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Carlo Cellucci
Università degli Studi di Roma La Sapienza (PhD)
  1. Philosophy at a Crossroads: Escaping From Irrelevance.Carlo Cellucci - 2018 - Syzetesis (1):13-53.
    Although there have never been so many professional philosophers as today, most of the questions discussed by today’s philosophers are of no interest to cultured people at large. Specifically, several scientists have maintained that philosophy has become an irrelevant subject. Thus philosophy is at a crossroads: either to continue on the present line, which relegates it into irrelevance, or to analyse the reasons of the irrelevance and seek an escape. This paper is an attempt to explore the second alternative.
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  2.  27
    Rethinking Knowledge.Carlo Cellucci - 2015 - Metaphilosophy 46 (2):213-234.
    The view that the subject matter of epistemology is the concept of knowledge is faced with the problem that all attempts so far to define that concept are subject to counterexamples. As an alternative, this article argues that the subject matter of epistemology is knowledge itself rather than the concept of knowledge. Moreover, knowledge is not merely a state of mind but rather a certain kind of response to the environment that is essential for survival. In this perspective, the article (...)
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  3. The Nature of Mathematical Explanation.Carlo Cellucci - 2008 - Studies in History and Philosophy of Science Part A 39 (2):202-210.
    Although in the past three decades interest in mathematical explanation revived, recent literature on the subject seems to neglect the strict connection between explanation and discovery. In this paper I sketch an alternative approach that takes such connection into account. My approach is a revised version of one originally considered by Descartes. The main difference is that my approach is in terms of the analytic method, which is a method of discovery prior to axiomatized mathematics, whereas Descartes’s approach is in (...)
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  4. Rethinking Philosophy.Carlo Cellucci - 2014 - Philosophia 42 (2):271-288.
    Can philosophy still be fruitful, and what kind of philosophy can be such? In particular, what kind of philosophy can be legitimized in the face of sciences? The aim of this paper is to answer these questions, listing the characteristics philosophy should have to be fruitful and legitimized in the face of sciences. Since the characteristics in question demand that philosophy search for new knowledge and new rules of discovery, a philosophy with such characteristics may be called the ‘heuristic view’. (...)
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  5. Knowledge, Truth and Plausibility.Carlo Cellucci - 2014 - Axiomathes 24 (4):517-532.
    From antiquity several philosophers have claimed that the goal of natural science is truth. In particular, this is a basic tenet of contemporary scientific realism. However, all concepts of truth that have been put forward are inadequate to modern science because they do not provide a criterion of truth. This means that we will generally be unable to recognize a scientific truth when we reach it. As an alternative, this paper argues that the goal of natural science is plausibility and (...)
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  6.  46
    Mathematical Beauty, Understanding, and Discovery.Carlo Cellucci - 2015 - Foundations of Science 20 (4):339-355.
    In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which hypothesis to (...)
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  7.  8
    Diagrams in Mathematics.Carlo Cellucci - forthcoming - Foundations of Science:1-22.
    In the last few decades there has been a revival of interest in diagrams in mathematics. But the revival, at least at its origin, has been motivated by adherence to the view that the method of mathematics is the axiomatic method, and specifically by the attempt to fit diagrams into the axiomatic method, translating particular diagrams into statements and inference rules of a formal system. This approach does not deal with diagrams qua diagrams, and is incapable of accounting for the (...)
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  8.  9
    Reconnecting Logic with Discovery.Carlo Cellucci - 2017 - Topoi:1-12.
    According to a view going back to Plato, the aim of philosophy is to acquire knowledge and there is a method to acquire knowledge, namely a method of discovery. In the last century, however, this view has been completely abandoned, the attempt to give a rational account of discovery has been given up, and logic has been disconnected from discovery. This paper outlines a way of reconnecting logic with discovery.
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  9.  47
    Philosophy of Mathematics: Making a Fresh Start.Carlo Cellucci - 2013 - Studies in History and Philosophy of Science Part A 44 (1):32-42.
    The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the (...)
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  10. Mente Incarnata E Conoscenza [Embodied Mind and Knowledge].Carlo Cellucci - 2005 - In Eugenio Canone (ed.), Per una storia del concetto di mente. Olschki.
    La mente non è sempre esistita ma è stata inventata: inventata nel senso che, a un certo punto, qualcuno ha introdotto il concetto di mente. Chi lo abbia introdotto per primo è una questione controversa. Per esempio, Putnam a f f er ma c he , a nc he s e «i n que s t os e c ol os i pa r l a c ome s e l a me nt e f os s e qua s (...)
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  11.  10
    Top-Down and Bottom-Up Philosophy of Mathematics.Carlo Cellucci - 2013 - Foundations of Science 18 (1):93-106.
  12. How Should We Think About the Meaning of Life?Carlo Cellucci - unknown
    In the past few decades the question of the meaning of life has received renewed attention. However, much of the recent literature on the topic reduces the question of the meaning of life to the question of meaning in life. This raises the problem: How should we think about the meaning of life? The paper tries to give an answer to this problem.
     
