SILFS 1 SILFS1 Philosophy of Science New Essays in Logic and SILFS
The papers collected in this volume are based on the best contributions to the conference of the Italian Society for SILFS Logic and Philosophy of Science (SILFS) that took place in Milan on 8-10 October 2007. The aim of the Society, New Essays in Logic and since its foundation in 1952, has always been that of bringing together scholars — working in the broad areas of Logic, Philosophy of Science and History of Science — Philosophy of Science who share an open-minded approach to their disciplines and regard them as essentially requiring continuous confrontation and bridge-building to avoid the danger of over-specialism. In this perspective, logicians and philosophers of science should not indulge in inventing and cherishing their own “internal problems” — although these may occasionally be an opportunity for conceptual clarifi cation — but should primarily look at the challenging conceptual and methodological questions that arise in any genuine attempt to extend our objective knowledge. As Ludovico Geymonat used to put it: “[good] philosophy should be sought in the folds of science itself”.
Contributions are distributed into six sections, fi ve of which — “Logic and Computing”, “Physics and Mathematics”, “Life Sciences”, “Economics and Social Sciences”, “Neuroscience and Philosophy of Mind” — are devoted Corrado Sinigaglia Telmo Pievani Federico Laudisa Giulio Giorello Marcello D’Agostin to the discussion of cutting-edge problems that arise Editors from current-day scientifi c research, while the remaining section on “General Philosophy of Science” is focused on foundational and methodological questions that are common to all areas.
Editors Marcello D’Agostino Giulio Giorello Federico Laudisa Telmo Pievani Corrado Sinigaglia
SILFS
Volume 1
New Essays in Logic and Philosophy of Science
Volume 1 New Essays in Logic and Philosophy of Science Marcello D’Agostino, Federico Ladisa, Telmo Pievani and Corrado Sinigaglia, eds
SILFS Series Editor Marcello D’Agostino [email protected]
New Essays in Logic and Philosophy of Science
Edited by Marcello D’Agostino, Federico Laudisa, Telmo Pievani, and Corrado Sinigaglia
© Individual author and College Publications 2010. All rights reserved.
ISBN 978-1-84890-003-5
College Publications Scientific Director: Dov Gabbay Managing Director: Jane Spurr Department of Computer Science King’s College London, Strand, London WC2R 2LS, UK http://www.collegepublications.co.uk
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Table of contents
Editors’ preface ix
List of contributors xi
PART I LOGIC AND COMPUTING 1 Umberto Rivieccio A bilattice for contextual reasoning 3 Francesca Poggiolesi Reflecting the semantic features of S5 at the syntactic level 13 Gisele` Fischer Servi Non monotonic conditionals and the concept I believe only A 27 Carlo Penco, Daniele Porello Sense and Proof 37 Andrea Pedeferri Some reflections on plurals and second order logic 47 G. Casini, H. Hosni Default-assumption consequence relations in a preferential setting: reasoning about normality 53 Bianca Boretti, Sara Negri On the finitization of Priorean linear time 67 Riccardo Bruni Proof-theoretic aspects of quasi-inductive definitions 81 Giacomo Calamai Remarks on a proof-theoretic characterization of polynomial space functions 95
PART II PHYSICS AND MATHEMATICS 115 Vincenzo Fano, Giovanni Macchia How contemporary cosmology bypasses Kantian prohibition against a science of the universe 117 Giulia Giannini Poincar´e and the electromagnetic world picture. For a revaluation of his conventionalism 131 Marco Toscano “Besides quantity”: the epistemological meaning of Poincar´e’s qualitative analysis 141 vi
Laura Felline Structural explanation from special relativity to quantum mechanics 153 Miriam Cometto When the structure is not a limit. On continuity through theory-change 163 Gianluca Introzzi Approaches to wave/particle duality: historical analysis and critical remarks 173 Marco Pedicini, Mario Piazza An application of von Neumann algebras to computational complexity 183 Miriam Franchella Phenomenology and intuitionism: the pros and cons of a research program 195 Luca Bellotti A note on the circularity of set-theoretic semantics for set theory 207 Valeria Giardino The use of figures and diagrams in mathematics 217 Paola Cantu` The role of epistemological models in Veronese’s and Bettazzi’s theory of magnitudes 229
