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Zermelo's set theory axioms in Frege's "Begriffsschrift" notation

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zbegriff

Zermelo's set theory axioms in Frege's "Begriffsschrift" notation

This pdf shows the conjunction of Zermelo's original list of axioms for set theory, in Gottlob Frege's "Begriffsschrift" notation. Frege was the inventor of what is now known as first-order logic, and his "Begriffsschrift" was the original notation system for mathematical expressions with nested quantifiers.

Frege's notation proved unwieldly for actual mathematical use, and was overtaken by the now-standard Peano notation (backwards E's and upside-down A's for quantifiers, with expressions resembling traditional mathematical formulas). "Begriffsschrift" has long been consigned to the realm of aesthetic curiosity, mentioned only in passing by logicians & philosophers who feel they owe it a tip-of-the-hat because of its historical priority. To my knowledge, nobody other than me has taken the time to write any substantial mathematical expressions in "Begriffsschrift" since Frege.

This pdf was the culmination of a personal project in which I first translated the axioms from standard first-order logic notation into "Begriffsschrift" (mostly by doodling in class notebooks), and then used a special LaTeX package to typeset the resulting image into the nice pretty pdf you see here. Unfortunately I no longer have the TeX file, just the finalized pdf.

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