This article derives from a project attempting to show that Western formal logic, from Aristotle onward, has both been partially constituted by, and partially constitutive of, what has become known as racism. In the present article, I will first discuss, in light of Frege’s honorary role as founder of the philosophy of mathematics, Reuben Hersh’s What is Mathematics, Really? Second, I will explore how the infamous section of Frege’s 1924 diary (specifically the entries from March 10 to April 9) supports (...) Hersh's claim regarding the link between political conservatism and the (historically and currently) dominant school of the philosophy of mathematics (to which Frege undeniably belongs). Third, I will examine Frege’s attempt at a more reader-friendly introduction to his philosophy of mathematics, The Foundations of Arithmetic. And finally, I will briefly analyze Frege’s Begriffsschrift to see how questions of race arise even at the heights of his logical abstraction. (shrink)
The present article reviews the Polish-language edition of Gottlob Frege’s scientific correspondence. In the article, I discuss the material hitherto unpublished in Polish in relation to the remainder of Frege’s works. First of all, I inquire into the role and nature of definitions. Then, I consider Frege’s recognition criteria for sameness of thoughts. In the article’s third part, I study letters devoted to the principle of semantic compositionality, while in the fourth part I discuss Frege’s remarks concerning the context principle.
Although the connections between Frege’s and Russell’s investigations are commonly known, there are some topics in their letters which do not seem to have been analysed until now: 1. Paradoxes formulated by Russell on the basis of Frege’s rules: a) „»ξ can never take the place of a proper name« is a false proposition when ξ is a proposition”; b) “A function never takes the place of a subject”. A solution of this problem was based on the reference/sense theory and (...) on the distinction between the first- and second-level names. 2. The inconsistency in Frege’s system may be avoided by the introduction of: a) a new kind of objects called quasi-objects ; b) logical types ; c) mathematics without classes ; d) some restrictions on the domain of function. 3. Since the inconsistency is connected with a class, what is class? In one of the letters, Frege compared a class to a chair composed of atoms. This approach seems to be similar to the collective understanding of a set. 4. Russell doubted that the difference between sense and reference of expressions was essential. Hence, Frege found some additional reasons to distinguish between them: semiotic, epistemological, from identity, and from mathematical practice. This discussion can be seen as a next step in developing the theory of descriptions by Bertrand Russell. (shrink)
ABSTRACTA short piece by Frege, heretofore overlooked, containing a précis of his views on the concept of number, is presented, after some very brief questions about Frege's possible involvement in the wider intellectual milieu.
"By looking at Frege's lectures on logic through the eyes of the young Carnap, this book casts new light on the history of logic and analytic philosophy. As two introductory essays by Gottfried Gabriel and by Erich H. Reck and Steve Awodey explain, Carnap's notes allow us to better understand Frege's deep influence on Carnap and analytic philosophy, as well as the broader philosophical matrix from which both continental and analytic styles of thought emerged in the 20th century."--BOOK JACKET.
