The main aim of our paper is to show that interpretative issues belonging to classical General Relativity (GR) might be preliminary to a deeper understanding of conceptual problems stemming from on-going attempts at constructing a quantum theory of gravity. Among such interpretative issues, we focus on the meaning of general covariance and the related question of the identity of points, by basing our investigation on the Hamiltonian formulation of GR. In particular, we argue that the adoption of a peculiar gauge-fixing (...) within the canonical reduction of ADM metric gravity may yield a new solution to the debate between substantivalists and relationists, by suggesting a \emph{tertium quid} between these two age-old positions. Such a third position enables us to evaluate the controversial relationship between entity realism and structural realism in a well-defined case study. After having indicated the possible developments of this approach in Quantum Gravity, we discuss the structuralist and holistic features of the class of spacetime models that are used in the above mentioned canonical reduction. (shrink)

A critical re-examination of the history of the concepts of space (including spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlighting the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein “giving up the extensional continuum … is like to breathe in airless space”). On the other hand, Planck’s discovery of the atomization of action leads to the fundamental recognition (...) of an ontology of non-spatial, abstract entities (Quine) for the quantum level of reality (QT), as distinguished from the necessarily spatio-temporal, experimental revelations (measurements). The elementary quantum act (measured by Planck’s constant) has neither duration nor extension, and any genuinely quantum process literally does not belong in the Raum and time of our experience. As Heisenberg stresses: “Während also die klassische Physik ein objectives Geschehen in Raum and Zeit zum Gegenstand hat, für dessen Existenz seine Beobachtung völlig irrelevant war, behandelt die Quantentheorie Vorgänge, die sozusagen nur in den Momenten der Beobachtung als raumzeitliche Phänomene aufleuchten, und über die in der zwischenzeit anschaulische physikalische Aussagen sinloss sind”. An admittedly speculative, hazardous conjecture is then advanced concerning the relation of such quantum ontology with the role of the pre-phenomenal continuum (Husserl) in the perception of macroscopically distinguishable objects in the Raum and time of our experience. Although rather venturesome, it brings together important philosophical issues. Coherently with recent general results in works on the foundations of QT, it is assumed that the linearity of quantum dynamical evolution does not apply to the central nervous system of living beings at a certain level of the evolutionary ramification and at the pre-conscious stage of subjectivity. Accordingly, corresponding to the onset of a non-linear dynamic evolution, a ‘primary spatial’ reduction is ‘continually’ taking place, thereby constituting the neural precondition for the experience of distinguishable macroscopic objects in the continuous spatial extension. While preventing the theoretically possible quantum superpositions of macroscopic objects from being perceivable by living beings, the ‘primary reduction’ has no effect on the standard processes concerning quantum level entities involved in laboratory man-made experiments. In this connection, an experimental check which might falsify the conjecture is briefly discussed. The approach suggested here, if sound, leads to a naturalization of that part of Kant’s Transcendental Aesthetics than can survive the Euclidean catastrophe. According to such naturalized transcendentalism, “space can well be transcendental without the axioms being so”, in agreement with a well-known statement by Boltzman. Finally, as far as QT is concerned, the conjecture entails that a scheme for quantum measurement of the von Neumann type cannot even ‘leave the ground’, vindicating Bohr’s viewpoint. A quantum theory of measurement, in a proper sense, turns out to be unnecessary and in fact impossible. (shrink)

”The last remnant of physical objectivity of space-time” is disclosed in the case of a continuous family of spatially non-compact models of general relativity. The physical individuation of point-events is furnished by the autonomous degrees of freedom of the gravitational field, which represent -as it were -the ontic part of the metric field. The physical role of the epistemic part is likewise clarified as embodying the unavoidable non-inertial aspects of GR. At the end the philosophical import of the Hole Argument (...) is substantially weakened and in fact the Argument itself dis-solved, while a specific four-dimensional holistic and structuralist view of space-time emerges, including elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real temporal change: this gives new evidence to the fact that statements like the frozen-time character of evolution, as other ontological claims about GR, are model dependent. (shrink)

