In: Vejnarová, J., Wilson, N. (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty, 16th European Conference, ECSQARU 2021, Prague, Czech Republic, September 21–24, 2021. Proceedings, Lecture Notes in Computer Science (2021). Springer Nature: 575-589

We investigate the application of a modal language à la Hennessy-Milner to the specific domain of evidence-based trust estimations. In particular, we refer to a context-aware notion of computational trust joining in a quantitative setting both assessment of subjective opinions and third-party recommendations. Moreover, for a comprehensive analysis of the proposed logics, we offer an axiomatization and provide soundness and completeness results.

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Synthese, 197(2020): 4639-4644

The publication of this Special Issue occurs in a period during which a number of important anniversaries concerning Lewis’s life and work are being marked: 50 years since the publication of Lewis’s first book “Convention: A Philosophical Study” in 1969 (based on his Ph.D. thesis at Harvard); the twentieth anniversary of the publication of the last volume of Lewis’s collected works in 2000; and 20 years since Lewis’s passing on October 14, 2001. This collection does not aim to reconstruct the development of Lewis’s thought, nor to provide an introduction to or overview of his work, for which excellent sources are already available. Rather, it aims to provide a window onto Lewis’s enormous philosophical legacy by examining some of the most important ways in which Lewis’s ideas continue to shape the development of contemporary philosophical research. This Special Issue collects 14 articles written by leading scholars, analysing some of the main themes in Lewis’s philosophy: from the analysis of modality to modal realism, from the theory of counterparts to the criticisms of different kinds of ersatzism, from the analysis of mereological monism and Humean supervenience to that of unrestricted composition, from the counterfactual approach to causality to the counterfactual analysis of dispositions, from the concept of change to the notion of time, and concluding with an analysis of Lewis’s epistemology.

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Il Sussidiario.net, May, 13, 2020

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Il Fumaiolo, 16(1)(2020): 6-8

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Published in 2021. Milan: Mimesis. ISBN: 978-88-5757-889-7

An introduction to the main authors, problems, classical texts and methods of the analytic philosophy of language. It presupposes no previous knowledge in the field, since basic concepts are fully explained in plain terms, arguments are spelled out explicitly, and a wealth of examples are used. The nine chapters deal respectively with: a general introduction to the philosophy of language, the linguistic turn and analytic philosophy; Frege and his legacy in logic, philosophy of mathematics, semantics and pragmatics, with special regard to the distinction between sense and reference; Bertrand Russell’s foundations of mathematics, theory of descriptions, logical atomism and semantic monism; the picture theory of propositions and the truth-conditional analysis of meaning in Wittgenstein’s Tractatus; the verificationist theory of meaning in Neopositivism and after; Carnap’s system of extension and intension, and the possible worlds semantics; meaning as use in Wittgenstein’s Philosophical Investigations; Quine’s rejection of intensions, analyticity and referential determinacy; Kripke’s and Putnam’s the theories of direct reference.

Each chapter presents its subject matter by following and explaining one or two classical texts of the respective authors (Frege’s “Sinn und Bedeutung” and “Der Gedanke”; Russell’s “On Descriptions” and “On Denoting”; Wittgenstein’s Tractatus; Carnap’s “Pseudoproblems in Philosophy”; Carnap’s Meaning and Necessity; Quine’s “Two Dogmas” and “Ontological Relativity”; Kripke’s Naming and Necessity and Putnam’s “Meaning, Reference and Stereotypes”). 

Some necessary basic elements of logic are also introduced: truth tables, material and ordinary conditionals, quantifiers, elementary notions of set theory. Besides, the handbook stresses the most relevant connections between the philosophy of language and metaphysics, epistemology, philosophy of science, philosophy of mathematics, philosophy of mind. Thus, it briefly discusses, among others, identity criteria, essences, universals, scientific realism and antirealism, scientific change, the nature of numbers. 

Each topic is dealt with on three distinct levels: a basic introduction, a more extensive and in-depth presentation, and a more advanced critical discussion, where each level can be followed independently of the next one.

Nuova Secondaria, 37(4)(2019): 60-63 

Blog Laurea Magistrale in Filosofia dell’Informazione, March, 1, 2020

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Nuova Secondaria, 38(2021): 63-68

Il nuovo libro di Giampaolo Bellini ed Evandro Agazzi riesamina la posizione esistenziale e intellettuale della persona umana nell’epoca della tecnoscienza, argomentando che la cultura odierna non può prescindere dalla nostra miglior scienza, mentre la conoscenza scientifica sarebbe monca senza il sapere umanistico e la profonda consapevolezza che ce ne deriva.

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In: Tassani, I. (ed.), M.Q. 90. Dualismo, entanglement, olismo - Special issue of Isonomia - Epistemologica, 11(2021): 17-34

The empirical underdetermination of theories is a classical objection to scientific realism. Realists reply that beside complying with empirical data, theories must satisfy theoretical requirements, such as coherence, simplicity, consilience, plausibility, explanatory power and methodological correctness. This is why historical cases of underdetermination never concerned more than two or three theories, and all have been solved in due time. But in current microphysics things are worse, because of the many alternative theories and interpretations among which we seem unable to decide. This does not refute realism, however, because all the main accounts share a significant core of theoretical assumptions, on which one can be realist while withdrawing one’s judgment on all the rest. Besides, we don’t have a stalemate because all the different theories and interpretations satisfy the theoretical requirements equally well, but because none satisfies them sufficiently. Therefore we may hope that in the future new empirical tests become possible, or the progress of background knowledge allows a new assessment of each competitor’s theoretical virtues, or the open problems are solved by a radically new approach. But even if some of them were to remain unsolved, realists hold that reality is independent of the knowing subject; unlike idealists, therefore, they grant that there might be factual limits to our capacity of knowing the world.

