Abstract
Based on an examination of Galileo’s mechanics, Peter Machamer and Andrea Woody (and Machamer alone in subsequent articles) proposed the scientific use of what they call models of intelligibility. As they define it, a model of intelligibility (MOI) is a concrete phenomenon that guides scientific understanding of problematic cases. This paper extends Machamer and Woody’s analysis by elaborating the semantic function of MOIs. MOIs are physical embodiments of theoretical representations. Therefore, they eliminate the interpretive distance between theory and phenomena, creating classes of concrete referents for theoretical concepts. Meanwhile, MOIs also provide evidence for historical analyses of concepts, like ‘body’ or ‘motion’, that are otherwise thought to be too basic for explicit explication. These points are illustrated by two examples also drawn from Galileo. First, I show how the introduction of the balance as an MOI leads Galileo to reject the Aristotelian conception of elemental natures. Second, Galileo’s rejection of medieval MOIs of circular motion constrains the reference of ‘conserved motion’ to curvilinear translations, thereby excluding the rotations that had been included in its scope. Both uses of MOIs marked important steps toward modern classical mechanics.
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Notes
- 1.
- 2.
My use of the term ‘phenomena’ here elides the important distinctions between physical entities, sensory givens, measurements, data, phenomena, and so on. A complete account would venture into territory far afield of the concerns addressed here. Likewise, the reader should not take this use of the term to imply any commitment to scientific realism. One can remain agnostic as to the precise ontological status of phenomena.
- 3.
This is not the place to delve into a characterization of scientific explanation. Deductions from law-like principles and boundary conditions can be taken as archetypical.
- 4.
Coordinative definitions have been viewed as necessary to interpret scientific language under the logical positivists’ “received view” of scientific theories and its post-positivist “syntactic view” descendants (sometimes under different names, such as ‘correspondence rules’). Many versions of the “semantic view” also presume coordinative definitions to link elements of a theoretical model with the world. The minority exception is that some semantic views rely on isomorphism between a theoretical model and the world to establish the reference of theoretical concepts, without coordinative definitions for each conceptual node in the model. See (Friedman 1999; Friedman 2001; Van Fraassen 2008; Brigandt 2010). See also the discussion in (Miller 2014, 4–6).
- 5.
(Machamer and Woody 1994, 219).
- 6.
In his subsequent papers, Machamer enumerates several additional Galilean examples, including bitumen thrown on a hot iron pan (as an MOI for sunspots), pendulums, water on pavement, and a moving ship (Machamer 1997, 149). For a close analysis of the application of the balance model to materials, see (Biener 2004). For an extensive list of additional examples, see (Meli 2006, 2).
- 7.
(Machamer and Woody 1994, 221).
- 8.
As Machamer and Woody point out, the concreteness of MOIs also distinguishes them from similar suggestions, especially Kuhnian exemplars. For Kuhn, exemplars are problem-solving schema, based perhaps on concrete examples. They can therefore involve MOIs, but they are not themselves MOIs. Exemplars are merely heuristics. They are not explananda. (Machamer and Woody 1994, 219).
- 9.
(Machamer and Woody 1994, 223).
- 10.
At this point, one might worry about ambiguities arising from the particularities of an MOI. Imagining a theoretician saying, “by ‘conserved motion’ I mean that” while ostending a ball rolling across a table, one could wonder how the listener would know to ignore the ball’s color, etc. But this is not the dialectic I have in mind. MOIs are used against the background of additional theoretical knowledge. Suppose a physics student learning about electrons. After learning what charge and mass and so on are, she learns that an electron has a certain charge and a certain mass. All of this is conceptual. But then the professor stands over a cloud chamber, points to one of spiral tracks and says, “That’s an electron.” And the student now knows that tracks with that shape are electrons. The representation constituted by the MOI (the cloud chamber track) is transparent in the sense that it conflates the concept ‘electron’ (particle with such and such charge, mass, and so on) with a thing in the world. The track is an ‘electron’ in an unqualified, direct way. Put more bluntly, the electron is an ‘electron’. That does not mean, however, that no learning or assumptions were required to get the student to the point of making that conflation. Likewise, when the theoretician says, “by ‘conserved motion’ I mean that,” one can assume she is stipulating a certain kind of motion, in response to a question like, “which motions count as ‘conserved motion’?” The concept of ‘motion’ itself is antecedently understood (perhaps in light of other coordinations). Moreover, in stipulating the coordination between the abstract mental concept and the concrete object, one is implicitly asserting that the object behaves according to its idealization—in this case, that the ball’s motion really is conserved—thereby setting aside accidental properties and imperfections (which might be addressed post hoc).
