arXiv · 0709.1387
A portrait of Kurt Goedel with emphasis on his work on relativity theory and idealistic philosophy.
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Ivan Todorov. 2008-02-15. Kurt Goedel and His Universe. https://arxiv.org/abs/0709.1387
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This paper argues that, where deterministic and indeterministic formulations agree on empirically corroborated structure while differing in their completion of structure that remains empirically underdetermined, features invariant across these formulations warrant ontological commitment, whereas any warrant attaching to features that vary across them is categorically more provisional. Because deterministic and indeterministic completions are always formally available, while additional grounds for preferring particular completions are contingent and defeasible, empirically corroborated structure alone cannot determine whether reality is fundamentally deterministic or indeterministic, or whether that very distinction belongs only to specific representations of it. On this basis, I advance a model-invariance criterion according to which structural features are candidates for realist commitment insofar as they are empirically corroborated within a regime and preserved across the admissible formulations of that structure. I show how such invariant content can be characterised in mathematically intelligible ways, yielding a fallibilist form of structural realism grounded in model-invariance rather than in the specific form of any given mathematical representation. Features such as conservation relations, invariant measures, symmetries, and probability or correlation structures over observable histories may satisfy this criterion. By contrast, the localisation of modal selection---whether in fine-grained initial conditions, stochastic outcomes, or state-update and collapse mechanisms---may vary across empirically admissible formulations and therefore constitute a gauge-like representational freedom. This framework offers a realist ontology for modern physics that combines empirical openness with resistance to metaphysical overreach.
Can we infer whether all of physical reality began to exist? Several novel results are offered suggesting a negative verdict. First, two necessary (but not necessarily sufficient) conditions are offered for a cosmic beginning. Second, I discuss three theorems which show that, in a wide range of spacetimes, observers cannot infer the global structure of their spacetime; one of the three shows that spacetimes satisfying a condition necessary for a cosmic beginning are observationally indistinguishable from spacetimes which do not satisfy that condition. Next, I offer two extensions to the aforementioned theorems. The two extensions show that, in an equally wide range of spacetimes, observers cannot collect sufficient data to determine whether the application conditions for the class singularity theorems are satisfied or whether their spacetime satisfies the two necessary conditions for a cosmic beginning. Lastly, a reply is offered to the objection that the skeptical consequences of the aforementioned theorems can be overcome with induction. Importantly, all past singular dust FLRW spacetimes are observationally indistinguishable from counterparts which, while sharing a number of important local properties, either do not include a singularity to the past of every point or else do not have the sort of time ordering intuitively required for a cosmic beginning.
This paper argues for the historical utility of general relativity textbooks written during, or shortly before, the Renaissance of general relativity. More so than research papers, textbooks offer a narrative account of the field--one that may differ substantially from the accounts of other authors addressing the same subject. Textbooks on general relativity therefore constitute a distinctive form of testimony to the intellectual forces that shaped general relativity, particularly during its reinvention period from 1955 to the mid-1970s. A second pillar of this argument is the observation that nearly all principal investigators at the research centers previously identified by Lalli et al.--centers that functioned as intellectual epicenters of the Renaissance of general relativity--eventually produced a textbook associated with their own school of thought. To situate this observation within the broader development of the field, the paper presents a concise history of general relativity textbooks from the theory's inception in 1915-16 to the 1980s. This history illustrates one way in which textbooks can serve as sources for reconstructing the intellectual dynamics of the Renaissance of general relativity.