Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard also in other (...) fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively. (shrink)

The first complete English translation of a groundbreaking work. An ambitious account of the relation of mathematics to logic. Includes a foreword by Crispin Wright, translators' Introduction, and an appendix on Frege's logic by Roy T. Cook. The German philosopher and mathematician Gottlob Frege (1848-1925) was the father of analytic philosophy and to all intents and purposes the inventor of modern logic. Basic Laws of Arithmetic, originally published in German in two volumes (1893, 1903), is Freges magnum opus. It was (...) to be the pinnacle of Freges lifes work. It represents the final stage of his logicist project the idea that arithmetic and analysis are reducible to logic and contains his mature philosophy of mathematics and logic. The aim of Basic Laws of Arithmetic is to demonstrate the logical nature of mathematical theorems by providing gapless proofs in Frege's formal system using only basic laws of logic, logical inference, and explicit definitions. The work contains a philosophical foreword, an introduction to Frege's logic, a derivation of arithmetic from this logic, a critique of contemporary approaches to the real numbers, and the beginnings of a logicist treatment of real analysis. As is well-known, a letter received from Bertrand Russell shortly before the publication of the second volume made Frege realise that his basic law V, governing the identity of value-ranges, leads into inconsistency. Frege discusses a revision to basic law V written in response to Russells letter in an afterword to volume II. The continuing importance of Basic Laws of Arithmetic lies not only in its bearing on issues in the foundations of mathematics and logic but in its model of philosophical inquiry. Frege's ability to locate the essential questions, his integration of logical and philosophical analysis, and his rigorous approach to criticism and argument in general are vividly in evidence in this, his most ambitious work. Philip Ebert and Marcus Rossberg present the first full English translation of both volumes of Freges major work preserving the original formalism and pagination. The edition contains a foreword by Crispin Wright and an extensive appendix providing an introduction to Frege's formal system by Roy T. Cook. Readership: Scholars and advanced students in philosophy of logic, philosophy of mathematics, and early analytic philosophy. (shrink)

This is the first single-volume edition and translation of Frege's philosophical writings to include his seminal papers as well as substantial selections from ...

Questo volume ripropone sei articoli fondamentali di Gottlob Frege nella versione italiana corredata dalla guida alla lettura di Carlo Lazzerini, che ha fatto di questa raccolta un’introduzione particolarmente felice alla logica moderna: un testo classico molto intenso viene proposto in modo tanto semplice da poter essere la porta di ingresso nella logica e nella filosofia della logica del Novecento anche per lettori che non ne hanno nessuna nozione e che ne iniziano da qui lo studio. Gli articoli di Frege, composti (...) in epoche diverse e caratterizzati da un’evoluzione verso una maggiore sistematicità, formano nel complesso un testo organico e seminale per lo sviluppo della logica matematica, della semantica e della filosofia del linguaggio del Novecento, come si constata anche ad una prima lettura, quando si tenga conto dell’influenza da un lato della geniale intuizione di Frege della distinzione nel significato dei nomi, dei concetti e delle proposizioni fra «senso» e «denotazione», e dall’altro della sua scoperta del valore funzionale del concetto. La lettura di Frege è un’occasione d’incontro tra cultura filosofica e scientifica. Se nell’antichità la logica (come, ad esempio, anche la fisica e la matematica) era intesa come disciplina filosofica, col volgere del tempo la logica è diventata sempre più una scienza autonoma, con un oggetto ben definito e finalità pratiche preminenti. Anzi, proprio la «logica matematica» promossa da Frege ha dato maggiore impulso a questo distacco, configurandosi sempre più come una tecnica precisa, un calcolo, come la forma elementare della matematica o come un ramo particolare della matematica stessa. Eppure, che gli scritti di Frege abbiano un valore filosofico, si avverte anche ad una lettura superficiale, nonostante l’impressione di tecnicismo che gli argomenti da lui preferiti possono dare. La ricerca matematica di Frege, il suo interesse per il problema dei «fondamenti» ed il suo inevitabile sconfinare di continuo nella logica, non sono mai promossi né da esigenze di applicazione, né di costruzione «all’in su» della scienza, ma sempre da un’esigenza di perfezionamento teoretico, verso il profondo. Dalla matematica ai fondamenti e dai fondamenti alla logica: se questo è l’itinerario della ricerca di Frege la sua qualità filosofica non è data dalla direzione dell’itinerario stesso, dal fatto che approda alla logica, ma dal modo della ricerca, che gli fa trascurare le possibilità costruttive della scienza (e da ciò viene la legittima diffidenza dei matematici suoi contemporanei), per tener dietro alle prospettive teoretiche che si aprono, una dopo l’altra, in direzioni del tutto imprevedibili. (shrink)

