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In the search for alternative conceptions of space that transcend the traditional substantivalist and relationist dichotomy, a host of different strategies stand out in the recent literature: the positivist-inspired definitional approach favored by Stein and DiSalle; the various formulations of a property theory defended by Sklar and Teller, to name only a few; and the structural realist conception of space put forward by Dorato, Rickles, and several others. While some of these third-way approaches have been previously discussed, this chapter will provide an examination of their content and overall viability in greater detail, in particular, the property theory, §5.1, and the structural realist conceptions of space (spacetime), §5.2. In keeping with the stated goals of our inquiry, the emphasis will be placed on exploring aspects of these alternative hypotheses that both correlate with the key elements of Newton and Leibniz" views as well as improve upon the standard substantivalist and relationist categories that they seek to replace. However, the relationship between these contemporary alternative spatial ontologies and seventeenth century spatial ontologies will not be taken up until later in Part II (Chap.  7, in particular) and Part III.

DOI: 10.1007/978-3-319-44868-8_5

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