No coin nor oath required. For personal study only.
BOOK NOTES [J. F. I. and ( 3) Better yet, the original and the translated texts are arranged, paragraph by paragraph, on opposing pages of the book, so that a direct comparison of both is possible in the most convenient manner. The present reviewer, who is fully conversant with German, has repeatedly checked the accuracy of Mr. Austin's translation, by preparing his own English version of a sentence or two at a time in various parts of the book and comparing it with his. In all instances Mr. Austin's version was either identical with that of this reviewer or superior to it in conveying the logical niceties of Frege's arguments.
The necessity, in a text of this nature, of rendering, as it were, verbatim, the rational content of the author's statements in German makes it unavoidable that the English version becomes somewhat stilted. Unavoidably too, much of the original style and mood has been lost.
Despite its formidable subject, Frege's original text makes delightful reading. The first half of the book is devoted to the presentation of the views of other writers on the nature of arithmetical propositions, on the concept of Number, and on those of Unity and One. Systematically, Frege takes Kant, Leibniz, Hankel, Mills, Hobbes, Locke and a host of less illustrious predecessors to task, quoting their statements on the subject and neatly plucking them apart with a wry smile. Mills, in particular, as a proponent of empiricism, comes in for a large share of genteel sarcasm.
The second half of the book contains demonstrations of Frege's thesis that "a statement of number contains an assertion about a concept," so that the laws of arithmetic are analytic judgments and, consequently, a priori.
In the concluding section the statement occurs: "Arithmetic is but an extension of logic and every proposition of arithmetic is a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts (observation itself already includes within it a logical activity) ; calculation is deduction." A thoroughly modern point of view ! OTTO R. SPIES
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