Book contents
- Frontmatter
- Contents
- Preface
- Continuous Functionals of Dependent and Transfinite Types
- Degree-Theoretic Aspects of Computably Enumerable Reals
- Simplicity and Independence for Pseudo-Algebraically Closed Fields
- Clockwork or Turing U/universe? - Remarks on Causal Determinism and Computability
- A Techniques Oriented Survey of Bounded Queries
- Relative Categoricity in Abelian Groups
- Computability and Complexity Revisited
- Effective Model Theory: The Number of Models and Their Complexity
- A Survey on Canonical Bases in Simple Theories
- True Approximations and Models of Arithmetic
- On the Topological Stability Conjecture
- A Mahlo-Universe of Effective Domains with Totality
- Logic and Decision Making
- The Sheaf of Locally Definable Scalars over a Ring
- Human Styles of Quantificational Reasoning
- Recursion Theoretic Memories 1954–1978
- Fields Definable in Simple Groups
- A Combinatory Algebra for Sequential Functionals of Finite Type
- Model Theory of Analytic and Smooth Functions
Clockwork or Turing U/universe? - Remarks on Causal Determinism and Computability
Published online by Cambridge University Press: 17 May 2010
- Frontmatter
- Contents
- Preface
- Continuous Functionals of Dependent and Transfinite Types
- Degree-Theoretic Aspects of Computably Enumerable Reals
- Simplicity and Independence for Pseudo-Algebraically Closed Fields
- Clockwork or Turing U/universe? - Remarks on Causal Determinism and Computability
- A Techniques Oriented Survey of Bounded Queries
- Relative Categoricity in Abelian Groups
- Computability and Complexity Revisited
- Effective Model Theory: The Number of Models and Their Complexity
- A Survey on Canonical Bases in Simple Theories
- True Approximations and Models of Arithmetic
- On the Topological Stability Conjecture
- A Mahlo-Universe of Effective Domains with Totality
- Logic and Decision Making
- The Sheaf of Locally Definable Scalars over a Ring
- Human Styles of Quantificational Reasoning
- Recursion Theoretic Memories 1954–1978
- Fields Definable in Simple Groups
- A Combinatory Algebra for Sequential Functionals of Finite Type
- Model Theory of Analytic and Smooth Functions
Summary
ABSTRACT. The relevance of the Turing universe as a model for complex physical situations (that is, those showing both computable and incomputable aspects) is discussed. Some well-known arguments concerning the nature of scientific reality are related to this theoretical context.
The close relationship between computability, mechanism and causal determinacy is basic to post-Newtonian science, and underpins the familiar notion of a Laplacian ‘clockwork’ Universe, which provided a clear mathematical model of physical reality for over a century and a half — the discovery in the 1930s of the possibility of an explicit mathematical description of the model providing a key ingredient in its eventual demise. Acceptance of such a model has never been total of course, even amongst scientists. But in recent times the need for a mathematical alternative to that of Laplace, subsuming and extending according to the changing theoretical and empirical environment, has become increasingly overdue. The purpose of this note is to argue that the genesis of such a precise and intuitively natural model lies in Alan Turing's response, in a more limited mathematical context, to the newly discovered incomputabilities of the decade 1927–1936.
Laplacian determinism
A perceived algorithmic content for reality is peculiar to our time and culture. Its origins are commonly traced back to the ancient Greeks, as is the development of the notion of proof, providing a useful infrastructure for mathematical and scientific truth, having been rediscovered (largely via Arab texts) in the late Middle Ages and developed during and after the Renaissance.
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- Models and Computability , pp. 63 - 116Publisher: Cambridge University PressPrint publication year: 1999
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