In the previous paper of this volume, Kojman and Shelah solved our long standing problem of collapsing cardinal κ0 to ω1 by the forcing for singular κ with countable cofinality. The aim of the present paper is to give an explicit construction of the Boolean matrix for this collapse.

We investigate the following weak Ramsey property of a cardinal κ: If χ is coloring of nodes of the tree κ <ω by countably many colors, call a tree ${T \subseteq \kappa^{ < \omega}}$ χ-homogeneous if the number of colors on each level of T is finite. Write ${\kappa \rightsquigarrow (\lambda)^{ < \omega}_{\omega}}$ to denote that for any such coloring there is a χ-homogeneous λ-branching tree of height ω. We prove, e.g., that if ${\kappa < \mathfrak{p}}$ or ${\kappa > \mathfrak{d}}$ (...) is regular, then ${{\kappa \rightsquigarrow (\kappa)^{ < \omega}_{\omega}}}$ and that ${\mathfrak{b}}$ ${(\mathfrak{b})^{ < \omega}_{\omega}}$ and ${\mathfrak{d}}$ ${(\mathfrak{d})^{ < \omega}_{\omega}}$ . The arrow is applied to prove a generalization of a theorem of Hurewicz: A Čech-analytic space is σ-locally compact iff it does not contain a closed homeomorphic copy of irrationals. (shrink)

We prove the existence of p-ideals that are nonmeagre subsets of P(ω) under various set-theoretic assumptions.

Despite their flaws, large language models (LLMs) deserve a fair chance to prove their mettle against human experts, who are often plagued with biases, conflicts of interest, and other frailties. For epistemically unprivileged laypeople struggling to access expert knowledge, the accessibility advantages of LLMs could prove crucial. While complaints about LLMs' inconsistencies and arguments for human superiority are often justified (for now), they distract from the urgent need to prepare for the likely scenario of LLMs' continued ascent. Experimentation with both (...) the capabilities and institutional architecture of LLMs is necessary. Neither tech-bashing nor excessive gatekeeping will suffice. As LLMs are here to stay and they keep improving, it is high time we started thinking about how to navigate the impending wave of their proliferation. (shrink)

Between the zone of certainty beyond all doubt and the zone of incomprehensible uncertainty, the sources of which are nothing but chance, we need to use solid results from a vast interdisciplinarity. We wish to give here a sense of the factors in play and the state of the debate and advance in the territory of how interdisciplinarity may help to solve problems which are common in many areas of knowledge. Chaos and complexity certainly put limits on what we can (...) know. High complexity, asymmetry and/or non-linearity are universal types of imprecision. Can hazard have purpose and direction?The idea is that the more effort we put into project design to cover as many details and possible consequences as possible we can grasp in our in-depth analysis aiming to create the project (in art or science or society), the greater the chances that the random occurrence of the unpredictable event will settle on the project's purpose and direction and not on contrary to them. There is no vicious circle here. This kind of method can explain many good results already obtained in such circumstances. Simplicity, beauty, rationalistic optimism, are features of unshakeable scientific results We may call this feature of scientific theory or art _uniqueness. _Uniqueness is strongly correlated with _essentialization. _Science is working in that sense: to simplify a phenomenon to its essence in order to study it easily without losing anything important in the analysis. That is _essentialization. _Why and how complex systems move to the edge of chaos? And what do they do to stay there? They are in constant struggle to create or keep order in complexity. That is the pattern of self-organization, the specific feature of human nature. That is why our action is meant to build resilience to deal better with unpredictable events and prevent the emergence of a critical threshold. Uncertainty, indeterminacy, randomness, and contradictions appear, not as non-essential substances of debate to be eliminated by explanation, but as everlasting ingredients of our conception of reality. There are compelling reasons to believe that it is impossible to make accurate, nontrivial predictions concerning human behavior. Logic and reason are and remain priority, but unpredictability forces us to imagination and creative thinking. Indeed we are confronted with a new human landscape. The anomalies become the new normal. (shrink)

Analyzing different philosophical and theological components of Aquinas’s view regarding the relation between human agency and divine providence, the monograph shows this view to be compatibilist, based on a determinist conception of causation and an aristocratic understanding of goodness.