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In: Calosi, C., Graziani, P., Pietrini, D., Tarozzi, G. (eds.), Experience, Abstraction and the Scientific Image of the World. Festschrift for Vincenzo Fano on his 60th Birthday (2021). Milano: Franco Angeli: 185-197

There is a tension in Fano’s works, between a tendency (of positivistic descent) to think that ultimately only science provides authentic knowledge, and the classical idea (revived by phenomenology) that still philosophy, and even metaphysics, have an important role to play. Therefore, the paper explores the following questions in the light of the answers given or suggested by Fano’s writings: Can philosophy yield knowledge? If so, only in dependence of science or autonomously? Can philosophy be naturalized? Is there any non-scientific knowledge? Is there any non-scientific factual knowledge (e.g., ordinary, metaphysical, religious)? Is metaphysics possible? Is non-empirical, i.e. a priori, metaphysics possible? Is “armchair”, i.e. a priori, philosophy possible? Does common sense provide knowledge, and can it be a basis for philosophy? Should we believe the manifest image of the world or the scientific one? 

Axiomathes, 31(2021): 779-789

In an earlier article on this journal I argued that the problem of empirical underdetermination can for the largest part be solved by theoretical virtues, and for the remaining part it can be tolerated. Here I confront two further challenges to scientific realism based on underdetermination. First, there are four classes of theories which may seem to be underdetermined even by theoretical virtues. Concerning them I argue that (i) theories produced by trivial permutations and (ii) “equivalent descriptions” are compatible with the truth of standard theories; instead (iii) “as if” versions of standard theories are much worse from the point of view of theoretical virtues; finally (iv) mathematically intertranslatable theories either may become empirically decidable in the future, or can be discriminated by theoretical virtues, or realists may simply plead ignorance about their claims. Secondly, I consider Stanford’s underdetermination with respect unconceived alternatives, arguing that it essentially relies on the pessimistic meta-induction from the falsity of all past theories. Therefore, it can be resisted by (a) considering the radical advancement of present with respect to past science, and (b) arguing with selective realism that past successful theories, even if false, always included some true components.

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Foundations of Science. Published in OnlineFirst on August, 10, 2020

Many formulations of scientific realism (SR) include some commitment to metaphysical realism (MR). On the other hand, authors like Schlick, Carnap and Putnam held forms of scientific realism coupled with metaphysical antirealism (and this has analogies in Kant). So we might ask: do scientific realists really need MR? or is MR already implied by SR, so that SR is actually incompatible with metaphysical antirealism? And if MR must really be added to SR, why is that so? And which additional arguments scientific realists need to support it? After reviewing and classifying a number of different kinds of realisms, metaphysical and not, I answer that SR and MR are logically independent of each other, so that there is no logical inconsistency in holding SR while rejecting MR. However, I argue that the “no miracle” argument (NMA) not only is the “ultimate” argument for SR, but by the same token it also supports MR. Therefore one cannot effectively defend SR without also subscribing to MR, but this can be done at no additional argumentative cost. I show this by discussing not only the standard version of the NMA, but also three more versions which are not usually considered as such in the literature.

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In: Lyons, T., Vickers, P. (eds.), Contemporary Scientific Realism: The Challenge from the History of Science (2021). Oxford: Oxford University Press: 183-215

Deployment Realism resists Laudan’s and Lyons’ objections to the “No Miracle Argument” by arguing that a hypothesis is most probably true when it is deployed essentially in a novel prediction. However, Lyons criticized Psillos’ criterion of essentiality, maintaining that Deployment Realism should be committed to all the actually deployed assumptions. But since many actually deployed assumptions proved false, he concludes that the No Miracle Argument and Deployment Realism fail. I reply that the essentiality condition is required by Occam’s razor. In fact, there is a simpler formulation of essentiality which escapes Lyons’ criticisms and rescues the No Miracle Argument and Deployment Realism from their purported historical counterexamples: a hypothesis is essential when it has no proper parts (in Yablo’s sense) sufficient to derive the same prediction. Although essentiality so conceived cannot be detected prospectively, this is just natural, and it is not a problem but an advantage for Deployment Realism.

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Axiomathes-Epistemologia, 29(6)(2019): 621-637

The empirical underdetermination of theories is a philosophical problem which until the last century has not seriously troubled actual science. The reason is that confirmation does not depend only on empirical consequences, and theoretical virtues allow to choose among empirically equivalent theories. Moreover, I argue that the theories selected in this way are not just pragmatically or aesthetically better, but more probably (and/or largely) true. At present in quantum mechanics not even theoretical virtues allow to choose among many competing theories and interpretations, but this is because none of them possess those virtues to a sufficient degree. However, first, we can hope for some future advancement (new empirical tests, or new theories). Second, even if no further progress came forth, all the most credited competitors agree on a substantial core of theoretical assumptions. Therefore underdetermination does not show that we cannot be realist on unobservable entities in general, but at most that in particular fields our inquiry may encounter some de facto limits.

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In: Gosh, S., Icard, T. (eds.), Logic, Rationality, and Interaction. LORI 2021 (2021). Dordrecht: Springer: 31-40

The semantic paradoxes and the paradoxes of vagueness (‘soritical paradoxes’) display remarkable family resemblances. In particular, the same non-classical logics have been (independently) applied to both kinds of paradoxes. These facts have been taken by some authors to suggest that truth and vagueness require a unified logical framework (see e.g. [3,5]). Some authors go further, and argue that truth is itself a vague or indeterminate concept (see e.g. [4,7]). Importantly, however, there currently is no identification of what the common features of semantic and soritical paradoxes exactly consist in. This is what we aim to do in this work: we analyze semantic and soritical paradoxes, and develop our analysis into a theory of paradoxicality. The unification of the paradoxes of truth and vagueness we propose here has a wide scope, but for the sake of concreteness we focus on four threevalued logics.

