Most areas of philosopher Edmund Husserl’s thought have been explored, but his views on logic, mathematics, and semantics have been largely ignored. These essays offer an alternative to discussions of the philosophy of contemporary mathematics. The book covers areas of disagreement between Husserl and Gottlob Frege, the father of analytical philosophy, and explores new perspectives seen in their work.

"This volume assembles twelve texts published between 1892 and 1915.... The editors allow one to see the genesis of the ideas of Duhem, philosopher and historian, of the variety of his styles, and sometimes also the limits of his work.... A useful index, probably unique in the field of Duhemian studies, completes the book.... The English-language public may be assured an exemplary translation and a reliable critical apparatus." --Jean Gayon, _Revue d'Histoire des Sciences_.

Quine’s criticism of the notion of analyticity applies, at best, to Carnap’s notion, not to those of Frege or Husserl. The failure of logicism is also the failure of Frege’s definition of analyticity, but it does not even touch Husserl’s views, which are based on logical form. However, some relatively concrete number-theoretic statements do not admit such a formalization salva veritate. A new definition of analyticity based not on syntactical but on semantical logical form is proposed and argued for.

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (shrink)

überall einen richtigen Gebrauch der reinen Vernunft giebt, in welchem Fall es auch einen Canon derselben geben muß, so wird dieser nicht den speculativen, sondernden pr.ntischen Vernunftgebrauch betreffen, den wir also iezt ...

Quine’s criticism of the notion of analyticity applies, at best, to Carnap’s notion, not to those of Frege or Husserl. The failure of logicism is also the failure of Frege’s definition of analyticity, but it does not even touch Husserl’s views, which are based on logical form. However, some relatively concrete number-theoretic statements do not admit such a formalization salva veritate. A new definition of analyticity based not on syntactical but on semantical logical form is proposed and argued for.

Part I: Inductivism and its Critics:. 1. Some Historical Background: Inductivism, Russell and the Cambridge School, the Vienna Circle and Popper. 2. Popper’s Critique of Inductivism. 3. Duhem’s Critique of Inductivism. Part II: Conventionalism and the Duhem-Quine Thesis:. 4. Poincare’s Conventionalism of 1902. 5. The Duhem Thesis and the Quine Thesis. Part III: The Nature of Observation:. 6. Observation Statements: the Views of Carnap, Neurath, Popper and Duhem. 7. Observation Statements: Some Psychological Findings. Part IV: The Demarcation between Science and (...) Metaphysics:. 8. Is Metaphysics Meaningless? Wittgenstein, the Vienna Circle and Popper’s Critique. 9. Metaphysics in relation to Science: the Views of Popper, Duhem and Quine. 10. Falsification in the light of the Duhem-Quine Thesis. (shrink)

Second-order logic has a number of attractive features, in particular the strong expressive resources it offers, and the possibility of articulating categorical mathematical theories (such as arithmetic and analysis). But it also has its costs. Five major charges have been launched against second-order logic: (1) It is not axiomatizable; as opposed to first-order logic, it is inherently incomplete. (2) It also has several semantics, and there is no criterion to choose between them (Putnam, J Symbol Logic 45:464–482, 1980 ). Therefore, (...) it is not clear how this logic should be interpreted. (3) Second-order logic also has strong ontological commitments: (a) it is ontologically committed to classes (Resnik, J Phil 85:75–87, 1988 ), and (b) according to Quine (Philosophy of logic, Prentice-Hall: Englewood Cliffs, 1970 ), it is nothing more than “set theory in sheep’s clothing”. (4) It is also not better than its first-order counterpart, in the following sense: if first-order logic does not characterize adequately mathematical systems, given the existence of non - isomorphic first-order interpretations, second-order logic does not characterize them either, given the existence of different interpretations of second-order theories (Melia, Analysis 55:127–134, 1995 ). (5) Finally, as opposed to what is claimed by defenders of second-order logic [such as Shapiro (J Symbol Logic 50:714–742, 1985 )], this logic does not solve the problem of referential access to mathematical objects (Azzouni, Metaphysical myths, mathematical practice: the logic and epistemology of the exact sciences, Cambridge University Press, Cambridge, 1994 ). In this paper, I argue that the second-order theorist can solve each of these difficulties. As a result, second-order logic provides the benefits of a rich framework without the associated costs. (shrink)

