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100-440: Microethics is a term introduced by Paul Komesaroff in 1995 and elaborated in a series of subsequent works. The concept, which draws especially on the work of the philosophers Edmund Husserl and Emmanuel Levinas , is based on the recognition that most ethical decisions in everyday life are not taken on the basis of explicit rational argument or calculation but rather occur in a continuous flux of relationships and dialogues. Often

200-702: A Privatdozent at Halle from 1887, then as professor, first at Göttingen from 1901, then at Freiburg from 1916 until he retired in 1928, after which he remained highly productive. In 1933, under racial laws of the Nazi Party , Husserl was expelled from the library of the University of Freiburg due to his Jewish family background and months later resigned from the Deutsche Akademie . Following an illness, he died in Freiburg in 1938. Husserl

300-462: A Privatdozent at the University of Halle . In 1891 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 . In 1901 Husserl with his family moved to

400-407: A chicken-and-egg problem. Does the lifeworld contextualize and thus compromise the gaze of the pure ego, or does the phenomenological method nonetheless raise the ego up transcendent? These last writings presented the fruits of his professional life. Since his university retirement Husserl had "worked at a tremendous pace, producing several major works." After suffering a fall in the autumn of 1937,

500-482: A doctorate for her from Heidelberg University without the need for an oral thesis defense. He was immobile for the last three years of his life, and died in Berlin from pneumonia . From 1870 until her death in 1891, Kovalevsky corresponded with Weierstrass. Upon learning of her death, he burned her letters. About 150 of his letters to her have been preserved. Professor Reinhard Bölling  [ de ] discovered

600-514: A feature that inheres in an object's essence founded in the relation between the object and the perceiver. 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 people perceive (or an assumption underlying how people perceive objects). The major dividing line in Husserl's thought

700-414: A general and indeterminate manner. It is, properly speaking, the most universal mathematics of all. Through the posit of certain indeterminate objects (formal-ontological categories) as well as any combination of mathematical axioms, mathematicians can explore the apodeictic connections between them, as long as consistency is preserved. According to Husserl, this view of logic and mathematics accounted for

800-565: A government official, and Theodora Vonderforst both of whom were Catholic Rhinelanders . His interest in mathematics began while he was a gymnasium student at the Theodorianum in Paderborn . He was sent to the University of Bonn upon graduation to prepare for a government position. Because his studies were to be in the fields of law, economics, and finance, he was immediately in conflict with his hopes to study mathematics. He resolved

900-475: A lecture Husserl gave to various Kant Societies in Frankfurt, Berlin, and Halle during 1931 entitled Phänomenologie und Anthropologie . In the war-time 1941 edition of Heidegger's primary work, Being and Time ( Sein und Zeit , first published in 1927), the original dedication to Husserl was removed. This was not due to a negation of the relationship between the two philosophers, however, but rather

1000-738: A long period of illness, but was able to publish mathematical articles that brought him fame and distinction. The University of Königsberg conferred an honorary doctor's degree on him on 31 March 1854. In 1856 he took a chair at the Gewerbeinstitut in Berlin (an institute to educate technical workers which would later merge with the Bauakademie to form the Technische Hochschule in Charlottenburg; now Technische Universität Berlin ). In 1864 he became professor at

1100-658: 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 people 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 people direct themselves toward and perceive those objects—is normally conceived of in what he called

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1200-425: A priori sciences as having an essentially empirical foundation and a prescriptive or descriptive nature. According to psychologism , logic would not be an autonomous discipline, but a branch of psychology, either proposing a prescriptive and practical "art" of correct judgement (as Brentano and some of his more orthodox students did) or a description of the factual processes of human thought. Husserl pointed out that

1300-440: A priori ' interconnection of bodies, given in perception, is what founds the interconnection of consciousnesses known as transcendental intersubjectivity , which Husserl would go on to describe at length in volumes of unpublished writings. There has been a debate over whether or not Husserl's description of ownness and its movement into intersubjectivity is sufficient to reject the charge of solipsism, to which Descartes, for example,

1400-628: A proper name denotes a non-existent object, it does not have a reference, hence concepts with no objects have no truth value in arguments. Moreover, Husserl did not maintain that predicates of sentences designate concepts. According to Frege the reference of a sentence is a truth value; for Husserl it is a "state of affairs." Frege's notion of "sense" is unrelated to Husserl's noema, while the latter's notions of "meaning" and "object" differ from those of Frege. In detail, Husserl's conception of logic and mathematics differs from that of Frege, who held that arithmetic could be derived from logic. For Husserl this