PART III LIFE SCIENCES 243 Pietro Omodeo Evolution by increasing complexity in the framework of Darwin’s theory 245 Stefano Giaimo, Giuseppe Testa Gene: an entity in search of concepts 257 Elena Casetta Categories, taxa, and chimeras 265 Flavio D’Abramo Final, efficient and complex causes in biology 279 Ludovica Lorusso The concept of race and its justification in biology 289
PART IV ECONOMICS AND SOCIAL SCIENCES 301 Marco Novarese, Alessandro Lanteri, Cesare Tibaldeschi Learning, generalization, and the perception of information: an experimental study 303 Andrea Pozzali Tacit knowledge and economics: recent findings and perspectives of research 319 vii
Viviana Di Giovinazzo From individual well-being to economic welfare. Tibor Scitovsky explains why (consumers’) dissatisfaction leads to a joyless economy 327 Federica Russo Explaining causal modelling. Or, what a causal model ought to explain 347 Enzo Di Nuoscio The epistemological statute of the rationality principle. Comparing Mises and Popper 363 Albertina Oliverio Evolution, cooperation and rationality: some remarks 377 Francesco Di Iorio Self-organization of the mind and methodological individualism in Hayek’s thought 389 Simona Morini Can ethics be naturalized? 403 Stefano Vaselli Searle’s collective intentionality and the “invisible hand” explanations 409 Sergio Levi The naturalness of religion and the action representation system 423 Andrea Zhok On value judgement and the ethical nature of economic optimality 433 Dario Antiseri Carl Menger, Ludwig von Mises, Friedrich A. von Hayek and Karl Popper: four Viennese in defense of methodological individualism 447 PART V NEUROSCIENCE AND PHILOSOPHY OF MIND 463 Fabio Bacchini Jaegwon Kim and the threat of epiphenomenalism of mental states 465 Wolfgang Huemer Philosophy of mind between reduction, elimination and enrichment 481 Laura Sparaci Discourse and action: analyzing the possibility of a structural similarity 493 Alessandro Dell’Anna Visuomotor representations: Jacob and Jeannerod between enaction and the two visual systems hypothesis 505 viii
Daniela Tagliafico Mirror neurons and the “radical view” on simulation 515 Vincenzo G. Fiore Multiple realizations of the mental states: hunting for plausible chimeras 529 Arturo Carsetti The embodied meaning and the “unfolding” of the mind’s eyes 539 Katja Crone Consciousness and the problem of different viewpoints 547 Giulia Piredda The whys and hows of extended mind 559 Carmela Morabito Movement in the philosophy of mind: traces of the motor model of mind in the history of science 571 Jean-Luc Petit The brain, the person and the world 585
PART VI GENERAL PHILOSOPHY OF SCIENCE 601 Gustavo Cevolani, Vincenzo Crupi, Roberto Festa The whole truth about Linda: probability, verisimilitude, and a paradox of conjunction 603 Antonino Freno Probabilistic Graphical Models and logic of scientific discovery 617 Massimiliano Carrara, Davide Fassio Perfected science and the knowability paradox 629 Luca Tambolo Two problems for normative naturalism 637 Silvano Zipoli Caiani Explaining the scientific success. A critique of an abductive defence of scientific realism 649 Mario Alai Van Fraassen, observability and belief 663 Marco Giunti Reduction in dynamical systems: a representational view 677 Alexander Afriat Duhem, Quine and the other dogma 695 Edoardo Datteri Bionic simulation of biological systems: a methodological analysis 711 Luca Guzzardi Some remarks on a heuristic point of view about the role of experiment in the physical sciences 725 Editors’ preface
The papers collected in this volume stem from the contributions delivered to the conference of the Italian Society for Logic and Philosophy of Science (SILFS) that took place in Milan on 8-10 October 2007. The aim of the So- ciety, since its foundation in 1952, has always been that of bringing together scholars — working in the broad areas of Logic, Philosophy of Science and History of Science — who share an open-minded approach to their disciplines and regard them as essentially requiring continuous confrontation and bridge- building to avoid the vanity of over-specialism. In this perspective, logicians and philosophers of science should not indulge in inventing and cherishing their own “internal problems” — although these