Develops a structuralist understanding of mathematics, as an alternative to set- or type-theoretic foundations, that respects classical mathematical truth while ...

Already in 1863, Jules Verne knew about Caselli's "pantelegraphy," which was what he described as a "photographic telegraphy, invented during the last century by Professor Giovanni Caselli of Florence."1 Following the mistaken belief that facsimile machines could not been invented until well after the nineteenth century, and wrongly assuming that Caselli was a fictional inventor, merely a figment of Verne's most productive fertile imagination (as such imaginative elements characterize his latter writings), some of Verne's readers mistakenly ascribed to him the (...) discovery of the possibility of the fax machine. They thus committed what I will call soon "a reversed actualist fallacy."In challenging actualist mistakes .. (shrink)

The title of our volume refers to what is well described by the following two quota tions:"Godcreated man in his own image"l and "Man creates God in his own image."2 Our approach to symmetry is subjective, and the term "personal" symmetry reflects this approach in our discussion of selected scientific events. We have chosen six icons to symbolize six areas: Kepler for modeling, Fuller for new molecules, Pauling for helical structures, Kitaigorodskii for packing, Bernal for quasicrystals, and Curie for dissymmetry. (...) For the past three decades we have been involved in learning, thinking, speaking, and writing about symmetry. This involvement has augmented our principal activities in molecular structure research. Our interest in symmetry had started with a simple fascination and has evolved into a highly charged personal topic for us. At the start of this volume, we had had several authored and edited symmetry related books behind 3 us. We owe a debt of gratitude to the numerous people whose interviews are quoted 4 in this volume. We very much appreciate the kind and gracious cooperation of Edgar J. Applewhite (Washington, DC), Lawrence S. Bartell (University of Michigan), R. (shrink)