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Profile: Carlo Cellucci (Sapienza University of Rome)
Profile: Carlo Cellucci
  1. Carlo Cellucci (forthcoming). Mathematical Beauty, Understanding, and Discovery. Foundations of Science:1-17.
    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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  2. 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.
  3. 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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  4. 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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  5. 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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  6. 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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  7. Carlo Cellucci (2007). La Filosofia della Matematica del Novecento. Laterza.
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  8. 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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  9. Carlo Cellucci & Paolo Pecere (eds.) (2006). Demonstrative and Non-Demonstrative Reasoning in Mathematics and Natural Science, Pp. 207-235. Edizioni dell'Università di Cassino.
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  10. 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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  11. Carlo Cellucci & Donald Gillies (eds.) (2005). Mathematical Reasoning and Heuristics. College Publications.
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  12. 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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  13. 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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  14. Carlo Cellucci (2000). Analytic Cut Trees. Logic Journal of the Igpl 8:733-750.
    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 <span class='Hi'>analytic</span> cut trees, a system from which cuts cannot be eliminated but satisfying the subformula property. Like tableaux <span class='Hi'>analytic</span> cut trees are a refutation system but unlike tableaux they have a single inference rule (a form of (...)
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  15. 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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  16. 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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  17. 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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  18. 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.
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  19. 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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  20. Carlo Cellucci (1974). On the Role of Reducibility Principles. Synthese 27 (1-2):93 - 110.
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  21. Carlo Cellucci (1970). Skolem's Paradox and Platonism. Critica 4 (11/12):43 - 54.
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  22. 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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