45 found
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  1. Plato's Problem: An Introduction to Mathematical Platonism.Marco Panza & Andrea Sereni - 2013 - Palgrave-Macmillan.
  2. The Twofold Role of Diagrams in Euclid’s Plane Geometry.Marco Panza - 2012 - Synthese 186 (1):55-102.
    Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid’s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid’s plane geometry (EPG). Euclid’s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams (...)
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  3. Diagrams in Mathematics: History and Philosophy.John Mumma & Marco Panza - 2012 - Synthese 186 (1):1-5.
    Diagrams are ubiquitous in mathematics. From the most elementary class to the most advanced seminar, in both introductory textbooks and professional journals, diagrams are present, to introduce concepts, increase understanding, and prove results. They thus fulfill a variety of important roles in mathematical practice. Long overlooked by philosophers focused on foundational and ontological issues, these roles have come to receive attention in the past two decades, a trend in line with the growing philosophical interest in actual mathematical practice.
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  4. Functions and Generality of Logic.Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur (eds.) - 2015 - Springer Verlag.
    Part I of Frege’s Grundgesetze is devoted to the “exposition [Darlegung]” of his formal system.
     
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  5. From Lagrange to Frege: Functions and Expressions.Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur - 2015 - In Gabriel Sandu, Marco Panza & Hourya Benis-Sinaceur (eds.), Functions and Generality of Logic. Springer Verlag.
    Both Frege's Grundgesetze, and Lagrange's treatises on analytical functions pursue a foundational purpose. Still, the former's program is not only crucially different from the latter's. It also depends on a different idea of what foundation of mathematics should be like . Despite this contrast, the notion of function plays similar roles in their respective programs. The purpose of my paper is emphasising this similarity. In doing it, I hope to contribute to a better understanding of Frege's logicism, especially in relation (...)
     
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  6.  74
    The Varieties of Indispensability Arguments.Marco Panza & Andrea Sereni - 2016 - Synthese 193 (2):469-516.
    The indispensability argument comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA (...)
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  7. Classical Sources for the Concepts of Analysis and Synthesis.Marco Panza - 1997 - Boston Studies in the Philosophy of Science:365-414.
  8.  1
    Abstraction and Epistemic Economy.Marco Panza - 2016 - In Sorin Costreie (ed.), Early Analytic Philosophy – New Perspectives on the Tradition. Springer Verlag.
    Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I suggest (...)
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  9. Mathematical Proofs.Marco Panza - 2003 - Synthese 134 (1-2):119 - 158.
    The aim I am pursuing here is to describe some general aspects of mathematical proofs. In my view, a mathematical proof is a warrant to assert a non-tautological statement which claims that certain objects (possibly a certain object) enjoy a certain property. Because it is proved, such a statement is a mathematical theorem. In my view, in order to understand the nature of a mathematical proof it is necessary to understand the nature of mathematical objects. If we understand them as (...)
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  10.  28
    Processes Rather Than Descriptions?Domenico Napoletani, Marco Panza & Daniele C. Struppa - 2013 - Foundations of Science 18 (3):587-590.
    As a reply to the commentary (Humphreys in Found Sci, 2012), we explore the methodological implications of seeing artificial neural networks as generic classification tools, we show in which sense the use of descriptions and models in data analysis is not equivalent to the original empirical use of epicycles in describing planetary motion, and we argue that agnostic science is essentially related to the type of problems we ask about a phenomenon and to the processes used to find answers.
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  11.  37
    Artificial Diamonds Are Still Diamonds.Domenico Napoletani, Marco Panza & Daniele C. Struppa - 2013 - Foundations of Science 18 (3):591-594.
    As a reply to the commentary (Lenhard in Found Sci, 2012), we stress here that structural understanding of data analysis techniques is the natural counterpart to the lack of understanding of phenomena in agnostic science. We suggest moreover that the dynamics of computational processes, and their parallels with the dynamics of natural processes, will increasingly be, possibly, the driving force of the development of data analysis.
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  12.  45
    François Viète: Between Analysis and Cryptanalysis.Marco Panza - 2006 - Studies in History and Philosophy of Science Part A 37 (2):269-289.
    François Viète is considered the father both of modern algebra and of modern cryptanalysis. The paper outlines Viète’s major contributions in these two mathematical fields and argues that, despite an obvious parallel between them, there is an essential difference. Viète’s ‘new algebra’ relies on his reform of the classical method of analysis and synthesis, in particular on a new conception of analysis and the introduction of a new formalism. The procedures he suggests to decrypt coded messages are particular forms of (...)
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  13.  12
    Das velocidades às fluxões.Marco Panza - 2010 - Scientiae Studia 8 (4):509-546.
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  14.  6
    La révolution scientifique les révolutions et l'histoire des sciences.Marco Panza - 2001 - Revue de Synthèse 122 (2-4):411-424.
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  15.  7
    Frege’s Theory of Real Numbers: A Consistent Rendering.Francesca Boccuni & Marco Panza - forthcoming - Review of Symbolic Logic:1-42.
