Frege uses Greek letters in two different ways in his Begriffsschrift. One way is the familiar use of bound variables, in conjunction with variable-binding operators, to mark and close argument-places. The other, which is quite unfamiliar, employs letters to mark places for operators to reach into, without thereby closing these places. Frege thereby invents a powerful and compact notation for functional operations which can be recommended even today. His regrettable double use of Greek letters obscured his invention, and this, together (...) with the fact that in the Grundgesetze he no longer has need of function-valued functions, explains why the device was overlooked and has not passed into general use. (shrink)

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...

In his Grundlagen, Frege held that geometrical truths.are synthetic a priori, and that they rest on intuition. From this it has been concluded that he thought, like Kant, that space and time are a priori intuitions and that physical objects are mere appearances. It is plausible that Frege always believed geometrical truths to be synthetic a priori; the virtual disappearance of the word ‘intuition’ from his writings from after 1885 until 1924 suggests, on the other hand, that he became dissatisfied (...) with the notion of intuition as he had employed it in Grundlagen. The belief that a priori intuition is a source of knowledge does not in itself entail idealism: that is a question about what it is that makes true the propositions known in this way. In Grundlagen, Frege expressly states that geometrical truths are objective in the sense of being independent of our intuition. This shows that, even at that period, Frege did not draw the idealist conclusion drawn by Kant. (shrink)

The ideas of the German philosopher and mathematician Gottlob Frege lie at the root of the analytical movement in philosophy. Frege and Other Philosophers comprises all of Professor Dummett's published and previously unpublished essays on Frege, with the exception of those included in his Truth and Other Enigmas. In some of these essays he explores the relation of Frege's ideas to those of his predecessors and contemporaries. In others he considers critically some interpretations of Frege, and develops the argument for (...) a sound understanding of Frege's thought which he first delineated in The Interpretation of Frege's Philosophy. Several of the essays illustrate his contention that Frege's work remains the best starting point for the investigation of problems concerning truth, meaning, thought, and language, which are still among the most contentious issues in modern analytical philosophy. Any discussion of Frege's ideas is therefore also an exploration of fundamental and as yet unresolved issues of philosophy. (shrink)