The recognition of taboo words – i.e. socially inappropriate words – has been repeatedly associated to semantic interference phenomena, with detrimental effects on the performance in the ongoing task. In the present study, we investigated taboo interference in the context of reading aloud, a task configuration which prompts the overt violation of conventional sociolinguistic norms by requiring the explicit utterance of taboo items. We assessed whether this form of semantic interference is handled by habituative or cognitive control processes. In addition (...) to the reading aloud task, participants performed a vocal Stroop task featuring different conditions to dissociate semantic, task, and response conflict. Taboo words were read slower than non-taboo words, but this effect was subject to a quick habituation, with a decreasing interference over the course of trials, which allowed participants to selectively attend to goal-relevant information. In the Stroop task, only semantic conflict was significantly reduced by habituation. These findings suggest that semantic properties can be quickly and flexibly weighed on the basis of contextual appropriateness, thus characterising semantic processing as a flexible and goal-directed component of reading aloud. (shrink)

O artigo que segue pretende abordar o potencial transformador da ética do cuidado de Carol Gilligan destacando, por um lado, seu caráter de denúncia expresso no questionamento acerca da exclusão das experiencias das mulheres na produção do conhecimento e, por outro, a sua verve de resistência manifesta no fato de que a ética do cuidado traz a produção teórica de uma mulher que trata de experiencias femininas em sociedades patriarcais. Para tanto, serão explicitados os principais pontos da ética do cuidado (...) de Gilligan assim como as reflexões por elas suscitadas em termos de críticas e reações. (shrink)

This paper aims to examine a very specific passage of Sextus Empiricus’s work: the final section of the second book of the Outlines of Pyrrhonism (=ph ii, 229–259). Here Sextus concentrates his attention on a very limited yet crucial topic, namely the question of the validity or invalidity and ‘pragmatic dissolution’ of an allegedly strong tool such as sophisms and their dialectical structure. Indeed, Pyrrhonists do not wander about aimlessly nor lack effective tools through which to dismantle the logical industry (...) of sophisms; their reference point is completely different, since they agree about some evident facts and live their life in accordance with κοινὸς βίος. (shrink)

A lot of attention has recently been devoted to the notion of Trustworthy AI (TAI). However, the very applicability of the notions of trust and trustworthiness to AI systems has been called into question. A purely epistemic account of trust can hardly ground the distinction between trustworthy and merely reliable AI, while it has been argued that insisting on the importance of the trustee’s motivations and goodwill makes the notion of TAI a categorical error. After providing an overview of the (...) debate, we contend that the prevailing views on trust and AI fail to account for the ethically relevant and value-laden aspects of the design and use of AI systems, and we propose an understanding of the notion of TAI that explicitly aims at capturing these aspects. The problems involved in applying trust and trustworthiness to AI systems are overcome by keeping apart trust in AI systems and interpersonal trust. These notions share a conceptual core but should be treated as distinct ones. (shrink)

Risks connected with AI systems have become a recurrent topic in public and academic debates, and the European proposal for the AI Act explicitly adopts a risk-based tiered approach that associates different levels of regulation with different levels of risk. However, a comprehensive and general framework to think about AI-related risk is still lacking. In this work, we aim to provide an epistemological analysis of such risk building upon the existing literature on disaster risk analysis and reduction. We show how (...) a multi-component analysis of risk, that distinguishes between the dimensions of hazard, exposure, and vulnerability, allows us to better understand the sources of AI-related risks and effectively intervene to mitigate them. This multi-component analysis also turns out to be particularly useful in the case of general-purpose and experimental AI systems, for which it is often hard to perform both ex-ante and ex-post risk analyses. (shrink)

Famously, Kripke has argued that the central portion of the Philosophical Investigations describes both a skeptical paradox and its skeptical solution. Solving the paradox involves the element of the community, which determines correctness conditions for rule-following behavior. What do such conditions precisely consist of? Is it accurate to say that there is no fact to the matter of rule following? How are the correctness conditions sustained in the community? My answers to these questions revolve around the idea that a rule (...) is followed insofar as a convention is in place. In particular, I consider the game-theoretic definition of convention offered by David Lewis and I show that it illuminates essential aspects of the communitarian understanding of rule-following. Make the following experiment: say “It’s cold here” and mean “It’s warm here”. Can you do it?Ludwig Wittgenstein, Philosophical Investigations, 1953, §510.I can’t say “it’s cold here” and mean “it’s warm here”—at least, not without a little help from my friends.David Lewis, Convention. (shrink)

When we witness a great actor, musician, or sportsperson performing, we share something of their experience. Only recently has it become clear just how this sharing of experience is realised within the human brain. 'Mirrors in the brain' provides an accessible overview of mirror neurons, written by the man who first discovered them.

