Dossier Pierre Duhem

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## No 2 (2017)### Dossier Pierre Duhem**Pierre Duhem’s Philosophy and History of Science**### Full IssueView or download the full issue | [PDF](https://www.historiographyofscience.org/index.php/transversal/issue/viewIssue/6/7) ---|--- ### Table of Contents#### From the Editors[Historiography of Science: The Link between History and Philosophy in Understanding Science](https://www.historiographyofscience.org/index.php/transversal/article/view/49)Mauro L. Condé, Marlon Salomon | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/49/53)01 ---|--- #### Dossiers (Issue-specific topics)[Introduction](https://www.historiographyofscience.org/index.php/transversal/article/view/51)Fábio Rodrigo Leite, Jean-François Stoffel | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/51/55)03 ---|--- [Duhem’s Analysis of Newtonian Method and the Logical Priority of Physics over Metaphysics](https://www.historiographyofscience.org/index.php/transversal/article/view/39)Eduardo Salles de Oliveira Barra, Ricardo Batista dos Santos | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/39/45)07 ---|--- [The French Roots of Duhem’s early Historiography and Epistemology](https://www.historiographyofscience.org/index.php/transversal/article/view/33)Stefano Bordoni | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/33/39)20 ---|--- [Duhem’s Critical Analysis of Mechanicism and his Defense of a Formal Conception of Theoretical Physics](https://www.historiographyofscience.org/index.php/transversal/article/view/44)José R. N. Chiappin, Cássio Costa Laranjeiras | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/44/50)36 ---|--- [Anti-Scepticism and Epistemic Humility in Pierre Duhem’s Philosophy of Science](https://www.historiographyofscience.org/index.php/transversal/article/view/45)Marie Gueguen, Stathis Psillos | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/45/51)54 ---|--- [Duhem: Images of Science, Historical Continuity, and the First Crisis in Physics](https://www.historiographyofscience.org/index.php/transversal/article/view/37)Michael Liston | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/37/48)73 ---|--- [Duhem in Pre-War Italian Philosophy: The Reasons of an Absence](https://www.historiographyofscience.org/index.php/transversal/article/view/53)Roberto Maiocchi | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/53/58)85 ---|--- [Was Pierre Duhem an Esprit de finesse?](https://www.historiographyofscience.org/index.php/transversal/article/view/41)Víctor Manuel Hernández | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/41/49)93 ---|--- [Was Duhem Justified in not Distinguishing Between Physical and Chemical Atomism?](https://www.historiographyofscience.org/index.php/transversal/article/view/22)Paul Needham | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/22/42)108 ---|--- [Bon sens and noûs](https://www.historiographyofscience.org/index.php/transversal/article/view/35)Roberto Estrada Olguin | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/35/41)112 ---|--- [Duhem’s Legacy for the Change in the Historiography of Science: An Analysis Based on Kuhn’s Writings](https://www.historiographyofscience.org/index.php/transversal/article/view/48)Amélia Oliveira | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/48/56)127 ---|--- [Poincaré and Duhem: Resonances in their First Epistemological Reflections](https://www.historiographyofscience.org/index.php/transversal/article/view/40)João Príncipe | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/40/46)140 ---|--- #### Dossier - Book Reviews[Pierre Duhem: Between Physics and Metaphysics](https://www.historiographyofscience.org/index.php/transversal/article/view/32)Dámian Islas Mondragon | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/32/38)157 ---|--- [The New French Edition of Pierre Duhem’s The Aim and Structure of the Physical Theory](https://www.historiographyofscience.org/index.php/transversal/article/view/54)Jean-François Stoffel | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/54/62)160 ---|--- [When Historiography Met Epistemology](https://www.historiographyofscience.org/index.php/transversal/article/view/55)Jean-François Stoffel | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/55/61)163 ---|--- #### Articles[A Development of the Principle of Virtual Laws and its Conceptual Framework in Mechanics as Fundamental Relationship between Physics and Mathematics](https://www.historiographyofscience.org/index.php/transversal/article/view/8)Raffaele Pisano | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/8/47)166 ---|--- [Michael Scot and the Four Rainbows](https://www.historiographyofscience.org/index.php/transversal/article/view/28)Tony Scott | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/28/43)204 ---|--- [Galileo and the Medici: Post-Renaissance Patronage or Post-Modern Historiography](https://www.historiographyofscience.org/index.php/transversal/article/view/47)Michael