<i>Axiomatization of the Theory of Relativity</i>

Reichenbach, Hans; Agassi, Joseph

doi:10.1063/1.3022688

Cited by 59 publications

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“…Unlike, say, 'consistency', which has long since been usefully assimilated into the culture, and is no longer recognised as coming out of the logicians toolboxdefinability plays a fairly minor role in everyday discourse. Definability is a key concept for those trying to formulate theories about the real universe, with foundational work in this context going back to Hans Reichenbach [58] in 1924, and somewhat later, Carl Gustav Hempel [29]. The mathematical framework within which definability is discussed nowadays was formulated over a period of years, and first appeared in Alfred Tarski's 1931 paper [73] (translated, and reprinted, in [74]).…”

Section: Definability and Emergent Structurementioning

confidence: 99%

From Descartes to Turing: The Computational Content of Supervenience

Cooper

2011

Information and Computation

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Mathematics can provide precise formulations of relatively vague concepts and problems from the real world, and bring out underlying structure common to diverse scientific areas. Sometimes very natural mathematical concepts lie neglected and not widely understood for many years, before their fundamental relevance is recognised and their explanatory power is fully exploited. The notion of definability in a structure is such a concept, and Turing's [77] 1939 model of interactive computation provides a fruitful context in which to exercise the usefulness of definability as a powerful and widely applicable source of understanding. In this article we set out to relate this simple idea to one of the oldest and apparently least scientifically approachable of problems -that of realistically modelling how mental properties supervene on physical ones.Mathematics can provide precise formulations of relatively vague concepts and problems from the real world, and bring out underlying structure common to diverse scientific areas. Sometimes very natural mathematical concepts lie neglected and not widely understood for many years, before their fundamental relevance is recognised and their explanatory power is fully exploited. Previously we have argued that the notion of definability in a structure is such a concept, and pointed to Turing's [77] 1939 model of interactive computation as providing a fruitful context in which to exercise the usefulness of definability as a powerful and widely applicable source of understanding.Below, we relate this simple idea to one of the oldest and apparently least scientifically approachable of problems -that of realistically modelling how mental properties supervene on physical ones. We will first briefly review the origins with René Descartes of mind-body dualism, and the problem of mental causation. We will then summarise the subsequent difficulties encountered, and their current persistence, and the more recent usefulness of the concept of supervenience in * Research supported by EPSRC research grant No. Computing with Partial Information: Definability in the Local Structure of the Enumeration Degrees.1 From Descartes to Turing: The Computational Content of Supervenience 2 providing a philosophical workspace in which to make mind-body connectionsand the parallel recognition of emergence as a tool for giving supervenience a non-reductive physical content. The rise and fall of the British emergentists will provide a salutary warning of the pitfalls of working with too vague a formulation of emergence, and of the need for a test for emergence.Following on from this, we will further clarify emergence by looking at mathematical analogues, and at approaches to emergence -such as synergetics -with a strong mathematical or scientific content. This will move us away from the empirical quest for emergent phenomena as something surprising towards formalisations of self-organisation in terms of the two-way interaction between physical phenomena, and their descriptions and representations. We w...

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Section: Definability and Emergent Structurementioning

confidence: 99%

From Descartes to Turing: The Computational Content of Supervenience

Cooper

2011

Information and Computation

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“…It has been analyzed in any respect in the early days of relativity and discussed also on its fundamental meaning [1]. Since then it has been assumed that no anisotropy can be revealed until the frontier of special relativity is crossed.…”

Section: Introductionmentioning

confidence: 99%

Angular Momentum Effects in Michelson–Morley Type Experiments

Tartaglia

Ruggiero

2002

General Relativity and Gravitation

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The effect of the angular momentum density of a gravitational source on the times of flight of light rays in an interferometer is analyzed. The calculation is made imagining that the interferometer is at the equator of an axisymmetric steadily rotating gravity source. In order to evaluate the size of the effect in the case of the Earth a weak field approximation for the metric elements is introduced. For laboratory scales and non-geodesic paths the correction due to the angular momentum turns out to be comparable with the sensitivity expected in gravitational waves interferometric detectors, whereas it drops under the threshold of detectability when using free (geodesic) light rays. PACS number 04.80.C

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“…As Hans Reichenbach (Hilary Putnam is perhaps his best-known student) found in the 1920s onwards, formalising definability in the real world comes into its own when we need to clarify and better understand the content of a hard-to-grasp description of reality, such as Einstein's theory of general relativity. Reichenbach's seminal work 79 on axiomatising relativity has become an ongoing project, carried forward today by Istvan Nemeti, Hajnal Andreka and their co-workers (see, for example, Andréka, Madarász, Németi and Székely 2 ). One can think of such work as paralleling the positive developments that models of computation enabled during the early days of computer science, bringing a surer grip on practical computation.…”

Section: Introductionmentioning

confidence: 99%

Definability in the Real Universe

Cooper¹

2011

Computability in Context

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Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and computability theory."If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics lead me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress."

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Axiomatization of the Theory of Relativity

Cited by 59 publications

References 0 publications

From Descartes to Turing: The Computational Content of Supervenience

From Descartes to Turing: The Computational Content of Supervenience

Angular Momentum Effects in Michelson–Morley Type Experiments

Definability in the Real Universe

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