This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same reducibility degree (under the notion of reducibility for equivalence relations usually called “computable reducibility”), or in the same isomorphism type (with the isomorphism induced by a computable function), or in the same strong isomorphism type (with the isomorphism induced by a computable permutation (...) of the natural numbers). We observe, e.g., that every ceer is isomorphic to the word problem of some c.e. semigroup, but (answering a question of Gao and Gerdes) not every ceer is in the same reducibility degree of the word problem of some finitely presented semigroup, nor is it in the same reducibility degree of some non‐periodic semigroup. We also show that the ceer provided by provable equivalence of Peano Arithmetic is in the same strong isomorphism type as the word problem of some non‐commutative and non‐Boolean c.e. ring. (shrink)

[1] [without special title] -- 2. La distribuzione del bene negli enti.

This paper is part of a project that is based on the notion of a dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In Amidei et al. (2016, Rev. Symb. Logic, 9, 1–26) and Amidei et al. (2016, Rev. Symb. Logic, 9, 299–324), we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasi-dialectical systems, that enrich Magari’s systems with a natural mechanism (...) of revision. In the present paper we consider a third class of systems, that of p-dialectical systems, that naturally combine features coming from the two other cases. We prove several results about p-dialectical systems and the sets that they represent. Then we focus on the completions of first-order theories. In doing so, we consider systems with connectives, i.e. systems that encode the rules of classical logic. We show that any consistent system with connectives represents the completion of a given theory. We prove that dialectical and q-dialectical systems coincide with respect to the completions that they can represent. Yet, p-dialectical systems are more powerful; we exhibit a p-dialectical system representing a completion of Peano Arithmetic that is neither dialectical nor q-dialectical. (shrink)

The complexity of equivalence relations has received much attention in the recent literature. The main tool for such endeavour is the following reducibility: given equivalence relations R and S on natural numbers, R is computably reducible to S if there is a computable function f:ω→ω that induces an injective map from R-equivalence classes to S-equivalence classes. In order to compare the complexity of equivalence relations which are computable, researchers considered also feasible variants of computable reducibility, such as the polynomial-time reducibility. (...) In this work, we explore Peq, the degree structure generated by primitive recursive reducibility on primitive recursive equivalence relations with infinitely many equivalence classes. In contrast with all other known degree structures on equivalence relations, we show that Peq has much more structure: e.g., we show that it is a dense distributive lattice. On the other hand, we also offer evidence of the intricacy of Peq, proving, e.g., that the structure is neither rigid nor homogeneous. (shrink)

We make some beginning observations about the category Eq of equivalence relations on the set of natural numbers, where a morphism between two equivalence relations R and S is a mapping from the set of R-equivalence classes to that of S-equivalence classes, which is induced by a computable function. We also consider some full subcategories of Eq, such as the category Eq(Σ01) of computably enumerable equivalence relations (called ceers), the category Eq(Π01) of co-computably enumerable equivalence relations, and the category Eq(Dark*) (...) whose objects are the so-called dark ceers plus the ceers with finitely many equivalence classes. Although in all these categories the monomorphisms coincide with the injective morphisms, we show that in Eq(Σ01) the epimorphisms coincide with the onto morphisms, but in Eq(Π01) there are epimorphisms that are not onto. Moreover, Eq, Eq(Σ01), and Eq(Dark*) are closed under finite products, binary coproducts, and coequalizers, but we give an example of two morphisms in Eq(Π01) whose coequalizer in Eq is not an object of Eq(Π01). (shrink)

Computably enumerable equivalence relations received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility \. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the \ case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by \ on the \ equivalence relations. (...) A special focus of our work is on the existence of infima and suprema of c-degrees. (shrink)

