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  • Draft: please do not cite or circulate Marco Romani Mistretta

    1 Harvard University, Department of the Classics

    Boylston Hall, 1350 Massachusetts Avenue 02138 Cambridge, MA (USA)

    Platonic Hypotheses: Galileos Analytic Method and the Phaedo


    Galileo often resembles an epistemological Proteus. Because of his unquestionable status

    as one of the founding fathers of modern science, his methodological tenets have not only been

    constantly bent to support whichever theory of natural science is en vogue at any given moment,

    but his fundamentally Classical allegiances have accordingly experienced major shifts.1 Is Galileo

    a Platonist or an Aristotelian? Is he a realist or an instrumentalist? Does he ever prove to be

    an Archimedean scientist? Or perhaps none of the above? What ancient sources, if any, inform

    his conception of the workings and methods of physics?

    The dichotomy of Platonism and Aristotelianism, in particular, seems to dominate

    early- and mid-twentieth-century Galilean scholarship. A. Koyr's seminal article (1943),2 for

    instance, establishes a polarizing contrast between Platonic and Aristotelian natural science,

    based on the role assigned to mathematics in making sense of the physical world. Koyr argues

    that, whereas Aristotle conceives of the workings of nature as being intelligible in purely empirical

    terms, without the need for mathematical formalization, Plato (in the Timaeus) describes the

    structure of nature as being inherently geometrical, and therefore only subject to explanation

    through mathematical concepts. According to Koyr (followed by Crombie and others), Galileo is

    essentially a Platonist insofar as he attributes a crucial importance to the use of mathematics in

    1 See e.g. Wallace 1974: 79 (with references); McMullin 1978: 210. 2 Koyr's views concerning the predominance of natural philosophy (in the Aristotelian sense) over the application of mathematical reasoning to the physical world constitute one the main underpinnings of his well-known denial that the ancients ever developed any technology in the modern sense of the term (cf. especially From the Closed World to the Infinite Universe, Baltimore - London 1957).

  • Platonic Hypotheses


    natural science (ubi mathematica, ibi Plato).3 C. Dollo (1989), however, has rightly pointed out

    that Galileos Platonism is constituted by well-defined and circumscribed elements of method and

    cosmological content, rather than by a mere set of Platonic ideas, vaguely related to the

    mathematization of the world, but devoid of factual significance.4

    Other scholars, most notably T.P. McTighe (1968) and E. McMullin (1978), have

    emphasized the Aristotelian character of Galileo's epistemology by drawing attention to his

    conception of physics - and of mechanics in particular - as a demonstrative science, or a science

    of the necessary. Demonstration, for Aristotle provides the gnoseological foil against which the

    explanatory power of any other science is to be measured: an extremely influential idea, if one

    thinks - for example - of Veblen's claim that the formulation of a science endowed with necessity

    and sufficiency is the goal of any investigations of the foundations of geometry.5 Moreover,

    building upon an intuition originally suggested by Cassirer,6 A.C. Crombie (1953) and N. Jardine

    (1976) have shown striking affinities between Galileo's account of scientific demonstration and

    the Aristotelian theories of Paduan Renaissance intellectuals such as Agostino Nifo and Giacomo

    3 It is now known that the principal experiments described in Galileo's Discorsi, and thought by Koyr to be pure thought experiments, were in fact performed (see e.g. Dubarle 1968: 305). 4 Similarly, J. Hankins (2000) rightly warns against the tendnecy of much Galilean scholarship to approach the Platonic problem from an unhistorical perspective: rather, we should understand Platonism in terms of what it meant for Galileo in his own time, rather than in terms of what it means for us now. For example, Ficinos view on how the planets motion is a composite of rectilinear and circular motion is much closer than Platos Timaeus to Galileos own cosmogonic account (cf. Hankins 2004: 159). 5 Veblen 1903: 309. 6 Cassirer 1906: 134-141. A fundamental innovation of Paduan Aristotelianism consists, according to Cassirer, in bringing together the compositional and the analytical method, in order to establish procedures for acquiring knowledge that move from effects to causes and viceversa. Such a method is not so much a way of resolving phenomena into fundamental principles as it is about shedding light on the hidden causes of those phenomena: in fact, it is an essentially causal-explanatory procedure. Cassirer sees in the role of mathematics the main, decisive difference between Zabarellas regressus and Galileos own scientific method. Aristotelian syllogistics cannot, however, escape from the issue of whether and how the first principles can be proven: hence, for the new science, a need for hypotheses.

