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Scientific Imagination, Geometry, and Motion in the Late Medieval calculatores Tradition

From: 2019-11-11 To:2019-11-13

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  • Thematic Line

    Medieval & Early Modern Philosophy
  • Research Group

    Reason, Politics & Society
  • Research seminar.

    Daniel A. Di Liscia* (Ludwig-Maximilians Universität München / Munich Center for Mathematical Philosophy)

    Scientific Imagination, Geometry, and Motion in the Late Medieval calculatores Tradition

    11, 12 and 13 November 2019
    10h00 - 13h00 | Sala de Reuniões 2
    Faculdade de Letras da Universidade do Porto

    “Geometry” and “motion” are two notions intrinsically united in modern physics, especially after Galileo, whose “new science of motion” is nothing but a geometrization of – as he himself wrote in his Discorsi – “an old topic about which the philosopher have already written enough comprehensive books”.  In fact, it seems that for the previous period, influenced by Aristotle and his followers, geometry and motion are hardly compatible.

    Sometimes, history is a good tool to reflect on scientific and philosophical issues. The present seminar will deal with a special development in late medieval thought which is connected to both, the history of classical philosophy and the history of science (physics and mathematics). By reading and discussing original sources we intend to question the traditional clear-cut understanding of the overused notion of “Scientific Revolution”. As we will see, from the 14th century onward and during the entire 15th century there was a widespread approach based on the mathematization of motion and qualities. Initiated by the Oxford calculatores, this way of thinking was so successful that it became a completely new discipline, a new “middle science” – as it was usually called – included in the university curriculum along with other similar disciplines like optics and astronomy.

    In the first session (“The epistemological background and the sophismata-tradition”) we will discuss the problem of a mathematized science of nature in Aristotle, Robert Grosseteste and Thomas Aquinas. In addition, we will analyze some texts belonging to the sophismata tradition to consider the role of logic and philosophy of language. In the second session (“Configurationes and latitudines”) we will go in medias res by reading some passages of Nicole Oresme’ treatise De configurationibus and of the Pseudo-Oresme De latitudinibus formarum. We will focus on the geometrical approach as the background for this new discipline. In the third and final session (“A new ‘Middle Science’ and the New Science of Motion”) we will discussion the relationship between the late medieval geometrization of motion and the new approach presented by Galileo Galilei.


    The seminar sessions are open, but attendance should be confirmed by email: lqueiroz@letras.up.pt


    1st Session

    11 November (Sala de Reuniões 2, 10h00-13h00)

    The epistemological background and the sophismata-tradition

    Texts (1-5)


    2nd Session

    12 November (Sala de Reuniões 2, 10h00-13h00)

    Configurationes and latitudines

    Texts (9-10)


    3rd Session

    13 November (Sala de Reuniões 2, 10h00-13h00)

    A new ‘Middle Science’ and the New Science of Motion

    Texts (11-13)


    Texts available here: https://drive.google.com/open?id=1ehnVLBuepvRyPxMRhRg7WQwiV0fK18fS


    Supporting bibliography

    Daniel A. Di Liscia, La «latitud de las formas» y la geometrización de la ciencia del movimiento, Mediaevalia. Textos e estudos, 36 (2017) 75-114.


    E. Sylla, «Oxford Calculators», The Cambridge History of Later Medieval Philosophy: From the Rediscovery of Aristotle to the Disintegration of Scholasticism, 1100-1600, ed. J. Pinborg, A. Kenny, Cambridge University Press, 1988.



    *Daniel A. Di Liscia

    Daniel A. Di Liscia studied philosophy at the University of Buenos Aires with a specialization in the history of late medieval and early modern philosophy (1989). With support first from the DAAD (German Academic Exchange Service) and later from the Antorchas Foundation, he completed his Ph. D. at the LMU München (summa cum laude). After three years of collaboration at the Munich Copernicus Edition, he came to the Kepler-Kommission in the Bavarian Academy of Sciences, where he worked for six years, the final four as “Wissenschaftlicher Leiter”.

    His research interests are in the history of philosophy and science from late medieval to early modern times. His focus lies on two branches of research: the history of Renaissance cosmology, especially in connection with Nicolaus Copernicus and Johannes Kepler, and the tradition of the “calculators”. The background for both subjects is the same: the late Aristotelian tradition in logic, epistemology and, above all, natural philosophy.

    1. Late medieval history of logic and philosophy of language: theory of „consequentiae“; syllogistic and concept of deduction in medieval logic and mathematics.

    2. Modern cosmology and history of science: Gravity in Copernicus and Kepler; Kepler on pneumatics; mathematics and metrology in Kepler; the late Aristotelian Tradition and the new cosmology; Renaissance epistemology (the “middle sciences”, regressus demonstrativus and the kind of scientific proofs).

    Selected Publications

    - Daniel A. Di Liscia, Zwischen Geometrie und Naturphilosophie. Die Entwicklung der Formlatitudenlehre im deutschen Sprachraum, als Mikrofiche erschienen (München, Universitätsbibliothek, sign.: 0001/UMC 18387).

    - D. A. Di Liscia, E. Kessler, Ch. Methuen (eds.): Method and Order in Renaissance Philosophy of Nature. The Aristotle Commentary Tradition, Adeshot – Brookfield – Singapore – Sidney, Ashgate, 1997.

    - F. Boockmann, D. A. Di Liscia, H. Kothmann (eds.), Miscellanea Kepleriana. Festschrift für Volker Bialas zum 65. Geburtstag, Augsburg: Dr. Erwin Rauner Verlag, 2005.

    - Johannes Kepler. Gesammelte Werke, vol. XXI.2.1. Manuscripta Astrologica – Manuscripta Pneumatica, München, Beck Verlag, 2009.

    - «Velocidad quo ad effectus y velocidad quo ad causas: la tradición de los calculadores y la metodología aristotélica», in, Method and Order ... D. A. Di Liscia, E. Kessler, Ch. Methuen (eds.), pp. 143–176.

    - «Die fallenden Körper und die Rätsel des Domingo de Soto», in Der ungebändigte Galilei. Beiträge zu einem Symposion, M. Segre, E. Knobloch (eds.), Stuttgart, Franz Steiner Verlag, 2001, pp. 9–22.

    - «‘El libro encadenado’: Eine Sammelhandschrift naturphilosophischer Schriften von Jean Buridan“ (Ms. Buenos Aires, Biblioteca Nacional 342R)», Vivarium 39/1 (2001), pp. 52–86.

    - «Der von Amplonius Rattinck dem Oresme zugeschriebene Tractatus de terminis confundentibus und dessen verschollene Handschrift (Hs. Pommersfelden, Graf von Schönborn Schloßbibliothek, 236 [2858])» Traditio 56 (2001), pp. 89–108.

    Project From Data to Wisdom. Philosophizing Data Visualizations in the Middle Ages and Early Modernity (13th-17th Century) - FDTW (POCI-01-0145-FEDER-029717)
    Instituto de Filosofia da Universidade do Porto - FIL/00502
    Fundação para a Ciência e a Tecnologia (FCT)

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