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, ...

Frege's life and character -- The project -- Frege's new logic -- Defining the numbers -- The reconception of the logic, I-"Function and concept" -- The reconception of the logic, II- "On sense and meaning" and "on concept and object" -- Basic laws, the great contradiction, and its aftermath -- On the foundations of geometry -- Logical investigations -- Frege's influence on recent philosophy.

Let me start with a well-known story. Kant held that logic and conceptual analysis alone cannot account for our knowledge of arithmetic: “however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what is the sum [7+5]” (KrV, B16). Frege took himself to have shown that Kant was wrong about this. According to Frege’s logicist thesis, every arithmetical concept can be defined in purely logical terms, and (...) every theorem of arithmetic can be proved using only the basic laws of logic. Hence, Kant was wrong to think that our grasp of arithmetical concepts and our knowledge of arithmetical truth depend on an extralogical source—the pure intuition of time (Frege 1884, §89, §109). Arithmetic, properly understood, is just a part of logic. (shrink)

The paper scrutinizes Frege's Euclideanism - his view of arithmetic and geometry as resting on a small number of self-evident axioms from which non-self-evident theorems can be proved. Frege's notions of self-evidence and axiom are discussed in some detail. Elements in Frege's position that are in apparent tension with his Euclideanism are considered - his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential (...) abilities. The resolution of the tensions indicates that Frege maintained a sophisticated and challenging form of rationalism, one relevant to current epistemology and parts of the philosophy of mathematics. (shrink)

A summary of the philosophical career and intellectual contributions of Gottlob Frege (1848–1925), including his invention of first- and second-order quantified logic, his logicist understanding of arithmetic and numbers, the theory of sense (Sinn) and reference (Bedeutung) of language, the third-realm metaphysics of “thoughts”, his arguments against rival views, and other topics.

This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik, with introduction and annotation. The importance of Frege's ideas within contemporary philosophy would be hard to exaggerate. He was, to all intents and purposes, the inventor of mathematical logic, and the influence exerted on modern philosophy of language and logic, and indeed on general epistemology, by the philosophical framework.

The first systematic exposition of all the central topics in the philosophy of logic, Susan Haack's book has established an international reputation for its accessibility, clarity, conciseness, orderliness, and range as well as for its thorough scholarship and careful analyses. Haack discusses the scope and purpose of logic, validity, truth-functions, quantification and ontology, names, descriptions, truth, truth-bearers, the set-theoretical and semantic paradoxes, and modality. She also explores the motivations for a whole range of non-classical systems of logic, including many-valued logics, (...) fuzzy logic, moddal and tense logics, and relevance logics. Persupposing only an elementary knowledge of formal logic, this book includes many useful summary tables and diagrams, as well as a helpful glossary of technical terms. Wide-ranging, informative, and eminently readable, this book has proven a valuable resource for generations of students and scholars in a variety of disciplines outside philosophy needing guidance on the philosophy of logic. (shrink)

Bertrand Russell was one of the greatest logicians since Aristotle, and one of the most important philosophers of the past two hundred years. As we approach the 125th anniversary of the Nobel laureate's birth, his works continue to spark debate, resounding with unmatched timeliness and power. The Problems of Philosophy, one of the most popular works in Russell's prolific collection of writings, has become core reading in philosophy. Clear and accessible, this little book is an intelligible and stimulating guide to (...) those problems of philosophy which often mistakenly lead to its status as too lofty and abstruse for the lay mind. Focusing on problems he believes will provoke positive and constructive discussion, Russell concentrates on knowledge rather than metaphysics, steering the reader through his famous 1910 distinction between "knowledge by acquaintance and knowledge by description," and introducing important theories of Descartes, Kant, Hegel, Hume, Locke, Plato, and others to lay the foundation for philosophical inquiry by general readers and scholars alike.With a new introduction by John Perry, this valuable work is a perfect introduction to the field and will continue to stimulate philosophical discussion as it has done for nearly forty years. (shrink)

In Rationality and Logic, Robert Hanna argues that logic is intrinsically psychological and that human psychology is intrinsically logical. He claims that logic is cognitively constructed by rational animals and that rational animals are essentially logical animals. In order to do so, he defends the broadly Kantian thesis that all rational animals possess an innate cognitive "logic faculty." Hanna 's claims challenge the conventional philosophical wisdom that sees logic as a fully formal or "topic-neutral" science irreconcilably separate from the species- (...) or individual-specific focus of empirical psychology.Logic and psychology went their separate ways after attacks by Frege and Husserl on logical psychologism--the explanatory reduction of logic to empirical psychology. Hanna argues, however, that--despite the fact that logical psychologism is false--there is an essential link between logic and psychology. Rational human animals constitute the basic class of cognizers or thinkers studied by cognitive psychology; given the connection between rationality and logic that Hanna claims, it follows that the nature of logic is significantly revealed to us by cognitive psychology. Hanna 's proposed "logical cognitivism" has two important consequences: the recognition by logically oriented philosophers that psychologists are their colleagues in the metadiscipline of cognitive science; and radical changes in cognitive science itself. Cognitive science, Hanna argues, is not at bottom a natural science; it is both an objective or truth-oriented science and a normative human science, as is logic itself. (shrink)

This article develops Frege's conception of answerability, and his correlative views on psychologism of the first sort. Compared to prior philosophers, such as British empiricists, Frege is a minimalist in the demands he sets on answerability. If he is ever less than minimalist, that is something that flows out of his particular conception of logic. The article then turns to Wittgenstein's conception of answerability, by which Frege is not quite minimalist enough. That allows us to see how the pursuit of (...) answerability might lead to psychologism of the second kind. (shrink)

Challenges current interpretations of Frege's work arguing that they anachronistically project late twentieth century concerns and categories onto the thought of a nineteenth-century mathematical logician.

