Author
L. Smail
Bio: L. Smail is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 5 citations.
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TL;DR: Divergent series have appeared in mathematics for a long time as mentioned in this paper and have been used widely throughout the 17th and 18th centuries, sometimes with great profit and sometimes without.
Abstract: Divergent series have appeared in mathematics for a long time. They were used widely throughout the 17th and 18th centuries, sometimes with great profit and sometimes without. Many mathematicians who used them were frequently in doubt about their validity while others seemed totally unconcerned. Throughout the period, controversy surrounded the use of divergent series mainly because contradictions were often derived through their application. One of the earliest discussions regarding a divergent series occurred when the infinite series
24 citations
TL;DR: In this paper, the authors argue that Field's program for nominalizing science is unlikely to succeed generally, since no nominalistic variant will provide us with the kind of physical insight into the phenomena that the standard theory supplies.
Abstract: I argue on the basis of an example, Fourier theory applied to the problem of vibration, that Field's program for nominalizing science is unlikely to succeed generally, since no nominalistic variant will provide us with the kind of physical insight into the phenomena that the standard theory supplies. Consideration of the same example also shows, I argue, that some of the motivation for mathematical fictionalism, particularly the alleged problem of cognitive access, is more apparent than real.
12 citations
01 Jan 1994
TL;DR: In this paper, the authors discuss the mathematical and epistemological importance of Borel's theory of divergent series and its role in the rational modification of mathematical practice, making use of diverse and original sources.
Abstract: Taking into account the renewed interest in the applications of the theory of divergent series, we consider it proper to revaluate this little known part of Borel's works. We begin With the analysis of the circumstances and main sources which support Borel's early research. Then we briefiy describe how Borel built his theory. Finally, making use of diverse and original sources, we intend to clarify the mathematical and epistemological importance of Borel's theory and its role in the rational modification of mathematical practice.
4 citations