This open access book investigates the role played by identity of proofs in proof-theoretic semantics. It develops a conception of proof-theoretic semantics as primarily concerned with the relationship between proofs (understood as abstract entities) and derivations (the linguistic representations of proofs). It demonstrates that identity of proof is a key both to clarify some —still not wholly understood— notions at the core of proof-theoretic semantics, such as harmony; and to broaden the range of the phenomena which can be analyzed using (...) the tools of this semantic paradigm, so as to include for instance paradoxes. The volume covers topics such as the philosophical significance of different criteria of identity of proofs, and adequacy conditions for an intensional account of the notion of harmony. The author also examines the Prawitz-Tennant analysis of paradoxes by investigating on the one hand the prospects of turning it into a theory of meaning for paradoxical languages, and on the other hand two distinct kinds of phenomena, first observed by Crabbe and Ekman, showing that the Tennant-Prawitz criterion for paradoxicality overgenerates. This volume is of interest to scholars in formal and philosophical logic. (shrink)

Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the (...) graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics. (shrink)

The notions of common knowledge or common belief play an important role in several areas of computer science , in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of “agents”, agreement or coordinated actions. In the following we will present several deductive systems for common knowledge above epistemic logics –such as K, T, S4 and S5 –with a fixed number of agents. We focus on structural and proof-theoretic properties of these (...) calculi. (shrink)

In this paper, I will discuss the various ways in which intentions can be said to be conditional, with particular attention to the internal conditions on the intentions’ content. I will first consider what it takes to carry out a conditional intention. I will then discuss how the distinctive norms of intention apply to conditional intentions and whether conditional intentions are a weaker sort of commitments than the unconditional ones. This discussion will lead to the idea of what I call (...) the ‘deep structure’ of intentions. Roughly, this is the idea that the conditional nature of our intentions is only partially made explicit in the expressions we use to communicate our intentions and in the explicit form of our thinking about and reasoning with them. Most conditions that qualify our intentions are part of a deep functional structure that can be evinced by observing the actual psychological functioning of intentions and by considering the rational requirements that they engage. I will argue that the deep structure of intentions is characteristically conditional. Genuinely unconditional intentions are only limiting instances of conditional intentions and their contribution to agency can only be understood in light of this fact. I will conclude by showing that the characteristic conditional structure of intentions is intimately related to distinctive features of human agency, especially to its unity over time. (shrink)

The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit not only to (...) establish advantages and limitations of our approach with respect to related ones, but also to give, by means of a substructural analysis, a new proof-theoretic method for investigating decidability and complexity of (some of) the logics we consider. All of our deduction systems have been implemented in the generic theorem prover Isabelle, thus providing a simple and natural environment for interactive proof development. Labelled Non-Classical Logics is essential reading for researchers and practitioners interested in the theory and applications of non-classical logics. (shrink)

Timothy Smiley’s wonderful paper ‘Rejection’ (1996) is still perhaps not as well known or well understood as it should be. This note first gives a quick presentation of themes from that paper, though done in our own way, and then considers a putative line of objection – recently advanced by Julien Murzi and Ole Hjortland (2009) – to one of Smiley’s key claims. Along the way, we consider the prospects for an intuitionistic approach to some of the issues discussed in (...) Smiley’s paper. (shrink)

Crispin Wright has given an explanation of how a first time warrant can fall short of transmitting across a known entailment. Formal epistemologists have struggled to turn Wright’s informal explanation into cogent Bayesian reasoning. In this paper, I analyse two Bayesian models of Wright’s account respectively proposed by Samir Okasha and Jake Chandler. I argue that both formalizations are unsatisfactory for different reasons, and I lay down a third Bayesian model that appears to me to capture the valid kernel of (...) Wright’s explanation. After this, I consider a recent development in Wright’s account of transmission failure. Wright suggests that his condition sufficient for transmission failure of first time warrant also suffices for transmission failure of supplementary warrant. I propose an interpretation of Wright’s suggestion that shield it from objections. I then lay down a fourth Bayesian framework that provides a simplified model of the unified explanation of transmission failure envisaged by Wright. (shrink)

This paper focuses on whether static images can depict motion. It is natural to say that pictures depicting objects caught in the middle of a dynamic action—such as Henri Cartier-Bresson’s (1932) Behind the Gare St. Lazare—are pictures of movement, but, given that pictures themselves do not move, can we make sense of such an idea? Drawing on results from experimental psychology and cognitive sciences, I show that we can. Psychological studies on implicit motion and representational momentum indicate that motion is (...) really perceived in some static images: our visual system is built in order to detect motion, even where it is only implied, and to anticipate the probable outcomes of others’ actions—even when the ‘others’ are only the subject matters of pictures’. I argue that, consequently, a range of popular depiction theories—perceptualist theories of depiction—can accommodate depicted motion. (shrink)

