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When characterizing 'Schopenhauer as Educator,' in the essay of that title, Nietzsche acknowledges the value of Schopenhauer's writings but reserves special praise for Schopenhauer as a model to emulate: Schopenhauer, in Nietzsche's telling, has lived the exemplary philosophical life. The former colleagues and students who have come together here are bound by a like estimate of the influence of Hans Herzberger on their thoughts. Hans's writings, in a variety of areas, are recognized to have had an important impact, but those who have had the good fortune to know him will testify in addition to the lasting imprint of his scholarly personality: the memory of his quiet, insistent hunger for understanding, independence of mind and intellectual honesty. The essays collected here are dedicated to Hans with affection and gratitude for both his profound work and his lasting example.

The editors would like to sadly note the absence of Hans's inseparable graduate school friend Jerrold Katz from the list of contributors. He was an enthusiastic supporter of this tribute project and planned to add a paper, before his untimely passing.

Isaac Levi addresses the question of in what sense, if any, a rational agent should be seen as a maximizer of some cognitive value (be it utility, preference, or something else). Levi wishes to go even further than Herzberger had in attacking this idea and develops a distinctive rule for the guidance of choice, agreeing with Herzberger that 'rationality does not mandate maximizing preference' in situations where one's choices are 'incomparable.'

Calvin Normore turns to the surprisingly vexing concept of logical validity. Medieval philosophers raised difficulties for the standard notion in which validity is defined in terms of truth (e.g., it is impossible for the premises of a valid argument to be true and the conclusion [End Page vii] false). As Herzberger noted, some medievals had the logical machinery needed for a more subtle approach. Normore explores some of these that retain interest to this day.

Jamie Tappenden's essay opens a window on Frege's life and work, which has been almost completely closed for a hundred years: the local influences on both his doctrines and his understanding of the nature of mathematics and its philosophy. Tappenden explores in particular the remarkably gifted, but under-regarded, mathematician Ernst Abbe with whom Frege had very close contact and by whom he was deeply influenced in a number of ways. The link to Herzberger here is tangential but delightfully surprising.

Alasdair Urquhart tackles a subject that was a perennial interest of Herzberger, the inexpressible. Frege's peculiar, and — seemingly — obviously incorrect (if not ridiculous), remark that 'the concept horse is not a concept' is Urquhart's particular target: the 'limits of expression in Frege's system.' Urquhart argues that Frege's puzzling remark is a natural consequence of his rigid systematic views about linguistic or mathematical entities, such as functions and their values (objects). Like Wittgenstein, Frege is forced to write nonsense, but nonsense that is also somehow illuminating.

Achille Varzi's lighthearted essay takes us back to Flatland, where we discover a long lost document written by A. Square, in which it is shown how the geometry of Flatland is neither obvious in its nature nor yet inaccessible to thought and investigation.

Finally, Steven Yablo once again takes off from Frege and expressibility, this time based on Frege's somewhat cryptic remark that the content of a sentence can be 'carved' in multiple ways, the comparative virtues of which ways is relative to a number of more or less familiar considerations. Yablo's reflections on this notion extend far beyond Frege, to an intricate metaphysical analysis of content and carvings, and from there to the issue of mathematical realism. [End Page viii]