may occasionally be an op- portunity for conceptual clarification — but should primarily look at the challenging conceptual and methodological questions that arise in any gen- uine attempt to extend our “objective” knowledge of the physical, biological, social and intellectual environment in which we are embedded. As Ludovico Geymonat used to put it: “[good] philosophy should be sought in the folds of science itself”. Accordingly, the accepted contributions were distributed into six sections, five of which — “Logic and Computing”, “Physics and Mathematics”, “Life Sciences”, “Economics and Social Sciences”, “Neuroscience and Philosophy of Mind” — were devoted to the discussion of cutting-edge problems that arise from current-day scientific research, while the remaining section on “Gen- eral Philosophy of Science” was focused on foundational and methodological questions that are common to all areas. The very good response to the call for abstracts and the high quality of the accepted presentations persuaded the SILFS President, Giulio Giorello, to launch the idea of a refereed volume based on the best contributions. Authors were therefore invited to submit papers, inspired by their talks, which were anonimously refereed and subsequently revised before being finally accepted for publication in this volume. So, what we are presenting here is by no means the proceedings of the conference, but rather the result of a long (and, alas, time-consuming) process that started after the conference, although being inspired by it. We do hope that readers may enjoy the result of this collective effort and appreciate the strong inderdisciplinary spirit that pervades it. We wish to thank all the authors and, especially, Luca Guzzardi who gen- erously offered us his competent support in editing this volume. M.D’A, G.G., F.L, T.P. C.S.
Milano, 31 July 2010
List of contributors
Alexander Afriat, Department of Philosophy, University of West Brittany Mario Alai, Department of Philosophy, University of Urbino Dario Antiseri, Department of Political Sciences, LUISS, Rome Fabio Bacchini, Faculty of Architecture of Alghero, University of Sassari Luca Bellotti, Department of Philosophy, University of Pisa Bianca Boretti, Department of Philosophy, University of Helsinki Riccardo Bruni, Department of Philosophy, University of Florence Giacomo Calamai, Department of Mathematics and Information Sciences “Roberto Magari”, University of Siena Paola Cantu`, Centre d’Epist´emologie et Ergologie Comparatives, Univer- sit´e de Provence, Aix-en-Provence Massimiliano Carrara, Department of Philosophy, University of Padua Arturo Carsetti, Department of Philosophy, University of Rome “Tor Ver- gata” Elena Casetta, Department of Philosophy, University of Turin Giovanni Casini, Scuola Normale Superiore di Pisa Gustavo Cevolani, Department of Philosophy, University of Bologna Miriam Cometto, Department of Philosophy, University of Rome III Katja Crone, Department of Philosophy, Humboldt University, Berlin Vincenzo Crupi, Department of Critical Care, University of Florence Flavio D’Abramo, Department of Philosophical and Epistemological Stud- ies, University of Rome “La Sapienza” Edoardo Datteri, Department of Human Sciences, University of Milan- Bicocca Alessandro Dell’Anna, Department of Philosophy, University of Genoa Viviana Di Giovinazzo, Department of Sociology and Social Research, Uni- versity of Milan-Bicocca Francesco Di Iorio, LUISS University, Rome and EHESS-CREA, Ecole Polytechnique, Paris Enzo Di Nuoscio, Faculty of Human Sciences, University of Molise Enzo Fano, Department of Philosophy, University of Urbino Davide Fassio, Department of Philosophy, University of Padua Laura Felline, Department of Education Science and Philosophy, Univer- sity of Cagliari Roberto Festa, Department of Philosophy, Languages, and Literatures, University of Trieste Vincenzo G. Fiore, Laboratory Of Computational Embodied Neuroscience, Institute of Cognitive Sciences and Technologies, CNR Gisele´ Fischer Servi, Department of Philosophy, Univeristy of Parma Miriam Franchella, Department of Philosophy, University of Milan Antonino Freno, Information Engineering Department, University of Siena xii
