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Begriffsschrift
Begriffsschrift (German for, roughly, 'concept-writing') is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book.
Begriffsschrift is usually translated as concept writing or concept notation; the full title of the book identifies it as "a formula language, modeled on that of arithmetic, for pure thought." Frege's motivation for developing his formal approach to logic resembled Leibniz's motivation for his calculus ratiocinator. (Despite that, in the foreword Frege clearly denied that he achieved this aim, and also that his main aim would be constructing an ideal language like Leibniz's, which Frege declared to be a quite hard and idealistic—though not impossible—task.) Frege went on to employ his logical calculus in his research on the foundations of mathematics, carried out over the next quarter-century. This is the first work in analytic philosophy, a field that British and American philosophers later further developed.
The calculus contains the first appearance of quantified variables, and is essentially classical bivalent second-order logic with identity. It is bivalent in that sentences or formulas denote either True or False; second-order because it includes relation variables in addition to object variables and allows quantification over both. The modifier "with identity" specifies that the language includes the identity relation, =. Frege stated that his book was his version of a characteristica universalis, a Leibnizian concept that would be applied in mathematics.
In the first chapter, Frege defines basic ideas and notation: judgement, conditionality, negation, identity of content, functions and generality.
Frege presents his calculus in an idiosyncratic two-dimensional notation, based on negation, material conditional and universal quantification. Other connectives and existential quantification are provided as definitions. Parentheses are not needed.
The conditional () is expressed by 
. Regarding its meaning Frege wrote:
Now
stands for the judgment that the third of those possibilities does not take place, but one of the three others does."
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Begriffsschrift
Begriffsschrift (German for, roughly, 'concept-writing') is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book.
Begriffsschrift is usually translated as concept writing or concept notation; the full title of the book identifies it as "a formula language, modeled on that of arithmetic, for pure thought." Frege's motivation for developing his formal approach to logic resembled Leibniz's motivation for his calculus ratiocinator. (Despite that, in the foreword Frege clearly denied that he achieved this aim, and also that his main aim would be constructing an ideal language like Leibniz's, which Frege declared to be a quite hard and idealistic—though not impossible—task.) Frege went on to employ his logical calculus in his research on the foundations of mathematics, carried out over the next quarter-century. This is the first work in analytic philosophy, a field that British and American philosophers later further developed.
The calculus contains the first appearance of quantified variables, and is essentially classical bivalent second-order logic with identity. It is bivalent in that sentences or formulas denote either True or False; second-order because it includes relation variables in addition to object variables and allows quantification over both. The modifier "with identity" specifies that the language includes the identity relation, =. Frege stated that his book was his version of a characteristica universalis, a Leibnizian concept that would be applied in mathematics.
In the first chapter, Frege defines basic ideas and notation: judgement, conditionality, negation, identity of content, functions and generality.
Frege presents his calculus in an idiosyncratic two-dimensional notation, based on negation, material conditional and universal quantification. Other connectives and existential quantification are provided as definitions. Parentheses are not needed.
The conditional () is expressed by . Regarding its meaning Frege wrote:
Now
stands for the judgment that the third of those possibilities does not take place, but one of the three others does."
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