Vincenzo Fano

Mechanical intelligence and Godelian Arguments

In the present paper we attempt to evaluate the legacy of Turing’s ideas concerning the consequences of Godel’s Incompleteness Theorems for philosophy of mind. These Theorems were almost immediately seen as tools for rejecting the mechanistic thesis. Turing himself took this fact to be an implication of the theorems; beside him, P. Rosenbloom, G. Kemeny and E. Nagel and J.R. Newman, in the 1950’s, developed argumentations based on the idea that Godel’s Theorems could provide a logical tool to refute the philosophical thesis of mechanism. Despite this tradition, a famous Godelian anti-mechanists argument is usually associated with the name of the English philosopher John Randolf Lucas (1961). This issue was addressed by Godel already in 1951, but his considerations became known only in recent times, in the 1990’s, when many scholars were already aware of Benacerraf’s (1967) and Chihara’s (1972) analyses on it. Benacerraf and Chihara, in fact, discussing Lucas’ paper, arrived at the same conclusions as Godel in the fifties, but in a more formal way. Lucas’s argument was rejuvenated by R. Penrose (1989; 1994): he formulated and defended a version of it, but without mentioning (or perhaps knowing of) Benacerraf’s and Chihara’s papers. After Penrose’s provocative arguments many scholars analyzed the questions, in particular S. Shapiro (1998) shed light on it. In the present paper we offer a broad and clear reconstruction of the debate and the contributions made to it by different authors, its reemergence at different times in similar forms, the necessary philosophical premises of Godel’s argument and more in general of Godelian arguments. Nel presente lavoro esamineremo l’eredita delle idee di Turing in riferimento alle conseguenze per la filosofia della mente dei Teoremi di Incompletezza di Godel. Questi teoremi sono stati quasi immediatamente visti come strumenti per confutare la tesi meccanicista. Turing per primo analizzo tale implicazione dei teoremi; dopo di lui pensatori come P. Rosenbloom, G. Kemeny e E. Nagel e J.R. Newman, nel 1950, svilupparono argomentazioni basate sull’idea che i Teoremi di Godel avrebbero potuto fornire uno strumento di logica per confutare la tesi filosofica del meccanicismo. Nonostante questa tradizione, il piu famoso argomento (godeliano) antimeccanicista e di solito associato al nome del filosofo inglese John Randolf Lucas (1961). Si noti che questa implicazione e stata indagata dallo stesso Godel nel 1951, ma le sue conside- razioni divennero note solo in tempi recenti, gli anni novanta dello scorso secolo, quando tuttavia molti studiosi erano venuti gia a conoscenza degli studi di Benacerraf (1967) e Chihara (1972) che analizzando l’articolo di Lucas arrivarono (in modo piu formale) alle stesse conclusioni alle quali Godel era pervenuto negli anni Cinquanta. L’argomento di Lucas e stato riproposto da R. Penrose (1989, 1994) il quale ha formulato e difeso una versione di esso, ma senza menzionare i lavori di Benacerraf e Chihara. Dopo l’argomento provocatorio di Penrose molti altri studiosi hanno analizzato la questione, in particolare S. Shapiro (1998). Nel presente lavoro, offriamo una ricostruzione ampia e chiara del dibattito e dei contributi ad esso apportati da diversi autori, il suo riemergere in tempi diversi in forme simili, le necessarie premesse filosofiche dell’argomento di Godel e piu in generale degli argomenti godeliani.

Space and time : a priori and a posteriori studies

The articles in this volume focus on the ontology of space and time, including the themes of substantivalism vs. relationism, continuity vs. discreteness, and time travel. In the current debate on these issues, there is a tendency to separate too rigidly between a priori and a posteriori approaches. This volume aims to bridge the gap between these two perspectives, showing the fruitfulness of combining them to the greatest extent possible.

A Threat for Physicalism : a New Gedankenexperiment

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 (i) either Minimal Physicalism is unable to give an adequate account of the new thought experiment we present or (ii) 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. Presentiamo qui un nuovo esperimento mentale, che costituisce un problema per il fisicalismo, inteso come la tesi secondo cui le proprieta mentali sopravvengono su quelle fisiche. Mostriamo che se il fisicalismo fosse vero, dovremmo spiegare il fatto che due individui numericamente distinti ma fisicamente indistinguibili hanno coscienza diversa a causa della loro differente collocazione spaziale. Questa conclusione e fortemente in contrasto con la nostra attuale immagine scientifica del mondo.