Simon Critchley's first book, The Ethics of Deconstruction, was originally published to great acclaim in 1992. This edition contains three new appendices and a new preface where Critchley reflects upon the origins, motivation and reception of The Ethics of Deconstruction.

In this book, Petre Petrov argues that Soviet ideology, in the form in which it solidified during the Stalinist period, should not be seen as a member of a known political ideology. Rather, Soviet ideology is its own kind of political ideology, whose original life calls for an innovative conceptual treatment.

Gilles Deleuze’s engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems – for example, the problem of individuation – and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze’s philosophy, (...) as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. -/- In the wake of Alain Badiou’s recent and seemingly devastating attack on the way the relation between mathematics and philosophy is configured in Deleuze’s work, Simon Duffy offers a robust defence of the structure of Deleuze’s philosophy and, in particular, the adequacy of the mathematical problems used in its construction. By reconciling Badiou and Deleuze’s seeming incompatible engagements with mathematics, Duffy succeeds in presenting a solid foundation for Deleuze’s philosophy, rebuffing the recent challenges against it. -/- Simon B. Duffy is a Senior Lecturer in Philosophy at Yale-NUS College, Singapore, and Honorary Research Associate in the Department of Philosophy at the University of Sydney, Australia. He is the author of The Logic of Expression: Quality, Quantity, and Intensity in Spinoza, Hegel and Deleuze (2006). (shrink)

Le devenir-autre de l'existence est une étude phénoménologique à la fois systématique et historique. En prenant pour fil conducteur un problème systématique, celui de l'événementialité de l'apparaître et de la subjectivité, elle confronte cinq représentants majeurs de la phénoménologie contemporaine française : Maldiney, Romano, Marion, Barbaras et Richir. L'étude entre dans la phénoménologie avec Husserl avant de présenter plusieurs concepts-clés forgés par les deux générations de philosophes qui jalonnent la voie menant à la phénoménologie contemporaine (Heidegger, Sartre, Straus, Merleau-Ponty, Patocka, (...) Lévinas). Puis elle se focalise sur la phénoménologie de l'événement de Maldiney et de Romano qui envisagent l'existant et le monde dans leur coappartenance : l'événement est considéré avant tout comme co-naissance du sujet et du monde. Or, puisque l'existence qui devient-autre est nécessairement une existence finie radicalement séparée de la transcendance métaphysique du monde, on est conduit à intégrer à la discussion trois autres philosophes : d'abord Marion dont l'adonné est conçu comme limite de la donation, puis Barbaras et Richir qui thématisent la subjectivité au sein d'une métaphysique"--Page 4 of cover. (shrink)

This bestselling dictionary is written by one of the leading philosophers of our time, and it is widely recognized as the best dictionary of its kind. Comprehensive and authoritative, it covers every aspect of philosophy from Aristotle to Zen. With clear and concise definitions, it provides lively and accessible coverage of not only Western philosophical traditions, but also themes from Chinese, Indian, Islamic, and Jewish philosophy. New entries on philosophy of economics, social theory, neuroscience, philosophy of the mind, and moral (...) conceptions, bring this authoritative third edition up to date. It is the ideal introduction to philosophy for anyone with an interest in the subject, and it is an indispensable work of reference for students and teachers. (shrink)

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying “xis true” and satisfying the “dequotation schema”for all sentences φ? This problem is investigated in the frame of Łukasiewicz infinitely valued logic.

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for (...) the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics. (shrink)

Procedural justifications of democracy emphasize inclusiveness and respect and by doing so come into conflict with instrumental justifications that depend on voters’ competence. This conflict raises questions about jury theorems and makes their standing in democratic theory contested. We show that a type of no-regret learning called meta-induction can help to satisfy the competence assumption without excluding voters or diverse opinion leaders on an a priori basis. Meta-induction assigns weights to opinion leaders based on their past predictive performance to determine (...) the level of their inclusion in recommendations for voters. The weighting minimizes the difference between the performance of meta-induction and the best opinion leader in hindsight. The difference represents the regret of meta-induction whose minimization ensures that the recommendations are optimal in supporting voters’ competence. Meta-induction has optimal truth-tracking properties that support voters’ competence even if it is targeted by mis/disinformation and should be considered a tool for supporting democracy in hyper-plurality. (shrink)