Abstract
Besides the reflection on representations of existing spatial knowledge, the expansion of spaces of experience is a motor for conceptual development, whether these are the geographical spaces known through political expansion, trade, and exploration, the cosmological spaces known through observation, or the microcosmic spaces known through engineering and experimentation. The chapter presents three examples for processes of concept formation and the generalization of spatial concepts that were promoted by such expansions of experiential spaces. The first example refers to the systematic accumulation of geographical knowledge, which laid the foundation for the introduction of a global system of terrestrial coordinates. This allowed landmarks to be related no longer just to other landmarks but also to a mathematically determined, abstract geographical space. The second example refers to the accumulation over centuries of astronomical and mechanical knowledge, which, by a process of reflective integration, brought about the Newtonian concept of a homogeneous, isotropic, absolute space independent of its matter content. The third example relates to the expansion of knowledge of microscopic space by institutionalized research on electric and magnetic forces, which brought about and stabilized the concept of the electromagnetic field.
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Notes
- 1.
Malkin (2011).
- 2.
Harley and Woodward (1987, 148–149).
- 3.
See Strabo (1982–1995) for a modern edition with an English translation.
- 4.
On the different arguments for the centrality of the earth found in Aristotle and Ptolemy, see Omodeo and Tupikova (forthcoming).
- 5.
The hypothesis of a close relation between astronomical instruments and cosmological theory is discussed in Szabó and Maula (1982). That the knowledge about the dependency of the celestial appearances on geographical position does not necessarily lead to the hypothesis of a spherical earth is suggested by the Chinese case. The very same phenomena that Eratosthenes exploited in his estimation of the size of the spherical earth (see below)—the variation along the north-south direction of the gnomon shadow length at noon—were used in China to determine the height of the heavens above a flat earth. (I am grateful to Irina Tupikova for pointing this out to me.) See Cullen (1976, 122–127).
- 6.
- 7.
See Harley and Woodward (1987, 138–139).
- 8.
Harley and Woodward (1987, 151).
- 9.
- 10.
See Harley and Woodward (1987, 166).
- 11.
Stückelberger and Graßhoff (2006–2009, 10–11).
- 12.
On Ptolemy’s sources, see Stückelberger and Graßhoff (2006–2009, 16–20).
- 13.
A famous example of such a ‘topological’ map is the Roman Peutinger Map from around 300 CE, which represents the oikoumene in a highly distorted way; see, e.g., Talbert (2007).
- 14.
- 15.
See Mach (1989, 1–3) .
- 16.
The authorship of the Mechanical Problems is disputed, which is why its author is usually referred to as Pseudo-Aristotle . There is a contemporary, independent emergence of theoretical reflections on mechanical arrangements and phenomena in China , documented in the Mohist Canon , which apparently had virtually no influence on the later course of Chinese intellectual history; see Renn and Schemmel (2006).
- 17.
Abattouy et al. (2001, 4–5 and 9–10).
- 18.
- 19.
- 20.
See Hunger and Pingree (1999).
- 21.
See Saliba (1994).
- 22.
See, e.g., Johnson (1937, 111–112).
- 23.
Pierre Duhem is correct, of course, when he points out that Newton could not find his laws by generalizing Kepler’s laws, that he could not “extract [them] from experiment” (Duhem 1962, 191) by means of induction. Duhem argues that Newton’s set of laws and Kepler’s set of laws actually contradict each other and that therefore the one cannot be derived from the other (Duhem 1962, 190–195). It is true that the relation between Newton’s mechanics and preclassical mechanics is not one of formal deductivity. The form of reasoning that connects the mutually incompatible but genetically related conceptual systems is non-monotonic and involves content-dependent cognitive structures such as mental models (see below).
- 24.
A prominent example for the gradual understanding of the conceptual implications of a theory’s physico-mathematical formalism, which is itself evolving, is provided by the history of general relativity; see Renn (2007, vols. 1 and 2); see also the next chapter.
- 25.
- 26.
Three-dimensionality and Euclidicity are not particular to Newton’s concept of space, of course; both are accepted properties in ancient, medieval, and early modern theories of space. In the Aristotelian cosmos, for instance, natural motions follow the elements of Euclidean geometrical figures, straight lines and circles. However, while in the Aristotelian case the application of these elements is restricted due to the finiteness of the cosmos, such a restriction does not apply to infinite Newtonian space (see below).
- 27.
Newton (1978, 133). This is A.R. and M.B. Hall’s translation of Newton’s unpublished manuscript De gravitatione et aequipondio fluidorum, the Latin original reads: “Ad eundem modum intra aquam claram etsei nullas videmus materiales figuras, tamen insunt plurimae quas aliquis tantum color varijs ejus partibus inditus multimodo faceret apparere” (Newton 1978, 100).
- 28.
Earman (1989, 11).
- 29.
Newton (1978, 133).
- 30.
Newton (1978, 133).
- 31.
Newton (1978, 134).
- 32.
