Nikokora Philosophie der Arithmetik The philosophy of Edmund Husserl in its development from his mathematical interests to his first concept of phenomenology in Logical Investigations. Philosophiques36 2: Gottlob Frege — — G. Translations are mine, unless otherwise specified, and modified where required, without notice. Create lists, bibliographies and reviews: This field of psychology I call descriptive. Die Frage nach dem Ursprung der Geometrie als intentional-historiches Problem: Hence, the question we should rather ask, is: Introduction and notes by D.
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He was born into a Jewish family, the second of four children. His father was a milliner. Then Husserl traveled to Vienna to study at the Realgymnasium there, followed next by the Staatsgymnasium in Olomouc Ger.
At Leipzig he was inspired by philosophy lectures given by Wilhelm Wundt , one of the founders of modern psychology. Then he moved to the Frederick William University of Berlin the present-day Humboldt University of Berlin in where he continued his study of mathematics under Leopold Kronecker and the renowned Karl Weierstrass.
In Berlin he found a mentor in Thomas Masaryk , then a former philosophy student of Franz Brentano and later the first president of Czechoslovakia. Herbert Spiegelberg writes, "While outward religious practice never entered his life any more than it did that of most academic scholars of the time, his mind remained open for the religious phenomenon as for any other genuine experience.
Yet already Husserl had felt the desire to pursue philosophy. Then professor Weierstrass became very ill. Husserl became free to return to Vienna where, after serving a short military duty, he devoted his attention to philosophy.
In at the University of Vienna he attended the lectures of Franz Brentano on philosophy and philosophical psychology. Stuart Mill , and David Hume. Husserl was so impressed by Brentano that he decided to dedicate his life to philosophy; indeed, Franz Brentano is often credited as being his most important influence, e. In their daughter Elizabeth was born, in their son Gerhart , and in their son Wolfgang.
Elizabeth would marry in , and Gerhart in ; Wolfgang, however, became a casualty of the First World War. He started when he was in as a Privatdozent at the University of Halle. In he published his Philosophie der Arithmetik.
Psychologische und logische Untersuchungen which, drawing on his prior studies in mathematics and philosophy, proposed a psychological context as the basis of mathematics. It drew the adverse notice of Gottlob Frege , who criticized its psychologism.
Just prior to this a major work of his, Logische Untersuchungen Halle, — , was published. Volume One contains seasoned reflections on "pure logic" in which he carefully refutes "psychologism". Kant and Descartes were also now influencing his thought. In he became joint editor of the journal Logos. During this period Husserl had delivered lectures on internal time consciousness, which several decades later his former student Heidegger edited for publication. His important work Ideen  was published in its first issue.
In October both his sons were sent to fight on the Western Front of World War I and the following year one of them, Wolfgang Husserl, was badly injured. On 8 March , on the battlefield of Verdun , Wolfgang was killed in action. The next year his other son Gerhart Husserl was wounded in the war but survived.
His own mother Julia died. In November one of his outstanding students and later a noted philosophy professor in his own right, Adolf Reinach , was killed in the war while serving in Flanders.
The mathematician Hermann Weyl began corresponding with him in Husserl gave four lectures on Phenomenological method at University College, London in The University of Berlin in called on him to relocate there, but he declined the offer. In Heidegger dedicated his book Sein und Zeit Being and Time to him "in grateful respect and friendship. A Festschrift to celebrate his seventieth birthday was presented to him on 8 April Despite retirement, Husserl gave several notable lectures.
It remains, however, alone unconnected. On 6 April Husserl was banned from using the library at the University of Freiburg, or any other academic library; the following week, after a public outcry, he was reinstated. By contrast, in July Husserl resigned from the Deutsche Akademie. The apolitical Husserl before had specifically avoided such historical discussions, pointedly preferring to go directly to an investigation of consciousness. Merleau-Ponty and others question whether Husserl here does not undercut his own position, in that Husserl had attacked in principle historicism , while specifically designing his phenomenology to be rigorous enough to transcend the limits of history.
Does the lifeworld contextualize and thus compromise the gaze of the pure ego, or does the phenomenological method nonetheless raise the ego up transcendent? Since his university retirement Husserl had "worked at a tremendous pace, producing several major works. Edmund Husserl died at Freiburg on 27 April , having just turned His wife Malvine survived him. Eugen Fink , his research assistant, delivered his eulogy. Heidegger and the Nazi era[ edit ] Husserl was incorrectly rumoured to have been denied the use of the library at Freiburg as a result of the anti-Jewish legislation of April It was also rumoured that his former pupil Martin Heidegger informed Husserl that he was discharged, but it was actually the previous rector.
In the summer of Husserl had studied carefully selected writings of Heidegger, coming to the conclusion that on several of their key positions they differed: e. Husserl, of course, had died three years earlier. In post-war editions of Sein und Zeit the dedication to Husserl is restored. The complex, troubled, and sundered philosophical relationship between Husserl and Heidegger has been widely discussed.
He analyzes the psychological process needed to obtain the concept of number and then tries to build up a systematical theory on this analysis. To achieve this he uses several methods and concepts taken from his teachers. From Weierstrass he derives the idea that we generate the concept of number by counting a certain collection of objects.
From Brentano and Stumpf he takes over the distinction between proper and improper presenting. In other words, you can have a proper presentation of an object if it is actually present, and an improper or symbolic, as he also calls it one if you only can indicate that object through signs, symbols, etc.
While often simplistically summarised as "aboutness" or the relationship between mental acts and the external world, Brentano defined it as the main characteristic of mental phenomena, by which they could be distinguished from physical phenomena.