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HOPOS, 11(1)(2021): 282-304

Since the beginning of the twentieth century, prominent authors including Jean Piaget have drawn attention to Edmond Goblot's account of mathematical thought experi¬ments. But his contribution to today's debate has been neglected so far. The main goal of this article is to reconstruct and discuss Goblot's account of logical operations (the term he used for thought experiments in mathematics) and its interpretation by Piaget against the theoretical background of two open questions in today's debate: (1) the re¬lationship between empirical and mathematical thought experiments and (2) the ques¬tion of whether mathematical thought experiments can play a justificatory function in proofs. The main corollary of this analysis is that Piaget's interpretation is seriously flawed and insufficiently appreciative of important theses of Goblot's account. First, Goblot can be easily defended against Piaget's main criticism, and second, Goblot developed ideas about mathematical thought experiments that still deserve attention.

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Axiomathes, 31(2021): 743-762

Unlike empirical science, philosophy has no limit whatever as far as its possible objects are concerned. To say that there is no limit whatever to the possible objects of philosophy is to say that, strictly speaking, it has no object at all and must find its object outside itself, that is, in common sense knowledge and the naturaland human sciences. Against the background of this conception, the paper argues that philosophy of science, as a critical reflection on common sense knowledge and the natural or human sciences, inherits from philosophy in general this two-faced Janus nature, which in the philosophy of science shapes the epistemological status of the discipline in an even more prominent way. To show this in detail, the paper enunciates eleven theses that derive from the intimate connection of unity and distinction that exists between philosophy of science on the one hand and the particular and specialized scientific knowledge on the other.

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Forthcoming in: Wuppuluri, S. (ed.), From Electrons to Elephants and Elections: Saga of Content and Context. Berlin: Springer

In the literature of the last decades, it has become clear that medicine must find some way to combine its scientific and humanistic sides. In other words, an adequate notion of medicine requires an integrative position that mediates between the analytic-reductionist and the normative-holistic tendencies we find therein. This is especially important as these different styles of reasoning separate "illness" (something perceived and managed by the whole individual in concert with their environment) and "disease" (a “mechanical failure” of a biological element within the body). While the demand for an integrative view has typically been motivated by ethical concerns, we claim that it is also motivated, perhaps even more fundamentally, by epistemological and methodological reasons. Evidence-based bio-medicine employs experimental and statistical techniques which eliminate important differences in the ways that conscious humans evaluate, live with, and react to disease and illness. However, it is precisely these experiences that underpin the concepts and norms of bio-medicine. Humanistic disciplines, on the other hand, have the resources to investigate these experiences in an intersubjectively testable way. Medicine, therefore, cannot afford to ignore its nature as a human science (i.e., a science that studies humans); it must be concerned not only with disease and illness, but also with the ways in which patients as persons respond to malady. Insofar as attitudes and expectations influence the criteria of illness and disease, they must be studied as part of the genuine subject matter of medicine as a human science. In general, we urge that this is a necessary step to overcome today's trend to split evidence-based and clinical medicine.)

The British Journal for the Philosophy of Science, 72(2021): 865-891

We put forward a new, ‘coherentist’ account of quantum entanglement, according to which entangled systems are characterized by symmetric relations of ontological dependence among the component particles. We compare this coherentist viewpoint with the two most popular alternatives currently on offer—structuralism and holism—and argue that it is essentially different from, and preferable to, both. In the course of this article, we point out how coherentism might be extended beyond the case of entanglement and further articulated. 

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Mathematical Logic Quarterly, 66(2021): 380-394

We present a theory of stratified truth  𝖲𝖳𝜇  with a μ-operator, where terms representing fixed points of stratified monotone operations are available. We prove that  𝖲𝖳𝜇  is relatively intepretable into Quine's  𝖭𝖥  (or subsystems thereof). The motivation is to investigate a strong theory of truth, which is consistent by means of stratification, i.e., by adopting an implicit type theoretic discipline, and yet is compatible with self-reference (to a certain extent). The present version of  𝖲𝖳𝜇  is an enhancement of the theory presented in [2].

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Forthcoming in: Oliveri, G., Ternullo, C., Boscolo, S. (eds.), Objects, Structures and Logic. Berlin: Springer: 1-22

The problem is whether truth (qua a primitive notion) is to play an independent role in the philosophy of mathematics and in the foundational investigations. The problem is handled by surveying axiomatic theories of truth and their implications, with a main concern for ontological and epistemological issues.

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In: Knox, E., Wilson, A. (eds.), Routledge Companion to the Philosophy of Physics (2021). London: Routledge: 620-631

Symmetry breaking is ubiquitous in almost all areas of physics. It is a feature of everyday phenomena as well as in more specific contexts within physics when considering elementary particles described by quantum fields, quantum mechanical descriptions of condensed matter systems or general relativistic descriptions of the entire universe. Symmetry and symmetry breaking are, in a sense, the two faces of the same coin. In terms of the scientific notion of symmetry, i.e., invariance under a group of transformations, this can be made very precise. On the one hand, a symmetry of a given order can be seen as the result of a higher-order symmetry being broken to a lower-order symmetry, where the order of a symmetry is the order of the corresponding symmetry group. The discovery of the violation of parity, soon followed by the observation of other violations of the discrete space and time symmetries, brought a change in the above “contingency view.”

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Studies in History and Philosophy of Science Part A, 89(2021): 103-113

We discuss Manchak (2009a)'s result that there are locally (but not globally) isometric universes observationally indistinguishable from our own. This theorem makes the epistemic predicament of modern cosmology particularly problematic and the prospects of ever gaining knowledge of the global structure of the universe rather unlikely in the context of general relativity. We argue however that this conclusion is too quick; indeed, Manchak's theorem deploys spacetimes which are not physically reasonable, since they have features which are not the product of any physical process. This ultimately rests on the fact that local isometry between two spacetimes is not sufficient to guarantee that they are both physically reasonable. We propose an additional condition to properly define when a spacetime is physically reasonable, and we show that Manchak's spacetimes do not satisfy this further demand.