Stefano Giaimo, European School of Molecular Medicine and FIRC Insti- tute of Molecular Oncology, Milan Giulia Giannini, Department of Human Sciences, University of Bergamo Valeria Giardino, Institute Jean Nicod (CNRS-EHESS-ENS), Paris Marco Giunti, Department of the Science of Education and Philosophy, University of Cagliari Luca Guzzardi, Astronomical Observatory of Brera, Milan Hykel Hosni, Scuola Normale Superiore di Pisa Wolfgang Huemer, Department of Philosophy, University of Parma Gianluca Introzzi, Department of Nuclear and Theoretical Physics, Uni- versity of Pavia Alessandro Lanteri, European School of Economics, Milan Sergio Levi, Department of Philosophy, University of Milan Ludovica Lorusso, Department of Economics, Business and Regulation, University of Sassari Giovanni Macchia, Department of Philosophy, University of Urbino Carmela Morabito, Department of Philosophy, University of Rome “Tor Vergata” Simona Morini, Faculty of Design and Arts, IUAV, Venice Sara Negri, Department of Philosophy, University of Helsinki Marco Novarese, Centre for Cognitive Economics, Department of Legal Sciences and Economics, University of West Piedmont, Vercelli Albertina Oliverio, Faculty of Human Sciences, University of Chieti and Pescara Pietro Omodeo, Department of Evolutionary Biology, University of Siena Andrea Pedeferri, Department of Philosophy, George Washingotn Uni- versity, Washington DC Marco Pedicini, CNR — Istituto per le Applicazioni del Calcolo M. Picone, Roma Carlo Penco, Department of Philosophy, University of Genoa Jean-Luc Petit, Faculty of Philosophy, Linguistics and the Science of Ed- ucation, University of Strasbourg and College de France, Paris Mario Piazza, Department of Philosophy, University of Chieti and Pescara Giulia Piredda, Institute Jean Nicod (CNRS-EHESS-ENS), Paris Francesca Poggiolesi, Department of Philosophy and Moral Sciences, Vrije Universiteit Brussel Daniele Porello, Department of Philosophy, Univeristy of Genoa Andrea Pozzali, European University of Rome Umberto Rivieccio, Department of Philosophy, University of Genoa Federica Russo, Department of Philosophy, University of Kent Laura Sparaci, Neuroscience Department, Child Neuropsychiatry Unit, Children’s Hospital “Bambino Ges`u”, Rome Daniela Tagliafico, Laboratory of Ontology, University of Turin Luca Tambolo, Department of Philosophy, Languages, and Literatures, University of Trieste Giuseppe Testa, Laboratory of Stem Cell Epigenetics, European Institute of Oncology and European School of Molecular Medicine, Milan xiii
Cesare Tibaldeschi, Department of Legal Sciences and Economics, Uni- versity of West-Piedmont, Vercelli Marco Toscano, Department of Human Sciences, University of Bergamo Stefano Vaselli, Department of Philosophical and Epistemological Studies, University of Rome “La Sapienza” Silvano Zipoli Caiani, Department of Philosophy, University of Milan Andrea Zhok, Department of Philosophy, University of Milan
PART I
LOGIC AND COMPUTING
A bilattice for contextual reasoning Umberto Rivieccio
1 Introduction Bilattices are algebraic structures introduced by Ginsberg [4] as a uniform framework for inference in Artificial Intelligence. In the last two decades the bilattice formalism proved useful in many fields: however it has never been applied to contextual reasoning so far. My aim here is to sketch one such possible application. The basic idea is to treat contexts as “truth values” that form a bilattice, that is a lattice equipped with two partial orders. We shall employ a bilattice construction introduced in [4] for the “justifications” of a Truth Maintenance System, i.e. sets of premises used for derivations, but we will apply it to sets of formulas representing not premises in the usual logical sense but cognitive contexts. The usual logical connectives will then be defined as lattice operators on the set of truth values, for instance conjunction and disjunction correspond re- spectively to the meet and join with respect to the so called “truth ordering”. Non classical connectives may also be defined, such as those corresponding to the meet and join w.r.t. the second partial order, usually called the “knowl- edge ordering”. The next step would be to construct a suitable inference mechanism for contextual bilattices. This has been done for the general case (see for instance [4] and [1]), but it remains to show that such mechanisms may be successfully applied to contextual reasoning. In section 4 we shall see an example of a possible application.
