摘要：Over the course of the nineteenth century mathematicians became vividly aware that great advances in intuitive “understanding” could be obtained if novel definitions were devised for old notions such as “conic section”, for one thereby often gained a deeper appreciation for why old theorems in the subject had to be true (the new definitions were said to have proved “more fruitful” in these regards). From a naïve philosophical standpoint, such definitional alterations look as if they must properly displace the “propositional contents” of the very theorems they seek to illuminate. Haven’t our reformers merely “changed the subject”, rather than truly provided the conceptual enlightenment they claim? Many practitioners of the time claimed that “Science” enjoys a special prerogative to ignore “surface content” in its search for truth, a sentiment with which Frege often concurs, at least in his early writings. Yet it is hard to render these opinions consistent with his official views on sense and reference, as this essay details. It also surveys Russell’s views on such topics, although he was generally less aware than Frege of the revolutionary mathematical work pursued within the “search for fruitful definitions” program.
关键词：definition; 19th century definitional practice; objective content; sense; meaning; reference; Frege; Russell
