This volume contains all of Frege's extant unpublished writings on philosophy and logic other than his correspondence, written at various stages of his career.

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)

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)

Moritz Pasch is usually seen today as a precursor of Hilbert. The Vorlesungen über neuere Geometrie is indeed one of the few works Hilbert referred to in the Grundlagen. Unfortunately, Hilbert's epoch-making book has eclipsed Pasch's achievement; so much so that Pasch's Vorlesungen has not been yet translated into English. But as Pollard emphasizes, it would be a mistake to reduce Pasch's research to his work on the foundations of geometry. Pasch published another book on the foundations of real analysis (...) and arithmetic in 1882, and two other works, respectively, in 1909 and in 1914 . Pasch thus aimed not only to analyze the foundations of geometry but also to elaborate a complete theory of mathematical knowledge. This ambition brought him close to the logicists . But, unlike them, Pasch was a resolute empiricist: he considered that ‘geometry and number theory are branches of empirical science’ 1 and that all mathematical concepts must be derived from a set of notions abstracted from our experience.Pasch made his whole career in Giessen — that is, outside of the major German research centers. Heavily burdened with administrative duties, Professor Pasch seems to have found time for his research only in 1917, when he retired at the age of 67. As Pollard notes, nearly half of Pasch's published output appeared after his sixty-eighth birthday! This volume is a translation of fourteen articles dating from the later period of Pasch's life, ordered by the time of their publication. The papers are preceded by a substantial introduction by Stephen Pollard, the editor and translator of all the papers. Aside from his correspondence with Frege, this volume is thus the first translation of Pasch's work …. (shrink)

A painstakingly-argued, well-documented, scholarly work arguing for a sophisticated representative realism. Heuristically the analysis centers principally around Brentano, Meinong, Frege, and Bergmann. Some distinctive theses are mind is not substantial but a pluralism of momentary mental acts in which a subsequent act may have a predecessor for its object; things are really states of affairs; bare particulars are individuating principles; every mental act is propositional—its content does not intend a particular; possible states of affairs, which are nothing but could be, (...) can be intended ; thought-world, language-world correspondences do not coincide ; and a behavioristic reduction of intentional contexts would not account for "how certain mental phenomena give rise to the occurrence of intentional contexts". The organizational theme is the idealist-realist controversy in perception, with the nominalist-realist controversy covered by excellent discussions of universals and relations.—P. S. (shrink)

Description: The book points to a new logic of singular designators based upon a close analysis of work in the area by contemporary philosophers of language. The philosophers range from Frege, Russell, Quine, Strawson and Dummett to Kripke, Hintikka, Plantinga, Kaplan, Donnellan, Searle and Burge. It is generally taken for granted that proper names are rigid designators, having no meaning content, which explains their intranslatability into other languages. However, they do have their modes of presentation that must constitute their sense. (...) There is little room for contradiction here in admitting that proper names have a sense, which does not amount to meaning. One of the advantages of this position is that it blocks the emergence of the Kripkean puzzle about belief by accepting different belief contents corresponding to a variation in the senses of the names involved. Is Kripke's distinction between rigid and non-rigid designators finally valid' the author asks, questioning the corollaries that are supposed to follow from the distinction, viz., that proper names do not have descriptive backing, and that there are contingent a priori truths. He draws our attention to predicative occurrences of proper names, in the modal context, matching corresponding occurrences of definite descriptions. His explanation of contingency, where proper names or definite descriptions are involved, is innovatively straight, simple and broad-based, at par with situations having ordinary predicates. Parts of the book have taken a final shape in response to comments by Strawson, Dummett and Burge. (shrink)

A brief, non-technical introduction to technical and philosophical aspects of Frege's philosophy of arithmetic. The exposition focuses on Frege's Theorem, which states that the axioms of arithmetic are provable, in second-order logic, from a single non-logical axiom, "Hume's Principle", which itself is: The number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence.

