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This book is the only full scale biography of Johnson to be written so far. As such it is a valuable addition to our knowledge. It was originally written as a senior honors project at Yale, and although expanded, still bears signs of its origins. It is strong on the development of the Harlem stride piano style and has a good chapter on Johnson's pianistic approach.
However, it also has some flaws: it is based largely on secondary sources, has little to say about Johnson's "serious" music (most of which was not rediscovered until after 1986), is unbalanced in its emphasis on the 1920s while neglecting Johnson's jazz revival in the 1940s, and offers only limited analysis of his recordings.
Bob Hilbert's discography is a very useful addition, although it is now 15 years out of date and therefore omits both CD releases and some recent discoveries.
For Johnson fans or those interested in the history of stride piano or in the New York jazz scene of the 1920s, this is well worth getting. However, it is not the definitive scholarly biography that Johnson's stature ultimately deserves.
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But it is a good story with a different viewpoint. Does one accept a common humanity and collaborate with the German-- who after all does not seem that evil.... or does one forgo that for the pride of being French.... and being the conquored....
Honestly, everything having to do with WWII is biased.... or most everything.... this portrait is at least honest about it.... and fairly nonpoliticized... though that is another topic entirely....
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It is a lot of work to use this book. The content may be good, but if you're looking for guidance on something specific, you're going to have to dig to find it. A guide should be easy to use, not a chore, in and of itself.
It isn't always as detailed as a writer might like on usage, but if you have a strong handle on usage, then this shouldn't be a problem.
The book is small and compact, so it doesn't take up a lot of shelf space, but it is full of useful information. It's also great as a writer's traveling companion. Information is quick and easy to find. I recommend keeping this one nearby when proofreading and editing one's work.
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Brown is desperately in need of an editor, or at least a proofreader. There are countless grammatical and typographical errors which really ought not to be in a final edition; and while most of these do little more than make the text seem unpolished and amateurish, some obscure the subject matter: for example, because of Brown's extreme laziness in bracket-counting, his proof of Gödel's second incompleteness theorem (chapter 5) is quite incomprehensible unless the reader is adept enough at playing Sherlock Holmes to come up with the proof Brown *really* meant to give.
But Brown doesn't just need an editor to fix his mechanical errors: he needs someone to help him choose what to print. In chapter 8, on constructive mathematics, Brown fills up a full page with lengthy quotes from Brouwer, admitting that "This is pretty obscure stuff," (116) but declining to elucidate Brouwer's point except with more quotation, which he admits is "no better".
There is interesting material in this book, but the presentation is far from perfect, and often aggravating. Brown is to be credited with a sense for what is interesting, but he would put that sense to better use advising another writer than writing himself. If you can't find another introduction to the philosophy of mathematics, this book is worth reading; if you can, I strongly advise you to investigate your alternatives.
He shows why philosophers argue against Platonism, and which are the biases and confusions they make that apparently they show a rejection to it.
It discusses subjects such as numbers, sets, geometrical objects, graphs, and even fractals, and how Platonism can recognize all of them as abstract objects, and how pictures can help us psychologically to grasp these abstract objects.
However, with all of this I have only one problem. He proposes a kind of "mind's eye" by which we are able to "grasp" these abstract objects. Although he presents a very keen argument for refuting the argument that only through sensible experience we are able to know anything about the world, I still feel uneasy and not satisfied about his epistemological account. The hypothesis of this "mind's eye" is the reason why most philosophers find the Platonist proposal so objectionable. In order to account for our knowledge of abstract objects, we must posit a kind of myserious mystic faculty of the "mind's eye".
I think that Husserl's categorial intuition and categorial abstraction (which he proposes in his "Logical Investigations") or Katz proposal of intellectual intuition (in his "Realistic Rationalism") are much more acceptable proposals than Brown's "mind's eye".
Despite this difference, I highly recommend this book, along with Jerrold Katz's "Realistic Rationalism", as a great and serious exposition of the Platonist proposal in philosophy of mathematics that I have ever found. It also serves as a good introduction to philosophy of mathematics.
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