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McMullin, Ernan. “Formalism and Ontology in Early Astronomy."

According to Ernan McMullin, there are several crucial challenges to the relations between quantum mechanics and theology. First, the discussion of both quantum mechanics and theology often relies on a realist interpretation, but some of the most energetic critics of realism are philosophers of quantum mechanics. Second, in dealing with mechanics in general, and with quantum mechanics in particular, the move from the mathematical formalism to its ontological interpretation is highly problematic. The fact that quantum formalism yields two different ontologies (those of Bohr and Bohm) leads to further problems: how can this be so, and how is one to decide between them? Finally, one is faced with the “troubling strangeness” of quantum ontology.

In this essay, McMullin limits his concern to the history of the relation between formalism and ontology in astronomy in order to show that similar difficulties arose throughout this history. First he clarifies terms. Mathematical formalism tells us nothing about the world until it is interpreted in terms of measurable quantities, thus becoming a physical formalism such as quantum mechanics. Both the Copenhagen interpretation and Bohm’s interpretation are then second level interpretations between the physical formalism and ontology, and it is here that issues arise which divide scientific realists and nonrealists.

With this in place, McMullin turns to the early history of astronomy and finds similar difficulties in moving from formalism to ontology. He starts with Greek astronomy, where the celestial regularities invited explanation in terms of an underlying physical structure. Aristotle, for example, regarded the mathematical formalism of concentric spheres as implying a causal explanation based on the ontology of a single interlocking system of spheres. But Apollonius and Hipparchus showed that a complex, mathematical model based on the eccentric and the epicycle could explain the data equally well, and this posed something similar to the problem we find in quantum physics: how can two radically different ontologies explain the same phenomena? Perhaps there is no genuine connection between formalism and ontology; if there is, the criterion of “saving the appearances” is clearly not enough in itself to reveal it.

McMullin next examines the Copernican revolution from geocentrism to heliocentrism. Although both formalisms could equally well save the appearances, Copernicus’s system offered important advantages. It eliminated unwanted elements of Ptolemy’s formalism and it explained phenomena that were mere coincidences in the Ptolemaic system. In addition, Copernicus could specify the order of the planets outwards from the sun, their distances from the Earth, their periods of revolution, and their retrograde motion. All of this disclosed such a degree of harmony that, for Copernicus, it proved the reality of the earth’s motion and pointed to God as its creator. McMullin closes this section by challenging Kuhn’s assessments of the epistemic merits of Copernicus’s system.

Kepler, we are next told, strongly supported Copernicus’s realist arguments for the motion of the earth, both for religious reasons and because Copernicus offered such a convincing explanation of the phenomena. His extensive analysis of Tycho Brahe’s observations of Mars led Kepler to explain its orbit as elliptical and to suggest a physics that could make such an orbit possible. Kepler’s “theory of gravity” was analogous to magnetism and gave the Sun causal primacy in determining planetary motion. But it was only with Newton that we at last have a case “sufficient to warrant reasonable belief” in the heliocentric system. What then of ontology? Certainly Newton’s system employed terms like ‘force’ and ‘attraction’, but with his rejection of action-at-a-distance, the challenge of finding an ontology to match the formalism remained. As McMullin points out, this situation is obviously similar to the current problems in interpreting quantum mechanics.

McMullin closes by drawing a philosophical moral from this history of mechanical systems: moving from a valid formalism to an underlying ontology has always been a “contentious matter. Mechanical agency has all along proved to be an uncommonly elusive quarry.” On the other hand, this history has forced us to expand our intuitive notions of agency and, given the challenges raised by quantum mechanics, it seems clear that further expansion is necessary. He also offers us a theological moral from his historical account: if our explanation of motion at its most basic level is more complicated and mysterious than earlier generations imagined, how much more complex and mysterious must divine agency be, and how hesitant ought we to be in discussing it.

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