He attacked those who fell into remote, artificial constructions which, with the intent of building the elementary arithmetic concepts out of their ultimate definitional properties, interpret and change their meaning so much that totally strange, practically and scientifically useless conceptual formations finally result.
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As soon as one comes to the ultimate, elemental concepts, Husserl reasoned, all defining has to come to an end. All one can then do is to point to the concrete phenomena from or through which the concepts are abstracted and show the nature of the abstractive process. A verbal explanation should place us in the proper state of mind for picking out, in inner or outer intuition, the abstract moments intended and for reproducing in ourselves the mental processes required for the formation of the concept.
He said that his analyses had shown with incontestable clarity that the concepts of multiplicity and unity rest directly upon ultimate, elemental psychical data, and so belong among the indefinable concepts.
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Since the concept of number was so closely joined to them, one could scarcely speak of defining it either. All these points are made on the only pages of Philosophy of Arithmetic that Husserl ever explicitly retracted.
In On the Concept of Number, Husserl had set out to anchor arithmetical concepts in direct experience by analyzing the actual psychological processes to which he thought the concept of number owed its genesis. To obtain the concept of number of a concrete set of objects, say A, A, and A, he explained, one abstracts from the particular characteristics of the individual contents collected, only considering and retaining each one insofar as it is a something or a one. Regarding their collective combination, one thus obtains the general form of the set belonging to the set in question: one and one, etc.
The enthusiastic espousal of psychologism of On the Concept of Number is not found in Philosophy of Arithmetic. Husserl later confessed that doubts about basic differences between the concept of number and the concept of collecting, which was all that could be obtained from reflection on acts, had troubled and tormented him from the very beginning and had eventually extended to all categorial concepts and to concepts of objectivities of any sort whatsoever, ultimately to include modern analysis and the theory of manifolds, and simultaneously to mathematical logic and the entire field of logic in general.
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He did not see how one could reconcile the objectivity of mathematics with psychological foundations for logic. Years later, Husserl would explain in Formal and Transcendental Logic that his.
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 , 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 His views took an idealistic turn in the Ideas Toward a Pure Phenomenology Husserl wrote little from then until the late s, when he developed his idealism in a new direction in Formal and Transcendental Logic and Cartesian Meditations It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide.
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Husserl Trans. Cairns - Formal and Transcendental Logic | Phenomenology (Philosophy) | Logic
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