    Frege's definition of the real numbers, as envisaged in the second volume of Grundgesetze der Arithmetik, is fatally flawed by the inconsistency of Frege's ill-fated Basic Law V. We restate Frege's definition in a consistent logical framework and investigate whether it can provide a logical foundation of real analysis. Our conclusion will deem it doubtful that such a foundation along the lines of Frege's own indications is possible at all.
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  16.  23
    The Logical System of Frege's Grundgestze: A Rational Reconstruction.Méven Cadet & Marco Panza - 2015 - Manuscrito 38 (1):5-94.
    This paper aims at clarifying the nature of Frege's system of logic, as presented in the first volume of the Grundgesetze. We undertake a rational reconstruction of this system, by distinguishing its propositional and predicate fragments. This allows us to emphasise the differences and similarities between this system and a modern system of classical second-order logic.
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  17.  6
    From Logic to Practice.Giorgio Venturi, Marco Panza & Gabriele Lolli (eds.) - 2015 - Springer International Publishing.
    In the Tractatus, it is stated that questions about logical formatting cannot be meaningfully formulated, since it is precisely the application of logical rules which enables the formulation of a question whatsoever; analogously, Wittgenstein’s celebrated infinite regress argument on rule-following seems to undermine any explanation of deduction, as relying on a logical argument. On the other hand, some recent mathematical developments of the Curry-Howard bridge between proof theory and type theory address the issue of describing the “subjective” side of logic, (...)
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  18.  19
    The Agnostic Structure of Data Science Methods.Domenico Napoletani, Marco Panza & Daniele Struppa - unknown
    In this paper we want to discuss the changing role of mathematics in science, as a way to discuss some methodological trends at work in big data science. More specifically, we will show how the role of mathematics has dramatically changed from its more classical approach. Classically, any application of mathematical techniques requires a previous understanding of the phenomena, and of the mutual relations among the relevant data; modern data analysis appeals, instead, to mathematics in order to identify possible invariants (...)
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  19. Analysis and Synthesis in Mathematics,.Michael Otte & Marco Panza (eds.) - 1997 - Kluwer Academic Publishers.
  20. Analysis and synthesis in mathematics, Boston studies in the philosophy of science, vol. 196.Michaël Otte & Marco Panza - 1999 - Revue Philosophique de la France Et de l'Etranger 189 (1):99-99.
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  21. Analysis and Synthesis in Mathematics History and Philosophy.Michael Otte & Marco Panza - 1997
  22. Reviews: Mathematics and Logic-Analysis and Synthesis in Mathematics. History and Philosophy. [REVIEW]Michael Otte, Marco Panza & I. Grattan-Guinness - 1998 - Annals of Science 55 (4):436-437.
  23. Breathing Fresh Air Into the Philosophy of Mathematics: Paolo Mancosu : The Philosophy of Mathematical Practice. Oxford, New York: Oxford University Press, 2008, Xii+448pp, £58.95, $100.00 HB.Marco Panza - 2011 - Metascience 20 (3):495-500.
    Breathing fresh air into the philosophy of mathematics Content Type Journal Article DOI 10.1007/s11016-010-9470-8 Authors Marco Panza, IHPST, 13, rue du Four, 75006 Paris, France Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  24.  9
    De la Nature Épargnante aux Forces Généreuses: Le Principe de Moindre Action Entre Mathématiques Et Métaphysique. Maupertuis Et Euler, 1740-1751/From Nature That Economizes to Generous Forces: The Principle of Least Action Between Mathematics and Metaphysics, Maupertuis and Euler, 1740-1751. [REVIEW]Marco Panza - 1995 - Revue d'Histoire des Sciences 48 (4):435-520.
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  25.  1
    Discussion Note On: “Semantic Nominalism: How I Learned to Stop Worrying and Love Universals” by G. Aldo Antonelli.Marco Panza & Robert May - 2016 - In Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. Filmat Studies in the Philosophy of Mathematics. Springer Verlag.
    Editorial NoteThe following Discussion Note is an edited transcription of the discussion on G. Aldo Antonelli’s paper “Semantic Nominalism: How I Learned to Stop Worrying and Love Universals”, held among participants at the IHPST-UC Davis Workshop Ontological Commitment in Mathematics which took place, in memoriam of Aldo Antonelli, at IHPST in Paris on December, 14–15, 2015. The note’s and volume’s editors would like to thank all participants in the discussion for their contributions, and Alberto Naibo, Michael Wright and the personnel (...)
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  26. Espace Et Horizon de Réalité Philosophie Mathématique de Ferdinand Gonseth.Marco Panza & Jean-Claude Pont - 1992
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  27.  1
    Enthymemathical Proofs and Canonical Proofs in Euclid’s Plane Geometry.Marco Panza & Abel Lassalle-Casanave - 2018 - In Hassan Tahiri (ed.), The Philosophers and Mathematics: Festschrift for Roshdi Rashed. Springer Verlag. pp. 127-144.