"The last remnant of physical objectivity of space-time" is disclosed, beyond the Leibniz equivalence, in the case of a continuous family of spatially non-compact models of general relativity. The physical individuation of point-events is furnished by the intrinsic degrees of freedom of the gravitational field, (viz, the "Dirac observables") that represent - as it were - the "ontic" part of the metric field. The physical role of the "epistemic" part (viz. the "gauge" variables) is likewise clarified. At the end, a (...) peculiar four-dimensional "holistic and structuralist" view of space-time emerges which includes elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real "temporal change" and thereby provide a counter-example to the thesis of the "frozen-time" picture of evolution. (shrink)

The Hamiltonian structure of General Relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: i) the "Hole Argument" can be bypassed by means of a specific "physical individuation" of point-events of the space-time manifold M^4 in terms of the "autonomous degrees of freedom" of the vacuum gravitational field (Dirac observables), while the "Leibniz equivalence" is reduced to differences in the "non-inertial appearances" (connected to gauge variables) of (...) the same phenomena. ii) the chrono-geometric structure of a solution of Einstein equations for given, gauge-fixed, initial data (a "3-geometry" satisfying the relevant constraints on the Cauchy surface), can be interpreted as an "unfolding" in mathematical global time of a sequence of "achronal 3-spaces" characterized by "dynamically determined conventions" about distant simultaneity. This result stands out as an important conceptual difference with respect to the standard chrono-geometrical view of Special Relativity (SR) and allows, in a specific sense, for an "endurantist" interpretations of ordinary physical objects in GR. (shrink)

This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called "Hole Argument" in general relativity. Such achievements include: 1) the analysis of the "Hole" phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the "weak" ADM energy; 2) a re-interpretation of "active" diffeomorphisms as "passive and metric-dependent" (...) dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (up to now unknown) connection to gauge transformations on-shell; understanding such connection also enlightens the real content of the Hole Argument or, better, dis-solves it together with its alleged "indeterminism"; 3) the utilization of the Bergmann-Komar "intrinsic pseudo-coordinates", defined as suitable functionals of the Weyl curvature scalars, as tools for a peculiar gauge-fixing to the super-hamiltonian and super-momentum constraints; 4) the consequent construction of a "physical atlas" of 4-coordinate systems for the 4-dimensional "mathematical" manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent "Dirac observables"). Such construction embodies the "physical individuation" of the points of space-time as "point-events", independently of the presence of matter, and associates a "non-commutative structure" to each gauge fixing or four-dimensional coordinate system; 5) a clarification of the multiple definition given by Peter Bergmann of the concept of "(Bergmann) observable" in general relativity. This clarification leads to the proposal of a "main conjecture" asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) "change" in the observable quantities of general relativity. 6) a clarification of the physical role of Dirac and gauge variables as their being related to "tidal-like" and "inertial-like" effects, respectively. This clarification is mainly due to the fact that, unlike the standard formulations of the equivalence principle, the Hamiltonian formalism allows to define notion of "force" in general relativity in a natural way; 7) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a "standard of space-time" more or less like atomic clocks define standards of time. We conclude that, besides being operationally essential for building measuring apparatuses for the gravitational field, the role of matter in the non-vacuum gravitational case is also that of "participating directly" in the individuation process, being involved in the determination of the Dirac observables. This circumstance leads naturally to a peculiar new kind of "structuralist" view of the general-relativistic concept of space-time, a view that embodies some elements of both the traditional "absolutist" and "relational" conceptions. In the end, space-time point-events maintain a "peculiar sort of objectivity". Some hints following from our approach for the quantum gravity programme are also given. (shrink)