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  13. Mathematical Discourse Vs. Mathematical Intuition.Carlo Cellucci - 2005 - In Carlo Cellucci & Donald Gillies (eds.), Mathematical Reasoning and Heuristics. College Publications. pp. 137-165..
    The aim of this article is to show that intuition plays no role in mathematics. That intuition plays a role in mathematics is mainly associated to the view that the method of mathematics is the axiomatic method. It is assumed that axioms are directly (Gödel) or indirectly (Hilbert) justified by intuition. This article argues that all attempts to justify axioms in terms of intuition fail. As an alternative, the article supports the view that the method of mathematics is the analytic (...)
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  14. L'illusione di Una Filosofia Specializzata [The Illusion of a Specialized P Hilosophy].Carlo Cellucci - 2002 - In Marcello D'Agostino, Giulio Giorello & Salvatore Veca (eds.), Logica e politica. Per Marco Mondadori. Mondadori.
    Secondo un recente bilancio della filosofia del Novecento di Rossi e Viano, nel nostro secolo «il successo maggiore è toccato alle dottrine filosofiche che si sono proposte di offrire alternative alla conoscenza tecnico-scientifica e che sostengono la possibilità di alleggerire i vincoli che il sapere positivo porrebbe al modo di pensare e ai progetti di azione»2. Tali dottrine prospettano un ritorno all’antica metafisica, a cui «si ricorre non come a una forma di sapere sistematico, bensì come alla testimonianza di una (...)
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  15. Filosofia & Matematica, Introduction.Carlo Cellucci - 2006 - In Reuben Hersh (ed.), 18 Unconventional Essays on the Nature of Mathematics. Springer.
    Mathematics has long been a preferential subject of reflection for philosophers, inspiring them since antiquity in developing their theories of knowledge and their metaphysical doctrines. Given the close connection between philosophy and mathematics, it is hardly surprising that some major philosophers, such as Descartes, Leibniz, Pascal and Lambert, have also been major mathematicians.
     
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  16.  22
    Is Mathematics Problem Solving or Theorem Proving?Carlo Cellucci - 2017 - Foundations of Science 22 (1):183-199.
    The question that is the subject of this article is not intended to be a sociological or statistical question about the practice of today’s mathematicians, but a philosophical question about the nature of mathematics, and specifically the method of mathematics. Since antiquity, saying that mathematics is problem solving has been an expression of the view that the method of mathematics is the analytic method, while saying that mathematics is theorem proving has been an expression of the view that the method (...)
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  17. From Closed to Open Systems.Carlo Cellucci - 1993 - In J. Czermak (ed.), Philosophy of Mathematics, pp. 206-220. Hölder-Pichler-Tempsky.
    While Gödel's (first) incompleteness theorem has been used to refute the main contentions of Hilbert's program, it does not seem to have been generally used to stress that a basic ingredient of that program, the concept of formal system as a closed system - as well as the underlying view, embodied in the axiomatic method, that mathematical theories are deductions from first principles must be abandoned. Indeed the logical community has generally failed to learn Gödel's lesson that Hilbert's concept of (...)
     