Every mental phenomenon, every psychological act, has a content, is directed at an object the intentional object. Every belief, desire, etc.
Brentano used the expression "intentional inexistence" to indicate the status of the objects of thought in the mind. The property of being intentional, of having an intentional object, was the key feature to distinguish mental phenomena and physical phenomena, because physical phenomena lack intentionality altogether.
Knowledge of essences would only be possible by " bracketing " all assumptions about the existence of an external world. These new concepts prompted the publication of the Ideen Ideas in , in which they were at first incorporated, and a plan for a second edition of the Logische Untersuchungen. From the Ideen onward, Husserl concentrated on the ideal, essential structures of consciousness.
The metaphysical problem of establishing the reality of what we perceive, as distinct from the perceiving subject, was of little interest to Husserl in spite of his being a transcendental idealist. Husserl proposed that the world of objects—and of ways in which we direct ourselves toward and perceive those objects—is normally conceived of in what he called the "natural standpoint", which is characterized by a belief that objects exist distinct from the perceiving subject and exhibit properties that we see as emanating from them.
Husserl proposed a radical new phenomenological way of looking at objects by examining how we, in our many ways of being intentionally directed toward them, actually "constitute" them to be distinguished from materially creating objects or objects merely being figments of the imagination ; in the Phenomenological standpoint, the object ceases to be something simply "external" and ceases to be seen as providing indicators about what it is, and becomes a grouping of perceptual and functional aspects that imply one another under the idea of a particular object or "type".
In order to better understand the world of appearances and objects, phenomenology attempts to identify the invariant features of how objects are perceived and pushes attributions of reality into their role as an attribution about the things we perceive or an assumption underlying how we perceive objects. Husserl tries new methods of bringing his readers to understand the importance of phenomenology to scientific inquiry and specifically to psychology and what it means to "bracket" the natural attitude.
In it, Husserl for the first time attempts a historical overview of the development of Western philosophy and science , emphasizing the challenges presented by their increasingly one-sidedly empirical and naturalistic orientation. In the former, sense-perception in correspondence with the material realm constitutes the known reality, and understanding is premised on the accuracy of the perception and the objective knowability of what is called the "real world".
He identified several different kinds of names. For example, there are names that have the role of properties that uniquely identify an object. Each of these names expresses a meaning and designates the same object. There are names which have no meaning, but have the role of designating an object: "Aristotle", "Socrates", and so on. Finally, there are names which designate a variety of objects. These are called "universal names"; their meaning is a " concept " and refers to a series of objects the extension of the concept.
The way we know sensible objects is called " sensible intuition ". Husserl also identifies a series of "formal words" which are necessary to form sentences and have no sensible correlates. Examples of formal words are "a", "the", "more than", "over", "under", "two", "group", and so on. Every sentence must contain formal words to designate what Husserl calls "formal categories". There are two kinds of categories: meaning categories and formal- ontological categories.
Meaning categories relate judgments; they include forms of conjunction , disjunction , forms of plural , among others. Formal-ontological categories relate objects and include notions such as set, cardinal number , ordinal number , part and whole, relation, and so on.
The way we know these categories is through a faculty of understanding called "categorial intuition". Through sensible intuition our consciousness constitutes what Husserl calls a "situation of affairs" Sachlage.
It is a passive constitution where objects themselves are presented to us. To this situation of affairs, through categorial intuition, we are able to constitute a " state of affairs " Sachverhalt. One situation of affairs through objective acts of consciousness acts of constituting categorially can serve as the basis for constituting multiple states of affairs. For example, suppose a and b are two sensible objects in a certain situation of affairs.
For Husserl a sentence has a proposition or judgment as its meaning, and refers to a state of affairs which has a situation of affairs as a reference base.
Logic is a formal theory of judgment , that studies the formal a priori relations among judgments using meaning categories. Mathematics, on the other hand, is formal ontology ; it studies all the possible forms of being of objects. Hence for both logic and mathematics, the different formal categories are the objects of study, not the sensible objects themselves.
The problem with the psychological approach to mathematics and logic is that it fails to account for the fact that this approach is about formal categories, and not simply about abstractions from sensibility alone. The reason why we do not deal with sensible objects in mathematics is because of another faculty of understanding called "categorial abstraction.
Thanks to "eidetic intuition" or "essential intuition" , we are able to grasp the possibility, impossibility, necessity and contingency among concepts and among formal categories. Categorial intuition, along with categorial abstraction and eidetic intuition, are the basis for logical and mathematical knowledge.
Structure[ edit ] The Philosophy of Arithmetic constitutes the first volume of a work which Husserl intended to comprise two volumes, of which the second was never published. Comprehensively it would have encompassed four parts and an Appendix. The first volume is divided in two parts, in the first of which Husserl purports to analyse the "Proper concepts of multiplicity, unity and amount" Die eigentliche Begriffe von Vielheit, Einheit und Anzahl and in the second "The symbolic amount-concepts and the logical sources of amount-arithmetic" Die symbolischen Anzahlbegrife und die logischen Quellen der Anzahlen-Arithmetik. Content[ edit ] The basic issue of the book is a philosophical analysis of the concept of number , which is the most basic concept on which the entire edifice of arithmetic and mathematics can be founded. In order to proceed with this analysis, Husserl, following Brentano and Stumpf, uses the tools of psychology to look for the "origin and content" of the concept of number. He begins with the classical definition, already given by Euclid , Thomas Hobbes and Gottfried Wilhelm Leibniz , that "number is a multiplicity of unities" and then asks himself: what is multiplicity and what is unity? Anything that we can think of, anything we can present, can be considered at its most basic level to be "something".
Filosofía de la aritmética (1891)
philosophie der arithmetik von husserl