This paper investigates the epistemic assumptions that David Lewis makes in his account of social conventions. In particular, I focus on the assumption that the agents have common knowledge of the convention to which they are parties. While evolutionary analyses show that the common knowledge assumption is unnecessary in certain classes of games, Lewis’ original account (and, more recently, Cubitt and Sugden’s reconstruction) stresses the importance of including it in the definition of convention. I discuss arguments pro et contra to (...) argue that, although the assumption might be relevant to a descriptively adequate account of social convention, it is not required for its rational reconstruction. I then point out that Lewis’ account, properly speaking, is of common reason to believe, rather than of common knowledge, and argue that, in order to formalize aptly the distinction between reason to believe and belief, standard formal epistemic models need to be supplemented with so-called awareness structures. Finally, I stress that the notion of knowledge implicit in Lewis’ text involves interesting elements that cannot be captured in the standard propositional formalizations, but need the full expressive force of quantified epistemic logic. (shrink)

While growing empirical evidence suggests a continuity between human and non-human psychology, many philosophers still think that only humans can act and form beliefs rationally. In this paper, we challenge this claim. We first clarify the notion of rationality. We then focus on the rationality of beliefs and argue that, in the relevant sense, humans are not the only rational animals. We do so by first distinguishing between unreflective and reflective responsiveness to epistemic reasons in belief formation and revision. We (...) argue that unreflective responsiveness is clearly within the reach of many animals. We then defend that a key demonstration of reflective responsiveness would be the ability to respond to undermining defeaters. We end by presenting some empirical evidence that suggests that some animal species are capable of processing these defeaters, which would entail that even by the strictest standards, humans are not the only rational animals. (shrink)

Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossible worlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically impossible worlds to which the agents are taken to have access; since such worlds need not behave consistently, the agents’ knowledge is fallible relative to logical (...) omniscience. The two approaches are known to be equally expressive in propositional systems interpreted over Kripke semantics. In this paper I show that the two approaches are equally expressive in propositional systems interpreted over Montague-Scott (neighborhood) semantics. Furthermore, I provide predicate systems of both awareness and impossible worlds structures interpreted on neighborhood semantics and prove the two systems to be equally expressive. (shrink)

Praise for First Edition: `This book is highly recommended to a wide range of people as a clear and systematic introduction to phenomenological psychology... the book has set the stage for possible new colloquia between the phenomenological and other approaches in psychology' - Changes `As a trainee interested in matters existential, I have been put off in the past by the long-winded and confusing texts usually available in academic libraries. Thankfully, here is a text that remedies that situation... [it] provides (...) a readable and insightful account' - Clinical Psychology Forum 'Spinelli’s classic introduction to phenomenology should be essential reading on all person-centred, existential and humanistic trainings, and any other counselling or psychotherapy course which aims to help students develop an in-depth understanding of human lived-experience. This book is sure to remain a key text for many years to come' - Mick Cooper, Senior Lecturer in Counselling, University of Strathclyde 'This is by far the most monumental, erudite, comprehensive, authoritative case that Existentialism and Phenomenology (a) have a rightful place in the academy; (b) are tough-minded bodies of thought; (c) have rigorous scientific foundations; (d) bequeath a distinctive school of psychotherapy and counselling; and (e) are just as good as the more established systems of psychology' - Alvin R. Mahrer, Ph.D. University of Ottawa, Canada, Author of The Complete Guide To Experiential Psychotherapy 'This book’s rich insight into the lacunae of modern psychological thinking illustrates the contribution that existential phenomenology can make to founding a coherently mature Psychology that is both fully human(e) and responsibly ‘scientific’ in the best sense of that term' - Richard House, Ph.D., Magdalen Medical Practice, Norwich; Steiner Waldorf teacher. The Interpreted World, Second Edition, is a welcome introduction to phenomenological psychology, an area of psychology which has its roots in notoriously difficult philosophical literature. Writing in a highly accessible, jargon-free style, Ernesto Spinelli traces the philosophical origins of phenomenological theory and presents phenomenological perspectives on central topics in psychology - perception, social cognition and the self. He compares the phenomenological approach with other major contemporary psychological approaches, pointing up areas of divergence and convergence with these systems. He also examines implications of phenomenology for the precepts and process of psychotherapy. For the Second Edition, a new chapter on phenomenological research has been added in which the author focuses on the contribution of phenomenology in relation to contemporary scientific enquiry. He describes the methodology used in phenomenological research and illustrates the approach through an actual research study. The Interpreted World, Second Edition demystifies an exciting branch of psychology, making its insights available to all students of psychology, psychotherapy and counselling. (shrink)

