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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From Kant’s point of view, existence claims were thought to be synthetic and in need of justification by the faculty of intuition.

At Engilsh, Frege attended lectures by Ernst Karl Abbe, who subsequently became Frege’s mentor and who had a significant intellectual and personal influence on Frege’s life. See May b for a nice discussion of the question of whether Frege believed that the sense of a name varies from person to person.

Wright, Basic Laws of Arithmetic: Selected ReadingsCambridge: Philosophy of MathematicsCambridge, MA: Black in Black []Geach and Black [] pp. These are the statements involving function applications and the simple predications which fall out as a special case. Begrirfsschrift what follows, however, we shall continue to use the notation of the modern predicate calculus instead of Frege’s notation. Concepts are functions which map every argument to one of the truth-values.

The intuitive idea is easily grasped if we consider begriffsschrft relation x is the father of y. We now work toward a theoretical description of the denotation of the sentence as a whole. Philosophers today still find that work insightful.


I’d like to thank to Emily Bender, who pointed out that I hadn’t observed the distinction between relative and subordinate clauses in discussing Frege’s analysis of belief reports. In the latter, Frege criticized Hilbert’s understanding and use of the axiomatic method see the entry on the Frege-Hilbert controversy.

Frege, but also facts about ancestrals of relations and natural numbers Philosophers only recently appreciated the importance of this work C.

In Aristotelian logic, these inferences have nothing frefe common.

Gottlob Frege > Chronological Catalog of Frege’s Work (Stanford Encyclopedia of Philosophy)

We discuss these developments in the following subsections. Yet, at the same time, Frege clearly accepted Riemann’s practice and methods derived from taking functions as fundamental, as opposed to Weierstrass’s focus on functions that can be represented or analyzed in terms of other mathematical objects e.

To see this more clearly, here are the formal representations of the above informal arguments: Is e an element of itself? Cantor, Zur Lehre vom Transfiniten: To see this more clearly, here are the formal representations of the above informal arguments:. In the modern predicate calculus, functional application is analyzable in terms of predication, as we shall soon see. Kluge in McGuinness [] begriffsscnrift.

Gottlob Frege

Its sense may be described as beggiffsschrift. Indeed, some recent scholars have a shown how Frege’s work in logic was informed in part by his understanding of the analogies and disanalogies between geometry and number theory Wilsonand b shown that Frege was intimately familiar with the division among late 19th century mathematicians doing complex analysis who split over whether it is better to use the analytic methods of Weierstrass or the intuitive geometric methods of Riemann Tappenden Blackwell, third edition, Klasseengllsh, pp.


In what has come to be regarded as a seminal treatise, Die Grundlagen der ArithmetikFrege began work on the idea of deriving some of the basic principles of arithmetic from what he thought were more fundamental logical principles and logical concepts. Carnap attended these lectures and took notes. Translated as Critique of Pure Reason by P. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen DenkensHalle a. MendelsohnInquiry But this conception has not yet been articulated in a widely accepted way, and so elements common to Frege’s and Bwgriffsschrift conception may yet play a role in our understanding of what logic is.