Many authors believe that the manuscripts Frege wrote in 1924–1925 are not theoretically of interest. They are rather a product of his emotional despair and theoretical dead-end which he reached in the last years of his life. Such is also the judgement of Michael Dummett delivered in his seminal book Frege: Philosophy of Language. According to Dummett, “the few fragmentary writings of Frege’s final period—1919–1925—are not of high quality: they are interesting chiefly as showing that Frege did, at least at (...) the very end of his life, acknowledge the failure of the logicist programme” (Dummett 1981, p. 664). In this paper we will try to show that the widely accepted negative assessment of Frege’s latest writings is due to a lack of understanding of their true idea. In fact, the change in Fre-ge’s mind in the last two or three years of his life was result of long deliberations on a severe tension in his founding intuitions. The change itself made his logico-philosophical project more coherent and, thus, is of utmost theoretical importance. (shrink)
Michael Dummett has shown that the fragment ‘17 Kernsätze zur Logik’ is evidence that Frege knew Lotze's Logik Dummett’s dating of this fragment prior to 1879, however, must be rejected.The present paper shows that there are other articles of Frege’s which bear clear traces of Lotze's LogikFirst of all, the expressions Vorstellungsverlauf from ‘Über die wissenschaftliche Berechtigung einer Begriffsschrift’, and veranlassenden Ursachen, from ‘Logik’, certainly are borrowed from Lotze.Second, there are links between ‘Booles rechnende Logik und die Begriffsschrift’ and Lotze's (...) Logik. Furthermore, it is shown that Frege’s ‘Kernsätze’, the ‘Dialog mit Pünjer über Existenz’, and his ‘Logik’ are intimately connected.All of this indicates that these texts were written in roughly the same period, namely the early 1880s.Conclusive evidence for this is that the terms Vorstellung and Vorstellungsverbindung are used indiscriminately in both a psychological and a logical sense in the ‘Begriffsschrift’, a fact which contradicts the ‘Kernsätze’. (shrink)
In a letter to Frege of 29 December 1899, Hilbert advances his formalist doctrine, according to which consistency of an arbitrary set of mathematical sentences is a sufficient condition for its truth and for the existence of the concepts described by it. This paper discusses Frege's analysis, as carried out in the context of the Frege-Hilbert correspondence, of the formalist approach in particular and the axiomatic method in general. We close with a speculation about Frege's influence on Hilbert's later work (...) in foundations, which we consider to have been greater than previously assumed. This conjecture is based on a hitherto neglected revision of Hilbert's talk "Über den Zahlbegriff". (shrink)
This book contains English translations of nearly all Frege's published writings other than Begriffsschrift, Grundlagen, and Grundgesetze. The works translated are selected from Kleine Schriften. About thirty percent of Collected Papers has never appeared in English before. This includes Frege's Göttingen dissertation, "On a Geometrical Representation of Imaginary Forms in the Plane", and his Jena Habilitationsschrift, "Methods of Calculation based on an Extension of the Concept of Quantity". Also translated for the first time are six brief reviews of mathematical works, (...) a reply to Cantor's review of Grundlagen, two short mathematical lectures: "Lecture on a Way of Conceiving the Shape of a Triangle as a Complex Quantity" and "Lecture on the Geometry of Pairs of Points in the Plane", and a satire, "On Mr. H. Schubert's Numbers". Everything else in Collected Papers has appeared in English before in various journals and books. Frege's only published works not translated here are three explanations of Begriffsschrift and a short lecture, "Ueber den Briefwechsel Leibnizens und Huygens mit Papin", which apparently has not been translated into English. Thus, with the exception of the complete Grundgesetze, the publication of this book, together with The Foundations of Arithmetic, Conceptual Notation, Philosophical and Mathematical Correspondence, and Posthumous Writings, makes almost all Frege's known surviving work, both published and unpublished, available in English. (shrink)
The short fragment of Frege's Nachlass which bears the above title, given to it by the editors, is in fact a sequence of connected comments by him on the Introduction to Lotze's Logik, or, more exactly, a response by him to that Introduction. It is thus very probably the earliest piece of writing from Frege's pen on the philosophy of logic surviving to us, and, when it is read in this light, the motivation for its author's puzzling selection of remarks (...) and the turns of phrase he employs become intelligible. We see here an early attempt by Frege to attain clarity about a topic that was to preoccupy him throughout his entire philosophical career, the nature of thoughts. (shrink)
Freges Werk eröffnete und leitete den Prozeß der Emanzipation der Logik von der ontologisch fundierten zur autarken, von allen nicht-logischen Voraussetzungen losgelösten Logik der Zeichen. Unmittelbaren Aufschluß über den Beginn dieser neuen Epoche gibt Freges Briefwechsel mit den führenden Theoretikern und Philosophen seiner Zeit. Kern des Bandes ist seine Korrespondenz mit Hilbert (über die Grundlagen der Geometrie), mit Husserl (über Sprachphilosophie) und mit Russell (über Logik).