1500-533: A reasonably rigorous definition of a limit as early as 1817 (and possibly even earlier) his work remained unknown to most of the mathematical community until years later, and many mathematicians had only vague definitions of limits and continuity of functions. The basic idea behind Delta-epsilon proofs is, arguably, first found in the works of Cauchy in the 1820s. Cauchy did not clearly distinguish between continuity and uniform continuity on an interval. Notably, in his 1821 Cours d'analyse, Cauchy argued that

1600-461: A reference base. Husserl sees ontology as a science of essences . Sciences of essences are contrasted with factual sciences : the former are knowable a priori and provide the foundation for the later, which are knowable a posteriori . Ontology as a science of essences is not interested in actual facts , but in the essences themselves, whether they have instances or not . Husserl distinguishes between formal ontology , which investigates

1700-417: A science of the mind (' Geisteswissenschaft ') must be established on as scientific a foundation as the natural sciences have managed: "It is my conviction that intentional phenomenology has for the first time made spirit as spirit the field of systematic scientific experience, thus effecting a total transformation of the task of knowledge." Husserl's thought is revolutionary in several ways, most notably in

1800-695: 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 people know these categories

1900-490: A theory of sense and reference before 1891. Commentators argue that Husserl's notion of noema has nothing to do with Frege's notion of sense, because noemata are necessarily fused with noeses which are the conscious activities of consciousness. Noemata have three different levels: Consequently, in intentional activities, even non-existent objects can be constituted, and form part of the whole noema. Frege, however, did not conceive of objects as forming parts of senses: If

2000-554: A visit to Franz Brentano his inspiring old teacher and to Constantin Carathéodory the mathematician. Kant and Descartes were also now influencing his thought. In 1910 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 students Edith Stein and Martin Heidegger edited for publication. In 1912 at Freiburg

2100-404: Is 'presented' to itself, and to each all others are 'presentiated' ( Vergegenwärtigung ), not as parts of nature but as pure consciousness". Ideen advanced his transition to a "transcendental interpretation" of phenomenology, a view later criticized by, among others, Jean-Paul Sartre . In Ideen Paul Ricœur sees the development of Husserl's thought as leading "from the psychological cogito to

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2200-582: Is clearly defined in that work. Frege's attack seems to be directed at certain foundational doctrines then current in Weierstrass's Berlin School, of which Husserl and Cantor cannot be said to be orthodox representatives. Furthermore, various sources indicate that Husserl changed his mind about psychologism as early as 1890, a year before he published the Philosophy of Arithmetic . Husserl stated that by

2300-423: Is considered the starting point for the formal theory of wholes and their parts known as mereology . Another important element that Husserl took over from Brentano was intentionality , the notion that the main characteristic of consciousness is that it is always intentional. While often simplistically summarised as "aboutness" or the relationship between mental acts and the external world, Brentano defined it as

2400-469: Is constituted by consciousness needs a noetic correlate (the subjective activities of consciousness). Husserl stated that logic has three strata, each further away from consciousness and psychology than those that precede it. The ontological correlate to the third stratum is the " theory of manifolds ". In formal ontology, it is a free investigation where a mathematician can assign several meanings to several symbols, and all their possible valid deductions in

2500-443: Is continuous at a point x = x 0 {\displaystyle \displaystyle x=x_{0}} if for each x {\displaystyle x} close enough to x 0 {\displaystyle x_{0}} , the function value f ( x ) {\displaystyle f(x)} is very close to f ( x 0 ) {\displaystyle f(x_{0})} , where

2600-424: Is not conditioned but rather transcendental: in Husserl's terms, pure consciousness of absolute Being. In Husserl's work, consciousness of any given thing calls for discerning its meaning as an "intentional object". Such an object does not simply strike the senses, to be interpreted or misinterpreted by mental reason; it has already been selected and grasped, grasping being an etymological connotation, of percipere ,

2700-409: Is not the case: mathematics (with the exception of geometry ) is the ontological correlate of logic, and while both fields are related, neither one is strictly reducible to the other. Reacting against authors such as John Stuart Mill , Christoph von Sigwart and his own former teacher Brentano, Husserl criticised their psychologism in mathematics and logic, i.e. their conception of these abstract and