For the past two decades, Einstein's Hole Argument (which deals with the apparent indeterminateness of general relativity due to the general covariance of the field equations) and its resolution in terms of "Leibniz equivalence" (the statement that pseudo-Riemannian geometries related by active diffeomorphisms represent the same physical solution) have been the starting point for a lively philosophical debate on the objectivity of the point-events of space-time. It seems that Leibniz equivalence makes it impossible to consider the points of the space-time (...) manifold as physically individuated without recourse to dynamical individuating fields. Various authors have posited that the metric field itself can be used in this way , but nobody so far has considered the problem of explicitly distilling the "metrical fingerprint" of point-events from the gauge-dependent elements of the metric field. Working in the Hamiltonian formulation of general relativity, and building on the results of Lusanna and Pauri (2002), we show how Bergmann and Komar's "intrinsic pseudo-coordinates" (based on the value of curvature invariants) can be used to provide a physical individuation of point-events in terms of the true degrees of freedom (the "Dirac observables") of the gravitational field, and we suggest how this conceptual individuation could in principle be implemented with a well-defined empirical procedure. We argue from these results that point-events retain a significant kind of physical objectivity. (shrink)

The so-called “New Atheism” is a relatively well-defined, very recent, still unfold- ing cultural phenomenon with import for public understanding of both science and philosophy. Arguably, the opening salvo of the New Atheists was The End of Faith by Sam Harris, published in 2004, followed in rapid succession by a number of other titles penned by Harris himself, Richard Dawkins, Daniel Dennett, Victor Stenger, and Christopher Hitchens.

This chapter sets aside the question of whether a Singularity will occur, to focus on the closely related issue of MU, specifically as presented by one of its most articulate proponents, David Chalmers. The fundamental premise of Chalmers' arguments about MU is some strong version of the Computational Theory of Mind (CTM). The chapter proceeds in the following fashion: first, it recalls Chalmers' main arguments; second, it argues that the ideas of MU and CTM do not take seriously enough the (...) fact that consciousness is a biological phenomenon, as pointed out in different contexts by both John Searle and Jerry Fodor, among others; third, it stipulates for the sake of argument that MU is somehow possible, and show that it would, at best, amount to a sort of mind cloning, but most certainly not to a preservation of anyone's consciousness in a medium different from one's own brain. (shrink)

Lettura prospettica di un caposaldo del pensiero hobbesiano: il sorgere del rapporto tra l'uomo ed il potere, tra la naturale condizione umana e la nozione di civiltà, attraverso due frammenti particolarmente rappresentativi della concezione hobbesiana del passaggio dallo stato di natura alla civiltà: il tredicesimo capitolo del Leviathan, sulla condizione naturale dell'uomo, ed il quinto capitolo, sulle cause ed origini della civitas, del De cive, giacché la mera esistenza dell'uomo ed il suo riconoscimento di una legge naturale, a giudizio di (...) Hobbes, non implica affatto necessariamente una qualsiasi forma consolidata di organizzazione sociale. Sebbene il De cive (pubblicato in latino nel 1642 e, in inglese, nel 1651) preceda cronologicamente il Leviathan (pubblicato, viceversa, dapprima in inglese, nel 1651, poi in latino, nel 1668), nell'ordine logico dell'esposizione qui presentata, il brano del Leviathan può essere considerato propedeutico al quinto capitolo del De cive, delineandone i presupposti, segnatamente la condizione di continuo pericolo per tutti causata dallo stato generale di reciproca guerra, che costituisce forse l'aspetto più noto (e frainteso) del pensiero hobbesiano. Per una migliore comprensione dei testi e delle differenti (spesso opposte) interpretazioni cui hanno dato vita, si è ritenuto di proporre, per quanto concerne i brani di Hobbes, tanto la loro traduzione in lingua italiana quanto le stesure originali in latino e inglese, presentate con i testi a fronte; tale scelta fornisce l'opportunità di osservare l'accurata scelta di alcuni dei vocaboli chiave della filosofia di Hobbes, la cui trasposizione da una lingua all'altra è stata spesso causa di fraintendimenti o volgarizzazioni in tutto o in parte ingiustificate. Allo scopo di offrire una più completa prospettiva del pensiero hobbesiano delineato nei brani selezionati, si è ritenuto di affiancare ad essi dei frammenti di interpreti novecenteschi (con delle sintetiche schede bio-bibliografiche) di alcuni concetti formulati da Hobbes e, segnatamente, di F. Tönnies, M. Horkheimer, L. Strauss, C. Schmitt, T. Parsons, N. Bobbio, H. Warrender. (shrink)