This essay gives an account of epistemic deference for agents with imprecise credences. I look at the two main imprecise deference principles in the literature, known as Identity Reflection and Pointwise Reflection (Moss, 2021). I show that Pointwise Reflection is strictly weaker than Identity Reflection, and argue that, if you are certain you will update by conditionalisation, you should defer to your future self according to Identity Reflection. Then I give a more general justification for Pointwise and Identity Reflection from (...) the assumption that you defer to someone whenever you consider their doxastic state to be better than yours, in the sense of leading to better decision-making. (shrink)

In this paper I address issues related to the problem of future contingents and the metaphysical doctrine of fatalism. Two classical responses to the problem of future contingents are the third truth value view and the all-false view. According to the former, future contingents take a third truth value which goes beyond truth and falsity. According to the latter, they are all false. I here illustrate and discuss two ways to respectively argue for those two views. Both ways are similar (...) in spirit and intimately connected with fatalism, in the sense that they engage with the doctrine of fatalism and accept a large part of a standard fatalistic machinery. (shrink)

This paper addresses a particular interpretation of quantum mechanics, i.e. superdeterminism. In short, superdeterminism i) takes the world to be fundamentally deterministic, ii) postulates hidden variables, and iii) contra Bell, saves locality at the cost of violating the principle of statistical independence. Superdeterminism currently enjoys little support in the physics and philosophy communities. Many take it to posit the ubiquitous occurrence of hard-to-digest conspiratorial and coincidental events; others object that violating the principle of statistical independence implies the death of the (...) scientific methodology. In this paper, we offer a defense to these and other objections. To counter the conspiracy objection, we draw upon the philosophical literature on time travel, and conclude that the picture of the world offered by the superdeterminist does not need to be particularly surprising or conspiratorial. We then move on to other recent objections, in particular those that focus on the methodology of science and the nature of the physical laws compatible with superdeterminism. A key ingredient of our arguments is that the principle of statistical independence may be violated in theory, but valid for practical purposes. Our overarching goal is to offer a defense of superdeterminism with respect to its main objections, so that it can earn its keep as a legitimate contender among the possible interpretations of quantum mechanics. (shrink)

Kaum ein anderes semantisches Feld durchzieht Platons Werk von den ersten Dialogen an bis zum Spätwerk so prägend und zugleich so spannungsreich wie das der Mimesis. Von der Sprachphilosophie über die Ästhetik und Moralpsychologie bis hin zur Metaphysik, Kosmologie und Theologie: in erstaunlich vielen Themenbereichen gewinnt die Semantik der Mimesis bei Platon hohe Relevanz. Der Tagungsband „Platonic Mimesis Revisited“ bietet eine umfassende und kontextsensible Neubetrachtung der Mimesis in allen einschlägigen Dialogen. Anders als frühere monographische Behandlungen des Themas vereint er eine (...) bedeutende Auswahl wissenschaftlicher Perspektiven aus Philosophie und Philologie und gibt so einen breiten Einblick in moderne Forschungsansätze.Mit Beiträgen vonMichele Abbate, Alexandra V. Alván Leon, Laura Candiotto, Andrea Capra, Elenio Cicchini, Michael Erler, Francesco Fronterotta, José Antonio Giménez Salinas, Stephen Halliwell, Irmgard Männlein-Robert, Lidia Palumbo, Anna Pavani, Julia Pfefferkorn, Antonino Spinelli, Benedikt Strobel und Justin Vlasits. (shrink)