2800-464: Is the turn to transcendental idealism. In a later period, Husserl began to wrestle with the complicated issues of intersubjectivity , specifically, how communication about an object can be assumed to refer to the same ideal entity ( Cartesian Meditations , Meditation V). 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"

2900-503: Is through a faculty of understanding called "categorial intuition". Through sensible intuition, consciousness constitutes what Husserl calls a "situation of affairs" ( Sachlage ). It is a passive constitution where objects themselves are presented. To this situation of affairs, through categorial intuition, people 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

3000-781: The Catholic University of Leuven in Belgium by the Franciscan priest Herman Van Breda . There they were deposited at Leuven to form the Husserl-Archives of the Higher Institute of Philosophy . Much of the material in his research manuscripts has since been published in the Husserliana critical edition series. In his first works, Husserl combined mathematics, psychology, and philosophy with

3100-783: The Deutsche Akademie . Later Husserl lectured at Prague in 1935 and Vienna in 1936, which resulted in a very differently styled work that, while innovative, is no less problematic: Die Krisis (Belgrade 1936). Husserl describes here the cultural crisis gripping Europe, then approaches a philosophy of history, discussing Galileo , Descartes, several British philosophers, and Kant . 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

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3200-563: The Philosophy of Arithmetic helped turn Husserl towards modern Platonism , but he had already discovered the work of Bernard Bolzano independently around 1890/91. In his Logical Investigations , Husserl explicitly mentioned Bolzano, G. W. Leibniz and Hermann Lotze as inspirations for his newer position. Husserl's review of Ernst Schröder , published before Frege's landmark 1892 article, clearly distinguishes sense from reference ; thus Husserl's notions of noema and object also arose independently. Likewise, in his criticism of Frege in

3300-612: The Philosophy of Arithmetic , Husserl remarks on the distinction between the content and the extension of a concept. Moreover, the distinction between the subjective mental act, namely the content of a concept, and the (external) object, was developed independently by Brentano and his school , and may have surfaced as early as Brentano's 1870s lectures on logic. Scholars such as J. N. Mohanty , Claire Ortiz Hill , and Guillermo E. Rosado Haddock , among others, have argued that Husserl's so-called change from psychologism to Platonism came about independently of Frege's review. For example,

3400-594: The University of Freiburg (in Freiburg im Breisgau ) where he continued bringing his work in philosophy to fruition, now as a full professor. Edith Stein served as his personal assistant during his first few years in Freiburg, followed later by Martin Heidegger from 1920 to 1923. The mathematician Hermann Weyl began corresponding with him in 1918. Husserl gave four lectures on Phenomenological method at University College London in 1922. The University of Berlin in 1923 called on him to relocate there, but he declined

3500-514: The University of Göttingen , where he taught as extraordinarius professor . Just prior to this a major work of his, Logische Untersuchungen (Halle, 1900–1901), was published. Volume One contains seasoned reflections on "pure logic" in which he carefully refutes "psychologism". This work was well received and became the subject of a seminar given by Wilhelm Dilthey ; Husserl in 1905 traveled to Berlin to visit Dilthey. Two years later in Italy he paid

3600-518: The University of Halle , seeking to obtain his habilitation which would qualify him to teach at the university level. There, under Stumpf's supervision, he wrote Über den Begriff der Zahl ( On the Concept of Number ) in 1887, which would serve later as the basis for his first important work, Philosophie der Arithmetik (1891). In 1887 Husserl married Malvine Steinschneider, a union that would last over fifty years. In 1892 their daughter Elizabeth

3700-494: The University of Leipzig from 1876 to 1878, Husserl studied mathematics, physics, and astronomy. 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 1878 where he continued his study of mathematics under Leopold Kronecker and

3800-478: The racial laws of the new National Socialist German Workers Party were enacted. 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. Yet his colleague Heidegger was elected Rector of the university on 21–22 April, and joined the Nazi Party . By contrast, in July Husserl resigned from

3900-616: The "close enough" restriction typically depends on the desired closeness of f ( x 0 ) {\displaystyle f(x_{0})} to f ( x ) . {\displaystyle f(x).} Using this definition, he proved the Intermediate Value Theorem. He also proved the Bolzano–Weierstrass theorem and used it to study the properties of continuous functions on closed and bounded intervals. Weierstrass also made advances in

