Abstract
Olaf Müller’s book (More Light) develops a new case for underdetermination (prismatic equivalence), and, as he is focusing on theories of a ‘limited domain’, this assumes the containability of the theories. First, the paper argues that Müller’s theory of darkness is fundamentally Newtonian, but for Newton’s optical theory the type of theoretical structure Müller adopts is problematic. Second, the paper discusses seventeenth-century challenges to Newton (by Huygens and Lucas), changes in the proof-structure of Newton’s optical theory, and how these affect Müller’s reconstruction. Müller’s book provides empirically equivalent theories, yet the historical theories were not empirically equivalent, and the same experiments were used to extract different bodies of evidence to rebut the opponent. Third, Goethe’s multi-layered critique of Newton’s experimental proof is investigated, including his developmental account of prismatic colours, the role of experimental series in rejecting Newton’s observations, and his incorporation of the ‘limited domain’ of prismatic colours in a broader framework. Two key elements of Goethe’s method, polarity and strengthening are discussed in contrast to Müller, who only utilises polarity in his account. Finally Neurath’s attempts to come to grips with the optical controversies and the prism-experiments with ‘blurred edges’ are recalled. Müller also discusses in detail some of these experiments and heavily draws on Quine. Neurath developed Duhem’s and Poincaré’s conventionalist insights and had good reasons to be pessimistic about theory-containment. Their differences provide some additions to the history of the Duhem–Quine thesis.
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Notes
This research partly overlapped with his work on ‘the auxiliary motive’ and ‘pseudorationalism’, see also the last section of (Biddle 2013).
Both Hooke and Huygens used two colours (explananda) to account for colours, as opposed to Newton’s indefinite number of colours. These modificationist accounts belonged to the class of theories that Newton rejected in his New Theory, the basic colours were different, but the two-colour hypothesis was supported by parsimony. Huygens pointed out the simplicity of a mechanical model operating with only two colours, and stated that Newton’s theory could be a very plausible hypothesis (Turnbull 1959, 235–236).
There are many subtle shifts in position, opponents cornered Newton after his early exposition of the optical theory. Müller’s rays are ‘strongly immutable’ (they exist before the first refraction), and he assumes a Naturkonstant. Newton’s argument in extending the reasoning from the second prism to the first in the crucial experiment also employs a principle of economy—a notion used in optics at least since the Catoptrics of Hero of Alexandria (Cohen and Drabkin 1948 (1969))—but this has been challenged in the controversy, and helped Newton restructure his proof (no experiment is called crucial in the Opticks). Müller notes that he is probably the only one who thinks Newton’s theory follows from the crucial experiment (§I.5.17, 117).
Before Newton, the coloured fringes were connected to the “ancient theory of the nature of the rainbow’s colors, a theory which held that a succession of modifications of sunlight by the droplets of a rain cloud produced the colors of the bow”. In mechanical hypotheses, it was generally “a minor perturbation restricted primarily to the edges of the homogeneous beam of sunlight”. The mixture of light and shade “at the region of contact between the refracted beam and the dark” is a result of “varying ‘condensation’ and ‘rarefaction’ produced at the edges of the beam”, or it might emerge “by some other mechanical modification” (Kuhn 1958, 30–31).
Goethe describes the ways in which light interacts with darkness, white with black to show that “without a boundary […] no colors appear. That is, the boundary condition is fundamental” (Sepper 1988, 222). As Jonathan Westphal notes, “the crucial claim made by Goethe, which is at the centre of his polemic against Newton, [is] that (as we would say) colour is an edge-phenomenon” (Westphal 1987, 9).
This is what Müller at points attributes to Goethe, over-exploiting the source, and equivocating his non-modificationist alternative to Newton with Goethe’s views. In Müller’s early treatment Goethe would have rejected rays of darkness, his criticism of the “ray-concept” is discussed (§II.3.5 p. 152), after accrediting Goethe with thinking of the lack of light (Abwesenheit) as causal counter-idea (§II.3.3 p. 150), by the end of the book Goethe is accredited and praised for formulating the heterogeneity of darkness (“der von ihm formulierten Heterogenität des Finsternis” §4.7.7., p. 419). In his recent article Goethe’s dissolving, splitting, and scattering “black image” is praised as the idea that “darkness and blackness are composite phenomena” (LA I.7, 86, Müller 2016).
Dennis Sepper adds that “One intriguing aspect of Goethe's exposition of the phenomena is that it incorporates a fundamental concept of modern mathematics and mathematical physics, the limit of a series, potentially if not actually infinite. The superexperiment, whether continuously or discretely varied, allows one to approach phenomenally a limit that may not be reachable in fact - for instance, an aperture with the breadth of a mathematical point” (Sepper 1988, 75). Sepper also cites a manuscript, where Goethe derives straight-line boundaries from a curved boundary by performing what amounts to a continuous topological deformation of space to transform a circle to a line by changing viewing angles in subjective prismatic experiments (ibid. 76), and Ribe draws an analogy between Goethe’s modificationist model and differential equations (Ribe 1985, 330).
As the late Goethe criticises his own earlier work: “The composition lacks the consummating concept of two of Nature's activating forces: polarity and progression” (Müller 1989, 245).
Goethe’s observational method delimited the applicability of the toolset to specific domains. In botany, for example, he gave up on giving an account of the subterranean parts of plants. If no advancement can be traced, then his comparative method is not applicable. Given the scope of his method, this was an unjust demand (“Unbillige Forderung”): “it is advance solely that could attract me, hold me, and sweep me along my course” (Müller 1989, 118).
As an account of objective colours, it equates colour with a property of a theoretical entity outside the observer. An earlier attempt developed Locke’s inverted spectrum thought experiment to discuss relations among consciousness, brain, behaviour, and scientific explanation, exploring isomorphism constraints in subjective colour-perception (Palmer 1998).
In the Opticks I/2, Exp. 5. Newton writes about the separated (‘pure’) spectral colours being further refracted: “For by this Refraction the Colour of the Light was never changed in the least. If any Part of the red Light was refracted it remained totally of the same red Colour as before…The like Constancy and Immutability I found also in the blue, green, and other Colours” (Newton 1952, 122–123). Yellow is suspiciously not listed, as here further fringes are visible.
Goethe aims to show that the ‘experimental’ proof that Newton uses has superfluous parts (FL-PT §35–39), concluding that the description is endowing Newton’s experiments with purity (FL-PT §41). To talk of -ibilities and -ities (“Ibilitäten,… Keiten” FL-PT §29) is far-fetched, unsupported, the proposition is not established, but only supported by the experiments. At points Goethe interferes even more with the process of idealisation, claiming that it is invalid.
The method is also reflexive, it enables Goethe to display his own development as a scientist. For Goethe as a historian of science can use it to develop models for social science: the intertwining polarities (authority and experience) are displayed by Roger Bacon, a typical ‘scientist’ in the irregular Medieval period (atypical for the lack of progress).
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Acknowledgements
The work was supported by the MTA Lendület Science and Morals Research Group and the “Integrative Argumentation Studies” NKFI-OTKA K 109456 Grant. I appreciate the helpful comments by István Danka and two anonymous reviewers.
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Zemplén, G.Á. Theory-Containment in Controversies: Neurath and Müller on Newton, Goethe, and Underdetermination. J Gen Philos Sci 49, 533–549 (2018). https://doi.org/10.1007/s10838-017-9391-y
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DOI: https://doi.org/10.1007/s10838-017-9391-y