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In: Hemmo, M., Shenker, O. (eds.), Quantum, Probability, Logic (2020). Berlin: Springer: 233-256

In a series of related papers and in a book (Healey R. The quantum revolution in philosophy. Oxford University Press, Oxford, 2017b), Richard Healey has proposed and articulated a new pragmatist approach to quantum theory that I will refer to as PQT. After briefly reviewing PQT by putting it into a more general philosophical context, I will discuss Healey’s self-proclaimed quantum realism by stressing that his agent-centered approach to quantum mechanics makes his position rather close to a sophisticated form of instrumentalist, despite his claims to the contrary. My discussion of the possible sources of incompatibility between PQT and the view that agents can be regarded as physical systems (agent physicalism) will allow me to compare Healey’s view of quantum theory with Pitowsky’s. In particular, by focusing on the measurement problem, I will discuss the role of observers and the notion of information in their respective philosophical approach.

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In: Zilioli, U. (ed.), Atomisms in Philosophy: A History From Antiquity To The Present (2020). London: Bloomsbury: 342-355

Quantum Studies: Mathematics and Foundations, 7(2020): 233–245

I begin by examining the question of the quantum limits of knowledge by briefly presenting the constraints of the theory that derive from its mathematical structure (in particular the no-go theorems formulated by von Neumann and Kochen and Specker). I then argue that these theorems reflect on a formal level those practical and experimental settings that are needed to come to know the properties of physical systems. In particular, I discuss some aspects of this relationist and contextualist conception of reality by comparing, in their apparent diversity, Bohr’s holistic, and Rovelli’s relationist interpretation of the formalism, that deep down share a unifying metaphysics of dispositions and propensities. Both interpretations are based on the widely shared fact that quantum mechanics does not describe previously definite quantities. In the final part, I show that, as a consequence of a relationist and perspectival approach to quantum mechanics, the quantum state of the universe regarded as an isolated system cannot be known in principle, so that the universe must be described “from within” by dividing it into two arbitrary parts. This is in fact the only way in which the two systems can exchange information by being physically correlated.

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(2019). Milano: Cortina Editore

La progressiva specializzazione delle nostre conoscenze rende inevitabile il ricorso a forme rappresentative e non dirette di democrazia. È solo in una democrazia rappresentativa che, attraverso libere elezioni, si possono delegare rappresentanti più competenti dei cittadini a trovare i mezzi opportuni per realizzare l’interesse generale. Malgrado inevitabili differenze, ci sono profonde analogie con i meccanismi che regolano la crescita della conoscenza scientifica. Quanto più cresce la conoscenza scientifica, tanto più si specializza e tanto più nascono linguaggi tecnici sempre meno accessibili al grande pubblico. La delega conoscitiva tipica delle comunità scientifiche si riflette nella necessità di affidare il compito di realizzare i nostri fini a rappresentanti più competenti di noi. Preservando la nostra autonomia di scelta, tale delega politica può al contempo impedire la formazione di tecnocrazie, in cui pochi tecnici decidano per tutti.

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Philosophy of Science, 86(4)(2019): 807-813

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In: Campo, A., Gozzano, S. (eds.), The quarrel of time. Einstein vs Bergson (2021). Berlin: de Gruyter: 65-82

By relying on a quotation by F.L. Pogson to be found in the introduction to his translation of Bergson’s Time and Free Will essay, in this paper I discuss Bergson’s theory of the relation between time and free will by analysing three key notion of his philosophy, namely that of creative power of nature, of memory and of duration. In particular, I discuss a possible reinterpretation of his metaphysics by using the growing block model of reality, and his anti-associationist philosophy of mind—by him identified with determinism—which seems to require a finite duration of the present experience. Finally, I propose a reinterpretation of his conception of free action by using Kane’s contemporary approach to the problem.

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Argumenta (2021): 1-18

In the dispute between presentism and eternalism, the affective dimensions of the debate have been somewhat neglected. Contemporary philosophers of time have not tried to relate these ontological positions with two of the most discussed maxims in the history of ethics – “live in the present” vs. “look at your life under the aspect of the eternity” (sub specie aeternitatis)– that since the Hellenistic times have been regarded as strictly connected with them. Consequently, I raise the question of whether the endorsement of one of these two ontological views can make a practical difference in the way we should live.

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Forthcoming in Marmodoro, A., Austin, C., Rosselli, A. (eds.), Time, Law and Free Will. Dordrecht: Springer 

I discuss various attempts to reject the conclusion of the consequence argument as it has been formulated by van Inwagen’s infamous paper (van Inwagen 1983) by showing that neither a Humean compatibilist solution nor an indeterministic metaphysics can avoid the difficulties posed by the argument. Rather, I will suggest that, in order to advance the discussion, it is opportune to connect it to the problem of the status of the laws of nature, that is indispensable to understand the notion of determinism and indeterminism, and in this respect I will defend an ontology of dispositions and capacities.

Forthcoming in: Calosi, C., Graziani, P., Tarozzi, G. (eds.), Experience, Abstraction and the Scientific Image of the World. Festschrift for Vincenzo Fano on his 60th Birthday. Milano: Franco Angeli 

In this paper I review and evaluate Vincenzo Fano’s philosophy from the perspective of the problem of the relationship between physics and metaphysics. In particular, I examine the different ways in which this relationship can be constructed by discussing the important role that the phenomenological constraint play in the question of scientific realism.

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Phenomenology and the Cognitive Sciences, 19(4)(2019): 747-771

We discuss the three dominant models of the phenomenological literature pertaining to temporal consciousness, namely the cinematic, the retentional, and the extensional model. This is first done by presenting the distinction between acts and contents of consciousness and the assumptions underlying the different models concerning both the extendedness and duration of these two components. Secondly, we elaborate on the consequences related to whether a perspective of direct or indirect realism about temporal perceptions is assumed. Finally, we review some relevant findings from the psychology and neuroscience of temporality in order to decide which of the three models of time consciousness is better confirmed from an empirical viewpoint. Depending on the time scale, all three models of temporal consciousness might apply. We specifically argue in favor of an extensional model of time consciousness for the experienced present where the acts and contents of consciousness are both extended. The retentional model might apply to longer time intervals covered by working memory. In addition, a predictive component is highlighted as decisive for an understanding of temporality.