4000-516: The "natural attitude", which is characterized by a belief that objects exist distinct from the perceiving subject and exhibit properties that people see as emanating from them (this attitude is also called physicalist objectivism ). Husserl proposed a radical new phenomenological way of looking at objects by examining how people, in their many ways of being intentionally directed toward them, actually "constitute" them (to be distinguished from materially creating objects or objects merely being figments of

4100-478: The (pointwise) limit of (pointwise) continuous functions was itself (pointwise) continuous, a statement that is false in general. The correct statement is rather that the uniform limit of continuous functions is continuous (also, the uniform limit of uniformly continuous functions is uniformly continuous). This required the concept of uniform convergence , which was first observed by Weierstrass's advisor, Christoph Gudermann , in an 1838 paper, where Gudermann noted

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4200-639: The Friedrich-Wilhelms-Universität Berlin, which later became the Humboldt Universität zu Berlin . In 1870, at the age of fifty-five, Weierstrass met Sofia Kovalevsky whom he tutored privately after failing to secure her admission to the university. They had a fruitful intellectual, and kindly personal relationship that "far transcended the usual teacher-student relationship". He mentored her for four years, and regarded her as his best student, helping to secure

4300-556: The anti-Jewish legislation of April 1933. However, among other disabilities Husserl was unable to publish his works in Nazi Germany [see above footnote to Die Krisis (1936)]. It was also rumoured that his former pupil Martin Heidegger informed Husserl that he was discharged, but it was actually the previous rector. Apparently Husserl and Heidegger had moved apart during the 1920s, which became clearer after 1928 when Husserl retired and Heidegger succeeded to his university chair. In

4400-620: The application of drugs or other therapeutic techniques also requires specific examination of the needs of individual patients, including their health conditions, their cultural preferences, their personal values and those of their families, and economic and other considerations. The negotiation of these latter considerations occurs within the field of microethics. Edmund Husserl Edmund Gustav Albrecht Husserl ( / ˈ h ʊ s ɜːr l / HUUSS -url ; US also / ˈ h ʊ s ər əl / HUUSS -ər-əl , German: [ˈɛtmʊnt ˈhʊsɐl] ; 8 April 1859 – 27 April 1938 )

4500-420: The assistant to Karl Weierstrass . 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 1884 at the University of Vienna he attended the lectures of Franz Brentano on philosophy and philosophical psychology. Brentano introduced him to

4600-415: The basis for constituting multiple states of affairs. For example, suppose a and b are two sensible objects in a certain situation of affairs. It can be used as the basis to say, " a < b " and " b > a ", two judgments which designate the same state 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

4700-582: The conflict by paying little heed to his planned course of study but continuing private study in mathematics. The outcome was that he left the university without a degree. He then studied mathematics at the Münster Academy (which was even then famous for mathematics) and his father was able to obtain a place for him in a teacher training school in Münster . Later he was certified as a teacher in that city. During this period of study, Weierstrass attended

4800-544: The definition of the continuity of a function and complex analysis , proved the intermediate value theorem and the Bolzano–Weierstrass theorem , and used the latter to study the properties of continuous functions on closed bounded intervals. Weierstrass was born into a Roman Catholic family in Ostenfelde, a village near Ennigerloh , in the Province of Westphalia . Weierstrass was the son of Wilhelm Weierstrass,

4900-675: 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 sensible objects are not dealt with in mathematics is because of another faculty of understanding called "categorial abstraction." Through this faculty people are able to get rid of sensible components of judgments, and just focus on formal categories themselves. Thanks to " eidetic reduction " (or "essential intuition"), people are able to grasp

5000-472: The distinction between "natural" and "phenomenological" modes of understanding. 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". Phenomenological understanding strives to be rigorously "presuppositionless" by means of what Husserl calls " phenomenological reduction ". This reduction

5100-681: The doctor and the patient, including non-linguistic and affective responses, often signified by small adjustments in facial expressions, posture, tone of voice or choice of words, and the great variety of meanings and values and which both participants call. Ethical considerations in biomedicine , engineering and other technical professions include issues relating both to large societal problems and to particular professions and professional conduct. Pharmaceuticals present particular macroethical challenges. Drug designers seek to prevent and treat diseases by modifying of stem cells and producing targeting drugs that have specific targeting mechanisms. However,

