Pierluigi Graziani

The enormous increasing of connections between people and the noteworthy enlargement of domains and methods in sciences have augmented extraordinarily the cardinality of the set of meaningful human symbols. We know that complexity is always on the way to become complication, i.e. a non-tractable topic. For this reason scholars engage themselves more and more in attempting to tame plurality and chaos. In this book distinguished scientists, philosophers and historians of science reflect on the topic from a multidisciplinary point of view. Is it possible to dominate complexity through reductionism? Are there other conceptual instruments useful to take account of complexity? What is complexity in biology, mathematics, physics and philosophy of mind? These are some of the questions which are faced in this volume.

Achille Varzi è uno dei maggiori metafisici viventi. Nel corso degli anni ha scritto testi fondamentali di logica, metafisica, mereologia, filosofia del linguaggio. Ha sconfinato nella topologia, nella geografia, nella matematica, ha ragionato di mostri e confini, percezione e buchi, viaggi nel tempo, nicchie, eventi e ciambelle; e non ha disdegnato di dialogare con gli abitanti di Flatlandia, con Neo e con Terminator. Tra le sue opere principali: Holes and Other Superficialities e Parts and Places. The Structures of Spatial Representation, entrambi scritti insieme a R. Casati per MIT Press; Il mondo messo a fuoco, Laterza; e il suo libro più recente: Le tribolazioni del filosofare, con C. Calosi, per Laterza. Da una giornata all’Università di Urbino nasce questa conversazione a molte voci sulla e con la filosofia di Achille C. Varzi. In un dialogo critico al quale l’Autore si presta con generosità e onestà intellettuale, Andrea Borghini, Francesco Calemi, Claudio Calosi, Elena Casetta, Valeria Giardino, Pierluigi Graziani, Patrizia Pedrini, Daniele Santoro e Giuliano Torrengo lo interrogano e mettono alla prova sui temi affrontati, nel corso degli anni, in campi diversi. Il risultato è un percorso che si snoda attraverso molti mondi, dalla logica alla metafisica, dalla filosofia del linguaggio alla filosofia della matematica, dalla mereologia alla filosofia del tempo, spingendosi in qualche caso oltre i confini del saggio filosofico.

La storia della nascita, utilizzo e declino delle notazioni scientifiche costituisce un’area di indagine importante che può aiutare le nostre analisi del pensiero scientifico e la sua evoluzione. […] this history constitutes a mirror of past and present conditions in mathematics which can be made to bear on the notational problems now confronting mathematics. The successes and failures of the past will contribute to a more speedy solutions of the notational problems of the present times.Questa storia, ovviamente, coinvolge anche le notazioni della logica. Il presente contributo intende proporre un nuovo insieme di simboli per una particolare teoria logica: la Mereologia Formale, in considerazione del fatto che questa teoria, pur avendo avuto trattazioni sistematiche, non ha allo stato attuale ancora raggiunto un sistema di notazioni condiviso dagli studiosi. Tale stato dell’arte è espressione, da un lato, di un legame della teoria al suo nascere con la notazione polacca, e del suo confronto con la Teoria Assiomatica degli Insiemi; dall’altro, del fatto che essa ha ricevuto solo in tempi recenti sistematiche applicazioni alle scienze.94 In tale prospettiva ho ritenuto necessario definire in primo luogo dei criteri attraverso cui procedere alla costruzione del sistema di simboli. Criteri desunti in parte dalla storia delle notazioni scientifiche nella loro evoluzione, in parte dalla pratica personale nell’uso di strumenti formali.

Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal characterisations of the surprise notion, crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes.

In the logical context, ignorance is traditionally defined recurring to epistemic logic. In particular, ignorance is essentially interpreted as “lack of knowledge”. This received view has - as we point out - some problems, in particular we will highlight how it does not allow to express a type of content-theoretic ignorance, i.e. an ignorance of φ that stems from an unfamiliarity with its meaning. Contrarily to this trend, in this paper, we introduce and investigate a modal logic having a primitive epistemic operator I, modeling ignorance. Our modal logic is essentially constructed on the modal logics based on weak Kleene three-valued logic introduced by Segerberg (Theoria, 33(1):53–71, 1997). Such non-classical propositional basis allows to define a Kripke-style semantics with the following, very intuitive, interpretation: a formula φ is ignored by an agent if φ is neither true nor false in every world accessible to the agent. As a consequence of this choice, we obtain a type of content-theoretic notion of ignorance, which is essentially different from the traditional approach. We dub it severe ignorance. We axiomatize, prove completeness and decidability for the logic of reflexive (three-valued) Kripke frames, which we find the most suitable candidate for our novel proposal and, finally, compare our approach with the most traditional one.

