The aim of this special issue is broad in scope, since its contributions range over different topics in logic and philosophy of science. Following Sellars’ idea that “the aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term”, the issue includes papers dealing with foundational and philosophical problems in artificial intelligence, biology, cognitive sciences, computing, classical and non-classical logics, health sciences, mathematics, physics, and social sciences, as well as connections among all of these.

To better understand those connections, the Italian Society for Logic and Philosophy of Sciences (SILFS) organized its 4th Postgraduate Conference. The conference took place in Urbino, Italy, from June 3 to June 7, 2019. The success of the conference prompted the organizers to collect its contributions in a special issue of Foundations of Science.

The present special issue collects 17 articles written by leading scholars and young researchers, analyzing some of the main connections among foundational and philosophical problems in sciences. The special issue focuses on five distinct macro-themes, and each is developed through a series of articles by leading scholars who discuss important connections between concepts fundamental for their specific theme.

One of the themes is the analysis of problems relating to scientific realism and causality.

In his paper “Scientific Realism, Metaphysical Antirealism and the no miracle arguments” Mario Alai (University of Urbino) reviews and classifies a number of different kinds of realisms, metaphysical and not, analyzing both the relationship between scientific realism and metaphysical realism, and their link to the no miracle argument. Alai argues that scientific realism and metaphysical realism are logically independent, so that there is no logical inconsistency in holding the former and rejecting the latter. However, in the final part of the paper, Alai also argues that the “no miracle” argument is both the “ultimate” argument in favor of scientific realism and also metaphysical realism.

Alberto Corti (University of Urbino, University of Geneva) also discusses this connection between scientific and metaphysical realism. In his “Scientific Realism Without Reality? What Happens When Metaphysics is Left Out” he examines how weak the metaphysical commitments endorsed by scientific realists could be. Corti argues that the debate about scientific realism is independent of one's take on metaphysical realism. Finally, Corti presents a form of scientific realism devoid of any commitment to metaphysical realism.

Following similar lines of thought, Marco J. Nathan (University of Denver) discusses the concept of causality in both its metaphysical and explanatory role. In “Causation vs. Causal Explanation: Which Is More Fundamental?”, he examines the relation between causation and causal explanation, distinguishing two prominent roles that causes play within the sciences: causes as metaphysical posits and causes as explanatory postulates. Nathan uses this distinction to revisit longstanding philosophical issues, such as overdetermination and causal pluralism, and he highlights that it also inspires a provocative reframing of Russell’s famous, even though notoriously elusive, remarks on the nature of causation.

A second theme of the issue deals with the foundations of quantum mechanics.

Gino Tarozzi (University of Urbino) and Giovanni Macchia (University of Urbino) bridge the gap between the two concepts of realism and causality and apply their reflections to the foundations of quantum mechanics. In their paper “No-Thing and Causality in Realistic Non-Standard Interpretations of the Quantum Mechanical Wave Function: Ex Nihilo Aliquid?”, they show how a realistic non-standard interpretation of quantum mechanics, which attributes some form of weak physical reality to the wave function, conflicts with causality in its Cartesian formulation. They also discuss a more radical realistic interpretation according to which physical properties can also be assigned to a non-metaphysical relative nothing, seen as the simple absence of a particle such as a photon, but not of its corresponding state (no-photon), which is considered real.

The theme of the foundations of quantum mechanics is also covered by another important paper by F.A. Muller (Erasmus University Rotterdam, Utrecht University). “The Influence of Quantum Physics on Philosophy” continues the discussion on quantum physics. The paper is devoted to the question whether quantum physics has had any influence on philosophy, and if not, whether it ought to have had any. After considering the problems in Chalmers-Bouget list and discussing more specifically the influence of quantum mechanics in philosophy of mind, logic, metaphysics, ethics, and philosophy of science, Muller concludes that although quantum physics has influenced philosophy in the sense that it has grown a new flourishing and blossoming branch of the tree of philosophy, called philosophy of physics, quantum physics has had hardly any influence on philosophy at all, and at best has had some influence on metaphysics.

A third theme of the special issue contains essays devoted to set theory. Those papers complete a volume that aims to analyze some of the main connections between foundational and philosophical problems in the sciences. The special issue hosts three papers on this topic.

“Russell’s Paradox and Free Zig Zag Solutions” opens the discussion on set theory. Ludovica Conti (Complutense University of Madrid) presents the traditional debate about the explanation of Russell’s paradox and proposes a new way to solve the contradiction that arises in Frege’s system. Conti examines two alternative explanations presupposed by many of the proposed solutions to Russell’s Paradox, showing how a controversial conclusion emerges from both. Then, she examines some particular zig zag solutions and proposes a new one obtained by the adoption of a negative free logic.

