1On the background of Frege’s Begriffsschrift, see Kreiser (), in particular Couturat’s contribution appeared in an English translation. Reproduktion in Begriffsschrift (). [Vortrag, gehalten in der Sitzung vom Juli der Jenaischen Gesellschaft für Medizin und Naturwissenschaft.]. In , Frege published his first book Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (Concept.

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Begriffsschrift – Wikipedia

Note the last line. Oxford University Press, third edition second edition, ; the first edition of is listed separately as Martinich [] McGuinnessB. Stoothoof in Stoothoff [], in Klemke [] pp. Even the sentences of Frege’s mature logical system are complex denoting terms; they are terms that denote truth-values. Sources were checked, errors were eliminated, and page numbers were added whenever possible. Unfortunately, Basic Law V implies a contradiction, englsih this was pointed out to Frege by Bertrand Russell just as the second volume of the Grundgesetze was going to press.

Concept Script: Frege

Jacquette in Jacquette []. The best way to understand this notation is by way of some tables, which show some specific examples of statements and how those are rendered in Frege’s notation and in the modern predicate calculus. In general, then, the Principle of Identity Substitution seems to take the following form, where S is a sentence, n and m are names, and S n differs from S m only by the fact that at least one occurrence of m replaces n:.


Leben, Werk, ZeitHamburg: Frege, therefore, would analyze this attitude report as follows: Thus, Frege analyzed the above inferences in the following general way: Each of these expressions has both a sense and a denotation.

This is the so-called “law of trichotomy “.

Despite Frege’s failure to provide a coherent systematization of the notion of an extension, we shall make use of the notion in what follows to explain Frege’s theory of numbers and analysis of number statements. To explain these puzzles, Frege suggested a that begriffsschrifg addition to having a denotation, names and begrfifsschrift also express a sense. Frege made a point of showing how every step in a proof of a proposition was justified either in terms of one of the axioms or in terms of one of the rules of inference or justified by a theorem or derived rule that had already been proved.

By using this site, you agree to the Terms of Use and Privacy Policy. To see this more clearly, here are the formal representations of the above informal arguments:.

Gottlob Frege (Stanford Encyclopedia of Philosophy)

The extension of a concept F records just those objects which F maps to The True. Here we can see the beginning of two lifelong interests of Frege, namely, 1 in how concepts and definitions developed for one domain fare when applied in a wider domain, and 2 in the contrast between legitimate appeals to intuition in geometry and illegitimate appeals to intuition in the development of pure number theory. This idea has inspired research in the field for begriffsshcrift a century and we discuss it in what follows.


The debate over which resources require an appeal to intuition and which do not is an important one, since Frege dedicated himself to the idea of eliminating appeals to intuition in the proofs of the basic propositions of arithmetic. Begrlffsschrift similar holds for surfaces and solid contents. Frege would say that any object that a concept maps to The True falls under the begricfsschrift.

Consider the following argument: Philosophers today still find that work insightful.

Johann Friedrich Hartknoch, 1st edition A; 2nd edition B Views Read Edit View history. Derived using concept-scriptOxford: There are distinct things x and y that fall under the concept F and anything else that falls under the concept F is identical to either x or y.

Kaal in McGuinness [] pp. Please notify the author if you find any remaining errors. Olms contains the English version of Frege [] AustinJ.

The function which maps The True to The True and maps all other objects to The False; used to express the thought that befriffsschrift argument of the function is a true statement.

Note the last row of the table — when Frege wants to assert that two conditions are materially equivalent, he uses the identity sign, since this says that they denote the same truth-value.