- 11.
(Machamer and Woody 1994, 223).
- 12.
Machamer hints at the semantic function of MOIs. In his 1998 paper, he notes that they can serve to “coordinate [a geometrical proof] with experience” (Machamer 1998, 70). Elsewhere, he notes that “mechanical models were a necessary part of the ‘proof’ or criteria of adequacy for determining a valid explanation” (Machamer 1997, 149). Suggestive as these comments are, they are made in passing, without elaboration.
- 13.
The manuscripts are preserved in the Biblioteca Nazionale Centrale in Florence as MS 71, available online at http://echo.mpiwg-berlin.mpg.de/content/scientific_revolution/galileo/photographicdocumentation. Favaro published them in Volume 1 of the Edizione Nazionale (Galilei 1890–1909, 1:243–419). For translations, see (Galilei 1960; Galilei and Fredette 2000). See (Wallace 1990; Giusti 1998; Fredette 2001) for a discussion of the history and dating of the manuscripts. I am here restricting my attention to the essay forms of De Motu, thus ignoring the earliest, dialogue form associated with the set.
- 14.
- 15.
(Galilei 1960, 16).
- 16.
Machamer has written on this subject, too. See (Machamer 1978).
- 17.
Aristotle himself refers to the motions of wood, bronze, gold, and lead; e.g., De Caelo, IV.1–2, 308a6–308b10.
- 18.
Aristotle offers fire, vapor, and smoke as examples of light bodies; e.g., Meteorology I.4, (341b1–341b17). In De Motu, Galileo devotes a chapter to refuting Aristotle’s ascription of lightness to fire (Galilei 1960, 55–61).
- 19.
(Galilei 1960, 20).
- 20.
(Galilei 1960, 21).
- 21.
(Galilei 1960, 21).
- 22.
(Galilei 1960, 22–23).
- 23.
(Galilei 1960, 23).
- 24.
- 25.
(Galilei 1960, 118).
- 26.
(Galilei 1960, 120).
- 27.
- 28.
See (Machamer 1998, 61).
- 29.
Though they do not put it in such terms, (Machamer and Hepburn 2004) show how Galileo uses a pendulum as an MOI for the concept ‘time’.
- 30.
- 31.
See the elaboration of Newton’s First Law of Motion: “A spinning hoop [or top; trochus], which has parts that by their cohesion continually draw one another back from rectilinear motions, does not cease to rotate, except insofar as it is retarded by the air” (Newton 1999, 416). Note that Newton uses a standard example, the trochus, discussed below.
- 32.
(Clagett 1959, 533).
- 33.
- 34.
(Galilei 1960, 65–66).
- 35.
(Galilei 1960, 63–64).
- 36.
(Galilei 1960, 75).
- 37.
(Galilei 1989, 172).
- 38.
Galileo does discuss the rotation of the rota aristotelica in Day 1, but the subject there is vacua in material substance, not mechanics. (Galilei 1989, 29–34).
- 39.
(Galilei 1989, 221).
- 40.
See (Miller 2014, ch. 5).
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Acknowledgments
My deepest gratitude to Peter Machamer, for letting me ask the questions I wanted to ask, and teaching me how to seek the answers. Thanks also to the editors of this volume, especially Adams and Biener, whose comments and suggestions improved this paper immensely.
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Miller, D.M. (2017). Models of Intelligibility in Galileo’s Mechanical Science. In: Adams, M., Biener, Z., Feest, U., Sullivan, J. (eds) Eppur si muove: Doing History and Philosophy of Science with Peter Machamer. The Western Ontario Series in Philosophy of Science, vol 81. Springer, Cham. https://doi.org/10.1007/978-3-319-52768-0_3
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