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Synthese, 199(2021): 601-616

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 (Synthese, 2007. https://doi.org/10.1007/s11229-017-1406-z).

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Axiomathes. Online First on August 13, 2020

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.

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In: Tassani, I. (ed.), M.Q. 90. Dualismo, entanglement, olismo - Special issue of Isonomia - Epistemologica, 11(2021): 35-49

In quantum mechanics, unbounded operators correspond to observables like position and momentum. These operators do not have eigenvectors for single value in standard Hilbert space. Fine (1971) and Teller (1979) brought this weird fact to the attention of philosophers. In the following we investigate the different proposed solutions of the problem. In section 2. we follow Weyl’s method of exponentiation of CCR; in part 3. we examine briefly rigged Hilbert space approach; in section 4. we discuss two papers by Halvorson, which face the question from many points of view and propose two different solutions; in section 5. we reject Teller’s too metaphysical proposal; some concluding remarks follow.

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Published in 2021. Rome: Carocci. ISBN: 9788829009480

Esistono infiniti di grandezza diversa e quantità infinitesime? Lo spazio, il tempo e la materia sono infiniti? Perché l'infinito è indispensabile per la comprensione della realtà? Il libro affronta queste domande fornendo una panoramica avvincente e aggiornata del problema in ambiti diversi. Dopo un'immersione nella storia e nella filosofia, illustra i risultati della teoria degli insiemi, dell'analisi matematica e della fisica contemporanea. Attraverso queste discipline, gli autori guidano il lettore nei meandri di un interrogativo che, come ha detto il matematico tedesco David Hilbert, «ha eccitato, più di ogni altro, l'animo umano».

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In: Calosi, C., Graziani, P., Pietrini, D., Tarozzi, G. (eds.), Experience, Abstraction and the Scientific Image of the World. Festschrift for Vincenzo Fano on his 60th Birthday (2021). Milano: Franco Angeli: 277-300

The present paper proposes to study what a geometric construction in the Elements is. To answer this question, the paper will be organized as follow: in §2, some points about the mainstream interpretation of geometric constructions will be discussed and a tentative taxonomy for geometric constructions, analysing an alternative view on them, will be suggested. In §3, arguments in favour of a general account of the role and nature of geometric constructions will be provided. In §4, some general conclusions will be discussed, completing the analysis.

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In: Montuschi, E., Omodeo, P. D. (eds.), Perché studiare la logica? (2020). Roma: Armando Editore: 50-70

Quale ruolo ha la logica formale negli studi della matematica antica? La logica formale può avere per lo storico del pensiero matematco antico  un qualche ruolo come strumento di indagine? Oppure deve essere confinata/riservata ad un diverso ambito di riflessione, magari più filosofico che storico? O addirittura deve essere trascurata nelle indagini storiche?. Il presente contributo intende affrontare queste domande mettendo in luce sotto quali condizioni la logica formale possa essere intesa non solo come un importante strumento di indagine della matematica antica, ma anche come questa applicazione della logica possa essere considerata un interessante campo di sviluppo delle stesse ricerche logiche.  Nel § 1 sarà introdotta la problematica; nel § 2 saranno considerate alcune possibili ragioni di diffidenza relative all’utilizzo della logica formale come strumento di studio dei testi matematici antichi. Nel § 3 saranno invece introdotti alcuni possibili principi e criteri sotto i quali guidare l’utilizzo degli strumenti formali nell’analisi di tali testi. Nel § 4 saranno tratte alcune conclusioni e descritte alcune prospettive di ricerca.

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In: Cleophas, L., Massink, M. (eds.), Software Engineering and Formal Methods. SEFM 2020. Lecture Notes in Computer Science (2021). Berlin: Springer: 214-230

When building artificial agents that have to make decisions, understanding what follows from what they know or believe is mandatory, but it is also important to understand what happens when those agents ignore some facts. This becomes especially relevant when such agents ignore their ignorance, since this hinders their ability of seeking the information they are missing. Given this fact, it might prove useful to clarify in which circumstances ignorance is present and what might cause an agent to ignore that he/she is ignoring. This paper is an attempt at exploring those facts. In the paper, the relationship between ignorance and beliefs is analysed. In particular, three doxastic effects are discussed, showing that they can be seen as a cause of ignorance. The effects are formalized in a bi-modal formal language for knowledge and belief and it is shown how ignorance follows directly from those effects. Moreover, it is shown that negative introspection is the culprit of the passage between simply ignoring a fact and ignoring someone’s ignorance about that fact. Those results could prove useful when artificial agents are designed, since modellers would be aware of which conditions are mandatory to avoid deep forms of ignorance; this means that those artificial agents would be able to infer which information they are ignoring and they could employ this fact to seek it and fill the gaps in their knowledge/belief base.

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Forthcoming in dialectica

Is it possible to name non-symmetric relations? If non-symmetric relations had distinct converses then the difficulty of picking out and distinguishing a non-symmetric relation from its converses would plausibly present an insuperable obstacle to introducing names for them. But, we argue that if non-symmetric relations lack converses then the aforementioned difficulty does not arise. Moreover, we argue, at the semantic level, that English or modest extensions of English have the expressive resources to name non-symmetric relations whose adicity is greater than 2. Van Inwagen’s case that it is impossible to name non-symmetric relations serves as our foil.

