Philosophy of Arithmetic: Psychological and Logical Investigations with Supplementary Texts from 1887–1901
dec. 2012 · Husserliana: Edmund Husserl – Collected Works Bog 10 · Springer Science & Business Media
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In his first book, Philosophy of Arithmetic, Edmund Husserl provides a carefully worked out account of number as a categorial or formal feature of the objective world, and of arithmetic as a symbolic technique for mastering the infinite field of numbers for knowledge. It is a realist account of numbers and number relations that interweaves them into the basic structure of the universe and into our knowledge of reality. It provides an answer to the question of how arithmetic applies to reality, and gives an account of how, in general, formalized systems of symbols work in providing access to the world. The "appendices" to this book provide some of Husserl's subsequent discussions of how formalisms work, involving David Hilbert's program of completeness for arithmetic. "Completeness" is integrated into Husserl's own problematic of the "imaginary", and allows him to move beyond the analysis of "representations" in his understanding of the logic of mathematics.
Husserl's work here provides an alternative model of what "conceptual analysis" should be - minus the "linguistic turn", but inclusive of language and linguistic meaning. In the process, he provides case after case of "Phenomenological Analysis" - fortunately unencumbered by that title - of the convincing type that made Husserl's life and thought a fountainhead of much of the most important philosophical work of the twentieth Century in Europe. Many Husserlian themes to be developed at length in later writings first emerge here: Abstraction, internal time consciousness, polythetic acts, acts of higher order ('founded' acts), Gestalt qualities and their role in knowledge, formalization (as opposed to generalization), essence analysis, and so forth.
This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time. Husserl's extensive and trenchant criticisms of Gottlob Frege's theory of number and arithmetic reach far beyond those most commonly referred to in the literature on their views.
Husserl's work here provides an alternative model of what "conceptual analysis" should be - minus the "linguistic turn", but inclusive of language and linguistic meaning. In the process, he provides case after case of "Phenomenological Analysis" - fortunately unencumbered by that title - of the convincing type that made Husserl's life and thought a fountainhead of much of the most important philosophical work of the twentieth Century in Europe. Many Husserlian themes to be developed at length in later writings first emerge here: Abstraction, internal time consciousness, polythetic acts, acts of higher order ('founded' acts), Gestalt qualities and their role in knowledge, formalization (as opposed to generalization), essence analysis, and so forth.
This volume is a window on a period of rich and illuminating philosophical activity that has been rendered generally inaccessible by the supposed "revolution" attributed to "Analytic Philosophy" so-called. Careful exposition and critique is given to every serious alternative account of number and number relations available at the time. Husserl's extensive and trenchant criticisms of Gottlob Frege's theory of number and arithmetic reach far beyond those most commonly referred to in the literature on their views.
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Born to Jewish parents in what is now the Czech Republic, Edmund Husserl began as a mathematician, studying with Karl Theodor Weierstrass and receiving a doctorate in 1881. He went on to study philosophy and psychology with Franz Brentano and taught at Halle (1887--1901), Gottingen (1901--16), and Freiburg (1916--29). Because of his Jewish background, he was subject to persecution by the Nazis, and after his death his unpublished manuscripts had to be smuggled to Louvain, Belgium, to prevent their being destroyed. Husserl is the founder of the philosophical school known as phenomenology. The history of Husserl's philosophical development is that of an endless philosophical search for a foundational method that could serve as a rational ground for all the sciences. His first major book, Philosophy of Arithmetic (1891), was criticized by Gottlob Frege for its psychologism, which changed the whole direction of Husserl's thinking. The culmination of his next period was the Logical Investigations (1901). His views took an idealistic turn in the Ideas Toward a Pure Phenomenology (1911). Husserl wrote little from then until the late 1920s, when he developed his idealism in a new direction in Formal and Transcendental Logic (1929) and Cartesian Meditations (1932). His thought took yet another turn in his late lectures published as Crisis of the European Sciences (1936), which emphasize the knowing I's rootedness in "life world." Husserl's influence in the twentieth century has been great, not only through his own writings, but also through his many distinguished students, who included Martin Heidegger, Maurice Merleau-Ponty, Jean-Paul Sartre, Eugen Fink, Emmanuel Levinas, and Roman Ingarden.
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