Vincenzo Fano

Harrigan and Spekkens, introduced the influential notion of an ontological model of operational quantum theory. Ontological models can be either “epistemic” or “ontic.” According to the two scholars, Einstein would have been one of the first to propose an epistemic interpretation of quantum mechanics. Pusey et al. showed that an epistemic interpretation of quantum theory is impossible, so implying that Einstein had been refuted. We discuss in detail Einstein’s arguments against the standard interpretation of QM, proving that there is a misunderstanding in Harrigan and Spekkens’ attribution of an epistemic perspective to Einstein, whose point of view was actually statistical, but in a quasi-classical sense.

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.

Abstract. An opposition between two conceptions of our knowledge of the external world is outlined. On the one hand physicists, like Dirac and Heisenberg, maintain that only what Physics considers real is actually real. On the other hand, psychologists, like Metzger, Kanizsa and Bozzi, believe that every sensible content is real, so that the Psychology of perception is the real Physics. We attempt to sketch a critical perspective, based on a reasonable criterion, in order to prospect a different solution to this question.

The present paper has three closely related aims. We first argue that Agazzi’s scientific realism about Quantum Mechanics is in line with Selleri’s and Tarozzi’s proposal of Quantum Waves. We then go on to formulate rigorously different metaphysical principles such as property compositional determinateness and mereological extensionalism. We argue that, contrary to widespread agreement, realism about Quantum Mechanics actually refutes only the former. Indeed we even formulate a new quantum mechanical argument in favor of extensionalism. We conclude by noting that, given the results of the work, Agazzi’s particular attitude towards Quantum Mechanics is still one of the most promising theoretical perspectives.

The arrow paradox is an argument purported to show that objects do not really move. The two main metaphysics of motion, the At–At theory of motion and velocity primitivism, solve the paradox differently. It is argued that neither solution is completely satisfactory. In particular it is contended that there are no decisive arguments in favor of the claim that velocity as it is constructed in the At–At theory is a truly instantaneous property, which is a crucial assumption to solve the paradox. If so the At–At theory faces the threat that most of our physical theories turn out to be non-Markovian. Finally it is considered whether all those threats and paradoxes are dispelled if only a new metaphysics of persistence is taken into account, namely four-dimensionalism.

Nella sua straordinaria opera scientifica, Franco Selleri si è sempre opposto alla rinuncia alla comprensione della struttura della realtà e della natura degli oggetti fisici, che egli considera come l’elemento caratterizzante delle principali teorie della fisica del Novecento e che è stata stigmatizzata da Karl Popper come tesi della “fine della strada in fisica”. Sin dalla fine degli anni ’60, egli ha sviluppato quella riflessione critica nei confronti delle teorie fondamentali della fisica moderna, in particolar modo della teoria delle particelle elementari e della meccanica quantistica, e in un secondo tempo delle teorie relativistiche, che contraddistingue il suo programma di ricerca. Nel corso della sua intensa e infaticabile attività scientifica, Selleri è entrato in proficuo contatto con molti grandi fisici e filosofi della scienza, instaurando un intenso dialogo critico con Louis de Broglie, John Bell e Karl Popper. Le sue originali e non convenzionali ricerche lo hanno portato a risultati significativi non solo nell’ambito dei fondamenti della fisica, ma anche della storia e della filosofia della fisica. Per questo abbiamo voluto dedicare un numero speciale di Isonomia al nostro impareggiabile amico e collega, sia per la sua passione instancabile e la sua profonda conoscenza dei fondamenti formali, concettuali e filosofici delle teorie della fisica contemporanea, sia e forse ancor più come maestro di una prospettiva perennemente critica che egli ha sempre seguito e proposto con particolare rigore ed estrema determinazione.