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5200-493: The domain of f {\displaystyle f} ,     | x − x 0 | < δ ⇒ | f ( x ) − f ( x 0 ) | < ε . {\displaystyle \displaystyle \ |x-x_{0}|<\delta \Rightarrow |f(x)-f(x_{0})|<\varepsilon .} In simple English, f ( x ) {\displaystyle \displaystyle f(x)}

5300-467: The draft of the letter she wrote to Weierstrass when she arrived in Stockholm in 1883 upon her appointment as Privatdocent at Stockholm University . Weierstrass was interested in the soundness of calculus, and at the time there were somewhat ambiguous definitions of the foundations of calculus so that important theorems could not be proven with sufficient rigour. Although Bolzano had developed

5400-471: The dynamics of microethical decision-making in a variety of practical, often intimate, contexts. If a researcher only acts within the bounds of one's research, i.e. exclusively microethical, the research may still be unacceptable from a societal perspective if it violates macroethical principles. Conversely, purely macroethical considerations are often disengaged from the concrete lifeworlds of ethical subjects and so lack coherence or relevance. For example, in

5500-434: The essence of objectivity in general , and regional ontologies , which study regional essences that are shared by all entities belonging to the region. Regions correspond to the highest genera of concrete entities : material nature, personal consciousness and interpersonal spirit. Husserl's method for studying ontology and sciences of essence in general is called eidetic variation . It involves imagining an object of

5600-550: The failure of anti-psychologists to defeat psychologism was a result of being unable to distinguish between the foundational, theoretical side of logic, and the applied, practical side. Pure logic does not deal at all with "thoughts" or "judgings" as mental episodes but about a priori laws and conditions for any theory and any judgments whatsoever, conceived as propositions in themselves. Since "truth-in-itself" has "being-in-itself" as ontological correlate, and since psychologists reduce truth (and hence logic) to empirical psychology,

5700-545: The field of calculus of variations . Using the apparatus of analysis that he helped to develop, Weierstrass was able to give a complete reformulation of the theory that paved the way for the modern study of the calculus of variations. Among several axioms, Weierstrass established a necessary condition for the existence of strong extrema of variational problems. He also helped devise the Weierstrass–Erdmann condition , which gives sufficient conditions for an extremal to have

5800-467: The first volume of his Logical Investigations , the Prolegomena of Pure Logic , Husserl, while attacking the psychologistic point of view in logic and mathematics, also appears to reject much of his early work, although the forms of psychologism analysed and refuted in the Prolegomena did not apply directly to his Philosophy of Arithmetic . Some scholars question whether Frege's negative review of

5900-563: The following way: if someone is standing in front of a house, they have a proper, direct presentation of that house, but if they are looking for it and ask for directions, then these directions (e.g. the house on the corner of this and that street) are an indirect, improper presentation. In other words, the person can have a proper presentation of an object if it is actually present, and an improper (or symbolic, as Husserl also calls it) one if they only can indicate that object through signs, symbols, etc. Husserl's Logical Investigations (1900–1901)

6000-525: The following year one of them, Wolfgang Husserl, was badly injured. On 8 March 1916, 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 1917 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 . Husserl had transferred in 1916 to

6100-487: The goal of providing a sound foundation for mathematics. He analyzed the psychological process needed to obtain the concept of number and then built up a theory on this analysis. He used methods and concepts taken from his teachers. From Weierstrass he derived the idea of generating the concept of number by counting a certain collection of objects. From Brentano and Stumpf he took the distinction between proper and improper presenting. In an example, Husserl explained this in

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6200-467: The highest genera. Husserl believed that truth-in-itself has as ontological correlate being-in-itself , just as meaning categories have formal-ontological categories as correlates. 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,

6300-499: 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". The notion of objects as real is not expelled by phenomenology, but "bracketed" as a way in which people regard objects—instead of

6400-578: The inevitable consequence is scepticism. Psychologists have not been successful either in showing how induction or psychological processes can justify the absolute certainty of logical principles, such as the principles of identity and non-contradiction. It is therefore futile to base certain logical laws and principles on uncertain processes of the mind. Karl Weierstrass Karl Theodor Wilhelm Weierstrass ( / ˈ v aɪ ər ˌ s t r ɑː s , - ˌ ʃ t r ɑː s / ; German: Weierstraß [ˈvaɪɐʃtʁaːs] ; 31 October 1815 – 19 February 1897)