Der vorliegende Band enthält den Text der vierstündigen Vorlesung, die Husserl im Wintersemester 1908/09 unter dem Titel "Alte und neue Logik" in Göttingen gehalten hat. Es handelt sich bei dieser Vorlesung zum einen um eine Umarbeitung und Neugestaltung seiner Logikvorlesung von 1902/03, die im Band 2 der Materialien veröffentlicht wurde, zum anderen um eine Vorstufe der in Band XXX der Gesammelten Werke unter dem späteren Titel "Logik und Allgemeine Wissenschaftslehre" veröffentlichten Vorlesung "Einleitung in die Logik und Erkenntnistheorie" von 1910/11. Husserl (...) konfrontiert in der Vorlesung nicht, wie der Titel anzukündigen scheint, die traditionelle Logik mit den zeitgenössischen Reformversuchen dieser Logik, sondern er entwickelt in kritischer Abwehr des Psychologismus, zu dem er ausdrücklich auch Brentanos Reform der Logik rechnet, seine eigene Konzeption der reinen Logik. Konstitutiv für diese Konzeption ist die Zweischichtung in Bedeutungslehre als reine Formenlehre der logischen Bedeutungen ("reine Grammatik") und Geltungslehre. Die konkreten Ausführungen sind vor allem einer umfassenden Darstellung der Formenlehre sowie der kritischen Erörterung von bedeutungstheoretischen Streitfragen gewidmet. (shrink)

Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them from (...) MSL. To make the book accessible to readers from different disciplines, whilst maintaining precision, the author has supplied detailed step-by-step proofs, avoiding difficult arguments, and continually motivating the material with examples. Consequently this can be used as a reference, for self-teaching or for first-year graduate courses. (shrink)

The articles in this volume represent a part of the philosophical literature on higher-order logic and the Skolem paradox. They ask the question what is second-order logic? and examine various interpretations of the Lowenheim-Skolem theorem.

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 Ausgabe innerhalb der Philosophischen Bibliothek bietet den vollständigen Wortlaut der beiden Originalausgaben von 1781 und 1787. Der Kantische Text wurde unter Wahrung der Interpunktion und sprachlicher Eigenheiten sehr behutsam an die heutigen orthographischen Regeln angeglichen. Die semantisch bedeutenden Korrekturvorschläge späterer Herausgeber sind, wo sie nicht in den Text Aufnahme gefunden haben, am Fuß der Seite verzeichnet. Alle wesentlichen Unterschiede zwischen den Originalausgaben sind durch Kursivdruck hervorgehoben, größere Abweichungen ganzer Textstücke – etwa in der Einleitung und im Kapitel über Phaenomena (...) und Noumena – wurden synoptisch gegenübergestellt, so daß Art und Umfang der Umarbeitung unmittelbar abgelesen werden können. (shrink)

In this paper six of the most important issues in the philosophy of logic are examined from a standpoint that rejects the First Commandment of empiricist analytic philosophy, namely, Ockham’s razor. Such a standpoint opens the door to the clarification of such fundamental issues and to possible new solutions to each of them.

In this short paper I am concerned with basically two especially important issues in Oswaldo Chateaubriand’s Logical Forms II; namely, the dispute between first- and higher-order logic and his conception of logical truth and related notions, like logical property, logical state of affairs and logical falsehood. The first issue was also present in the first volume of the book, but the last is privative of the second volume. The extraordinary significance of both issues for philosophy is emphasized and, though there (...) is a basic agreement with Chateaubriand’s views, some critical remarks are interspersed.Neste pequeno artigo considero basicamente duas questões particularmente importantes em Logical Forms II de Oswaldo Chateaubriand; a saber, a disputa entre a lógica de primeira e de segunda ordem e sua concepção de verdade lógica e noções relacionadas, como as de propriedade lógica, estado de coisas lógico e falsidade lógica. A primeira questão também estava presente no primeiro volume do livro, mas a última apenas aparece no segundo volume. Enfatizo o significado extraordinário de ambas as questões para a filosofia e, embora haja uma concordância básica com as visões de Chateaubriand, algumas observações críticas são inseridas. (shrink)

In this critical study I try to highlight some of the most important issues discussed in Chateaubriand’s excellent book. In particular, I discuss in some detail Chateaubriand’s criticism of one of the icons of analytic philosophy, namely, Quine, as well as some of his own valuable contributions to philosophy in this book – for example, his refutation of the various forms of the slingshot argument and his characterization of logical truth.