Boran Berčić, in the second volume of his recent book "Filozofija" , offers two responses to David Chalmers’s conceivability or modal argument against physicalism. This latter argument aims at showing that zombies, our physical duplicates who lack consciousness, are metaphysically possible, given that they are conceivable. Berčić’s first response is based on the principle of the uniformity of nature that states that causes of a certain type will always cause effects of the same type. His second response is based on (...) the assumption that the basic statements of physicalism in philosophy of mind are or should be contingently true. I argue that if Berčić’s first defence is aimed at the conceivability of zombies, it is unsatisfactory. Moreover, I argue that a quite similar argument, offered by John Perry in his book "Knowledge, Possibility and Consciousness" , is afflicted by a similar problem. Nevertheless, under a more plausible interpretation, Berčić’s argument might be taken to attack the metaphysical possibility of zombies. This version of the argument might be effective and has the merit to point out a so far overlooked link between the discussion of the Chalmers’s conceivability arguments against physicalism and the modal strength of causal links and natural laws. Then, I argue that Berčić’s second defence of physicalism, which cannot be combined consistently with his first one, in any case, should not be formulated in the terms of contingent physicalism. (shrink)

In this paper I intend to demonstrate how Merleau-Ponty develops in his late thought an insightful account of reality. In opposition to the ontological primacy Husserl and Heidegger bestow to man, Merleau-Ponty’s late perspective is based on a dynamic ontology, namely on a philosophical understanding of the strict relation between nature and consciousness. With this respect, Merleau- Ponty approaches the problem of negativity, in order to explain the differences within reality without adopting an Hegelian account of dialectic and, on the (...) other hand, avoiding a merely empirical view of contingency. (shrink)

Sleep strengthens memories by repeatedly reactivating associated neuron ensembles. Our studies show that although long-term memory for a medium number of word-pairs benefits from sleep, a large number does not. This suggests an upper limit to the amount of information that has access to sleep-dependent declarative memory consolidation, which is possibly linked to the availability of reactivation opportunities. Due to competing processes of global forgetting that are active during sleep, we hypothesized that even larger amounts of information would enhance the (...) proportion of information that is actively forgotten during sleep. In the present study, we aimed to induce such forgetting by challenging the sleeping brain with vast amounts of to be remembered information. For this, 78 participants learned a very large number of 640 word-pairs interspersed with periods of quiet awake rest over the course of an entire day and then either slept or stayed awake during the night. Recall was tested after another night of regular sleep. Results revealed comparable retention rates between the sleep and wake groups. Although this null-effect can be reconciled with the concept of limited capacities available for sleep-dependent consolidation, it contradicts our hypothesis that sleep would increase forgetting compared to the wake group. Additional exploratory analyses relying on equivalence testing and Bayesian statistics reveal that there is evidence against sleep having a detrimental effect on the retention of declarative memory at high information loads. We argue that forgetting occurs in both wake and sleep states through different mechanisms, i.e., through increased interference and through global synaptic downscaling, respectively. Both of these processes might scale similarly with information load. (shrink)

Math and reading are related, and math problems are often accompanied by problems in reading. In the present study, we used a dimensional approach and we aimed to assess the relationship of reading and math with the cognitive skills assumed to underlie the development of math. The sample included 97 children from 4th and 5th grades of a primary school. Children were administered measures of reading and math, non-verbal IQ, and various underlying cognitive abilities of math. We also included measures (...) of phonological awareness and working memory. Two approaches were undertaken to elucidate the relations of the cognitive skills with math and reading. In the first approach, we examined the unique contributions of math and reading ability, as well as their interaction, to each cognitive ability. In the second approach, the cognitive abilities were taken to predict math and reading. Results from the first set of analyses showed specific effects of math on number sense and number system knowledge, whereas counting was affected by both math and reading. No math-by-reading interactions were observed. In contrast, for phonological awareness, an interaction of math and reading was found. Lower performing children on both math and reading performed disproportionately lower. Results with respect to the second approach confirmed the specific relation of counting, number sense, and number system knowledge to math and the relation of counting to reading but added that each math-related marker contributed independently to math. Following this approach, no unique effects of phonological awareness on math and reading were found. In all, the results show that math is specifically related to counting, number sense, and number system knowledge. The results also highlight what each approach can contribute to an understanding of the relations of the various cognitive correlates with reading and math. (shrink)