In their paper “Maximality Principles in the Hyperuniverse Programme'' Sy-David Friedman (University of Vienna) and Claudio Ternullo (University of Barcelona) provide an overview of the maximality principles for V, the universe of sets, which have been investigated in the Hyperuniverse Programme. The principle expressing the width maximality of V is the Inner Model Hypothesis (IHM), which prescribes the maximality of the inner models of V, whereas the principle expressing height maximality is ‘#-generation’, arguably the strongest reflection principle compatible with the Axiom of Constructibility (V = L). The authors also consider several combinations of IMH with #-generation, and then proceed to show how optimal principles, expressing both width and height maximality, may be selected in a justifiable way, that is, by looking at their connections with the iterative concept of set and at their consequences for set-theoretic truth.

In his paper “Dynamical Phenomena and Their Models: Truth and Empirical Correctness”, Marco Giunti (University of Cagliari) shows applications of set theory to the topic of truth. He reviews two conceptions of truth (one sentence-based and one model-based) and two conceptions of empirical adequacy (again, one sentence-based and one model-based), pointing out their respective difficulties, and laying out an account of the theory-world relationship called Methodological Constructive Realism (MCR). The author also shows how the content of MCR can be formulated as an axiomatic extension of set theory, and can then be applied to the special case of deterministic dynamical phenomena and their correlated deterministic models.

These articles on set theory are part of a larger set of articles on logic. In particular the following four articles are devoted to the themes of mathematical logic and the applications of formal logic to the natural sciences.

“Molecular Biology Meets Logic: Context-Sensitiveness in Focus” by Giovanni Boniolo (University of Ferrara), Marcello D’Agostino (University of Milan), Mario Piazza (Scuola Normale Superiore of Pisa) and Gabriele Pulcini (Tor Vergata University of Roma) propose a development of the Zsyntax project. Such a project presents the idea that biochemical types could be represented as logical formulae and molecular processes as formal derivations. In particular, the authors describe and discuss the context sensitiveness phenomenon, as it emerges in molecular reactions and processes, through the lenses of the Zsyntax account. This logical account also allows the authors to revisit the relationship between logic and philosophy of science in general, and philosophy of biology, in particular.

Sara Negri (University of Genoa) and Edi Pavlović (Munich Center for Mathematical Philosophy) in their paper "Alternative Axiomatization for Logics of Agency in a G3 Calculus" investigate a decidable sequent calculus for the logic of agency, specifically with respect to a deliberative see-to-it-that modality, or dstit, formulated by Negri and Pavlović in 2020. In that paper, the adequacy of the system is demonstrated by showing the derivability of the axiomatization of dstit from Belnap et al. (2001). In their new paper, the authors prove that also the alternative axiomatization offered in Xu (1998) of dstit modality is likewise successfully and readily derivable in the system developed by Negri and Pavlović (2020).

Antonino Salibra (Ca’ Foscari University of Venice), Antonio Bucciarelli (CNRS and University of Paris), Antonio Ledda (University of Cagliari) and Francesco Paoli (University of Cagliari) in their paper “Classical Logic with n Truth Values as a Symmetric Many-Valued Logic” generalize the (algebraic) semantics of the classical propositional calculus, i.e. Boolean algebras, to the case of n–perfectly symmetric–truth-values, where n is an arbitrary natural number. As a consequence, they obtain a logic, nCL, in which every finite-valued tabular logic can be embedded into, and this embedding preserves validity. Finally, they define a confluent and terminating first-order rewriting system for deciding validity in nCL, and, via the embeddings, in all the finite tabular logics.

The paper “On Finch’s Conditions for the Completion of Orthomodular Posets'' by Davide Fazio (University of Cagliari), Antonio Ledda (University of Cagliari) and Francesco Paoli (University of Cagliari) contributes to clarify the relationship between partially ordered sets of “crisp” quantum events, called Orthomodular Posets (OMPs), and the models they are an abstraction of, i.e. lattices of closed subspaces of Hilbert spaces (HS). Indeed, the authors show that, although, as it is well known, the theory of OMPs falls short of capturing the algebraic properties of HS’s in their entirety, OMPs which can be naturally embedded into OMPs having an underlying partial order which is a complete lattice, share at an abstract level the same features which characterize HS’ among inner product spaces. Therefore, these results shed a new light, from an abstract perspective, upon celebrated results in the foundation of quantum theory like e.g. the Amemiya-Araki-Piron’s and Gudder’s characterizations of HS’.