Is a Space Interval a Set of Infinite Points? A Very Old Question

In this paper we will address the question whether a space interval is a set of infinite points . It is a very old problem, but despite its age it is still a live issue, and one we have to confront. We will analyze some topics regarding this question using the most influential objections against it, i.e. The Large and the Small paradox (in particular its Small Horn). We will consider classical contemporary reformulations of the argument (Grunbaum in Philosophy of Science 19:280–306, 1952; Grunbaum in Modern science and Zeno’s paradoxes. Allen and Unwin, London, 1968) and the possible ‘solutions’ to it. Finally, we will propose a new formulation of the paradox and analyze its consequences. In particular, we will bring further arguments supporting the standard thesis that it is possible that a segment of space is composed of a non-denumerable set of indivisible 0-length points.

A physical interpretation of Lewis’ discrepancy between personal and external time in time travels

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.

Are Gandy Machines Really Local

This paper discusses the empirical question concerning the physical realization (or implementation) of a computation. We give a precise definition of the realization of a Turing-computable algorithm into a physical situation. This definition is not based, as usual, on an interpretation function of physical states, but on an implementation function from machine states to physical states (as suggested by Piccinini G, Computation in physical systems. The Stanford encyclopedia of philosophy. http://plato.stanford.edu/archives/fall2012/entries/computation-physicalsystems. Accessed 5 Dec 2013, 2012). We show that our definition avoids difficulties posed by Putnam’s theorem (Putnam H, Representation and reality. MIT Press, Cambridge, 1988) and Kripke’s objections (Stabler EP Jr, Kripke on functionalism and automata. Synthese 70(1):1–22, 1987; Scheutz M, What is not to implement a computation: a critical analysis of Chalmers’ notion of implementation. http://hrilab.tufts.edu/publications/scheutzcogsci12chalmers.pdf. Accessed 5 Dec 2013, 2001). Using our notion of representation, we analyse Gandy machines, intended in a physical sense, as a case study and show an inaccuracy in Gandy’s analysis with respect to the locality notion. This shows the epistemological relevance of our realization concept. We also discuss Gandy machines in quantum context. In fact, it is well known that in quantum mechanics, locality is seriously questioned, therefore it is worthwhile to analyse briefly, whether quantum machines are Gandy machines.

Theory of Knowing Machines: Revisiting Gödel and the Mechanistic Thesis

Church-Turing Thesis, mechanistic project, and Godelian Arguments offer different perspectives of informal intuitions behind the relationship existing between the notion of intuitively provable and the definition of decidability by some Turing machine. One of the most formal lines of research in this setting is represented by the theory of knowing machines, based on an extension of Peano Arithmetic, encompassing an epistemic notion of knowledge formalized through a modal operator denoting intuitive provability. In this framework, variants of the Church-Turing Thesis can be constructed and interpreted to characterize the knowledge that can be acquired by machines. In this paper, we survey such a theory of knowing machines and extend some recent results proving that a machine can know its own code exactly but cannot know its own correctness (despite actually being sound). In particular, we define a machine that, for (at least) a specific case, knows its own code and knows to be sound.

Continuity of Motion in Whitehead’s Geometrical Space

The paper explores a neglected conception in the foundations of spacetime theories, namely the conception of gunk, point-free spaces inaugurated by De Laguna and Whitehead. Despite the epistemological merits of the proposal they argue that this would have rather unwelcome consequences for the description of motion that is provided by most of our physical theories, even simple ones such as classical mechanics. The tension, they claim, is generated by the following facts: (i) classical mechanics crucially adopts the notion of a point-particle in its description of motion; (ii) sets of (constructed) points in these Whiteheadian spaces turn out to be non-connected; (iii) connectedness is a necessary condition for continuity.

Holism as an empirically meaningful metaphysical hypothesis

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. Spesso si riconosce alla Meccanica Quantistica di aver mostrato chiaramente che il tutto e piu della somma delle parti. In questo lavoro vogliamo indagare se, e in quale senso, questo e effettivamente il caso. Si argomenta che esiste un senso in cui tale affermazione e vera. Il nostro argomento principale e che una anche minima interpretazione realistica della Meccanica Quantistica rende un principio che chiamiamo Property Compositional Determinateness falso. Ma esiste un altro principio metafisico riguardante la composizione che spesso viene interpretato come implicare che la composizione delle parti esaurisca il tutto che compongono, il cosiddetto Mereological Extensionalism. In questo caso, contrariamente al generale consenso, si argomenta che la Meccanica Quantistica non suggerisce alcuna ragione, diretta o indiretta, in favore dell’abbandono di tale principio.

The Search for a Quantum Reality

We argue that pursuing the aim of building satisfactory “views of quantum reality”, or “quantum ontologies”, is epistemologically legitimate and not subject to no-go theorems. The question as to what extent existing interpretations may be considered satisfactory from this point of view is dealt with on the basis of criteria elaborated within the post-Kantian philosophical tradition. The aim may also prove worth the effort from a purely scientific point of view, although it may imply such radical changes of the ordinary ways of thinking as to require very long times.