Different realistic attitudes towards wavefunctions and quantum states are as old as quantum theory itself. Recently Pusey, Barret and Rudolph on the one hand, and Auletta and Tarozzi on the other, have proposed new interesting arguments in favor of a broad realistic interpretation of quantum mechanics that can be considered the modern heir to some views held by the fathers of quantum theory. In this paper we give a new and detailed presentation of such arguments, propose a new taxonomy of different realistic positions in the foundations of quantum mechanics and assess the scope, within this new taxonomy, of these realistic arguments.

The Dunning–Kruger effect focuses our attention on the notion of invisibility of ignorance, i.e., the ignorance of ignorance. Such a phenomenon is not only important for everyday life, but also, above all, for some philosophical disciplines, such as epistemology of sciences. When someone tries to understand formally the phenomenon of ignorance of ignorance, they usually end up with a nested epistemic operator highly resistant to proper regimentation. In this paper, we argue that to understand adequately the ignorance of ignorance phenomenon we have to understand satisfactorily the concept of disbelief and, as we call it, the concept of “radical ignorance”. We propose also prerequisites that a notion of radical ignorance useful for the philosophy of science ought to fulfill, and we sketch a possible formalization of this notion. Finally, we propose some comments on the problem of propagation of ignorance proposed by Fine.

This volume is the first systematic and thorough attempt to investigate the relation and the possible applications of mereology to contemporary science. It gathers contributions from leading scholars in the field and covers a wide range of scientific theories and practices such as physics, mathematics, chemistry, biology, computer science and engineering. Throughout the volume, a variety of foundational issues are investigated both from the formal and the empirical point of view. The first section looks at the topic as it applies to physics. The section addresses questions of persistence and composition within quantum and relativistic physics and concludes by scrutinizing the possibility to capture continuity of motion as described by our best physical theories within gunky space times. The second part tackles mathematics and shows how to provide a foundation for point-free geometry of space switching to fuzzy-logic. The relation between mereological sums and set-theoretic suprema is investigated and issues about different mereological perspectives such as classical and natural Mereology are thoroughly discussed. The third section in the volume looks at natural science. Several questions from biology, medicine and chemistry are investigated. From the perspective of biology, there is an attempt to provide axioms for inferring statements about part hood between two biological entities from statements about their spatial relation. From the perspective of chemistry, it is argued that classical mereological frameworks are not adequate to capture the practices of chemistry in that they consider neither temporal nor modal parameters. The final part introduces computer science and engineering. A new formal mereological framework in which an indeterminate relation of part hood is taken as a primitive notion is constructed and then applied to a wide variety of disciplines from robotics to knowledge engineering. A formal framework for discrete mereotopology and its applications is developed and finally, the importance of mereology for the relatively new science of domain engineering is also discussed.

Lucas-Penrose type arguments have been the focus of many papers in the literature. In the present paper we attempt to evaluate the consequences of Gödel’s incompleteness theorems for the philosophy of the mind. We argue that the best answer to this question was given by Gödel already in 1951 when he realized that either our intellectual capability is not representable by a Turing Machine, or we can never know with mathematical certainty what such a machine is. But his considerations became known only in recent times when many scholars were already aware of Benacerraf’s and Chihara’s analyses on the consequences of Gödel’s incompleteness theorems for the philosophy of the mind. Benacerraf and Chihara, in fact, discussing Lucas’ paper, arrived at the same conclusions as Gödel in the sixties, but in a more formal way. After Penrose’s provocative arguments, Shapiro again shed light on the question. In our paper, after a broad and simple presentation of the contributions to the debate made by different authors, we show how to present Gödel’s argument in a rigorous way, highlighting the necessary philosophical premises of Gödel’s argument and more in general of Gödelian arguments.