6500-422: The journal Jahrbuch für Philosophie und Phänomenologische Forschung ("Yearbook for Philosophy and Phenomenological Research") was founded by Husserl and his school, and which published articles of their phenomenological movement from 1913 to 1930. His important work Ideen was published in its first issue (Vol. 1, Issue 1, 1913). Before beginning Ideen , Husserl's thought had reached the stage where "each subject

6600-403: The kind under investigation and varying its features. The changed feature is inessential to this kind if the object can survive its change, otherwise it belongs to the kind's essence . For example, a triangle remains a triangle if one of its sides is extended but it ceases to be a triangle if a fourth side is added. Regional ontology involves applying this method to the essences corresponding to

6700-677: The lectures of Christoph Gudermann and became interested in elliptic functions . In 1843 he taught in Deutsch Krone in West Prussia and from 1848 he taught at the Lyceum Hosianum in Braunsberg . Besides mathematics he also taught physics, botany, and gymnastics. Weierstrass may have had an illegitimate child named Franz with the widow of his friend Carl Wilhelm Borchardt . After 1850 Weierstrass suffered from

6800-420: The limits of all possible knowledge, Husserl redefined phenomenology as a transcendental-idealist philosophy. Husserl's thought profoundly influenced 20th-century philosophy , and he remains a notable figure in contemporary philosophy and beyond. Husserl studied mathematics, taught by Karl Weierstrass and Leo Königsberger , and philosophy taught by Franz Brentano and Carl Stumpf . He taught philosophy as

6900-400: The limits of history. On the contrary, Husserl may be indicating here that historical traditions are merely features given to the pure ego's intuition, like any other. A longer section follows on the " lifeworld " [ Lebenswelt ], one not observed by the objective logic of science, but a world seen through subjective experience. Yet a problem arises similar to that dealing with 'history' above,

7000-422: 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. has an object that it is about: the believed, the wanted. Brentano used the expression "intentional inexistence" to indicate the status of the objects of thought in

7100-547: The mathematical sciences. After obtaining his PhD in mathematics, Husserl began analyzing the foundations of mathematics from a psychological point of view. In his habilitation thesis , On the Concept of Number (1886) and in his Philosophy of Arithmetic (1891), Husserl sought, by employing Brentano's descriptive psychology , to define the natural numbers in a way that advanced the methods and techniques of Karl Weierstrass , Richard Dedekind , Georg Cantor , Gottlob Frege , and other contemporary mathematicians. Later, in

7200-412: The medical setting of end of life issues, the macroethical considerations may include abstract reflections on the nature of life and death and high level principles about the “sacredness” or otherwise of life, the nature of personhood and the relevance and ethical force of competing consequences. By contrast, the microethical processes relate to the internal details of the interactive engagements between

7300-418: 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. Some years after the 1900–1901 publication of his main work, the Logische Untersuchungen ( Logical Investigations ), Husserl made some key conceptual elaborations which led him to assert that to study

7400-558: The natural attitude. The Crisis of the European Sciences is Husserl's unfinished work that deals most directly with these issues. 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. Husserl declares that mental and spiritual reality possess their own reality independent of any physical basis, and that

7500-433: The objectivity of a series of mathematical developments of his time, such as n -dimensional manifolds (both Euclidean and non-Euclidean ), Hermann Grassmann 's theory of extensions , William Rowan Hamilton 's Hamiltonians , Sophus Lie 's theory of transformation groups , and Cantor's set theory . Jacob Klein was one student of Husserl who pursued this line of inquiry, seeking to "desedimentize" mathematics and

7600-508: The offer. In 1926 Heidegger dedicated his book Sein und Zeit ( Being and Time ) to him "in grateful respect and friendship." Husserl remained in his professorship at Freiburg until he requested retirement, teaching his last class on 25 July 1928. A Festschrift to celebrate his seventieth birthday was presented to him on 8 April 1929. Despite retirement, Husserl gave several notable lectures. The first, at Paris in 1929, led to Méditations cartésiennes (Paris 1931). Husserl here reviews

7700-399: The phenomenological epoché (or phenomenological reduction), presented earlier in his pivotal Ideen (1913), in terms of a further reduction of experience to what he calls a 'sphere of ownness.' From within this sphere, which Husserl enacts to show the impossibility of solipsism, the transcendental ego finds itself always already paired with the lived body of another ego, another monad. This '