This paper deals with those time travels mostly considered by physics, namely those in the form of the so-called closed timelike curves. Some authoritative scholars have raised doubts about the status of these journeys as proper time travels. By using David Lewis’ famous definition of time travels proposed in 1976, we show that this proper status may actually be recovered, at least in some cosmological contexts containing spacetime regions, such as those concerning black holes described by the Kerr–Newman metric, that allow the formation of local closed curves. But, the mathematical incompatibility between ordinary black hole solutions to Einstein field equations and the cosmological solutions induces us to take into consideration the more general issue pertaining to the slippery interplay between models related to local and global aspects of the world, highlighting, in particular, the different notions of time that these domains inevitably imply. This leads us to think that time is not a univocal entity of the world, but is a scale-related characteristic which claims the adoption, when investigating its ontological status, of a sort of regional approach. We also briefly dwell upon the most appropriate form of realism that such a kind of dispute between local and global models may involve.

In this paper, we address an infamous argument against divisibility that dates back to Zeno. There has been an incredible amount of discussion on how to understand the critical notions of divisibility, extension, and infinite divisibility that are crucial for the very formulation of the argument. The paper provides new and rigorous definitions of those notions using the formal theories of parthood and location. Also, it provides a new solution to the paradox of divisibility which does not face some threats that can possibly undermine the standard Lebesgue measure solution to such a paradox.

The present investigation reformulates a few Brentanian ideas concerning what is mental. In particular, an attempt to define the categorial structure implicit in the notion of consciousness and in that of inner perception, keeping in mind their connections with external perception and with unconscious, is outlined. Within the mental field is observed a formal violation of some elementary rules of ontology and mereology, and such violation can be interpreted in terms of an infinite multiplicity of the mental field itself.

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 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.

Quantum mechanics is often credited for having clearly shown that the whole is something over and above the sum of its parts. We want to assess whether this is really the case, and if so, in what sense. We argue that there is indeed a sense in which this is true. Our argument is that even a weak realistic interpretation of quantum mechanics renders a particular metaphysical principle about property instantiation, that we label Property Compositional Determinateness, untenable. Yet there is another metaphysical principle about composition that is usually maintained to imply that composition of parts exhausts the whole they are part of, namely Mereological Extensionalism. In this case, contrary to widespread agreement, we argue that quantum mechanics does not provide any reason, either direct or indirect, to abandon such principle.

A draft of a possible comparison between the use made of mathematics in classical field theories and in quantum mechanics is presented. Hilbert’s space formalism, although not only elegant and powerful but intuitive as well, does not give us a spatio-temporal representation of physical events. The picture of the electromagnetic field as an entity which is real in itself– i.e., as a wave without support – fostered by the emergence of special relativity can be seen as the first step, favored by many physicists and philosophers, of a gradual “escape” from intuition into a purely mathematical representation of the external world. After the introduction, in recent theoretical physics, of fiber bundle formalism the classical notion of field acquires a new spatio-temporal intuitiveness. This intuitiveness is clearly foreshadowed in the Kantian and Meinongian analysis of the notion of magnitude. At the end of the paper we show that, contrary to what happens in quantum mechanics, mathematics plays a truly explicative role in general relativity, without any loss of spatio-temporal intuitiveness.

Abstract: It seems that from an epistemological point of view comparative probability has many advantages with respect to a probability measure. It is more reasonable as an evaluation of degrees of rational beliefs. It allows the formulation of a comparative indifference principle free from well known paradoxes. Moreover it makes it possible to weaken the principal principle, so that it becomes more reasonable. But the logical systems of comparative probability do not admit an adequate probability updating, which on the contrary is possible for a probability measure. Therefore we are faced with a true epistemological dilemma between comparative and quantitative probability.

We present a new thought experiment that raises a threat for Minimal Physicalism, i.e. the thesis according to which mental properties supervene on physical properties. Our proposal is an example of the so called hard problems in philosophy of mind, in particular the problem of maximal consciousness. We do not however presuppose anything about its very nature apart from the minimal, weak assumption that it is determined by first order mental properties. We argue that either Minimal Physicalism is unable to give an adequate account of the new thought experiment we present or has to explain the fact that two numerically distinct but physically indistinguishable individuals have different maximal consciousness due to their spatial location. We contend that this last conclusion is strongly at variance with our contemporary scientific image of the world.