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  18.  23
    Definition in Mathematics.Carlo Cellucci - 2018 - European Journal for Philosophy of Science 8 (3):605-629.
    In the past century the received view of definition in mathematics has been the stipulative conception, according to which a definition merely stipulates the meaning of a term in other terms which are supposed to be already well known. The stipulative conception has been so absolutely dominant and accepted as unproblematic that the nature of definition has not been much discussed, yet it is inadequate. This paper examines its shortcomings and proposes an alternative, the heuristic conception.
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  19. The Growth of Mathematical Knowledge: An Open World View.Carlo Cellucci - 2000 - In Emily Grosholz & Herbert Breger (eds.), The Growth of Mathematical Knowledge, pp. 153-176. Kluwer Academic Publishers. pp. 153--176.
    In his book The Value of Science Poincaré criticizes a certain view on the growth of mathematical knowledge: “The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new ones, but to the continuous evolution of zoological types which develop ceaselessly and end by becoming unrecognizable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past” (Poincaré (...)
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  20. Mathematical Logic: What has It Done for the Philosophy of Mathematics?Carlo Cellucci - 1996 - In Piergiorgio Odifreddi (ed.), Kreiseliana. About and Around Georg Kreisel, pp. 365-388. A K Peters.
    onl y to discuss some claims concerning the relationship between mathematical logic and the philosophy of mathematics that repeatedly occur in his writings. Although I do not know to what extent they are representative of his present position, they correspond to widespread views of the logical community and so seem worth discussing anyhow. Such claims will be used as reference to make some remarks about the present state of relations between mathematical logic and the philosophy of mathematics.
     
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  21. The Universal Generalization Problem.Carlo Cellucci - 2009 - Logique Et Analyse 52.
    The universal generalization problem is the question: What entitles one to conclude that a property established for an individual object holds for any individual object in the domain? This amounts to the question: Why is the rule of universal generalization justified? In the modern and contemporary age Descartes, Locke, Berkeley, Hume, Kant, Mill, Gentzen gave alternative solutions of the universal generalization problem. In this paper I consider Locke’s, Berkeley’s and Gentzen’s solutions and argue that they are problematic. Then I consider (...)
     
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  22. Filosofia E Matematica.Carlo Cellucci - 2002 - Editori Laterza.
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  23.  18
    Is Philosophy a Humanistic Discipline?Carlo Cellucci - 2015 - Philosophia 43 (2):259-269.
    According to Bernard Williams, philosophy is a humanistic discipline essentially different from the sciences. While the sciences describe the world as it is in itself, independent of perspective, philosophy tries to make sense of ourselves and of our activities. Only the humanistic disciplines, in particular philosophy, can do this, the sciences have nothing to say about it. In this note I point out some limitations of Williams’ view and outline an alternative view.
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  24. Analytic Cut Trees.Carlo Cellucci - 2000 - Logic Journal of the IGPL 8 (6):733-750.
    It has been maintained by Smullyan that the importance of cut-free proofs does not stem from cut elimination per se but rather from the fact that they satisfy the subformula property. In accordance with such a viewpoint in this paper we introduce analytic cut trees, a system from which cuts cannot be eliminated but satisfying the subformula property. Like tableaux analytic cut trees are a refutation system but unlike tableaux they have a single inference rule and several branch closure rules. (...)
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  25. La Ragioni Della Logica.Carlo Cellucci - 1998 - Rome: Laterza.
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  26.  82
    Proof Theory and Complexity.Carlo Cellucci - 1985 - Synthese 62 (2):173-189.
  27. The Scope of Logic: Deduction, Abduction, Analogy.Carlo Cellucci - 1998 - Theoria 64 (2-3):217-242.
    The present form of mathematical logic originated in the twenties and early thirties from the partial merging of two different traditions, the algebra of logic and the logicist tradition (see [27], [41]). This resulted in a new form of logic in which several features of the two earlier traditions coexist. Clearly neither the algebra of logic nor the logicist’s logic is identical to the present form of mathematical logic, yet some of their basic ideas can be distinctly recognized within it. (...)
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  28. Review of M. Giaquinto, The Search for Certainty. [REVIEW]Carlo Cellucci - 2003 - European Journal of Philosophy 11 (3):420-423.
    Giaquinto’s book is a philosophical examination of how the search for certainty was carried out within the philosophy of mathematics from the late nineteenth to roughly the mid-twentieth century. It is also a good introduction to the philosophy of mathematics and the views expressed in the body of the book, in addition to being thorough and stimulating, seem generally undisputable. Some doubts, however, could be raised about the concluding remarks concerning the present situation in the philosophy of mathematics, specifically Zermelo's (...)
     