  • Draft: please do not cite or circulate Marco Romani Mistretta


    Zabarella, whose doctrines most probably acted as mediators between ancient (or medieval)

    Aristotelianism and Galileo's epistemology.7

    This paper focuses on a particular aspect of Galileos methodology, i.e. his metodo

    resolutivo, which I intend to relate to the Platonic (and neo-Platonic) concept of hypothetical

    method. In order to do so, I will examine Galileos conception of hypothesis and hypothetical

    reasoning, showing that his use of the term ipotesi is by no means unequivocal. However, at

    least one of his ways of employing the notion is, I will argue, eminently Platonic.

    Galileo the realist?

    The main piece of evidence for mathematical Platonism in Galileo's method of science is

    usually taken to be a well-known and oft-quoted passage from The Assayer (1623), in which

    Galileo polemizes against Orazio Grassi's failure to understand the mathematical language which

    constitutes the basis of the scientific intelligibility of the world:

    Il Saggiatore, 6.34-37 Parmi, oltre a ci, di scorgere nel Sarsi ferma credenza, che nel filosofare sia necessario

    appoggiarsi all'opinioni di qualche celebre autore, s che la mente nostra, quando non si maritasse col discorso d'un altro, ne dovesse in tutto rimanere sterile ed infeconda; e forse stima che la filosofia sia un libro e una fantasia d'un uomo, come l'Iliade e l'Orlando Furioso, libri ne quali la meno importante cosa che quello che vi scritto sia vero. Signor Sarsi, la cosa non ist cos. La filosofia scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l'universo), ma non si pu intendere se prima non s'impara a intender la lingua, e conoscer i caratteri, ne quali scritto. Egli scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezi impossibile a intenderne umanamente parola; senza questi un aggirarsi vanamente per un oscuro laberinto. (Galilei 2005: 99)

    It seems to me that I discern in Sarsi a firm belief that in practising philosophy it is

    essential to support oneself upon the opinion of some celebrated author, as if when our minds are not wedded to the reasoning of some other person they ought to remain completely barren and sterile. Possibly he thinks that philosophy is a book of fiction created by some man, like the Iliad or Orlando Furioso - books in which the least important thing is whether what is written in them is true. Well, Sig. Sarsi, that is not the way matters stand. Philosophy is written in this grand book - I mean the universe - which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other

    7 For the contemporary debate on Aristotelianism and Platonism in Galileo, cf. notably Cellucci 2012, De Caro 2012, Finocchiaro 2010, Hatfield 2004.

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    geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is vainly wandering about in a dark labyrinth. (Drake 1960: 183-184, modified)

    Reading this passage as an endorsement of (Platonic) mathematical realism would be

    reading too much into it and reading it out of context, as L. Geymonat already pointed out in his

    pioneering monograph.8 But it is not simply a plea for [...] independent-mindedness against

    established authority:9 it is Galileo's own version of the time-honored idea of the Book of Nature,

    which for Galileo is encoded in mathematical language, and therefore understandable to a (well-

    educated) human mind.

    Whether or not Galileo had Plato's Timaeus (53c-55c) in mind, according to which the

    structure of the world can be explained in terms of five (Platonic) solids that can in turn be

    reduced to triangles, Galileo's criticism of Sarsi (= Grassi) is clearly aimed at highlighting the

    latter's underestimation of the role of mathematics in natural science.10 In fact, the Assayer as a

    whole has been read as a heroic poem in prose, a Sarsiad, a protracted tale of right against

    wrong, good against evil, innocence against deceit