This is a very entertaining and after it gets going, a useful review. But why are the punches pulled? Below the opening lines of the review. It is unclear to me why the names/titles of the offending chapters are omitted. This is ersatz frankness. More important, I don't see what service is performed by this. (Of course,the editor and publisher can probably reverse engineer the identity of the offending chapters, but unless they have a lot of pride this will not prevent repeat performances.)
- 402 pages crammed with faint, tiny type cannot be good for anyone's eyes.
- There is enough overlap between the essays to discourage a line-by-line march to the finish. (Does anyone really need six introductions to the corollarial/theorematic distinction in the space of 173 pages?) In one case, a single page is enough to engender a feeling of déjà vu. Lines 2-4 of p. 272 read: "Non-Archimedean ordered fields, by contrast, always contain infinite as well as nonzero infinitesimal elements, the latter being the multiplicative inverses of the former." Lines 22-24 of the same page read: "Non-Archimedean ordered fields, by contrast, contain infinite as well as nonzero infinitesimal elements, the latter being the multiplicative inverses of the former."
- Edited volumes of previously unpublished essays have an upside and a downside. Freed from the heavy hand of referees, some contributors produce creative work with a distinctive flair; others lengthen their vitas with output below their usual standard. True to form, some of the New Essays are, let us say, unimpressive.
- Furthermore, this reviewer was unable to form a definite judgment about another of the essays because he found it largely unintelligible. Here is a sample (214). "The elementary axioms of the basic system of existential graphs thus support the idea -- central in philosophy (Presocratics, Peirce, Heidegger) -- that a first self-reflection of nothingness on itself is the spark that ignites the evolution of knowledge." Readers who find this sort of thing suggestive or inspiring should, by all means, dig in.
- Yet another essay, though admirable in some respects, casts Peirce as little more than a spear-carrier. In the first 21 pages, the author cites Peirce only six times while citing himself 67 times. Peirce rallies a bit in the last 26 pages, but cannot overcome the author's early advantage. The final tally: Peirce citations 22, self-citations 97. These numbers give an accurate impression of the essay's focus. This might not please those readers who peruse the New Essays on Peirce's Mathematical Philosophy because they are interested in Peirce's mathematical philosophy."
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