This book explores the relationship between cultural psychology and aesthetics, by integrating the historical, theoretical and phenomenological perspectives. It offers a comprehensive discussion of the history of aesthetics and psychology from an international perspective, with contributions by leading researchers from Serbia, Austria, Portugal, Norway, Denmark, and Brazil. The first section of the book aims at summarizing the debate of where the song comes from. It discusses undeveloped topics, methodological hints, and epistemological questions in the different areas of contemporary psychological sciences. (...) The second section of the book presents concrete examples of case-studies and methodological issues to stimulate further explorations. The book aims to bring art back into psychology, to provide an understanding for the art of psychology. An Old Melody in a New Song will be of interest to advanced students and researchers in the fields of educational and developmental psychology, cultural psychology, history of ideas, aesthetics, and art-based research. (shrink)

In one of his lectures at the Collège de France, Foucault observed that, prior to the eighteenth century, ‘population’ was a ‘present-absent’ object in the theories and practices of government. In this paper, I have attempted to reconstruct the genealogical history of proto-demographic thought as reflected in the works of three major Renaissance political theorists: Niccolò Machiavelli, Jean Bodin, and Giovanni Botero. While all three thinkers address the question of how to cultivate a large and flourishing population, the primary obstacle (...) to the emergence of a modern conception of population lies in the inability to influence human reproduction directly, an area traditionally regarded as subject to divine will.Botero, however, introduced the possibility of an ‘incentive’ policy, promoting marriage and child-rearing, which foreshadowed the natalist policies later advocated by Mercantilists. The case of ‘population’ and its peculiar ‘presence-absence’ in Renaissance political theories, as interpreted through Foucault’s hypothesis, sheds light on the broader history of scientific objects —objects that are neither ‘discovered’ nor ‘invented’, but rather acquire their reality gradually over centuries through political and scholarly debate. (shrink)

Both sustainability and identity are said to be paradoxical issues in organizations. In this study we look at the paradoxes of corporate sustainability at the individual level by studying the identity work of those managers who hold sustainability-dedicated roles in organizations. Analysing 26 interviews with sustainability managers, we identify three main tensions affecting their identity construction process: the business versus values oriented, the organizational insider versus outsider and the short-term versus long-term focused identity work tensions. When dealing with these tensions, (...) some interviewees express a paradoxical perspective in attempting to accept and maintain the two poles of each of them simultaneously. It emerges in particular that metaphorical reasoning can be used by sustainability managers in varied ways to cope with the tensions of identity work. We read these findings in light of the existing literature on the relation between paradoxes and identity work, highlighting and discussing their implications for both research and practice. (shrink)

This article posits an interpretation of Thomas More’sUtopiathat focuses on the ways in which the nature of justice within a putatively ideal state is illuminated by references to international relations and the law of nations. Like Plato’sRepublic,Utopiauses differences of scale to provide a lens through which to examine the operation in one context of a unitary concept that is more visible elsewhere. Justice is constructed as a single concept; thus, in the same way that Plato uses the justice of thekallipolisto (...) provide insight into the justice of an individual, More uses the justice of the international community to provide a macroscopic perspective on justice as it exists within a sovereign state. Through discussions of trade, diplomacy, war and empire, Utopian understandings of international law and justice are revealed. The ideal organisation of the state is then characterised as one in which the resulting notions of justice, defined as the correct operation of laws that accord with natural law, are institutionalised. (shrink)