7800-769: The phenomenon but did not define it or elaborate on it. Weierstrass saw the importance of the concept, and both formalized it and applied it widely throughout the foundations of calculus. The formal definition of continuity of a function, as formulated by Weierstrass, is as follows: f ( x ) {\displaystyle \displaystyle f(x)} is continuous at x = x 0 {\displaystyle \displaystyle x=x_{0}} if ∀   ε > 0   ∃   δ > 0 {\displaystyle \displaystyle \forall \ \varepsilon >0\ \exists \ \delta >0} such that for every x {\displaystyle x} in

7900-405: The philosopher became ill with pleurisy . Edmund Husserl died in Freiburg on 27 April 1938, having just turned 79. His wife Malvine survived him. Eugen Fink , his research assistant, delivered his eulogy . Gerhard Ritter was the only Freiburg faculty member to attend the funeral, as an anti-Nazi protest. Husserl was rumoured to have been denied the use of the library at Freiburg as a result of

8000-511: The possibility, impossibility, necessity and contingency among concepts and among formal categories. Categorial intuition, along with categorial abstraction and eidetic reduction, are the basis for logical and mathematical knowledge. Husserl criticized the logicians of his day for not focusing on the relation between subjective processes that offer objective knowledge of pure logic. All subjective activities of consciousness need an ideal correlate, and objective logic (constituted noematically ) as it

8100-585: The processes of microethical judgments are intuitive and may even go unrecognised at the time. It is the accumulation of infinitesimal microethical moments that composes the large-scale ethical landscapes in which we live. Macroethics tends to emphasise principles, universal claims and normative rules, while microethics is context-specific and local, and acknowledges the role of modalities of communication and decision-making that go beyond rational argumentation. Macroethics and microethics are complementary and coexist in most ethical settings. Komesaroff has elaborated

8200-602: The recent regime change in Germany and its consequences: The future alone will judge which was the true Germany in 1933, and who were the true Germans—those who subscribe to the more or less materialistic-mythical racial prejudices of the day, or those Germans pure in heart and mind, heirs to the great Germans of the past whose tradition they revere and perpetuate. After his death, Husserl's manuscripts, amounting to approximately 40,000 pages of " Gabelsberger " stenography and his complete research library, were in 1939 smuggled to

8300-533: The renowned Karl Weierstrass . In Berlin he found a mentor in Tomáš Garrigue Masaryk , then a former philosophy student of Franz Brentano and later the first president of Czechoslovakia . There Husserl also attended Friedrich Paulsen 's philosophy lectures. In 1881 he left for the University of Vienna to complete his mathematics studies under the supervision of Leo Königsberger (a former student of Weierstrass). At Vienna in 1883 he obtained his PhD with

8400-411: The review falsely accuses Husserl of subjectivizing everything, so that no objectivity is possible, and falsely attributes to him a notion of abstraction whereby objects disappear until all that remains are numbers as mere ghosts. Contrary to what Frege states, in Husserl's Philosophy of Arithmetic there are already two different kinds of representations: subjective and objective. Moreover, objectivity

8500-716: The root of "perceive". From Logical Investigations (1900/1901) to Experience and Judgment (published in 1939), Husserl expressed clearly the difference between meaning and object . 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. Examples of this are "the victor in Jena" and "the loser in Waterloo", or "the equilateral triangle" and "the equiangular triangle"; in both cases, both names express different meanings, but designate

8600-428: 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 people know sensible objects is called " sensible intuition ". Husserl also identifies

8700-448: The structure of consciousness, one would have to distinguish between the act of consciousness and the phenomena at which it is directed (the objects as intended). Knowledge of essences would only be possible by " bracketing " all assumptions about the existence of an external world. This procedure he called " epoché ". These new concepts prompted the publication of the Ideen ( Ideas ) in 1913, in which they were at first incorporated, and

8800-425: The summer of 1929 Husserl had studied carefully selected writings of Heidegger, coming to the conclusion that on several of their key positions they differed: e.g., Heidegger substituted Dasein ["Being-there"] for the pure ego, thus transforming phenomenology into an anthropology, a type of psychologism strongly disfavored by Husserl. Such observations of Heidegger, along with a critique of Max Scheler , were put into