I submit that philosophy makes progress, but it does so in a way that is distinct from the sense in which the word applies to science, and is more akin to what happens in allied fields such as mathematics and logic. I develop a model of philosophy as “evoking” (to use L. Smolin's term) a series of peaks in conceptually defined but empirically constrained, landscapes, or what N. Rescher calls “aporetic clusters.” I also discuss empirical evidence for the existence of (...) such clusters, following a statistical survey of philosophers’ views about their own field, carried out by D. Bourget and D.J. Chalmers. (shrink)

Lezioni tenute da Massimo Fagioli all'Università di Chieti-Pescara nel 2008.

Written between 1978 and 2006, these essays engagingly address the most hidden tradition in European political thought: the unpolitical.

17 lessons in the discipline of desire -- 18 lessons in the discipline of action -- 17 lessons in the discipline of assent.

Decision-making assisted by algorithms developed by machine learning is increasingly determining our lives. Unfortunately, full opacity about the process is the norm. Would transparency contribute to restoring accountability for such systems as is often maintained? Several objections to full transparency are examined: the loss of privacy when datasets become public, the perverse effects of disclosure of the very algorithms themselves, the potential loss of companies’ competitive edge, and the limited gains in answerability to be expected since sophisticated algorithms usually are (...) inherently opaque. It is concluded that, at least presently, full transparency for oversight bodies alone is the only feasible option; extending it to the public at large is normally not advisable. Moreover, it is argued that algorithmic decisions preferably should become more understandable; to that effect, the models of machine learning to be employed should either be interpreted ex post or be interpretable by design ex ante. (shrink)

In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path which lies at the heart of the deBroglie-Bohm “ pilot-wave” interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths. This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of (...) the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton–Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized. (shrink)

Topics in Cognitive Science, Volume 14, Issue 1, Page 143-162, January 2022.

In public philosophy, the question is how best to engage people with the fascinating yet complex mix of science and philosophy that underpins discussions of the good life. Reasoning about the good life implies adopting – consciously or not – a philosophy of life. For instance, the authors briefly compare three paths to the good life: Christianity (a religion), Stoicism (a philosophy), and Buddhism (which has both religious and philosophical strands). They discuss some of the issues that come up when (...) they engage in public philosophy about the good life by way of an in‐depth look at a particular example. Lastly, the authors explore a number of approaches to philosophical public discourse on these themes, based on their experiences as a public philosopher as well as on the published literature. (shrink)

Provides a broad, comprehensive, and yet concise introduction to Islamic philosophy covering a vast subject area in a relatively short book.

Conceived by Wagner as a way to recover the synthesis of arts at the core of the Greek tragedy, the Gesamtkunstwerk played a big role in post-Romantic aesthetics. This book revisits the "total work of art" as a variation of intermediality that captures the digital age's principle of open textuality through complex interplay and synergy of media.

The book is a critical reading of all the major writings on history by Benedetto Croce, which has never been attempted before. The study is not a summary but a critical assessment based on the relevance of Croce's aesthetics for his concept of history. My account differs from previous studies which are characterized by the exclusion or by minimizing the aesthetic, a process I call "defiguring." Within this framework Croce's concept of history is not a total philosophy but only an (...) allegory of history: a narrative of the impossibility of history. In other words, Croce's history is not unlike his definition of Hegel's Phenomenology or his system as fiction. It is also not unlike Vico's New Science, the other major influence on Croce's concept of history, as an imaginative science. My study realigns Croce's concept of history with Hegel's and Vico's to redefine, thanks to Croce, how we understand history. (shrink)