The aim of this paper is to reconstruct the logical structure of Melissus philosophy, building on Laks Most’s translation and Barnes’ seminal work on the Samian. This will allow us to shed some light on the subtle argumentations of Melissus. On top of that, we frame Melissus’ metaphysics employing modern logical instruments. On one side, this reformulation makes clear a few assumptions hidden in the deductions made by the Samian; on the other side, our paper shows that contemporary analytic metaphysics has forerunners dating back 2500 years.

This volume presents philosophy of science at its best, i.e. as a philosophical questioning informed by current scientific research, which carefully assesses and evaluates its commitments and consequences. As such it represents philosophy simpliciter at its best, for it is concerned with and dares to ask fundamental questions about the nature of the results of the natural sciences, arguably our most reliable sources of knowledge of the world. The contributions collected in this volume make clear that a philosophy that is disconnected from science is sterile and that the practice of science that is disconnected from a philosophical attempt to understand the natural world in its most general features is blind. Throughout the book we are confronted with questions about the nature of species, numbers, space, time, matter, consciousness and so on. Taking seriously these questions, along with other open problems in philosophy of sciences, and keeping the dialogue between science and philosophy wide open, is likely to be our best bet for a deeper understanding of what surrounds us. The book has a further, deeply important merit. Being the result of a post-graduate conference, it brings together not only leading, long established experts in the field but also new, young researchers, who usually find too small a place within the academic environment. Promoting exactly this kind of interaction is an essential step in constructing a new paradigm for an open, collaborative and fruitful scientific community.

Great scholars in philosophy possess a keen analytical mind, excel in logical reasoning, and exhibit meticulous attention to detail. They rigorously define terms, avoiding ambiguities and errors. Originality and the willingness to challenge conventions are their hallmarks. They make significant contributions across various philosophical fields. They transparently address the exact aim of their research, and what it is not. Finally, they anticipate the impact of their theories on the current literature, and how such an impact should blossom across the future generations. In this respect, great philosophers address open problems and propose big questions for the foreseeable research efforts of those who will follow. Mario Alai embodies the qualities of a great scholar in philosophy, and the various essays in this volume are an evidence to that. It is challenging to condense a lifetime of research in one book. However, the Editors of the present volume’s aim was to face this challenge, to make a collection dedicated to Mario Alai’s work not only possible but, as metaphysicians would say, actual. The book attempts to bring together the reflections of three different generations of scholars - i.e., mentors, colleagues, and students - on Alai’s thought. Viewed from this perspective, the extensive and valuable contributions that follow, crafted in honor of Mario Alai and his scholarly endeavors, come as no surprise. All the chapters focus on a theme that was very dear to the philosophical curiosity of Mario Alai. Moreover, in engaging with these different topics, the plethora of contributions gives us a sense of the work by Alai. To make sense of the different contributions as a unified enterprise, this volume is organized into three sections, which seek to gather writings that revolve around Mario’s most substantial contributions, while elucidating their contemporary significance in the global discourse. Moreover, it endeavors to offer precious insights into the origins and development of these contributions, as observed through Mario’s writings and responses. This represents a sort of closure of the theoretical circle, clearly showing how the work by Mario Alai has been appreciated through different generations, originating from his relation to his mentors, on the one hand, while also shedding new light on his students’ research interests, on the other. Editing such a wealth of material was, again, no small feat. Still, the taxonomy we have chosen for this book will assist readers in navigating the profound depths of Alai’s philosophical research. Consequently, the book is structured into the following three parts: 1. Realism in History of Philosophy, History of Science, and Metaphysics. 2. Scientific Realism. 3. Realism in Philosophy of Language, Epistemology, and Experimental Philosophy. Each contribution actively participates in a substantial conversation with Alai’s body of work, as a deep theoretical dialogue between the author and Mario. Consequently, it appeared fitting to let Alai conclude this conversation, with direct responses to these philosophy-provoking pieces in his honor. We shall refrain from further commentary on the works within this book and allow them to express their significance independently to appreciate the river of ideas flowing through Mario’s work1. Beyond their philosophical substance, they are a vivid testament to Alai’s enduring dedication and ongoing contributions, in different moments of his research life.