Gottlob Frege Profile: Born: 8 Nov 1848 in Wismar, Mecklenburg-Schwerin (now Germany) Died: 26 July 1925 in Bad Kleinen, Germany Professional Input Friedrich Ludwig Gottlob Frege (1848-1925) was a German mathematician, logician, and philosopher who worked at the University of Jena. Frege essentially reconceived the discipline of logic by constructing a formal system which, in effect, constituted the first ‘predicate calculus’. In this formal system, Frege developed an analysis of quantified statements and formalized the notion of a ‘proof’ in terms that are still accepted today.
Frege then demonstrated that one could use his system to resolve theoretical mathematical statements in terms of simpler logical and mathematical notions. One of the axioms that Frege later added to his system, in the attempt to derive significant parts of mathematics from logic, proved to be inconsistent. Nevertheless, his definitions (of the predecessor relation and of the concept of natural number) and methods (for deriving the axioms of number theory) constituted a significant advance.
To ground his views about the relationship of logic and mathematics, Frege conceived a comprehensive philosophy of language that many philosophers still find insightful. However, his lifelong project, of showing that mathematics was reducible to logic, was not successful. * played a crucial role in the emergence of modern logic and analytic philosophy. Frege’s logical works were revolutionary, and are often taken to represent the fundamental break between contemporary approaches and the older, Aristotelian tradition.
He invented modern quantificational logic, and created the first fully axiomatic system for logic, which was complete in its treatment of propositional and first-order logic, and also represented the first treatment of higher-order logic. In the philosophy of mathematics, he was one of the most ardent proponents of logicism, the thesis that mathematical truths are logical truths, and presented influential criticisms of rival views such as psychologism and formalism. His theory of meaning, especially his distinction between the sense and reference of linguistic expressions, as groundbreaking in semantics and the philosophy of language. He had a profound and direct influence on such thinkers as Russell, Carnap and Wittgenstein. Frege is often called the founder of modern logic, and he is sometimes even heralded as the founder of analytic philosophy. F. H. Bradley AKA Francis Herbert Bradley Profile: Born: 30-Jan-1846 Birthplace: Clapham, England Died: 18-Sep-1924 Location of death: Oxford, England Cause of death: unspecified Gender: Male Race or Ethnicity: White Occupation: Philosopher Nationality: England Executive summary: Appearance and Reality
British philosopher of the Absolute Idealist school, which argued that since we can only know our ideas directly the universe consists, for us, only of ideas. Although Bradley wrote widely on logic as well as the philosophy of history and psychology, he is best known today for his work in the area of ethics, epistemology, and metaphysical philosophy, the latter of which has been compared in structure to quantum mechanics. His best known works include Ethical Studies (1876), Principles of Logic (1883), and Appearance and Reality (1893). Bradley’s teachings had a marked impact on the work of T. S. Eliot.
Father: Charles Bradley (prominent Evangelical preacher) Mother: Emma Linton (eight children) Brother: A. C. Bradley (literary scholar) Professional Input: F. H. Bradley (1846–1924) was the most famous, original and philosophically influential of the British Idealists. These philosophers came to prominence in the closing decades of the nineteenth century, but their effect on British philosophy and society at large — and, through the positions of power attained by some of their pupils in the institutions of the British Empire, on much of the world — persisted well into the first half of the twentieth.
They stood out amongst their peers in consciously rejecting some main aspects of the tradition of their earlier compatriots, such as Hume and Mill, and responding, albeit in an original and critical fashion, rather to the work of Kant and Hegel. But it would involve a significant degree of distortion to depict the British Idealists as simply choosing Hegel over Hume, as the denomination ‘Neo-Hegelians’ all too easily suggests. On the contrary, they were open to a variety of influences, including the philosophy of an anti-idealist thinker such as J. F.
Herbart and of the subsequently forgotten but then prominent Hermann Lotze, an independent mind whose speculations are difficult to classify in terms of the idealist/realist opposition. Upon the whole, the Idealists revitalized British philosophy by making it permeable to a rich variety of continental ideas. In this way, they helped prepare the ground on which analytic philosophy would eventually flourish, as most Idealists were very well acquainted with the works of Frege’s contemporaries (e. g. Sigwart) and discussed their ideas in their logical treatises.
Bradley was a leading figure in this movement of original reappropriation of alien ideas, which he explicitly promoted as the sole antidote to dogmatism and intellectual sclerosis in the ‘Preface’ to Appearance and Reality. ‘The present generation’, he said, ‘is learning that to gain education a man must study in more than one school’ (p. viii). It is for his metaphysics that Bradley has become best known. He argued that our everyday conceptions of the world (as well as those more refined ones common among his philosophical predecessors) contain hidden contradictions which appear, fatally, when we try to think out their consequences.
In particular, Bradley rejected on these grounds the view that reality can be understood as consisting of many objects existing independently of each other (pluralism) and of our experience of them (realism). Consistently, his own view combined substance monism — the claim that reality is one, that there are no real separate things — with metaphysical idealism — the claim that reality consists solely of idea or experience. This vision of the world had a profound effect on the verse of T. S. Eliot, who studied philosophy at Harvard and wrote a Ph. D. thesis on Bradley.
On later generations of philosophers, however, Bradley’s contributions to moral philosophy and the philosophy of logic were far more influential than his metaphysics. His critical examination of hedonism — the view that the goal of morality is the maximization of general pleasure — was seminal and stands as a permanent contribution to the subject which can still be read with profit today. Some of the doctrines of his logic have become standard and unnoticed assumptions through their acceptance by Bertrand Russell, an acceptance which survived Russell’s subsequent repudiation of idealist logic and metaphysics.