2 Bilattices
Given a set B, a bilattice may be defined as a structure B,≤t, ≤k where B,≤t and B,≤k are both complete lattices. The elements of B are intended to represent truth values ordered according to the degree of truth and the degree of knowledge (or information): the rela- tion ≤t corresponds to the truth ordering and ≤k to the knowledge ordering. Intuitively, given two sentences p and q, v (p) ≤t v (q) means that the agent has stronger evidence for the truth of q than for the truth of p and weaker evidence for the falsity of q than for that of p, while v (p) ≤k v (q) means that the agent has stronger evidence for both the truth and falsity of q than for the truth and falsity of p (thus allowing for inconsistency). The meet and join operations on the two lattices correspond to proposi- tional connectives in the bilattice-based logics. Conjunction and disjunction 4 Umberto Rivieccio are defined respectively as the greatest lower bound and least upper bound with respect to the truth ordering. Given two sentences p, q and a valuation v,wehave: ∧ { } v (p q) = glbt v (p) ,v(q)
v (p ∨ q) = lubt {v (p) ,v(q)} The corresponding connectives relative to the knowledge ordering have been called consensus (⊗) and gullability (⊕) operator (see [3]). They are defined as follows: ⊗ { } v (p q)=glbk v (p) ,v(q)
v (p ⊕ q)=lubk {v (p) ,v(q)} Intuitively, we may interpret v (p)⊗v (q) as the most information that v (p) and v (q) agree on, while the gullability operator ⊕ simply accepts any information from both v (p) and v (q). We have a bilattice negation if there is a function ¬ : B → B such that:
1. if v (p) ≤t v (q) then ¬v (q) ≤t ¬v (p),
2. if v (p) ≤k v (q) then ¬v (p) ≤k ¬v (q),
3. v (p)=¬¬v (p).
In other words, we require that the negation be an involutive operator that reverses the truth ordering while leaving the knowledge ordering unchanged: this corresponds to the intuition that the amount of information one has con- cerning some sentence p should not be altered when considering its negation ¬p. The existence of such a negation operator is a minimal requirement for logical bilattices (indeed some authors consider it part of the basic definition of bilattice); for the kind of bilattices we will construct there is a straightforward way to define it (see below, section 3). The smallest non-trivial bilattice is the one corresponding to Belnap’s logic (see [2]), which has four elements, that is exactly the least and greatest el- ements with respect to the two orderings. This bilattice can be constructed from the cartesian product of the classical two-point truth set with itself: {0, 1}×{0, 1} = {(0, 1) , (1, 0) , (0, 0) , (1, 1)}. We may interpret the first el- ement of each ordered pair as representing the evidence for the truth of a sentence p, while the second element represents the evidence for the falsity of p. In this way we can understand Belnap’s values in terms of the classical ones: (1, 0) corresponds to “at least true”, (0, 1) to “at least false”, (0, 0) to “unknown” (i. e. not known to be either true or false) and (1, 1) to “contra- dictory” (i. e. known to be both true and false). Several more complex bilattices have been introduced in the literature for a variety of applications (for instance to deal with default reasoning, with modal operators etc.), many of them built like Belnap’s using two copies of some lattice, the first for the positive evidence and the second for the negative. In the next section we shall employ this procedure to construct a bilattice for contextual reasoning. A bilattice for contextual reasoning 5
3 Contexts as truth values In cognitive processes, the notion of context may be defined as a part of the epistemic state of an agent, i.e. as a set of implicit assumptions. These assumptions enable us to assign a reference to indexical expressions such as “this”, “here”, “now” etc., and so to determine the truth value of the sentences involving them. The simplest way to formalize this is to identify contexts with subsets of the knowledge base, i.e. sets of formulas. Let F be the set of all formulas in the knowledge base and let C1,...,Cn ⊆ F be sets of formulas intended to represent contexts. To each sentence p we + may associate the set C = {C1,...,Cn} of all contexts in which p holds. We assume each Ci to be a set of sentences, possibly