I shall make two main claims. My first main claim is that Frege started out with a view of logic that is closer to Kant’s than is generally recognized, but that he gradually came to reject this Kantian view, or at least totally to transform it. My second main claim concerns Frege’s reasons for distancing himself from the Kantian conception of logic. It is natural to speculate that this change in Frege’s view of logic may have been spurred by a (...) desire to establish the logicality of the axiom system he needed for his logicist reduction, including the infamous Basic Law V. I admit this may have been one of Frege’s motives. But I shall argue that Frege also had a deeper and more interesting reason to reject his early Kantian view of logic, having to do with his increasingly vehement anti-psychologism. (shrink)

In the opening to his late essay, Der Gedanke, Frege asserts without qualification that the word "true" points the way for logic. But in a short piece from his Nachlass entitled "My Basic Logical Insights", Frege writes that the word true makes an unsuccessful attempt to point to the essence of logic, asserting instead that "what really pertains to logic lies not in the word "true" but in the assertoric force with which the sentence is uttered". Properly understanding what Frege (...) takes to be at issue here is crucial for understanding his conception of logic and, in particular, what he takes to be its normative status vis-à-vis judgement, assertion, and inference. In this paper, I focus my attention on clarifying the latter claim and Frege's motivations for making it, exposing what I take to be a fundamental tension in Frege's conception of logic. Finally, I discuss whether Frege's deployment of the horizontal in his mature Begriffsschrift helps to resolve this tension. (shrink)

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.

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.

In the 1890's, when fields such as psychology and philosophy were just emerging, turf wars between the disciplines were common-place. Philosophers widely discounted the possibility that psychology's claim to empirical truth had anything relevant to offer their field. And psychologists, such as the crazed and eccentric Otto Weinegger, often considered themselves philosophers. Freud, it is held, was deeply influenced by his wife, Martha's, uncle, who was also a philosopher. The tension between the fields persisted, until the two fields eventually matured (...) and grew apart. Until the publication of Martin Kursch's masterly work Psychologism , few philosophers and psychologists have attended to their originally unhappy, turn-of-the-century engagement. Martin Kusch explores the origins of psychologism in Germany and fin de siecle Vienna by examining two major figures of twentieth century philosophy: Frege and Husserl. As one of the few serious works on Frege, Kusch trenchantly and clearly reconstructs the debate and the context in which it flourished. Psychologism will prove to be a key work of intellectual history on a subject which has largely been overlooked and, above all, understudied. (shrink)

In Frege's writings, the notions of truth, judgment, and objectivity are all prominent and important. This paper explores the close connections between them, together with their ties to further cognate notions, such as those of thought, assertion, inference, logical law, and reason. It is argued that, according to Frege, these notions can only be understood properly together, in their inter-relations. Along the way, interpretations of some especially cryptic Fregean remarks, about objectivity, laws of truth, and reason, are offered, and seemingly (...) opposed "realist" and "idealist" strands in his position reconciled. (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)

What is psychologism? What are its grounds? And why have so many philosophers been opposed to it? This dissertation addresses these questions through an analysis of the anti-psychologistic arguments that appear in the logical and epistemological writings of Gottlob Frege and Karl Popper. Psychologism emerges in each of these contexts as the thesis that statements can be justified by sense perceptions. As such, it has traditionally been associated with subjectivism, relativism, and other attempts to ground knowledge on something not rational (...) in character. ;Frege and Popper each opposed psychologism with the introduction of a third realm to insure the possibility of objective knowledge and objective standards for rationality. But owing to what I call an "epistemological paradigm shift," these terms--"objectivity", "rationality", and "third realm"--have different senses for Popper and Frege. Despite normal similarities, Fregean and Popperian anti-psychologisms are distinct and epistemologically opposed positions. ;Frege's opposition to psychologism insisted upon the necessity of a priori valid statements for justification, and hence objective knowledge. Here, rationality was equated with logical justification. And to that extent, I argue that Frege's anti-psychologism was meant to oppose fallibilism in logic and mathematics. But Popper's epistemology forsakes both a priori valid statements and the justified true belief theory of knowledge. Here, rationality is equated not with logical justification, but with logical criticism. And Popper's fallibilistic anti-psychologism can be seen as a lemma in his general argument against the possibility of rational justification: statements cannot be justified logically, and psychological justification won't do either! ;These epistemological differences are also reflected in different characterizations of the third realm. Whereas Frege construed third realm objects as eternal and immutable, completely independent of the human mind, Popper regards them as human creations. At base in this dispute is the question whether human knowledge is created or discovered. And here one can glean very real differences in attitude concerning cognitive authority. Whereas Frege's anti-psychologism proceeded from the recognition of the cognitive authority of classical logic and mathematics, Popper's anti-psychologism is but another expression of his general suspicion of cognitive authority of any kind. (shrink)

Tries to identify some strands in the birth of analytic philosophy and to identify in consequence some of its distinctive features.