The aim of this paper is to clarify what kind of normativity characterizes a convention. First, we argue that conventions have normative consequences because they always involve a form of trust and reliance. We contend that it is by reference to a moral principle impinging on these aspects (i.e. the principle of Reliability) that interpersonal obligations and rights originate from conventional regularities. Second, we argue that the system of mutual expectations presupposed by conventions is a source of agreements. Agreements stemming (...) from conventions are “tacit” in the sense that they are implicated by what agents do (or forbear from doing) and without that any communication between them is necessary. To justify this conclusion, we assume that: (1) there is a salient interpretation, in some contexts, of everyone’s silence as confirmatory of the others’ expectations (an epistemic assumption), and (2) the participating agents share a value of not being motivated by hostile attitudes (a motivational assumption). By clarifying the relation between conventions and agreements, the peculiar normativity of conventions is analyzed. (shrink)

The text examines the attempt by Jürgen Habermas to renew the tasks of critical theory. The systematic reconstruction of his writings reveals a system of typical functions: a) the rationalization of instrumental and strategic action in the material reproduction of social systems (social technology); b) the analysis of the pathologies in the symbolic reproduction of the world of life; c) the clarification of the cognitive, value and expressive models in the public sphere; d) the unveiling of false representations that dominate (...) the mainstream (critique of ideology); e) sketching out alternatives to the status quo, through the utopia of a non-reified communicative everyday practice. All these functions actualize the Enlightenment project to place the cultural tradition in the service of civil and social progress. This ambitious program, however, must recognize the limitations of critical theory, with respect to the need for consolation and hope of human existence. The dialogue between philosophy and religion, which marks the last decade of Habermas's reflection, should be understood in this light. (shrink)

Through the interpretations of artwork provided by Hegel, Kant, and Heidegger, the artwork presents itself as complex and often irreducible. The reading offered by Harman, grounded in Object-Oriented Ontology (OOO), constructs a historically significant interpretation but does not exhaust the problematic nature of artwork represents. Through this article, I have attempted to demonstrate the functionality of the concept of loop applied to artwork, providing general connotations and linguistic tools for interpreting artwork as a loop.

Paul Feyerabend, one of the most original and nonconformist epistemologists of the 20th century, is known for describing science as an essentially anarchic enterprise characterized by different, sometimes contradictory, methods, approaches and ways of reasoning. But it was through his reflections on art and myth that he developed an even more radical view: there are different forms of human thought, each characterized by a different rationality and reality, and science is only one of them. And in intellectual history there is (...) only change, but not progress. (shrink)

La posibilidad de entender al otro pasa de manera decisiva por la posibilidad de ser otro, de convertirse en otro. Pero ¿podemos nosotros, los animales humanos, entender lo que siente un murciélago, lo que siente una planta o, llevando el argumento al extremo, lo que siente un objeto? ¿Podemos nosotros, los seres humanos, empezar a entender los hiperobjetos a la luz de la imposibilidad de ser otro? Este artículo analiza la imposibilidad de la relación deleuziana del devenir- y la relación (...) con los hiperobjetos. (shrink)

Antinaturalistic Strategies in Beyond Good and Evil. Naturalistic interpretations of Nietzsche’s thought ultimately appeal to two arguments. On the one hand, when tracing various human phenomena back to processes sufficiently explicable by the natural sciences, it would appear that Nietzsche was pursuing a de facto naturalization program. On the other hand, in BGE 230, the need for the naturalization of human beings as a whole is often interpreted as an argument de jure. After outlining some basic features of contemporary naturalism (...) and showing its incompatibility with Nietzsche’s philosophy, I argue in this paper that neither the de jure nor the de facto argument can be understood in a naturalistic sense. The task of “translating man back into nature” in BGE 230 is indeed turned against a point of view held by “old metaphysical bird-catchers.” An analysis of the manuscript and a comparison of it with the preface to HH I, in which this figure is used in the opposite sense, suggests rather that Nietzsche conceives of the renaturalization of the human in a deceptive way, that is, as one of those numerous “snares and nets for unwary birds” scattered throughout his works. Widening this view, a similar dynamic arises with respect to the de facto argument. In the concluding section, I highlight how, in On the Prejudices of Philosophers, certain naturalization operations are countered by as many arguments to the contrary. Such sudden shifts in perspective seem to indicate, at least in Beyond Good and Evil, a desire to subvert naturalism from within. (shrink)