Segre | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/47/63)226 ---|--- #### Interviews[Interview: Helge Kragh](https://www.historiographyofscience.org/index.php/transversal/article/view/52)Gustavo Rodrigues Rocha, Helge Kragh | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/52/57)233 ---|--- #### Book Reviews[Galileo as a Critic of the Arts](https://www.historiographyofscience.org/index.php/transversal/article/view/36)Hallhane Machado | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/36/60)238 ---|--- [A Contribution to the Newtonian Scholarship: The “Jesuit Edition” of Isaac Newton’s Principia, a research in progress by Paolo Bussotti and Raffaele Pisano](https://www.historiographyofscience.org/index.php/transversal/article/view/50)Gustavo Rodrigues Rocha | [PDF](https://www.historiographyofscience.org/index.php/transversal/article/view/50/54)242 ---|--- **ISSN: 2526-2270** This work is licensed under a [Creative Commons Attribution 4.0 International License](https://creativecommons.org/licenses/by/4.0/).* * *About footnote #6 of *Duhem’s Critical Analysis of Mechanicism and his Defense of a Formal Conception of Theoretical Physics* {[Gueguen & Psillos (2017)](https://www.historiographyofscience.org/index.php/transversal/article/view/45)}:Recall that Frege’s 1884 definition of number (in *Die Grundlagen der Arithmetik: Eine logisch-mathematische Untersuchung über den Begriff der Zahl* ) is predicated upon the concept of function. His theory of number is a second-order functional calculus with individual variables (terms/objects/arguments denoting truth-values) and function variables (formulas denoting the “extension” or class of a given numerical *object* under a specific *concept* ). That’s how he thinks of “abstraction” in his war against psychologism and subjectivity in mathematical theory. For example, a binary function of two variables *x* and *y* , denoted *F* (( *x* ), ( *y* )), will stand for a class of objects falling under a given concept *F* if *F* (( *x* ), ( *y* )) is always a truth-value. In that kind of statements, the function operation replaces the classical predication. As for Russell’s theory of types, it is predicated upon a set theoretical view of variables of “concatenated” higher-orders. That’s how his theory may be thought of as having to do with abstraction of several degrees. For example, a variable for individuals, another for sets of individuals, another yet for sets of sets of individuals, etc.The parallel you further highlight by quoting Duhem from *Prémices philosophiques* (to clarify the Frege-Duhem connection footnoted in the *Anti-Scepticism and Epistemic Humility in Pierre Duhem’s Philosophy of Science* article, p. 57) does make a lot of sense when talking about Duhem’s view of the use of abstraction as essentially equivalent (as you point out) to “Oresme’s discovery of how to assign numbers (analogically) to qualities.” With reference to Frege, I would recap it by saying that there seems to be a legitimate connection between the Fregean view of numbers in terms of “extensions” (--> relations of analogy between classes, a number [in the Fregean sense] being a class of *similar* classes) and the Duhemian/Oresmean view about the epistemological function of “abstraction” in relation to physical theories. I’m not aware of any direct influence of Oresme’s own “triangle” on Pascal’s *triangle arithmétique*. I know not of any place Pascal may have mentioned he knew of *Le Livre du ciel et du monde*. But he very well might have, and even actually referred to it—without me knowing it, as I haven’t gone through a detailed reading of Pascal’s entire corpus, which also includes many letters (notably to Fermat in mid-1654, precisely on his triangle). It is associated to some extent with “the so-called intuitionism and formalism debate in mathematics.” But, more specifically, the anti-psychologism stance Frege and others took in relation to foundational problems in mathematics hinges around the objectivity of logic (of logical truth), which Frege expressly emphasized demonstrably obtains apart from empiricism and the psychological determinisms influencing mental processing. His discussion of “analogy” is not so clearly identified as being about “analogy.” But whether with respect to what he understands and defines *bedeutung* (reference) to mean in functional logic or to the definition of a number as a class of similar classes, the notion of analogous modes of representation (“extensions”) for a given referent is quite intrinsic to his semantic theory and its epistemological implications. In that regard, it may be said not to be without connection with (as I wrote before) the Duhemian/Oresmean view about the epistemological function of “abstraction” in relation to physical theories, even though Frege did not “discuss analogy directly, in the process of [indicatively] understanding how to assign numbers to qualities.”