cointaining contextual “axioms” such as “Speaker = . . . ”, “ Time = . . . ” etc., that logically imply p. We shall denote this writing v (p)=[C+]. This is the basic idea that provides a link with the multi-valued setting of bilattices, that is the idea to treat contexts as truth values. If we want to handle inconsistent beliefs, we may also consider the set C− of all contexts in which ¬p holds, without requiring that C+ and C− be disjoint, so that we may have some context in which both p and ¬p hold. Therefore, instead of writing only v (p)=[C+], meaning that the value of p is given by the contexts in which p holds, we shall write v (p)=[C+,C−], meaning that the value of p is given by the contexts in which p holds together with the contexts in which ¬p holds. Now we proceed to define an order relation on these “truth values”. We may order contexts in a natural way by set inclusion. For instance, C2 ⊆ C1 intuitively means that C2 is more general than C1, since C2 requires fewer assumptions than C1. (The most general context is thus the empty context, corresponding to sentences that are completely context-independent, while the least general context is simply the set of all formulas.) This intuition may be extended to sets of contexts as follows. Given two sets of contexts C = {C1,...,Cm} and D = {D1,...,Dn},we set C ≤ D iff for all Ci ∈ C there is some Dj ∈ D such that Dj ⊆ Ci. This means that, for every context in C, there is some context in D which is more general: so if we know that p holds in D and q holds in C, we can conclude that p is less context-dependent than q. So far the relation we have defined is in fact only a preorder, since we may have C ≤ D and D ≤ C but C = D. This happens for instance if C = {{p}} and D = {{p} , {p, q}}. However, to obtain an order we just need to consider the equivalence classes under this preorder; or, equivalently, we might require that each set of contexts be minimal, in the sense that for every C = {C1,...,Cm} there should be no Ci,Cj ∈ C such that Ci ⊆ Cj. In other words, what we are assuming is that all sets are free of redundant contexts (such as Cj in our example). Of course this is not the only possible way to define an order relation on (sets of) contexts. For instance one might consider the logical (instead of just the set inclusion) relationship between the propositions representing contexts. For suppose we have two contexts C and D such that C D and D C but D ⊆ th (C), that is C p for each sentence p ∈ D. Since D is contained 6 Umberto Rivieccio in the logical consequences of C, from a deductive point of view we might expect to have C ≤ D. According to this intuition, we should replace the previous definition with the more general one: C ≤ D iff D ⊆ th (C). However, we shall not employ this definition here because it would not allow to construct a lattice of contexts in an effective way. In fact, in order to determine if C ≤ D we would have to check if D ⊆ th (C), which is notoriously a complex task from a computational point of view. Instead, we prefer to adopt the simpler set inclusion definition, delaying the hard part of the job to a later stage of the inference process. So if p holds in C and q holds in D, with D ⊆ th (C), this relation will not be reflected in the values assigned to p and q by our initial valuation until we have applied some suitable closure operator (such as the one introduced in [4]). Adopting the set inclusion order relation we are now able to define a lattice of sets of contexts. Let F be the set of all formulas in the knowledge base and P (F ) its power set, that is the set of all possible contexts. If we denote the set of all sets of contexts by L = P (P (F )), then the structure L, ≤ is the lattice of sets of contexts. As we have said, in order to consider inconsistent beliefs we employ two copies of L, one for the contexts in which a sentence p holds and the other for those in which ¬p holds. In this way we obtain a structure that may be called a “contextual bilattice” L × L, ≤t, ≤k, the underlying set being formed by the ordered pairs [C+,C−] of elements of the lattice of sets of contexts. In this structure the truth and knowledge order relations may be defined as follows. For any two elements [C+,C−], [D+,D−] ∈ L × L: + − + − + + − − C ,C ≤t D ,D iff C ≤ D and C ≥ D