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  29.  19
    Skolem's Paradox and Platonism.Carlo Cellucci - 1970 - Critica 4 (11/12):43-54.
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  30. The Question Hume Didn't Ask: Why Should We Accept Deductive Inferences?Carlo Cellucci - 2006 - In Carlo Cellucci & Paolo Pecere (eds.), Demonstrative and Non-Demonstrative Reasoning in Mathematics and Natural Science. Edizioni dell'Università di Cassino. pp. 207-235.
    This article examines the current justifications of deductive inferences, and finds them wanting. It argues that this depends on the fact that all such justification take no account of the role deductive inferences play in knowledge. Alternatively, the article argues that a justification of deductive inferences may be given in terms of the fact that they are non-ampliative, in the sense that the content of the conclusion is merely a reformulation of the content of the premises. Some possible objections to (...)
     
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  31.  13
    On Quine's Approach to Natural Deduction'.Carlo Cellucci - 1995 - In Paolo Leonardi & Marco Santambrogio (eds.), On Quine: New Essays. Cambridge University Press. pp. 314--335.
    This article examines Quine's original proposal for a natural deduction calculus including an existential specification rule, it argues that it introduces a new paradigm of natural deduction alternative to Gentzen's but has some substantial defects. As an alternative the article puts forward a system of sequent natural deduction.
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  32. La Filosofia della Matematica del Novecento.Carlo Cellucci - 2007 - Laterza.
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  33.  9
    Existential Instantiation and Normalization in Sequent Natural Deduction.Carlo Cellucci - 1992 - Annals of Pure and Applied Logic 58 (2):111-148.
    ellucci, C., Existential instantiation and normalization in sequent natural deduction, Annals of Pure and Applied Logic 58 111–148. A sequent conclusion natural deduction system is introduced in which classical logic is treated per se, not as a special case of intuitionistic logic. The system includes an existential instantiation rule and involves restrictions on the discharge rules. Contrary to the standard formula conclusion natural deduction systems for classical logic, its normal derivations satisfy both the subformula property and the separation property and (...)
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  34.  27
    Frege on Thinking and Its Epistemic Significance. [REVIEW]Carlo Cellucci - 2017 - History and Philosophy of Logic 38 (1):92-95.
  35.  68
    On the Role of Reducibility Principles.Carlo Cellucci - 1974 - Synthese 27 (1-2):93 - 110.
  36.  8
    Review: Georg Kreisel, Gaisi Takeuti, Formally Self-Referential Propositions for Cut Free Analysis and Related Systems; Peter Pappinghaus, A Version of the ∑1 1 -Reflection Principle for CFA Provable in PRA. [REVIEW]Carlo Cellucci - 1985 - Journal of Symbolic Logic 50 (1):244-246.
  37.  3
    Teoria Della Dimostrazione. Normalizzazioni E Assegnazioni di Numeri Ordinali.Carlo Cellucci - 1982 - Journal of Symbolic Logic 47 (1):220-221.
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  38. Demonstrative and Non-Demonstrative Reasoning in Mathematics and Natural Science.Carlo Cellucci & Paolo Pecere (eds.) - 2006 - Edizioni dell'Università di Cassino.
     