Newton (1978, 104, 138). In fact, the assumption of an infinitely extended universe with a homogeneous matter distribution, which appears to be the most natural cosmological extension of Newtonian physics, causes problems for classical theory: the gravitational force on a test-body becomes indeterminate everywhere. Newton himself recognized the problem (and erroneously thought that he could solve it). The problem was rediscovered at the end of the nineteenth century by the astronomer Hugo von Seeliger (1895, 1896). The difficulties for Newtonian theory arising from infinitely extended material universes and the history of approaches to the problem, including Newton’s, are discussed in Norton (1999).
- 33.
Newton (1978, 137).
- 34.
Newton (1978, 137).
- 35.
Descartes, Principia, II, 37–39 (Descartes 1984, 59–61).
- 36.
Descartes’ theory of motion is thoroughly criticized by Newton in his De gravitatione ... (Newton 1978, 91–98, 123–131); references to Descartes are less explicit but still clearly discernible in Newton’s Principia, see below.
- 37.
Newton (1999, 412–413).
- 38.
According to Jammer (1954, 114), in Newton’s view, the mechanical arguments for the existence of space are subordinate to the theological-metaphysical ones in the sense that their major function is to provide evidence for the relation between absolute space and God . Jammer (1954, 108–114) traces the theological-metaphysical influence on Newton’s concept of space back to Jewish cabalistic and Neoplatonic thought, mediated by Henry More and Newton’s teacher Isaac Barrow.
- 39.
“Je ne veux pas entrer dans la discussion des objections, qu’on fait contre la réalité de l’espace & du lieu; car ayant démontré, que cette réalité ne peut plus être revoquée en doute, il s’ensuit nécessairement, que toute ces objections doivent être peu solides; quand même nous ne serions pas en état d’y répondre.” (Euler 1748, 330, English translation M.S. A German translation is found in Euler 1763, 1–18.) Euler then goes on to state that if one thinks, based on the principle of the identity of indiscernibles, that it is absurd that the different places or parts of space are mutually indistinguishable (as Leibniz did in his correspondence with Clarke), maybe the principle does not hold in general, pertaining to bodies and spirits but not to parts of space.
- 40.
Neumann (1870). Incidentally, this is the text in which Neumann, in a sort of resublimitation of the sublimate landmarks of Newtonian absolute space, introduces the notion of a “Body Alpha.”
- 41.
Lange (1886, 133–141) .
- 42.
Barbour (1989, 659).
- 43.
On the practical background of Gilbert’s work, see Zilsel (2000a).
- 44.
Chung (1997, 42).
- 45.
Faraday (1965, Vol. II, 286).
- 46.
Gilbert gives an account of ancient and later opinions on electricity and magnetism in his De magnete, Book II, Chap. 3, before stating his own view (Gilbert 1958, 60–64).
- 47.
In the case of gravitation, the search for a material explanation continued through post-Newtonian times and well into the twentieth century; see, e.g., van Lunteren (1991).
- 48.
On Faraday’s ideas of matter as a ‘plenum of powers’ being influenced by Priestley’s view, and the conflation of Priestley’s theory of matter with Roger Joseph Boscovich’s, see Harman (1982, 77).
- 49.
- 50.
- 51.
On Ørsted and Ampère, see Harman (1982, 30–32).
- 52.
Harman (1982, 73–78).
- 53.
Harman (1982, 82–84).
- 54.
Maxwell (1890, 527–528) .
- 55.
Harman (1982, 104).
- 56.
On Maxwell’s theories of the field, see Harman (1982, 84–98).
- 57.
Harman (1982, 101–102).
- 58.
On the distinction between mechanical models and dynamical systems, see Buchwald (1988, 20–23).
- 59.
For a detailed account of the history of conceptions of the ether’s state of motion in the light of the experiential knowledge of the time, see Janssen and Stachel (2004).
- 60.
This is how Einstein put it in retrospect; see Einstein (1922, 11).
- 61.
Einstein (1922, 11).
- 62.
“Der völlig starre Äther trat ferner so sehr aus dem Kreis der beeinflußbaren und damit näher erkennbaren Objekte heraus, daß auch die Relativitätstheorie möglich wurde, bei welcher der Begriff des Äthers nur als ein durch neue Erfahrungen vertiefter Raum-Zeitbegriff erscheint.” (Schwarzschild 1913, 598, English translation M.S.)
- 63.
‘Knowledge acquisition’ or ‘production’, depending on whether one wishes to stress the empirical or the constructive aspect of knowledge growth.
- 64.
Kant (1996, 78).
- 65.
On Kant’s empirical concept of matter, see Friedman (2001).
- 66.
Compare Kant’s statement above to the following contradicting one, made by David Hume in his Treatise concerning human nature: “the ideas of space and time are [...] no separate or distinct ideas, but merely those of the manner or order, in which objects exist”: “[...] ’tis impossible to conceive either a vacuum and extension without matter, or a time, when there was no succession or change in any real existence” (Hume 2007, 31). Hume here clearly advocates a position-quality concept of space.
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Schemmel, M. (2016). The Expansion of Experiential Spaces Over History. In: Historical Epistemology of Space. SpringerBriefs in History of Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-25241-4_6
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