Branching time is a popular theory of time that is intended to account for the openness of the future. Generally, branching-time models the openness of the future by positing a multiplicity of concrete alternative futures mirroring all the possible ways the future could unfold. A distinction is drawn in the literature among branching-time theories: those that make use of moment-based structures and those that employ history-based ones. In this paper, I introduce and discuss a particular kind of openness relative to (...) the possibility that time ends (doomsday). I then show that whereas moment-based branching structures cannot represent this kind of openness, history-based structures can account for it. The conclusion is that history-based structures have an advantage over moment-based ones. (shrink)

The goal of this paper is to defend the general tenet that time travelers cannot change the past within B-theoretical models of time, independently of how many temporal dimensions there are. Baron Pacific Philosophical Quarterly, 98, 129–147 offered a strong argument intended to reach this general conclusion. However, his argument does not cover a peculiar case, i.e. a B-theoretical one-dimensional model of time that allows for the presence of internal times. Loss Pacific Philosophical Quarterly, 96, 1–11 used the latter model (...) to argue that time travelers can change the past within such model. We show a way to debunk Loss’s argument, so that the general tenet about the impossibility of changing the past within B-theoretical models is maintained. (shrink)

Recent attempts to define and support realism in semantics seem to acknowledge, as the only defence from skeptical attacks to the notion of meaning, a flat acceptance of the existence of representational relations between language and things in the world. In this paper I reconsider part of the mistrust about the normative character of meaning, in order to show that some of the worries urging the realists to cling to representationalism actually rest on misconceptions. To the contrary, I suggest that (...) normativity is the main strength of a stable realist stance in semantics. Support to this suggestion comes from the reanalysis of some oft-ignored Sellarsian themes. (shrink)

The philosophy of language of Robert Brandom is based on a theoretical structure composed of three main elements: the normative analysis of linguistic practices, the inferential characterization of conceptual contents and the expressive articulation of the relations between the former two. Normative pragmatics aims to explain how linguistic practices are sufficient to confer contentful states in those who engage in them. Inferential semantics provides a theory of such pragmatic significances in terms of the inferential relations that articulate conceptual contents. Rational (...) expressivism is the thesis that concept application is essentially a process of turning something that can only be done into something that can also be said. Such a threefold structure is the core of normative inferentialism. This book is a concise, selfcontained and comprehensive presentation of this philosophical enterprise. It guides the reader through the analysis of Brandom’s imposing theoretical apparatus, the discovery of the roots of his approach in American pragmatism and German idealism, till the exploration of some of its most interesting and recent outcomes in pragmatics and semantics. It is a valuable resource for both those who approach Brandom’s work for the first time and those who are interested in the potential of normative inferentialism. (shrink)

Dynamic approaches to semantics like Discourse Representation Theory or Jaszczolt's Default Semantics provide more and more effective tools to represent how speakers handle meanings in linguistic practices. These deeper perspectives may give us a lever to lift some of the philosophical perplexities crowding semantics and to catch a glimpse of what hides beneath them. In this paper, I exploit these approaches with relation to the analysis of belief reports. However, it will emerge that, despite their benefits, the theories that support (...) these representational advances may be themselves question begging from a philosophical point of view. Brandom's remarks about normative character of intentional content offer an important contribution to bring into focus the right path to drive these representational improvements towards really acceptable answers to philosophical questions about semantics. (shrink)

Dispositionalism is the theory of modality according to which all (metaphysical and natural) modal truths are made true by some actual irreducibly dispositional property. The relationship between Dispositionalism and time is yet to be satisfactorily explored. In this paper we contribute to this task by examining how Dispositionalism deals with ‘dated truths’: propositions involving a specific time, e.g. “It might rain at 12.30”. We examine two possible accounts: the first, 'Dated Manifestations Strategy', is the idea that powers are very fine-grained, (...) and tend towards temporally very specific manifestations. We argue that such strategy should not be adopted, for it leads to unnecessary violations of ontological parsimony; it is unable to accommodate an ontology of platonic universals; and it is incapable of offering a principled explanation of the forward-looking nature of powers. We offer an alternative account, the "Duration Strategy", which relies on an independently determined arrow of time and the existence of some “duration facts” that specify how long a power takes to bring about its manifestation. We argue that the Duration Strategy is to be preferred. We then flesh out the account by exploring the connection between powers, duration facts, and processes. (shrink)