Alongside analyses of a logical nature, the special issue also contains several contributions highlighting the impact of foundational and methodological analysis in the fields of epistemology, neuroscience, artificial intelligence and decision making.

Ciro De Florio (Cattolica University of Milan) and Vincenzo Fano (University of Urbino) discuss Williamson’s arguments against luminosity. In their paper “Williamson on the Margins of Knowledge: A Criticism” they argue that Williamson’s arguments against luminosity and the KK principle do not work in general. Specifically, they show that this kind of arguments do not hold in a scientific context, where a so-called “buffer zone” (between situations in which one is in a position to know p and situations in which one is in a position to know ¬ p) is controlled by a quantitative measurement of the experimental error.

“Facing up to the Hard Problem of Consciousness as an Integrated Information Theorist” by Robert Chis-Ciure (University of Bucharest, University of Wisconsin - Madison) and Francesco Ellia (University of Wisconsin - Madison) provides a philosophical analysis of the Hard Problem of consciousness and the implications of conceivability scenarios for current neuroscientific research. In particular, they focus on Integrated Information Theory (IIT), arguing that it’s possible to disentangle a core problem of consciousness from a layered hard problem, the latter being essentially connected to Chalmers’ conceivability argument. The main result of their analysis is that IIT has the resources to give a comprehensive account of the core problem, as well as reject the conceivability argument on principled grounds, thus dissolving also the layered hard problem. Overall, their contribution illuminates a long-standing issue in the contemporary scientific study of consciousness, namely how IIT, as one of its major theories, faces up to the conceptual challenge posed by Chalmers’ Hard Problem.

“A New Definition of “Artificial” for Two Artificial Sciences” by Francesco Bianchini (University of Bologna) considers the conceptual issue concerning the framework of two special sciences: artificial intelligence and synthetic biology. Bianchini claims that the standard definition of “artificial” is no longer useful to describe some present-day artificial sciences, as the boundary between the natural and the artificial is not so sharp and clear-cut as it was in the past. Artificial intelligence and synthetic biology need a new, more specific, and refined definition of (the) “artificial”. Bianchini tries to formulate a brand-new, more useful definition for future understanding, practical, and epistemological purposes of these two artificial sciences.

“Reviewing the case of online interpersonal trust” by Mirko Tagliaferri (University of Urbino) analyses the problem of online trust. The problem of online trust is that of evaluating whether online environments have the proper design to enable trust. This paper tries to better qualify this problem by showing that there is no unique answer, but only conditional considerations that depend on the conception of trust assumed and the features that are included in the environments themselves. In this paper, the richness of the philosophical discussions about trust is brought into the analysis of online trust. Tagliaferri first provides a set of conditions that depend on the definition of trust that can be assumed and then discusses those conditions with respect to the design of online environments in order to determine whether they can enable (and under which circumstances) trust.

“The Cochrane Case: An Epistemic Analysis on Decision-Making and Trust in Science in the Age of Information” by Federico Boem (University of Twente), Stefano Bonzio (University of Cagliari), Barbara Osimani (Marche Polytechnic University) and Armando Sacco (University of Naples) discusses a recent controversy within the biomedical world, concerning the evaluation of safety of certain vaccines. This paper wants to highlight the value and the impact of strategic decisions when complex issues, as those analyzed, are at stake. In order to address this issue, authors adopt a game-theoretic approach arguing that such an approach can be useful in dissecting this type of issue.

Finally, we would like to add some acknowledgements.

We are grateful to the Editor in Chief of Foundations of Science for supporting the project of this special issue. We would also like to thank the authors, for accepting our invitation to contribute to the project, and the referees, for working alongside the authors and the editors in improving each individual paper. Lastly, we would like to thank SILFS and the colleagues from our respective universities for their continued support.

Work on this project was made possible by the generosity of our funding sources, whose support is gratefully acknowledged. Pierluigi Graziani’s work was supported by the Italian Ministry of Education, University and Research through the PRIN 2017 project “The Manifest Image and the Scientific Image” prot. 2017ZNWW7F_004. Roberto Giuntini and Giuseppe Sergioli work was supported by the Italian Ministry of Education, University and Research through the PRIN 2017 project “Logic and Cognition: theory, experiments, applications”, prot. 20173YP4N3. The 4th SILFS Postgraduate Conference was partly funded by the Autonomous Region of Sardinia, under the project “Per un’estensione semantica della Logica Computazionale Quantistica—Impatto teorico e ricadute implementative" prot. RASSR40341.