Frege's puzzle is a fundamental challenge for accounts of mental and linguistic representation. This piece surveys a family of recent approaches to the puzzle that posit representational relations. I identify the central commitments of relational approaches and present several arguments for them. I also distinguish two kinds of relationism—semantic relationism and formal relationism—corresponding to two conceptions of representational relations. I briefly discuss the consequences of relational approaches for foundational questions about propositional attitudes, intentional explanation, and compositionality.

A key idea in both Frege's development of arithmetic in theGrundlagen[7] and Zermelo's 1904 proof [10] of the well-ordering theorem is that of a “type reducing” correspondence between second-level and first-level entities. In Frege's construction, the correspondence obtains betweenconceptandnumber, in Zermelo's (through the axiom of choice), betweensetandmember. In this paper, a formulation is given and a detailed investigation undertaken of a system ℱ of many-sorted first-order logic (first outlined in the Appendix to [6]) in which this notion of (...) type reducing correspondence is accorded a central role and which enables Frege's and Zermelo's constructions to be presented in such a way as to reveal their essential similarity. By adapting Bourbaki's version of Zermelo's proof of the well-ordering theorem, we show that, within ℱ, any correspondencecbetween second-level entities (here calledconcepts) and first-level ones (here calledobjects) induces a well-ordering relationW(c) in a canonical manner. We shall see that, whencis the “Fregean” correspondence between concepts and cardinal numbers,W(c) is (the well-ordering of) the ordinalω+ 1, and whencis a “Zermelian” choice function on concepts,W(c) is a well-ordering of the universal concept embracing all objects.In ℱ an important role is played by the notion ofextensionof a concept. To each conceptXwe assume there is assigned an objecte(X) in such a way that, for any conceptsX, Ysatisfying a certain predicateE, we havee(X) =e(Y) iff the same objects fall underXandY. (shrink)

In his essay 'Thoughts',' Frege is to be found employing a regress-argument against the correspondence theory of truth. He seems to have felt that the argument is not only completely destructive of the correspondence theory, but that it could be deployed equally well against any attempt to provide a general definition of the notion of truth. In my view neither conclusion is warranted. But Frege's Regress can, nevertheless, be developed into an argument of the greatest significance.

Michael Dummett has advanced, very influentially, the view that Frege means truth conditions by his notion of thought (Gedanke). My aim in this paper is to argue that Dummett and others are mistaken in this claim. First, Frege's aversion of the correspondence theory of truth does not square well with Dummett's claim. Secondly, and more importantly, Grundgesetze I, §32, is the only place where Frege even appears to be talking about truth conditions in connection with his notion of thought (...) -- and even there, I shall show, he does not really identify thoughts with truth conditions, but states only the triviality that a statement such as, say, 'Leibniz is a philosopher' expresses the thought that Leibniz is a philosopher. (shrink)

Frege's doctrine that the demonstrative ‘I’ has a private, incommunicable sense creates tension within his theory of meaning. Fregean sense is supposed to be something objective, which exists independently of its being cognized by anyone. And the notion of a private sense corresponding to primitive aspects of an individual of which only he can be awaredoes violence both to Frege's theory of sense as well as to our notionof language as something essentially intersubjective. John Perry has arguedthat Frege was led (...) to the doctrine of private senses in spite of his beliefin the objectivity of sense through his attempt to solve a problem which indexicals posed for his theory. And while philosophers have argued about whether the notion of a private sense is in fact problematic for Frege, they have tended to share Perry's assumption about its origin. (shrink)

This paper aims to determine what kind of problem Frege's famous “Julius Caesar problem” is. whether it is to be understood as the metaphysical problem of determining what kind of things abstract objects like numbers or value‐courses are, or as the epistemological problem of providing a means of recognizing these objects as the same again, or as the logical problem of providing abstract sortal concepts with a sharp delimitation in order to fulfill the law of excluded middle, or as the (...) semantic problem of fixing the referents of the corresponding abstract singular terms. It is argued that, for Frege, the Caesar problem is a bundle of related problems of which the semantic problem is the most basic one. (shrink)