Nowadays, physicalism is arguably the received view on the nature of mental states. Among the arguments that have been provided in its favour, the inductive one seems to play a pivotal role in the debate. Leveraging the past success of materialistic science, the physicalist argues that a materialistic account of consciousness will eventually be provided, hence that physicalism is true. This article aims at evaluating whether this strategy can provide support for physicalism. According to the standard objection raised against the (...) inductive line of reasoning, the argument would beg the question by assuming some sort of metaphysical uniformity between consciousness and the rest of the natural domain. Here, I concede that there is a way to avoid this criticism. However, I argue that the argument still fails to support physicalism due to a structural problem of justification transmission. (shrink)

This paper explores mutable futurism, the view according to which the future can literally change—that is, it can happen that a future time t changes from containing an event E to lacking it. Mutable futurism has received little attention so far, and the details and implications of the view are underexplored in the literature. For instance, it currently lacks a precise metaphysical model and a formal semantics. Although we do not endorse mutable futurism, our goal here is to strengthen the (...) case for mutable futurism and help establish it as a worthy contender in the debate on the philosophy of time. To attain this goal, we try to make mutable futurism, along with its metaphysical and inferential commitments, as clear as possible, by providing it with a coherent metaphysical model and a plausible semantics, and we show that it can be backed by theoretical reasons. (shrink)

Starting from the early 2000s, paired associative stimulation protocols have been used in humans to study brain connectivity in motor and sensory networks by exploiting the intrinsic properties of timing-dependent cortical plasticity. In the last 10 years, PAS have also been developed to investigate the plastic properties of complex cerebral systems, such as the frontal ones, with promising results. In the present work, we review the most recent advances of this technique, focusing on protocols targeting frontal cortices to investigate connectivity (...) and its plastic properties, subtending high-order cognitive functions like memory, decision-making, attentional, or emotional processing. Overall, current evidence reveals that PAS can be effectively used to assess, enhance or depress physiological connectivity within frontal networks in a timing-dependent way, in turn modulating cognitive processing in healthy and pathological conditions. (shrink)

In lieu of an abstract, here is a brief excerpt of the content: Canti VI, Bruto Minore GIACOMO LEOPARDI (Translated by Steven J. Willett) To Peter Green After Italian Valor, lying in Thracian dust an immense ruin, had been uprooted, then in the valleys of green Hesperia, on Tiber’s shore, Fate prepares the tramp of barbarian horse, and from naked forests oppressed by the freezing Bear, calls forth the Gothic swords to overthrow Rome’s renowned walls; sitting alone, soaked in (...) brothers’ blood, through black night in a desolate site, Brutus is determined to die, and the implacable gods and Hell itself he accuses with savage cries and strikes the somnambulant air in vain. Fatuous Valor, the empty mists, the fields of unquiet phantoms are your schools, and behind you strides remorse. To you, marmoreal gods, (whether you reside in Phlegethon or the clouds), to you a laughingstock and mockery is the miserable race from whom you extort temples and a fraudulent law insulting to mortals. Is heaven’s wrath, then, so provoked by terrestrial piety? and do you then sit, Jove, impiety’s protector? and when storm clouds exult through the air, and when arion 27.1 spring/summer 2019 you hurl the swift thunderbolt, do you cast the sacred fire on the just and faithful? Invincible destiny and iron necessity crush the sickly slaves of death: and if nothing avails to end their indignities, the common man takes comfort in their necessity. Is the evil without cure less harsh? Does he feel no grief who’s stripped naked of hope? War to the death, eternal, o ignoble fate, the valorous man wages, incapable of surrender; and your tyrannical right hand, victorious as it bears him down, indomitable he shrugs off with a valiant show, when in his noble side the bitter blade runs with blood, and malignly he smiles at the darkening shadows. He displeases the gods who violently breaks into Tartarus. No such courage could be found in their feeble, eternal breasts. Perhaps our torments, perhaps our bitter accidents and wretched passions heaven created as a pleasing spectacle for their idle hours? Not between calamities and crimes, but free in the forests and pure Nature appointed us, once our queen and goddess. But since on earth impious custom has destroyed the blessed realms and subjected our miserable life to other laws; when a virile soul rejects his luckless days does Nature return, and accuse the arrow that’s not hers? 166 CANTI VI, bruto minore Ignorant of guilt and their own misfortunes are the fortunate beasts; serene old age guides them to an unforeseen passage. But if they dash their foreheads on rough tree-trunks or from a mountain cliff cast bodies headlong to the winds, moved by their anguish, against that miserable desire would stand no arcane law or shadowy conception. You alone, among the numerous progeny that heaven created, alone among all, children of Prometheus, regret life. Alone o wretched ones, to you Jove bans, if sluggish fate delays, the shores of death. And you, from the sea stained by our blood, you rise bright moon, and explore the unquiet night and the deadly battlefield of Italian Valor. The victor tramples on kinsmen’s breasts, the hills shudder, from her highest summits ancient Rome collapses— and are you so placid? You saw the birth of Lavinia’s offspring, and their years of happiness, and the memorable victories; and on the mountain peaks you pour your immutable silent light when, in the wreck of the servile Italian name, this solitary place will echo beneath the barbarian tramp. Giacomo Leopardi 167 Here among naked rocks or on green boughs, beast and bird, breasts heavy with their habitual oblivion, ignore the profound ruin and the altered destiny of the world: and as the rooftop of the industrious peasant first glows red, with its morning song the one will wake the valleys, while through high slopes the other will startle the helpless multitude of smaller creatures. Oh destiny! oh insensate race! we are an abject part of things; neither the bloodstained soil nor the howling caves has our calamity ever perturbed, and no human cares stain the stars. Neither to Olympus’ or Cocytus’ deaf kings, or to the unworthy earth, and... (shrink)

