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Profile: Carlo Cellucci (Sapienza University of Rome)
Profile: Carlo Cellucci
  1. Carlo Cellucci (2014). Rethinking Philosophy. Philosophia 42 (2):271-288.
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  2.  10
    Carlo Cellucci (2014). Knowledge, Truth and Plausibility. Axiomathes 24 (4):517-532.
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  3.  18
    Carlo Cellucci (forthcoming). Frege on Thinking and Its Epistemic Significance. History and Philosophy of Logic:1-3.
  4. Carlo Cellucci, How Should We Think About the Meaning of Life?
    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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  5.  2
    Carlo Cellucci (2013). Philosophy of Mathematics: Making a Fresh Start. Studies in History and Philosophy of Science 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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  6. Carlo Cellucci (2005). Mente Incarnata E Conoscenza [Embodied Mind and Knowledge]. 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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  7.  89
    Carlo Cellucci (2014). Knowledge, Truth and Plausibility. 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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  8.  9
    Carlo Cellucci (2015). Is Philosophy a Humanistic Discipline? 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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  9. Carlo Cellucci (2000). The Growth of Mathematical Knowledge: An Open World View. In Emily Grosholz & Herbert Breger (eds.), The Growth of Mathematical Knowledge, pp. 153-176. Kluwer 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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  10. Carlo Cellucci (2002). L'illusione di Una Filosofia Specializzata [The Illusion of a Specialized P Hilosophy]. 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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  11. Carlo Cellucci (1996). Mathematical Logic: What has It Done for the Philosophy of Mathematics? 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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  12. Carlo Cellucci (1993). From Closed to Open Systems. 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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  13. Carlo Cellucci (2006). Filosofia & Matematica, Introduction. 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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  14. Carlo Cellucci (2000). Analytic Cut Trees. 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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  15. Carlo Cellucci (1998). The Scope of Logic: Deduction, Abduction, Analogy. 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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  16. Carlo Cellucci (2005). Mathematical Discourse Vs. Mathematical Intuition. In Carlo Cellucci & Donald Gillies (eds.), Mathematical Reasoning and Heuristics. College Publications 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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  17. Carlo Cellucci (2008). The Nature of Mathematical Explanation. Studies in History and Philosophy of Science Part A 39 (2):202-210.
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  18.  9
    Carlo Cellucci (2014). Rethinking Philosophy. 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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  19. Carlo Cellucci (2003). Review of M. Giaquinto, The Search for Certainty. [REVIEW] European Journal of Philosophy 11:420-423.
    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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  20.  9
    Carlo Cellucci (forthcoming). Is Mathematics Problem Solving or Theorem Proving? Foundations of Science:1-17.
    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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  21.  14
    Carlo Cellucci (2013). Philosophy of Mathematics: Making a Fresh Start. Studies in History and Philosophy of Science Part A 44 (1):32-42.
  22. Carlo Cellucci (2009). The Universal Generalization Problem. 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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  23. Carlo Cellucci (2002). Filosofia E Matematica. Monograph Collection (Matt - Pseudo).
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  24.  11
    Carlo Cellucci (2008). The Nature of Mathematical Explanation. Studies in History and Philosophy of Science 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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  25. Carlo Cellucci (1998). La Ragioni Della Logica. Monograph Collection (Matt - Pseudo).
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  26.  9
    Carlo Cellucci (1995). On Quine's Approach to Natural Deduction'. In Paolo Leonardi & Marco Santambrogio (eds.), On Quine: New Essays. Cambridge University Press 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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  27.  21
    Carlo Cellucci (2015). Mathematical Beauty, Understanding, and Discovery. 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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  28. Carlo Cellucci (2006). The Question Hume Didn't Ask: Why Should We Accept Deductive Inferences? In Carlo Cellucci & Paolo Pecere (eds.), Demonstrative and Non-Demonstrative Reasoning in Mathematics and Natural Science. Edizioni dell'Università di Cassino 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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  29. Carlo Cellucci (2007). La Filosofia della Matematica del Novecento. Laterza.
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  30.  10
    Carlo Cellucci (2015). Rethinking Knowledge. 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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  31.  53
    Carlo Cellucci (1985). Proof Theory and Complexity. Synthese 62 (2):173-189.
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  32.  4
    Carlo Cellucci (1992). Existential Instantiation and Normalization in Sequent Natural Deduction. 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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  33.  43
    Carlo Cellucci (1974). On the Role of Reducibility Principles. Synthese 27 (1-2):93 - 110.
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  34.  3
    Carlo Cellucci (2014). Knowledge, Truth and Plausibility. Axiomathes 24 (4):517-532.
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  35.  8
    Carlo Cellucci (1985). 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] Journal of Symbolic Logic 50 (1):244-246.
  36.  13
    Carlo Cellucci (1970). Skolem's Paradox and Platonism. Critica 4 (11/12):43 - 54.
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  37.  1
    Carlo Cellucci (2013). Top-Down and Bottom-Up Philosophy of Mathematics. Foundations of Science 18 (1):93-106.
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  38. Carlo Cellucci (1985). Proof Theory and Complexity. Synthese 62 (2):173-189.
  39.  3
    Carlo Cellucci (1992). Existential Instantiation and Normalization in Sequent Natural Deduction. Annals of Pure and Applied Logic 58 (2):111-148.
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  40. Carlo Cellucci & Paolo Pecere (eds.) (2006). Demonstrative and Non-Demonstrative Reasoning in Mathematics and Natural Science. Edizioni dell'Università di Cassino.
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  41. Carlo Cellucci (2014). Does Logic Slowly Pass Away, or Has It a Future? In E. Moriconi & L. Tescari (eds.), Second Pisa Colloquium in Logic, Language and Epistemology. ETS 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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  42. Carlo Cellucci (1992). Dalla logica teoretica alla logica pratica. Rivista di Filosofia 83 (2):169.
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  43. Carlo Cellucci (1985). 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] Journal of Symbolic Logic 50 (1):244-246.
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  44. Carlo Cellucci (1969). La Filosofia Della Matematica. Journal of Symbolic Logic 34 (2):313-314.
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  45. Carlo Cellucci & Donald Gillies (eds.) (2005). Mathematical Reasoning and Heuristics. College Publications.
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  46. Carlo Cellucci (1982). Teoria Della Dimostrazione. Normalizzazioni E Assegnazioni di Numeri Ordinali. Journal of Symbolic Logic 47 (1):220-221.
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  47. Carlo Cellucci & Società Italiana di Logica E. Filosofia Della Scienza (1988). 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. [REVIEW] Cooperativa Libraria Universitaria Editrice Bologna.
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  48. Carlo Cellucci (2014). Why Should the Logic of Discovery Be Revived? In E. Ippoliti (ed.), Heuristic Reasoning. Springer 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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  49. 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). 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. [REVIEW] Edizioni Ets.
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  50.  28
    Emiliano Ippoliti, Carlo Cellucci & Emily Grosholz (eds.) (2011). Logic and Knowlegde. 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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