Frege famously endorsed a principle of Thought-Sentence Correspondence that can be spelt out as follows: (Corr1) For all sentences s, for all thoughts t, if r expresses t, then:if a sense is expressed by a part of s then it is part of t, &(Corr2) For all sentences s, for all thoughts t, if s expresses t, then:if a sense is part of t then it is expressed by at least one part of s. He clearly embraces Corr1 when (...) he writes in § 32 of Grundgesetze, vol. I: ‘If a name is part of the name of a trut... (shrink)

In this paper we compare the propositional logic of Frege’s Grundgesetze der Arithmetik to modern propositional systems, and show that Frege does not have a separable propositional logic, definable in terms of primitives of Grundgesetze, that corresponds to modern formulations of the logic of “not”, “and”, “or”, and “if…then…”. Along the way we prove a number of novel results about the system of propositional logic found in Grundgesetze, and the broader system obtained by including identity. In particular, we show (...) that the propositional connectives that are definable in terms of Frege’s horizontal, negation, and conditional are exactly the connectives that fuse with the horizontal, and we show that the logical operators that are definable in terms of the horizontal, negation, the conditional, and identity are exactly the operators that are invariant with respect to permutations on the domain that leave the truth-values fixed. We conclude with some general observations regarding how Frege understood his logic, and how this understanding differs from modern views. (shrink)

Frege overlooked the role of quantifiers as expressing, by their formal dependence on each other, the actual dependences between variables bound to them. The resulting flaw in Frege’s and other logicians’ logic began to be corrected only in IF logic. The dependence relations are codified in the Skolem functions that correspond to existential-force quantifiers. Their existence is the natural truth condition. Such functions are not adequately handled in first-order predicate logic. In any adequate logic, a fixed mode of identification (...) is presupposed. The frameworks of identification can be perspectival or public. Kripke makes the same mistake about quantifiers as Frege and in addition assumes that only perspectival indentification is needed in the last analysis. He also overlooks dependence relations between modal operators and quantifiers. (shrink)

Important aspects of its philosophical basis, and its significance for the foundations of mathematics, appeared in The Foundations of Mathematics (FA, 1884). Six years later, at the beginning of the 1890s, Frege published three articles that mark significant changes in his conception: "Function and Concept" (FC, 1891), "On Sense and Reference" (SR, 1892) and "Concept and Object" (1892). Notable among these changes are: (a) The systematic distinction between the sense and the reference of expressions as two separate ingredients of their (...) meaning. (b) The extension and generalization of the notion of function to include the conception of concepts and relations as functions to truth-values, and the corresponding conception of the two truth-values as objects. These changes were immediately incorporated in the mature, authoritative exposition of his logic in his magnum opus: Basic Laws of Arithmetic (BL), whose first volume appeared in 1893. (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 ...

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his (...) philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein. (shrink)

In the paper, I propose a novel approach to Frege’s view on the principle of compositionality, its relation to the propositional holism and the formation of concepts. The main idea is to distinguish three stages of constructing a logically perfect language. At the first stage, only a sentence as a whole expresses a Thought. It is impossible to assign meaning to less complex units. This is the stage of an ordinary language. The second phase concerns the proper level of (...) construction of a logically perfect language. We are forced to discriminate syntactic and semantic parts of sentences to account for the inference relations. We can distinguish senses and references of parts of sentences. Furthermore, it is possible here to choose between different ways of analysing the given Thought. Finally, at the third stage, every expression of the language has an unambiguous sense and this sense determines a unique reference. The logically perfect language is ready. We may view Thoughts as composed from primitive elements. Moreover, the senses of parts of a sentence correspond to the parts of a Thought, so that the structure of the sentence serves as the image of the structure of the Thought. The principle of compositionality is met and we can discern how understanding of the infinite numbers of Thoughts is possible and how languages are learnable. The main advantage of the presented view is that it allows accommodating some aspects of Frege’s philosophy that are often seen as mutually incompatible. Furthermore, I submit extensive textual data in favour of the discussed views and conceptions. (shrink)

"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.

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

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 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.

[Translation of Frege's 'Gedankengefüge' (1923)].

[Translation of Frege's 'Über das Trägheitsgesetz].