_Selections from Leopardi’s prose masterwork, _Zibaldone_, one of the great intellectual diaries in European literature, expertly translated by Tim Parks__ _Revenge__—Revenge is so sweet one often wishes to be insulted so as to be able to take revenge, and I don’t mean just by an old enemy, but anyone, or even by a friend_._—from _Passions_ The extraordinary quality of Giacomo Leopardi’s writing and the innovative nature of his thought were never fully recognized in his lifetime. _Zibaldone_, his 4,500-page intellectual (...) diary—a vast collection of thoughts on philosophy, civilization, literary criticism, linguistics, humankind and its vanities, and other varied topics—remained unpublished until more than a half-century after his death. But shortly before he died, Leopardi began to organize a small, thematic collection of his writings in an attempt to give structure and system to his philosophical musings. Now freshly translated into English by master translator, novelist, and critic Tim Parks, Leopardi’s _Passions _presents 164 entries reflecting the full breadth of human passion. The volume offers a fascinating introduction to Leopardi’s arguments and insights, as well as a glimpse of the concerns of thinkers to come, among them Nietzsche, Dostoyevsky, Wittgenstein, Gadda, and Beckett. (shrink)

One important distinction in the debate over the nature of epistemic justification is the one between propositional and doxastic justification. Roughly, while doxastic justification is a property of beliefs, propositional justification is a property of propositions. On a rather common view, which accounts for doxastic justification in terms of propositional justification plus the so-called ‘basing relation’, propositional justification is seen as the prior notion, and doxastic justification is explained in terms of it. According to the opposing view, the direction of (...) explanation needs to be reversed, and doxastic justification should be seen as primary. I distinguish between two notions of priority, and I argue that they give different verdicts with respect to the issue of which notion of justification comes first. The lesson may be taken to be that propositional and doxastic justification are in a relation of intertwinement. (shrink)

Husserl’s official account of essence is modal. It is also, I submit, incompatible with the role that essence is supposed to play, especially relative to necessity, in his overall philosophy. In the Husserlian framework, essence should rather be treated as a non-modal notion. The point, while not generally acknowledged, has been made before (by Kevin Mulligan for one); yet the arguments given for it, though perhaps sound, are not Husserlian. In this paper I present a thoroughly Husserlian argument for that (...) claim, as well as a Husserlian essentialist account of necessity. I also discuss the role of grounding within the account. (shrink)

We introduce a quite natural Frege-style set theory, which we call Strong-Frege-2 equation image, a sort of simplification of the theory considered in 13 and 1 . We give a model of a weaker variant of equation image, called equation image, where atoms and coatoms are allowed. To construct the model we use an enumeration “almost without repetitions” of the Π11 sets of natural numbers; such an enumeration can be obtained via a classical priority argument much in the style of (...) 5 and 15. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (shrink)