In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens / von Dr. Gottlob Frege,...Date de l'edition originale : 1879Ce livre est la reproduction fidele d'une oeuvre publiee avant 1920 et fait partie d'une collection de livres reimprimes a la demande editee par Hachette Livre, dans le cadre d'un partenariat avec la Bibliotheque nationale de France, offrant l'opportunite d'acceder a des ouvrages anciens et souvent rares issus des fonds patrimoniaux de la BnF.Les oeuvres faisant partie de cette collection ont ete numerisees (...) par la BnF et sont presentes sur Gallica, sa bibliotheque numerique.En entreprenant de redonner vie a ces ouvrages au travers d'une collection de livres reimprimes a la demande, nous leur donnons la possibilite de rencontrer un public elargi et participons a la transmission de connaissances et de savoirs parfois difficilement accessibles.Nous avons cherche a concilier la reproduction fidele d'un livre ancien a partir de sa version numerisee avec le souci d'un confort de lecture optimal. Nous esperons que les ouvrages de cette nouvelle collection vous apporteront entiere satisfaction.Pour plus d'informations, rendez-vous sur www.hachettebnf.frhttp://gallica.bnf.fr/ark:/12148/bpt6k65658c. (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.

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.

This volume contains all of Frege's extant unpublished writings on philosophy and logic other than his correspondence, written at various stages of his career.

Equality1 gives rise to challenging questions which are not altogether easy to answer. Is it a relation? A relation between objects, or between names or signs of objects? In my Begriffsschrift I assumed the latter. The reasons which seem to favour this are the following: a = a and a = b are obviously statements of differing cognitive value; a = a holds a priori and, according to Kant, is to be labeled analytic, while statements of the form a = (...) b often contain very valuable extensions of our knowledge and cannot always be established a priori. The discovery that the rising sun is not new every morning, but always the same, was one of the most fertile astronomical discoveries. Even to-day the identification of a small planet or a comet is not always a matter of course. Now if we were to regard equality as a relation between that which the names ‘a’ and ‘b’ designate, it would seem that a = b could not differ from a = a (i.e. provided a = b is true). A relation would thereby be expressed of a thing to itself, and indeed one in which each thing stands to itself but to no other thing. What is intended to be said by a = b seems to be that the signs or names ‘a’ and ‘b’ designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. But this relation would hold between the names or signs only in so far as they named or designated something. It would be mediated by the connexion of each of the two signs with the same designated thing. But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case the sentence a = b would no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means. But in many cases this is just what we want to do. If the sign ‘a’ is distinguished from the sign ‘b’ only as object (here, by means of its shape), not as sign (i.e. not by the manner in which it designates something), the cognitive value of a = a becomes essentially equal to that of a = b, provided a = b is true.. (shrink)

§ i. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. ...

... as 'logicism') that the content expressed by true propositions of arithmetic and analysis is not something of an irreducibly mathematical character, ...

Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard also in other (...) fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively. (shrink)

Translation of Frege's 'Über Begriff und Gegenstand' (1892). Translation by Peter Geach, revised by Max Black.

This volume contains English translations of Frege's early writings in logic and philosophy and of relevant reviews by other leading logicians. Professor Bynum has contributed a biographical essay, introduction, and extensive bibliography.