This paper argues for a conditional claim concerning a famous argument—developed by Church in elucidation of some remarks by Frege to the effect that the bedeutung of a sentence is the sentence’s truth-value—the Frege–Gödel–Church argument, or FGC for short. The point we make is this :if, and just to the extent that, Arthur Smullyan’s argument against Quine's use of FGC is sound, then essentially the same rejoinder disposes also of Davidson's use of FGC against ‘correspondence’ theories of truth. We (...) thus dispute a contention by Professor Davidson that it is coherent to accept that Smullyan’s rejoinder takes away the force of Quine’s version of FGC, while still consistently using FGC to establish that if true sentences (or utterances) correspond to anything, they all correspond to the same thing. We show that the differences between the cases discussed by Smullyan and Davidson’s version of FGC on which Davidson relies for his contention are irrelevant to the point under dispute. (shrink)

Translation of Frege's 'Über die Begriffsschrift des Herrn Peano und meine eigene' (1896). Translated by V.H. Dudman.

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).

Russell corresponded with Sir Michael Dummett (1925–2011) between 1953 and 1963 while the latter was working on a book on Frege, eventually published as Frege: Philosophy of Language (1973). In their letters they discuss Russell’s correspondence with Frege, translating it into English, as well as Frege’s attempted solution to Russell’s paradox in the appendix to vol. 2 of his Grundgesetze der Arithmetik. After Dummett visited the University of Münster to view Frege’s Nachlaß, he sent reports back to (...) Russell concerning both the philosophical materials Frege left behind, as well as information from Frege’s journal revealing his anti-semitic political opinions. Their interaction contains interpretive conjectures and insights on Dummett’s side, and some dark humor on Russell’s. (shrink)

(Translation of Frege's Grundgesetze II, §§ 86-137).

This paper argues for a conditional claim concerning a famous argument—developed by Church in elucidation of some remarks by Frege to the effect that the bedeutung of a sentence is the sentence’s truth-value—the Frege–Gödel–Church argument, or FGC for short. The point we make is this :if, and just to the extent that, Arthur Smullyan’s argument against Quine's use of FGC is sound, then essentially the same rejoinder disposes also of Davidson's use of FGC against ‘correspondence’ theories of truth. We (...) thus dispute a contention by Professor Davidson that it is coherent to accept that Smullyan’s rejoinder takes away the force of Quine’s version of FGC, while still consistently using FGC to establish that if true sentences (or utterances) correspond to anything, they all correspond to the same thing. We show that the differences between the cases discussed by Smullyan and Davidson’s version of FGC on which Davidson relies for his contention are irrelevant to the point under dispute. (shrink)

Translation of Frege's 'Über den Zweck der Begriffsschrift' (1882).

(Translation of Frege's "Le nombre entier", 1895).

This chapter clarifies that it was the works Giuseppe Peano and his school that first led Russell to embrace symbolic logic as a tool for understanding the foundations of mathematics, not those of Frege, who undertook a similar project starting earlier on. It also discusses Russell’s reaction to Peano’s logic and its influence on his own. However, the chapter also seeks to clarify how and in what ways Frege was influential on Russell’s views regarding such topics as classes, functions, meaning (...) and denotation, etc., and summarizes the correspondence between Frege and Russell and the light it sheds on the philosophical logic of both. (shrink)

It is well known that Frege and his writings were an important influence on Wittgenstein. There is no agreement, however, on the nature and scope of this influence. In this paper, I clarify the situation in three related ways: by tracing Frege's and Wittgenstein's actual interactions, i.e., their face‐to‐face meetings and their correspondence between 1911 and 1920; by documenting Wittgenstein's continued study of Frege's writings, until the very end of his life in 1951; and by constructing, on that basis, (...) a new framework for understanding the themes that connect Wittgenstein to Frege, both in his early and his later works. (shrink)

Frege's essay "Der Gedanke.Eine logische Untersuchung" was first published in the Beitrage zur Philosophie des Deutschen Idealismus for 1918-1919 and is one of three related logical studies published as a complete work by Gunther Patzig entitled Logische Untersuchungen in Gottingen, 1966 .