In: Zilioli, U. (ed.), Atomisms in Philosophy: A History From Antiquity To The Present (2020). London: Bloomsbury: 445-456

This paper explores the relationship between metaphysical atomism and a form of physics-based structuralism that has recently become popular among philosophers of science. Prima facie, it looks like there is a clear conflict between the two theses. However, this is by no means straightforwardly the case. Once atomism and structuralism are carefully examined, the conflict can in fact be shown to be quite circumscribed, and to depend on theoretical preferences, choices and assumptions that go beyond the core claims that characterise the two positions. It follows that the best way to approach the issue of the relationship between atomism and physics-based structuralism is to avoid sweeping claims and define instead a more nuanced taxonomy.

Philosophy Compass, 15(7)(2020): e12690

This is the first part of a two-tier overview article on fundamentality in metaphysics and the philosophy of physics. It provides an introduction to the notion of fundamentality in metaphysics, as well as to several related concepts. The key issues in the contemporary debate on the topic are summarised, making systematic reference to the most relevant literature. In particular, various ways in which the fundamental entities and the fundamental structure of reality may be conceived are illustrated and discussed. A final brief section looks at the methodological issue of naturalism, paving the way for the survey of fundamentality in the philosophy of physics, which is carried out in the second part.

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Philosophy Compass, 15(10)(2020): 1-14

This is the second part of an overview article on fundamentality in metaphysics and the philosophy of physics. Here, the notion of fundamentality is looked at from the viewpoint of the philosophical analysis of physics and physical theories. The questions are considered (1) whether physics can be regarded as fundamental with respect to other sciences, and in what sense; (2) what the label ‘fundamental physics’ should exactly be taken to mean; (3) on what grounds a particular physical theory should be considered fundamental; (4) what should be regarded as fundamental according to particular theories of physics; and (5) what indications come from contemporary physics concerning the fundamental structure of reality.

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In: Campo, A., Gozzano, S. (eds.), The quarrel of time. Einstein vs Bergson (2021). Berlin: de Gruyter

This paper discusses the view according to which time is not an objective feature of reality, independent of the knowing subject. Rather than attempting to provide an exhaustive historical reconstruction of the debate concerning the (un)reality of time, we will proceed by looking at two paradigmatic and rather different arguments to the effect that time is an illusion: a well-known, purely philosophical, argument due to McTaggart, and an argument (or, maybe better, a family of considerations) coming from contemporary research in physics, in particular quantum gravity. Interesting common aspects will be emphasized and, in closing, a few more general considerations will be made.

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Forthcoming in: De Caro, M., MacArthur, D. (eds.), The Routledge Handbook of Liberal Naturalism. London-New York: Routledge

Liberal naturalism has been recently presented by several authors as the most credible form of philosophical naturalism. Generally speaking, it is the view according to which there are non-scientific entities, and related forms of inquiry, which nevertheless fall under the scope of the ‘natural’. In this paper, I argue that there are a few weaknesses in liberal naturalism as it has been formulated so far in the literature, and suggest some amendments. The result is a view which is 1) primarily based on considerations concerning explanatory usefulness rather than on a fixed differentiation among types of entities; and 2) at the same time stricter and even more liberal in the definition of the domain of non-scientific yet naturalistically acceptable entities. 

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In: Bliss, R., Miller, J. (eds.), Routledge Handbook of Metametaphysics (2020). London: Routledge: 468-479

This chapter illustrates the meaning and motivation of various forms of naturalized metaphysics, and then provide arguments in favour of moderate naturalism about metaphysics. In particular, section 1 will briefly rehearse various ways of understanding metaphysics, and present reasons for adopting a science-oriented approach to it. Section 2 will first consider arguments that have been put forward in favour of radical naturalism, leading to either the elimination of metaphysics or its subordination to science, and then challenge the view on the basis of a trilemma. A case study concerning the ontological nature of quantum entities will be used to guide the reader by means of an example. Section 3 will argue that (a form of ) moderately naturalistic metaphysics sidesteps the trilemma and should in general be preferred by philosophers. Section 4 describes in more detail the sort of moderately naturalistic metaphysics which promises to strike the best balance between science and philosophy. A brief concluding section follows.

In: Glick, D., Marmodoro, A. (eds.), The Foundation of Reality: Fundamentality, Space and Time (2020). Oxford: Oxford University Press: 69-86

Ontic structuralism is a thesis about the fundamental – one whereby relations, not objects, are the basic building blocks of reality. However, there are in fact several dimensions to the structuralism-fundamentality link, and many alternative ways of cashing out the idea that reality is fundamentally structural. Arguably, these require a more systematic and detailed assessment than acknowledged in the literature so far. I provide such an assessment based on considerations coming from both physics and analytic metaphysics, and conclude by pointing to an hitherto quite neglected theoretical option. 

Synthese, 198(2021): 2773-2793

In this paper, it is argued that Aristotelian hylomorphism can supply a useful and informative account of composite entities as these are described by physical theory. In particular, a hylomorphic account of quantum entangled systems is defined in detail, and compared to other alternatives currently on offer—in particular, ontic structural realism. In closing, it is suggested that the view of entanglement outlined here meshes well with a recently proposed ‘coherentist’ conception.

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Forthcoming in dialectica

Traditionally, we distinguish between relations and their converses, e.g., above and below or before and after. This distinction poses a dilemma. Is a relation really distinct from its converse or are they one and the same? There are contrasting arguments that favor one or the other reply, both of them in Russell, who first opted for the former (in Principles of Mathematics) and then for the latter (in Theory of Knowledge). Since then accounts of relations that side with one or the other option have flourished. A hybrid approach to properties and relations (attributes), according to which there are both sparse and abundant attributes is here offered as a way out of the dilemma: distinct converses are acknowledged at the semantic or propositional level of abundant attributes, and rejected at the truthmaker or ontological level of sparse attributes. A positionalist account of relations is also adopted, role positionalism, according to which positions are understood as roles, which are ontological or semantic counterparts of the thematic roles invoked in linguistics. In this way, distinct abundant converses differ because of the different roles involved in them, but they are intimately connected in that they correspond to a single sparse relation.