8900-523: The time he published that book, he had already changed his mind—that he had doubts about psychologism from the very outset. He attributed this change of mind to his reading of Leibniz, Bolzano, Lotze, and David Hume . Husserl makes no mention of Frege as a decisive factor in this change. In his Logical Investigations , Husserl mentions Frege only twice, once in a footnote to point out that he had retracted three pages of his criticism of Frege's The Foundations of Arithmetic , and again to question Frege's use of

9000-471: The time, his mind remained open for the religious phenomenon as for any other genuine experience." At times Husserl saw his goal as one of moral "renewal". Although a steadfast proponent of a radical and rational autonomy in all things, Husserl could also speak "about his vocation and even about his mission under God's will to find new ways for philosophy and science," observes Spiegelberg. Following his PhD in mathematics, Husserl returned to Berlin to work as

9100-548: The transcendental cogito". As phenomenology further evolves, it leads (when viewed from another vantage point in Husserl's 'labyrinth') to " transcendental subjectivity ". Also in Ideen Husserl explicitly elaborates the phenomenological and eidetic reductions . Ivan Ilyin and Karl Jaspers visited Husserl at Göttingen. In October 1914 both his sons were sent to fight on the Western Front of World War I , and

9200-571: The word Bedeutung to designate "reference" rather than "meaning" (sense). In a letter dated 24 May 1891, Frege thanked Husserl for sending him a copy of the Philosophy of Arithmetic and Husserl's review of Ernst Schröder 's Vorlesungen über die Algebra der Logik . In the same letter, Frege used the review of Schröder's book to analyze Husserl's notion of the sense of reference of concept words. Hence Frege recognized, as early as 1891, that Husserl distinguished between sense and reference. Consequently, Frege and Husserl independently elaborated

9300-618: The work Beiträge zur Variationsrechnung ( Contributions to the Calculus of variations ). Evidently as a result of his becoming familiar with the New Testament during his twenties, Husserl asked to be baptized into the Lutheran Church in 1886. Husserl's father Adolf had died in 1884. Herbert Spiegelberg writes, "While outward religious practice never entered his life any more than it did that of most academic scholars of

9400-412: The writings of Bernard Bolzano , Hermann Lotze , J. 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.g., with regard to intentionality . Following academic advice, two years later in 1886 Husserl followed Carl Stumpf , a former student of Brentano, to

9500-400: Was a German mathematician often cited as the " father of modern analysis ". Despite leaving university without a degree, he studied mathematics and trained as a school teacher, eventually teaching mathematics , physics , botany and gymnastics . He later received an honorary doctorate and became professor of mathematics in Berlin. Among many other contributions, Weierstrass formalized

9600-410: Was an Austrian-German philosopher and mathematician who established the school of phenomenology . In his early work, he elaborated critiques of historicism and of psychologism in logic based on analyses of intentionality . In his mature work, he sought to develop a systematic foundational science based on the so-called phenomenological reduction . Arguing that transcendental consciousness sets

9700-908: Was born in 1859 in Proßnitz in the Margraviate of Moravia in the Austrian Empire (today Prostějov in the Czech Republic ). He was born into a Jewish family, the second of four children. His father was a milliner . His childhood was spent in Prostějov, where he attended the secular primary school. Then Husserl traveled to Vienna to study at the Realgymnasium there, followed next by the Staatsgymnasium in Olmütz . At

9800-624: Was born, in 1893 their son Gerhart , and in 1894 their son Wolfgang. Elizabeth would marry in 1922, and Gerhart in 1923; Wolfgang, however, became a casualty of the First World War . Gerhart would become a philosopher of law, contributing to the subject of comparative law , teaching in the United States and after the war in Austria . Following his marriage Husserl began his long teaching career in philosophy. He started in 1887 as

9900-689: Was subject. One argument against Husserl's description works this way: instead of infinity and the Deity being the ego's gateway to the Other, as in Descartes, Husserl's ego in the Cartesian Meditations itself becomes transcendent. It remains, however, alone (unconnected). Only the ego's grasp "by analogy" of the Other (e.g., by conjectural reciprocity) allows the possibility for an 'objective' intersubjectivity, and hence for community. In 1933,

10000-590: Was the result of a suggested censorship by Heidegger's publisher who feared that the book might otherwise be banned by the Nazi regime. The dedication can still be found in a footnote on page 38, thanking Husserl for his guidance and generosity. Husserl 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. On 4 May 1933, Professor Edmund Husserl addressed

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