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The convenience of the typesetter; notation and typography in Frege’s Grundgesetze der Arithmetik. (English) Zbl 1354.03001
Gottlob Frege is admired for his wholly original contributions to logic, to the philosophy of mathematics, and to the philosophy of language, and his work in each of these fields is often cited almost as if he were a contemporary. His contributions to logical notation were also wholly original, but now are generally passed over in silence or explicitly dismissed. (F. Cajori calls Frege’s notation “repulsive”, [A history of mathematical notations. Vol. I: Notations in elementary mathematics. 2nd ed. La Salle, IL.: The Open Court Publishing Company (1974; Zbl 0334.01003), p. 295]). Faint hints of his assertion sign may be found in the turnstile symbol (\(\vdash\)) for derivability, and of his way of expressing negation in the negation symbol (\(\neg\)) first used by Arend Heyting and now widely standard in logic (though not in computing nor in mathematics). For functions, he seems to have sought out the most obscure characters available at his local print shop, including those peculiar to particular languages (the German Eszett, or the Polish Dark Ell) and signs from the then recently begun International Phonetic Alphabet (IPA), and proceeded to make them more obscure by inverting them (easy with lead type, more difficult in computer fonts) or adding diacritical marks. The present logically informed paper will help discouraged historians of logic see some gleams of purpose in his practice.
MSC:
03-03 History of mathematical logic and foundations
01A55 History of mathematics in the 19th century
03A05 Philosophical and critical aspects of logic and foundations
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