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Butterfield does have a few of his own biases, speaking in the magisterial "we" when declaring our age a secularized one, or speaking of alleged Catholic irrationality. But these are minor faults, and easily accounted for, hardly marring lthis excellent essay.
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The modern reader has many choices of science history books from which to choose. For someone a little bit familiar with the field Butterfield's work is a good overview. For someone not familiar with the field, I think it would make difficult reading if not supplemented by other books or by classroom discussion. So far as his second goal goes, I think he is right about the importance of the Scientific Revolution, but his transition from what was to what became is weak. After Newton, Butterfield points out only that the numbers and organization of scientists increased. True, he points out that Newton's mathematization and simplification of the universe was tremendously influential on other fields of thought, but on the whole I don't think he's made the connection.
However, this does not mean that I think the work is without value. Rather, I find it well thought out and well written. The scope is necessarily limited by the original lecture format, but this also keeps the writing concise and focused. Although more recent historiography frowns on calling anyone a 'great mind', I'm sympathetic to the point of view that the men involved in early modern scientific thinking were in fact great and intelligent, and should be commended for their work. This does not mean that Butterfield has presented a laundry list of Dark Ages Ignorance that was overcome by the lone genius, but he has accurately described the prevailing world views of the fifteenth and sixteenth centuries and explained how much effort it took to change or overthrow them.
But what is most important in this book is its central historical thesis: that science is not a "revolution" that exploded out of nowhere with Galileo (or even worse, with that desperate catch-all of ignorant scribblers, the Renaissance), but rather a tradition, you might say almost an apostolical succession, that goes back as far as the thirteenth century; that is, it is coeval with the rise of the distinctive Western (rather than Christian or Roman) civilization, with its distinctive cultural institutions - Universities and the private commercial publication of books. Butterfield's ability to discriminate, his insight into what is genuinely scientific and what he would call "archaic", are used in the service of a historical theory that, as far as I am concerned, has not aged and is still valid.
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If I were an editor at Norton, I would give serious consideration to reissuing this book with a new introductory essay. To be perfectly honest, I am not sure who the Whig historians were, and am not quite certain what the relations between being a Whig historian and being a Whig politically is. The only Whig historian Butterfield mentions by name, Lord Acton, was, as Butterfield points out, a Tory. I think I would have profited far more from this book if I had not had to spend all my time wondering precisely who Butterfield's targets were.
Essentially, this book is a critique of imposing moral judgments in historical research. It is a defense of taking each historical epoch on its own terms, and not imposing one's own moral and cultural standards on figures and situations that existed with, perhaps, a different set of moral and cultural concerns. To this degree, the book is commonsensical and noncontroversial, and can be read with a great deal of profit.
The structural problem of the book is that the entire discussion is framed in extremely polemical terms. Perhaps Butterfield was a Whig Catholic, but given the examples he constantly brings up, and the barely disguised passion he brings to the debate, one wonders if he were not a Tory Catholic. Perhaps not, but one cannot help but wonder why he is so polemical. The same points--none of them especially controversial today, however they may have been in 1932--could have been expressed far more effectively in a nonpolemical fashion. But, again, perhaps an introductory essay by a contemporary historian could explain just why Butterfield chose such an inflammatory mode.
Nonetheless, any nonhistorian can read this book with great profit, even if they, like me, wonder about the context in which he wrote and who the Whig historians were.