In , Frege published his first book Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens (Concept. Frege Gottlob Frege was a German logician, mathematician and philosopher who Sometime after the publication of the Begriffsschrift, Frege was married to . The topic of the paper is the public reception of Gottlob Frege’s (–) Begriffsschrift right after its publication in According to a widespread.
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Gottlob Frege was a German logician, mathematician and philosopher who 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, was 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. Frege was born on November 8, in the coastal city of Wismar in Northern Germany.
His full christened name was Friedrich Ludwig Gottlob Frege. Little is known about his youth. His father, Karl Alexander Frege, and his mother, Auguste Bialloblotzsky Frege, both worked at a girl’s private school founded in part by Karl.
Both were also principals of the school at various points: Karl held the position until his deathwhen Auguste took over until her death in The German writer Arnold Frege, born in Wismar inmay have been Frege’s younger brother, but this has not been confirmed. Frege probably lived in Wismar until ; in the years from he is known to have studied at the Gymnasium in Wismar.
In SpringFrege began studies at the University of Jena. There, he studied chemistry, philosophy and mathematics, and must have solidly impressed Ernst Abbe in mathematics, who later become of Frege’s benefactors.
Lotze is sometimes thought to have had a profound impact on Frege’s philosophical views. Inwith the recommendation of Ernst Abbe, Frege received a lectureship at the University of Jena, where he stayed the rest of his intellectual life.
His position was unsalaried during his first five years, and he was supported by his mother. It involves the theory of complex mathematical functions, and contains seeds of Frege’s advances in logic and the philosophy of mathematics. Frege had a heavy teaching load during his first few years at Jena. However, he still had time to work on his first major work in logic, which was published in under the title Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens “Concept-Script: Therein, Frege presented for the first time his invention of a new method for the construction of a logical language.
Upon the publication of the Begriffsschrifthe was promoted to ausserordentlicher Professorhis first salaried position. However, the book was not well-reviewed by Frege’s contemporaries, who apparently found its two-dimensional logical notation difficult to comprehend, and failed to see its advantages over previous approaches, such as that of Boole. Sometime after the publication of the BegriffsschriftFrege was married to Margaret Lieseburg They had at least two children, who unfortunately died young.
Years later they adopted a son, Alfred. However, little else is known about Frege’s family life. Frege had aimed to use the logical language of the Begriffsschrift to carry out his logicist program of attempting to show that all of the basic truths of arithmetic could be derived from purely logical axioms.
However, on the advice of Carl Stumpf, and given the poor reception of the BegriffsschriftFrege decided to write a work in which he would describe his logicist views informally in ordinary language, and argue against rival views.
However, this work seems to have been virtually ignored by most of Frege’s contemporaries. Soon thereafter, Frege began working on his attempt to derive the basic laws of arithmetic within his logical language. However, his work was interrupted by changes to his views.
In the late s and early s Frege developed new and interesting theories regarding the nature of language, functions and concepts, and philosophical logic, including a novel theory of meaning based on the distinction between sense and reference. This maturation of Frege’s semantic and philosophical views lead to changes in his frgee language, forcing him to abandon an almost completed draft of his work in logic and the foundations of mathematics.
However, inFrege finally finished a revised volume, employing a slightly revised logical system. In the first volume, Frege presented his new logical language, and proceeded to use it to define the natural numbers and their begriffsachrift.
His aim was to make begrifsschrift the first of a three volume work; in the second and third, he would move on to the definition of real numbers, and the demonstration of their properties. Again, however, Frege’s work was unfavorably reviewed by his contemporaries.
Nevertheless, he was promoted once again innow to the position of Honorary Ordinary Professor. It is likely that Frege was offered a position as full Professor, begriiffsschrift turned it down to avoid taking on additional administrative duties.
Gottlob Frege – Wikipedia
His new position was unsalaried, but he was able to support himself and his family with a stipend from the Carl Zeiss Stiftunga foundation that gave money to the University of Jena, and with which Ernst Abbe was intimately involved.
Because of the unfavorable reception of his earlier works, Frege was forced to arrange to have volume II of the G rundgesetze published at his own expense. It was not until that Frege was able to make such arrangements. However, while the volume was already in the publication process, Frege received a letter from Bertrand Russell, informing him that it was possible to prove a contradiction in the logical system of the first volume of the G rundgesetzewhich included a naive calculus for classes.
For more information, see the article on ” Russell’s Paradox bwgriffsschrift. Frege was, in his own words, “thunderstruck”. He was forced to quickly prepare an appendix in response.
For the next couple years, he continued to do important work. However, aroundprobably due to some combination of poor health, the early loss of his wife infrustration with his failure to find an adequate solution to Russell’s paradox, and disappointment over the continued poor reception of his work, Frege seems to have lost his intellectual steam.