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  39. Does Logic Slowly Pass Away, or Has It a Future?Carlo Cellucci - 2014 - In E. Moriconi & L. Tescari (eds.), Second Pisa Colloquium in Logic, Language and Epistemology. ETS. pp. 122-136.
    The limitations of mathematical logic either as a tool for the foundations of mathematics, or as a branch of mathematics, or as a tool for artificial intelligence, raise the need for a rethinking of logic. In particular, they raise the need for a reconsideration of the many doors the Founding Fathers of mathematical logic have closed historically. This paper examines three such doors, the view that logic should be a logic of discovery, the view that logic arises from method, and (...)
     
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  40. Dalla logica teoretica alla logica pratica.Carlo Cellucci - 1992 - Rivista di Filosofia 83 (2):169-207.
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  41. Kreisel Georg and Takeuti Gaisi. Formally Self-Referential Propositions for Cut Free Analysis and Related Systems. Dissertationes Mathematicae , No. 118, Polska Akademia Nauk, Instytut Matematyczny, Warsaw 1974, 50 Pp.Päppinghaus Peter. A Version of the Σ1-Reflection Principle for CFA Provable in PRA. Archiv Für Mathematische Logik Und Grundlagenforschung, Vol. 20 , Pp. 27–40. [REVIEW]Carlo Cellucci - 1985 - Journal of Symbolic Logic 50 (1):244-246.
  42.  1
    La Filosofia Della Matematica.Carlo Cellucci - 1969 - Association for Symbolic Logic.
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  43. Mathematical Reasoning and Heuristics.Carlo Cellucci & Donald Gillies (eds.) - 2005 - College Publications.
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  44. Temi E Prospettive Della Logica E Della Filosofia Della Scienza Contemporanee Organizzato Dalla Società Italiana di Logica E Filosofia Delle Scienze : Cesena, 7-10 Gennaio 1987.Carlo Cellucci & Società Italiana di Logica E. Filosofia Della Scienza - 1988 - Cooperativa Libraria Universitaria Editrice Bologna.
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  45. Why Should the Logic of Discovery Be Revived?Carlo Cellucci - 2014 - In E. Ippoliti (ed.), Heuristic Reasoning. Springer. pp. 11-27.
    Three decades ago Laudan posed the challenge: Why should the logic of discovery be revived? This paper tries to answer this question arguing that the logic of discovery should be revived, on the one hand, because, by Gödel’s second incompleteness theorem, mathematical logic fails to be the logic of justification, and only reviving the logic of discovery logic may continue to have an important role. On the other hand, scientists use heuristic tools in their work, and it may be useful (...)
     
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  46. Logica E Filosofia Della Scienza, Problemi E Prospettive Atti Del Congresso Triennale Della Società Italiana di Logica E Filosofia Delle Scienze, Lucca, 7-10 Gennaio 1993.Maria Concetta Di Maio, Carlo Cellucci, Gino Roncaglia, Problemi E. Prospettive Società Italiana di Logica E. Filosofia Della Scienza & Congresso Logica E. Filosofia Della Scienza - 1994 - Edizioni Ets.
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  47.  40
    Logic and Knowlegde.Emiliano Ippoliti, Carlo Cellucci & Emily Grosholz (eds.) - 2011 - Cambridge Scholar Publishing.
    Logic and Knowledge -/- Editor: Carlo Cellucci, Emily Grosholz and Emiliano Ippoliti Date Of Publication: Aug 2011 Isbn13: 978-1-4438-3008-9 Isbn: 1-4438-3008-9 -/- The problematic relation between logic and knowledge has given rise to some of the most important works in the history of philosophy, from Books VI–VII of Plato’s Republic and Aristotle’s Prior and Posterior Analytics, to Kant’s Critique of Pure Reason and Mill’s A System of Logic, Ratiocinative and Inductive. It provides the title of an important collection of papers (...)
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