In: Declos, A., Tiercelin, C. (eds.), La métaphysique du temps: perspectives contemporaines (2021). Paris: Collège de France

According to presentism, there exists only what exists at the present time. Moderate presentism is a version of presentism that emphasizes that only present events exists and admits, as part of the present, past and future times and non-concrete past and future objects. This paper presents moderate presentism with some new details and defends it from the charge that it is not a form of presentism after all. Then, the paper further motivates moderate presentism by showing how it can tackle a recent objection to presentism regarding temporal change, put forward by Lisa Leininger. 

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Philosophy Kitchen, 13(2020): 99-109

The standard account of the micro-structure of time is based on Cantor’s conception of continuity and thus views the time line as consisting of undenumerably many instants ordered by the B-theoretic earlier than relation. This may seem problematic for an A-theory of time such as presentism, according to which only what is present exists, for it seems to leave no room for the instants of a Cantorean time line. This paper defends a version of presentism that can accommodate the Cantorean conception and more generally any approach to the micro-structure of time based on durationless instants.

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In: Zalta, E. N. (eds.), Stanford Encyclopedia of Philosophy

November, 25, 2020 Update

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Axiomathes. Online First on July, 10th, 2021

Categoricalism is a doctrine about properties according to which the dispositional aspects of properties are not essential to them. In opposition to categoricalism, dispositionalism holds that the dispositional aspects of properties are essential to them. In this article, I shall construct a new version of categoricalism that should be favoured over the other existing versions: Semi-Necessitarian Categoricalism. In Section 2 I shall elaborate on the distinction between categoricalism and dispositionalism and single out different ‘shades’ of both doctrines. I shall also illustrate the main advantages and problems that characterize categoricalism. In Section 3 I shall introduce Necessitarian Categoricalism—as it has been recently developed by Alexander Kelly and Deborah Smith, among others. Even if Necessitarian Categoricalism solves the aforementioned problems of categoricalism, it also loses its main advantages. In Section 4 I shall refine this version of Necessitarian Categoricalism, thus developing Semi-Necessitarian Categoricalism. In Section 5 I shall face some objections. Finally, in Section 6, I shall briefly draw some conclusions and compare my account with other accounts.

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Erkenntnis. Online First on May, 28th, 2021

Within some ontological theories, bare or thin particulars are the “kernel” of ordinary substances and they are supposed to clarify some key features of the latter, including their nature. In this article, I wish to offer a new theory of bare particulars, based on an interpretation of properties as modes and on a new reading of the dependence relations holding among entities in terms of respects of dependence. In Section 1, I shall introduce bare particulars, modes and respects of dependence. In Section 2, I shall consider the relationships between bare particulars, clothed particulars (i.e., ordinary substances) and their properties. I shall present two models and I shall examine some of their problems. In Section 3 and in Section 4, I shall present a new model by invoking modes and respects of dependence. This will ground my theory of the relationships between bare particulars, clothed particulars and their properties. Finally, in Section 5, I shall compare my model with the second model presented in Section 2 and, in Section 6, I shall deal with some objections against bare particulars and against my own theory.

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Metaphysica. Published as Ahead of Print on June, 10th, 2022

I shall refine in this article Jaegwon Kim's theory of events by appealing to modes, i.e., particular properties that also depend on their 'bearers' for their identity. Events will turn out to be occurrent modes, i.e., relational modes having further modes and times as their relata. In Section 1 I shall briefly present Kim's theory and some difficulties that affect it. In Section 2, after having made some preliminary assumptions on modes and universals, I shall introduce occurrent modes. In Section 3 I shall show how my theory can deal with the difficulties discussed in Section 1.

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Esercizi Filosofici, 16(1)(2021): 3-25

I shall elaborate in this article on the connection between ficta and metaontological pluralism, i.e., the view according to which there are irreducibly many dependence relations. More precisely, I shall consider the main tenets of an artifactualist theory of ficta and show how they can be expressed from the standpoint of a pluralist theory of dependence that accepts irreducibly many Respect-of-Dependence relations (in short, RD-relations). In Section 2, I shall introduce the artifactualist theory at stake and, in Section 3, I shall recall my theory of RD-relations. In Section 4, I shall show how ficta identity-depend, origin-depend and sustenance-depend on further entities. In Section 5, I shall anticipate and solve three problems. In Section 6, I shall briefly compare my account with other accounts. Finally, in Section 7, I shall draw some conclusions.

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Metaphysica, 22(2)(2021): 223-249

I offer in this article an account of the distinction between intrinsic and extrinsic properties based on the ontology of modes. Modes are particular properties that directly depend for their identity on their "bearers". In Section 1, I shall introduce the ontology of modes. In Section 2, I shall examine the problem of distinguishing between intrinsic and extrinsic properties by considering another, related problem: that of distinguishing between internal and external relations. In Section 3, I shall present my own account and I shall also single out different degrees of intrinsicality and extrinsicality. In Section 4, I shall deal with missing-relatum modes, namely, with modes that lack specific relata, such as Othello's loving someone. I shall introduce three different theories to deal with them. Finally, in Section 5, I shall solve some problems affecting the intrinsic/extrinsic distinction from the standpoint of my account.

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Theoria, 87(3)(2021): 813-836

Masks, interferers, finks, reverse finks, and mimickers are troublesome for powers metaphysics insofar as the latter concedes that there are powers with essential stimuli/activation conditions. In this article, I aim at offering a novel approach for solving this problem. In Section 1, I shall present the problem; and in Section 2, I shall briefly show how it also arises within non‐reductive views of powers. Subsequently, in Section 3, I shall examine the failure of the ceteris paribus solution. The pars construens will begin in Section 4, where I shall distinguish between the activation conditions, the background conditions, and the possession conditions of a power. Within each category, I shall draw further distinctions. In Section 5, I shall demonstrate how such distinctions may ground a solution to our problem. Finally, in Section 6, I shall anticipate and reply to four objections.

