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The Philosophy of Gottlob Frege

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Begriffsschrift was, as the subtitle announced, a formula language of pure
thought modeled upon the language of arithmetic. Frege borrowed the notation
for functions from arithmetic, and enlarged the realm of applicability
of a function beyond the domain of numbers. Then, supplanting the
subject/predicate division, which was characteristic of previous logical
systems, by a function/argument division, he created a logical notation,
a Begriffsschrift – literally, Concept Writing – which would serve to represent
thoughts about any objects whatsoever. Like the language of arithmetic,
his Begriffsschrift represented thoughts so that the inferential connections
between them were molded in the representations themselves.
The project was enormously successful. Not only did Frege create modern
quantificational logic, but he also provided the theoretical framework for
many subsequent philosophical developments in logic as well as in speculative
philosophy. As Dummett (1981a) correctly remarked, Frege’s work
shifted the central focus of philosophy from the epistemological issues
raised by Descartes back to the metaphysical and ontological issues that
were salient after Aristotle.

The function/argument analysis Frege (1879) presented was, however,
flawed. There was a significant confusion in his operating semantic
notion of the content [Inhalt] of a sentence. Frege came to recognize
that repairs were needed, and after much hard philosophical
work, the theory with which we are now familiar emerged in the early
1890s.
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