Inventing the Universe: Plato's Timaeus, the Big Bang, and the Problem of Scientific Knowledge(SUNY series in Ancient Greek Philosophy)

A parallel investigation of both Plato's Timaeusand the contemporary standard Big Bang model of the universe shows that any possible scientific knowledge of the universe is ultimately grounded in irreducible and undemonstrable propositions. These are inventions of the human mind. The scientific knowledge of the universe is entirely composed in a series of axioms and rules of inference underlying a formalized system. There is no logical relationship between the sensible perception of a world of becoming and the formalized system of axioms known as a "scientific explanation." The "irrational gap" between perception and explanation can be appraised historically and identified in three stages: Plato's Timaeus furnishes the first example of a scientific theory dealing with a realm of ideality that cannot be derived from immediate sensible perception; the Big Bang model is constituted on the basis of the purely geometrical notion of symmetry; and in the more recent Algorithmic Theory of Information, the analysis of the purely symbolic language expressing physical reality reveals the level of complexity of any given theory formulated in this language. The result is that the probability of the universe actually conforming with simple mathematics is zero. In a formal system, a theorem contains more information than can be found in the set of axioms of this system, and it remains undecidable. In Aristotle' s language, the theorems that can be proved within a theoretical model are already potentially contained in the system of axioms underlying these theorems.

Table of Contents:
Acknowledgments Introduction: The Problem of Scientific Knowledge Situating the problem: our essential presuppositions The procedure followed in this analysis The Model of the Universe in Plato's Timaeus The Big Bang Model of Cosmology Algorithmic Information Theory Notes Part I: The Model of the Universe in the Timaeus The date of the composition of the Timaeus The first twelve axioms of the cosmological model advanced in the Timaeus Plato's theory of matter and the cosmological axioms Plato's explanation of the complexity of sensible things Experimental verification in Plato's time Standards and instruments of measure in Plato's time The numbering system in Plato's time Experimentation in the Timaeus Notes Part II: Contemporary Big Bang Cosmology A. The standard Big Bang model: short description The "philosophical" presuppositions The geometric axioms Einstein's gravitation Einstein's dynamic axioms: matter and energy in the universe time and causality in the universe Solving Einstein's field equations Isotropy and homogeneity of the energy/matter content of the universe: the standard Friendmann-Robertson-Walker model B. The relation between the model and observation The Hubble law Cosmic microwave background radiation The relative abundance of light elements Observational limits in cosmology Problems affecting the FRW model: observations requiring additional axioms The inflationary scenario C. Modern theory of matter The central role of the concept of symmetry Notes Part III: What Knowledge is Conveyed by Science? The symbolic description of reality Algorithmic Information Theory: some relevant aspects The Turing machine A definition of science The science of the axioms in Aristotle's Posterior Analytics Final conclusions Notes Indices

About the Author :
Luc Brisson is Director of Research at Centre National de la Recherche Scientifique. He has published several books and articles. F. Walter Meyerstein is in the Philosophy Department at the Universitate Autonoma de Barcelona, and is studying the philosophical implications of modern science.