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Philosophia. Online First on January, 6th, 2022

In this article, I aim at showing how powers may ground different types of probability in the universe. In Section 1 I single out several dimensions along which the probability of something can be determined. Each of such dimensions can be further specified at the type-level or at the token-level. In Section 2 I introduce some metaphysical assumptions about powers. In Section 3 I show how powers can ground single-case probabilities and frequency-probabilities in a deterministic setting. Later on, in Section 4, I move to a theoretical framework where the falsity of determinism is assumed. Within such a framework, I first argue that some probabilities are grounded on basic powers (i.e., powers whose activation is not determined by anything else). Moreover, in Section 5, I introduce tendencies and suggest that they are endowed with specific degrees of activation that may change over time. Such degrees explain why tendencies are more likely to be activated than non-activated, or vice versa. In Section 6 I compare my account of tendencies with other accounts. Finally, in Section 7, I anticipate some general objections against my account – objections that it shares with propensity-accounts of probability – and against degrees of activation of tendencies.

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Acta Analytica. Online First on March, 11th, 2022

Relationism holds that objects entirely depend on relations or that they must be eliminated in favour of the latter. In this article, I raise a problem for relationism. I argue that relationism cannot account for the order in which non-symmetrical relations apply to their relata. In Section 1, I introduce some concepts in the ontology of relations and define relationism. In Section 2, I present the Problem of Order for non-symmetrical relations, after distinguishing it from the Problem of Differential Application. I also examine four main existing strategies to solve it. In Section 3, I develop my argument. The first step consists in arguing that—among those strategies—relationism can only accept directionalism. The second step consists in arguing that directionalism is affected by a serious problem: the Problem of Converses. I also show that relationists who embrace directionalism cannot solve this problem. In Section 4, I introduce and rebut several strategies on behalf of relationists to cope with my argument. In Section 5, I briefly draw some conclusions.

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Studia Neoaristotelica, 18(1)(2021): 31-68

In this article I discuss several apparent counterexamples to the asymmetry of ontological dependence. These counterexamples were introduced in discussions about grounding, but they can affect every theory of ontological dependence. I show that, if one adopts metaontological pluralism (i.e., the view according to which there are many dependence relations), one has some advantages when it comes to defending the asymmetry of dependence. In Section 1, I introduce metaontological pluralism and my own version of it, which is based on Respect-of-Dependence Relations (RD-Relations). I then single out five strategies to deal with apparent cases of symmetric dependence and show that only two of them are available to metaontological pluralists. In Sections 2, 3, and 4 I deal with cases of symmetric dependence by adopting these strategies. Finally, in Section 5, I anticipate and reply to three objections against my account.

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Acta Analytica, 36(3)(2021): 341-355

The thesis I wish to argue for in this article is that spatial relations such as occupying (a certain place) and being 1 km distant from (something) are external. In Section 1, I shall introduce the distinction between external and internal relations and some other basic concepts in the ontology of relations. Afterwards, in the subsequent sections, I shall deal with different theories of space: substantivalism and relationism (Section 2); the spatial property theory (Section 3); super-substantivalism and super-relationism (Section 4); spatial essentialism (Section 5). I shall demonstrate that, in all such theories, spatial relations need to be considered external. Otherwise, unacceptable consequences or spatial properties that are non-relational by mere façon de parler are in order. Finally, in Section 6, I shall briefly tackle length contraction in special relativity theory.

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Analytic Philosophy, 62(4)(2021): 336-358

In this article, I develop a metaphysical account of final causes grounded on contemporary powers metaphysics. After having presented some key elements of an Aristotle-inspired teleology, i.e., the study of final causes within Aristotelian tradition, I introduce powers. Moreover, I present some theses about their nature and features. Afterward, I distinguish between two kinds of powers that are expected to play the roles traditionally attributed to final causes: weakly teleological powers and strongly teleological powers. Weakly teleological powers are those powers that ground the possession of all the other powers of a substance. Strongly teleological powers are those powers that ground the activation of all the other powers of a substance. Within this framework, I then develop some options to deal with human teleology, i.e., with the study of human behavior in light of final causes. Finally, in the last Section, I briefly compare my account with other accounts of teleology and of specific sorts of powers that somehow resemble teleological powers.

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Forthcoming in Knnuttila, T., Carillo, N., Kosinken, R. (eds.), The Routledge Handbook of Philosophy of Scientific Modeling. London-New York: Routledge

Models are often described as representations of target systems that are of scientific interest. Although they are seldom addressed, target systems are an important topic in their own right. Targets have been addressed as data models and as subsets of features of a spatiotemporally located region of the world, among other characterizations. What makes an adequate target and how to obtain it are important methodological questions in science that still need more attention from philosophers.

Journal of Symbolic Computation, 97(2020): 31-55

In the current Information Society the organization of the information is key to ensure the information safekeeping and retrieval. It is of utmost importance that each and every user can find the information he/she is looking for, presented in such a way that best fit his/her needs. Geometry is no exception, the servers of geometric information should be easily and successfully searchable. By classifying the information contained in the servers of geometric information accordingly to several taxonomies, it will be possible to begin applying filters to the users' queries, adjusting them to the perceived user's needs. Having that in mind, the introduction of an adaptive filtering mechanisms into servers of geometric information is considered. Different taxonomies for different goals are presented. For educational purposes, a classification like Common Core Standards should be considered, but other considerations like the complexity of the construction, the provability, by a geometry automatic theorem prover, of a given conjecture and the readability of the resulting proof, should be taken into account. For research in automated deduction purposes, other issues must be considered, e.g. efficiency and applicability of the available automated provers. To validate the usefulness of these taxonomies it will be used, as a case study, their application to a server of geometric information. In particular, Thousands of Geometric problems for geometric Theorem Provers will be considered. TGTP is a Web-based repository of geometric problems being developed to support the testing and evaluation of geometric automated theorem proving systems. Using this system it will be analysed how the taxonomies could help to tailor the search for information adapted to each and every geometer.

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