Online research in philosophy

THE PRINCIPLE OF SUPERPOSITION. The need for a quantum theory Classical mechanics has been developed continuously from the time of Newton and applied to an ...

Recent developments in astrophysical cosmology have revived support for the design argument among a growing clique of astrophysicists. I show that the scientific/mathematical evidence cited in support of intelligent design of the universe is infected with a mathematical sharp practice: the concepts of two numbers being of the same order of magnitude, and of being within an order of each other, have been stretched from their proper meanings so as to doctor the numbers evidentially. This practice started with A. S. (...) Eddington and P. A. M. Dirac in the 1920s and 1930s, but it is still very much alive today. 1 Introduction 2 The birth of a sharp practice 3 High tide for the anthropic principle 4 How not to do things with numbers 5 The recalcitrant sloppiness of crud 6 How excited can excited carbon-12 be? 7 Is a pile of doubts a doubtful pile? 8 Conclusion. (shrink)

Analysis of Emmy Noether’s 1918 theorems provides an illuminating method for testing the consequences of “coordinate generality”, and for exploring what else must be added to this requirement in order to give general covariance its far-reaching physical significance. The discussion takes us through Noether’s first and second theorems, and then a third related theorem due originally to F. Klein. Contact will also be made with the contributions of, principally, J.L. Anderson, A. Trautman, P.A.M. Dirac, R. Torretti and the father (...) of the whole business, A. Einstein (an apparent shift in Einstein’s thinking on the significance of general covariance between 1916 and 1918 is highlighted). (shrink)