He produced very little work between and his retirement in However, he continued to influence others during this period. Russell had included an appendix on Frege in his Principles of Mathematics. It is from this that Frege came be to be a bit wider known, including to begriffsschrift Austrian student studying engineering in Manchester, England, named Ludwig Wittgenstein. Wittgenstein studied the work of Frege and Russell closely, and inhe wrote to both of them concerning his own solution to Russell’s paradox.
Frege invited him to Jena to discuss his views. Wittgenstein did so in late The two engaged in a philosophical debate, and while Wittgenstein reported that Frege “wiped the floor” with him, Frege was sufficiently impressed begriffsschrft Wittgenstein that he suggested that he go to Cambridge to study with Russell–a suggestion that had profound importance for the history of philosophy.
Moreover, Rudolf Carnap was one of Frege’s students from toand doubtlessly Frege had significant influence on Carnap’s interest in logic and semantics and his subsequent intellectual development and successes. However, these were not wholly new works, but later drafts of works he had initiated in the s.
Ina year before his death, Frege finally returned to the attempt to understand the foundations of arithmetic. However, by this time, he had completely given up on his logicism, concluding that the paradoxes of class or set theory made it impossible. He instead attempted to develop a new theory of the nature of arithmetic based on Kantian pure intuitions of space.
However, he was not able to write much or publish anything about his begfiffsschrift theory.
Frege died on July 26, at the age of At the time of his death, Frege’s own works were still not very widely known. He did not live to see the profound impact he would have on the emergence of analytic philosophy, nor to see his brand of logic–due to the championship of Russell–virtually wholly supersede ggottlob forms of logic. However, in bequeathing his unpublished work to his adopted son, Alfred, he wrote prophetically, “I believe there are things here which will one day be prized much more highly than they are now.
Take care that nothing gets lost. Unfortunately, however, they were destroyed in an Allied bombing raid on March 25, Although Scholz had made copies of some of the more important pieces, a good portion of Frege’s unpublished works were lost. Although he was a fierce, sometimes even satirical, polemicist, Frege himself was a quiet, reserved man.
He was right-wing in his political views, begriffsschriift like many conservatives of his generation in Germany, he is known to have been distrustful of foreigners and rather anti-semitic.
Himself Lutheran, Frege seems to have wanted to see all Jews brgriffsschrift from Germany, or at least deprived of certain political rights. This distasteful feature of Frege’s personality has gravely disappointed some of Frege’s intellectual progeny. Trained as a mathematician, Frege’s interests in logic grew out of his interests in the foundations of arithmetic.
Early in his career, Frege became convinced that the truths of arithmetic are logical, analytic truths, agreeing with Leibnizand disagreeing with Kantwho thought that arithmetical knowledge was grounded in “pure intuition”, as well as more empiricist thinkers such as J. Millwho thought that arithmetic was grounded in observation. In other words, Frege subscribed to logicism. His logicism was modest in one sense, but very ambitious in others.
Frege’s logicism was limited to arithmetic; unlike other important historical logicists, such as Russell, Frege did not think that geometry was a branch of logic. However, Frege’s logicism was very ambitious in another regard, as he believed that one could prove all of the truths of arithmetic deductively from a limited number of logical axioms. Indeed, Frege himself set out to demonstrate all of the basic laws of arithmetic within his own system of logic. Frege concurred with Leibniz that natural language was unsuited to such a task.
Begriffssvhrift, Frege sought to create a language that would combine the tasks of what Leibniz called a ” calculus ratiocinator ” and ” lingua characterica “, that is, a logically perspicuous language in which logical relations and possible inferences would be clear and unambiguous.
Frege’s own term for such a language, “Begriffsschrift” was likely borrowed from a paper on Leibniz’s ideas written by Adolf Trendelenburg. Although there had been attempts to fashion at least the core of such a language made by Boole and others working in the Leibnizian tradition, Frege found their work unsuitable for a number of reasons. Boole’s logic used some of the same signs used in mathematics, except with different logical meanings.
Frege found this unacceptable for a language which was to be used to bergiffsschrift mathematical truths, because the signs would be ambiguous. Boole’s logic, though innovative in some respects, was weak in others. It was divided into a “primary logic” and “secondary logic”, bifurcating its propositional and categorical elements, and could not deal adequately with multiple generalities.
It analyzed propositions in terms of subject and predicate concepts, which Frege found to be imprecise and antiquated. Frege saw the formulae of mathematics as the paradigm gittlob clear, unambiguous writing.
In order to make his logical language suitable for purposes other than arithmetic, Frege expanded the notion of function to allow arguments and values other than numbers.
Mathematics > History and Overview
He defined a begriffsscbrift Begriff as a function that has a truth-value, either of the abstract objects the True or the False, as its value for any object as argument.
See below for more on Frege’s understanding of concepts, functions and objects. The concept being human is understood as a function that has the True as value for any argument that is human, and the False as value for anything else.