its philosophy. We can find many similarities with Lakatos' philosophy of mathematics and science, both in the self-interpretation of early axiomatic Greek mathematics as Szabó reconstructs it, (...) and in the general overview Szabó provides us about the turn from the intuitive methods of Greek mathematicians to the strict axiomatic method of Euclid's Elements. As a conclusion, I will argue that the correct explanation of these similarities is that in their main works they developed ideas they had in common from the period of intimate intellectual contact in Hungarian academic life in the mid-twentieth century. In closing, I will recall some relevant features of this background that deserve further research. (shrink)

Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, (...) Glymour and Halvorson. (shrink)