Recently, certain philosophers of mathematics (Fallis [1997]; Womack and Farach [1997]) have argued that there are no epistemic considerations that should stop mathematicians from using probabilistic methods to establish that mathematical propositions are true. However, mathematicians clearly should not use methods that are unreliable. Unfortunately, due to the fact that randomized algorithms are not really random in practice, there is reason to doubt their reliability. In this paper, I analyze the prospects for establishing that randomized algorithms are reliable. I end by arguing that it would be inconsistent for mathematicians to suspend judgement on the truth of mathematical propositions on the basis of worries about the reliability of randomized algorithms.
Preparation of bicyclo[4.2.0]octa-2,4-dien-7-one via trapping with benzylideneacetoneiron tricarbonyl
作者:Maurice Brookhart、Gregory O. Nelson、Gary Scholes、R. A. Watson
DOI:10.1039/c39760000195
日期:——
The synthesis of bicyclo[4.2.0]octa-2,4-dien-7-one has been accomplished by trapping this unstable tautomer with benzylideneacetoneiron tricarbonyl to form the stable bicyclo[4.2.0]octa-2,4-dien-7-oneirontricarbonyl which was then oxidatively cleaved with ceric ammonium nitrate at –30 °C to yield the title ketone.
The synthesis of tricarbonyl(2,4-cycloheptadiene-1,6-dione)iron and tricarbonyl(2,4-cyclooctadiene-1,6-dione)iron
作者:Noboru Morita、Shunji Ito、Toyonobu Asao
DOI:10.1016/0022-328x(93)80359-j
日期:1993.11
Tricarbonyl(6-hydroxy-2,4-cycloheptadien-1-one)iron derived from tricarbonyl(tropone)iron was easily oxidized to give tricarbonyl(2,4-cycloheptadiene-1,6-dione)iron. This procedure was also extended to tricarbonyl(2-substituted tropone)iron and exo(bicyclo[5.1.O]octa-3,5-dien-2-one)tricarbonyliron to yield tricarbonyl(2-substituted 2,4-cycloheptadiene-1,6-dione)iron and tricarbonyl(2,4-cyclooctadiene-1