    Since the application of Postulate I.2 in Euclid’s Elements is not uniform, one could wonder in what way should it be applied in Euclid’s plane geometry. Besides legitimizing questions like this from the perspective of a philosophy of mathematical practice, we sketch a general perspective of conceptual analysis of mathematical texts, which involves an extended notion of mathematical theory as system of authorizations, and an audience-dependent notion of proof.
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  28.  33
    Frege’s Constraint and the Nature of Frege’s Foundational Program.Marco Panza & Andrea Sereni - 2019 - Review of Symbolic Logic 12 (1):97-143.
    Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ or ‘Frege Constraint’, the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and on whether it applies to (...)
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  29. From Nature That Economizes to Generous Forces: The Principle of Least Action Between Mathematics and Metaphysics, Maupertuis and Euler, 1740-1751. [REVIEW]Marco Panza - 1995 - Revue d'Histoire des Sciences 48 (4):435-520.
  30. Geometria, Flussioni E Differenziali.Marco Panza & Clara Silvia Roero (eds.) - 1995 - La Città Del Sole.
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  31.  25
    Infini, Logique, Geométrie.Marco Panza - 2016 - History and Philosophy of Logic 37 (4):396-399.
  32. Il Problema di Platone: Un'introduzione Storica Alla Filosofia Della Matematica.Marco Panza & Andrea Sereni - 2010 - Carocci.
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  33. Joseph Louis Lagrange.Marco Panza - 2008 - In T. Gowers (ed.), Princeton Companion to Mathematics. Princeton University Press. pp. 751--752.
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  34. La Forma Della Quantitáa Analisi Algebrica E Analisi Superiore : Il Problema Dell'unitáa Della Matematica Nel Secolo Dell'illuminismo = la Forme de la Quantit'e : Analyse Alg'ebrique Et Analyse Sup'erieure : Le Probláeme de l'Unit'e des Math'ematiques Dans le Siáecle des Lumiáeres.Marco Panza - 1992 - Sociâetâe Franðcaise d'Histoire des Sciences Et des Techniques Diffusion Belin.
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  35. L'objectivité Mathématique Platonismes Et Structures Formelles.Marco Panza & J. Salanskis - 1995
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  36. Les Savants Et l''epist'emologie Vers la Fin du Xixe Siáecle.Marco Panza & Jean-Claude Pont - 1995
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  37.  1
    Lagrange’s Theory of Analytical Functions and His Ideal of Purity of Method.Marco Panza & Giovanni Ferraro - 2012 - Archive for History of Exact Sciences 66 (2):95-197.
    We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, (...)
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  38. Pluralité de l'Algèbre À la Renaissance. [REVIEW]Marco Panza - 2013 - Isis 104:838-839.
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  39.  2
    Peirce et le continu.Marco Panza - 1998 - Revue de Synthèse 119 (4):603-611.
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  40. Pour une critique de la philosophie mathématique : le cas de Imre Lakatos.Marco Panza - 1988 - le Cahier (Collège International de Philosophie) 5:186-189.
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  41.  12
    Sabine Rommevaux;, Maryvonne Spiesser;, Maria Rosa Massa Esteve . Pluralité de l'Algèbre À la Renaissance. 348 Pp., Illus., Bibl., Index. Paris: Honoré Champion, 2012. €85. [REVIEW]Marco Panza - 2013 - Isis 104 (4):838-839.
  42. The Role of Algebraic Inferences in Na‘Īm Ibn Mūsā’s Collection of Geometrical Propositions.Marco Panza - 2008 - Arabic Sciences and Philosophy 18 (2):165-191.
    Nam ibn M recently edited and translated in French by Roshdi Rashed and Christian Houzel bit ibn Qurras treatise is its large use of a form of inferences that can be said in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic analyses that are mainly used to reduce the geometrical problems they are concerned with to al-Khw’s equations.
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  43. Was Frege a Logicist for Arithmetic?Marco Panza - 2018 - In Annalisa Coliva, Paolo Leonardi & Sebastiano Moruzzi (eds.), Eva Picardi on Language, Analysis and History. Palgrave. pp. 87-112.
    The paper argues that Frege’s primary foundational purpose concerning arithmetic was neither that of making natural numbers logical objects, nor that of making arithmetic a part of logic, but rather that of assigning to it an appropriate place in the architectonics of mathematics and knowledge, by immersing it in a theory of numbers of concepts and making truths about natural numbers, and/or knowledge of them transparent to reason without the medium of senses and intuition.
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  44.  1
    Forcing Optimality and Brandt’s Principle.Daniele Struppa, Marco Panza & Domenico Napoletani - 2017 - In Martin Carrier & Johannes Lenhard (eds.), Mathematics as a Tool. Tracing New Roles of Mathematics in the Sciences. Springer Verlag.
    We argue that many optimization methods can be viewed as representatives of “forcing”, a methodological approach that attempts to bridge the gap between data and mathematics on the basis of an a priori trust in the power of a mathematical technique, even when detailed, credible models of a phenomenon are lacking or do not justify the use of this technique. In particular, we show that forcing is implied in particle swarms optimization methods, and in modeling image processing problems through optimization. (...)
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  45. Publications de la SMF.Marco Panza - 1986 - History of Science 24:125-144.
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