On the controversy, I shall focus on an account of the views of one important relationalist and one importantĮarman (1989 ) is a standard reference, so I shall employ its terminology and notation in discussing his Rather than attempting a (necessarily superficial) review of the vast philosophical literature Provoked by the hole argument and how it has led a number of participants from each camp to adopt this The fiber bundle approach, motivated in Section 3Īnd treated in more detail in Section 4.3, allows a rigorous formulation of this viewpoint inīut first, I shall give a brief account of the controversy between relationalists and substantivalists Space-time structure (see Stachel, 2005 ). “substantivalism” and “relationalism,” fraught with so many unwanted implications it placesĮmphasis on diachronic aspects of structure and its application is not confined to theories of I have called it dynamic structural realism (see Stachel, 2006a ), which has several advantages. These concepts lead to a viewpoint on the nature of space-time that has been given various names, such as structural spacetime realism 71Īnd sophisticated substantivalism (see Pooley, 2000, summarized in Section 5.3). Nature of coordinatization in Section 5.6, which establishes a correspondence between the two (for a fuller Mathematical structures, they lead to succinct discussions of algebraic and geometric structures and the These concepts are discussed in Appendix B and briefly reviewed in Section 5.5. internal and external relations, and between.In the light of the hole argument, I find it more fruitful to frame discussion in terms of two otherĭistinctions, leading to a point of view about space-time distinct from either substantivalism or Spacetime substantivalism ( Norton, 2011 ). ![]() One view is that spacetime is a substance,Ī thing that exists independently of the processes occurring within spacetime. ![]() Spacetime, and we inquire into its status. In that context, space and time are fused into a single entity, The hole argument arose when these questions were asked in the context of Processes with temporal durations? These questions have long been debated and continue That is, is there no space and time until there are things with spatial properties and They akin to parenthood there is no parenthood until there are parents and children? Onto which an artist paints they exist whether or not the artist paints on them? Or are Them? Or is their existence parasitic on these things and processes? Are they like a canvas What is space? What is time? Do they exist independently of the things and processes in To Section 4: Some Philosophical Concepts Nijenhuis on the Formal Definition of Natural Bundles Groups and partially background-independent space-times Internal and external, quiddity and haecceityĭoes “general relativity” extend the principle of ![]() Relationalism versus substantivalism: Is that all there Manifolds and diffeomorphisms, covariance and general covarianceīundles: principal bundles, associated bundles, frame bundles, natural Misunderstand coordinate transformations?Īnd geometric, permutability and general permutability The Cauchy problem for the Einstein equations: from Hilbert ![]() Theory to the search for a theory of gravityįrom the hole argument back to general covariance
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