scholarly journals “I have Learned Non-Euclidean Geometry Just from this Book” - Some facets of the correspondence between Friedrich Engel and David Hilbert

2021 ◽  
Vol 76 (3) ◽  
Author(s):  
Peter Ullrich

AbstractFriedrich Engel and David Hilbert learned to know each other at Leipzig in 1885 and exchanged letters in particular during the next 15 years which contain interesting information on the academic life of mathematicians at the end of the 19th century. In the present article we will mainly discuss a statement by Hilbert himself on Moritz Pasch’s influence on his views of geometry, and on personnel politics concerning Hermann Minkowski and Eduard Study but also Engel himself.

Author(s):  
Janet Folina

The mathematical developments of the 19th century seemed to undermine Kant’s philosophy. Non-Euclidean geometries challenged Kant’s view that there is a spatial intuition rich enough to yield the truth of Euclidean geometry. Similarly, advancements in algebra challenged the view that temporal intuition provides a foundation for both it and arithmetic. Mathematics seemed increasingly detached from experience as well as its form; moreover, with advances in symbolic logic, mathematical inference also seemed independent of intuition. This paper considers various philosophical responses to these changes, focusing on the idea of modifying Kant’s conception of intuition in order to accommodate the increasing abstractness of mathematics. It is argued that far from clinging to an outdated paradigm, programs based on new conceptions of intuition should be seen as motivated by important philosophical desiderata, such as the truth, apriority, distinctiveness and autonomy of mathematics.


2021 ◽  
Vol 34 (01) ◽  
pp. 280-309
Author(s):  
Eduard O. Heyfetz

Euclid’s fifth postulate has been accepted as a theorem since the time of ancient Greece. The efforts to prove it have been going on for nearly 2 000 years. Non-Euclidean geometry, based on its rejection, emerged in the first half of the 19th century. The author of the present article returns to the problem by addressing the metaphysical foundations of physics. The author has found the ideal instrument for analyzing infinity to be an infinitely small unit, which cannot be divided further. With the help of this instrument, the fundamental properties of the so-called space were found. It was concluded that there are no oblique or curved lines on the basic level. The apparent curved and oblique lines are stairs with negligibly fluent changing or constant steps, correspondingly. Hence, the refutation of non-Euclidean geometries and seeking a new proof of the postulate. Inter alia, it was found that the requirement to conclude the proof from Euclid’s other four axioms only diverted the attention of mathematicians from the true problem. The author proved the fifth postulate on a plane. Its application to a pair of skew lines is considered. In conclusion, the author describes the basic properties of the so-called space.


1967 ◽  
Vol 40 (3) ◽  
pp. 777-785
Author(s):  
Friedrich Linhardt

Abstract Vulcanized rubber has an unusual property, known early in the 19th century, but not understood until 1935: it increases in stiffness with rise in operating temperature. A strip of rubber loaded with a weight and heated does not stretch; on the contrary, it contracts to some extent. Theoretical interpretations of this effect showed deformation of rubber, as well as its softness and high extensibility, to be determined by entropy, among other things. “Entropy elasticity” was looked upon as a peculiarity of rubber. It was thus only logical, when materials were classified as “rubbers” that they should be distinguished from all other materials by using the expression “entropy elastic behavior”. To be sure, one is inclined today to consider entropy elasticity a characteristic of all high polymers, including those not crosslinked. The present article reports an experimental approach to this problem.


2013 ◽  
Vol 58 (1) ◽  
Author(s):  
Clara Reiter

AbstractThe present article focuses on court interpreters at the Imperial court of Vienna, who were employed in the Habsburg Monarchy from the early 16th century until the end of the 19th century. Based on the methodological concepts of professional intercultures introduced by Anthony Pym the article discusses the question whether or not court interpreters formed a professional group at the court. Different aspects of their profession such as competencies, remuneration, duties, reputation and their place in the organization of the court are discussed. For the application of Anthony Pyms model it will be shown that two main components, time and the intern differentiation of the group, are necessary to apply the model on a professional group like the court interpreters that was a highly complex group characterized by strong changes throughout their existence.


1970 ◽  
Vol 63 (8) ◽  
pp. 690-692
Author(s):  
Phillip E. Johnson

Georg Canttor created and largely developed the theory of sets in approximately the year. 1874-1897. In contrast to such developments as the calculus and non-Euclidean geometry, The creation of set theory was, according to all indications, Cantor's alone. AIso, set theory was not preceded by a long evoIutionary period such as is usually the case with big mathematical breakthroughs. The present article will concern itself primarily with the very earliest set-theoretic works of Cantor, namely, his first two papers in this area.1


Author(s):  
Miina Norvik

The objective of this article is to present the main findings of research into Livonian syntax. As is typical of the Finnic languages other than Estonian and Finnish, in the past, syntax-related issues have received little attention. For instance, the only scientific grammar of Livonian, which was written in German and published in the 19th century, remains the most comprehensive overview of Livonian syntax. In recent times, however, interest in syntax-related issues has grown and there are several separate studies on specific issues of Livonian syntax. Furthermore, a contemporary Livonian reference grammar will be published in a few years and it will also contain a chapter on syntax. The present article is meant to give a research overview of the main topics discussed previously and point out the main challenges for future research.Kokkuvõte. Miina Norvik: Liivi keele süntaksi uurimine: varasemad tulemused ning eesseisvad ülesanded. Artikli eesmärgiks on esitleda peamisi liivi keele süntaksi uurimisel saadud tulemusi esimese teadusliku grammatika ilmumisest 1861. aastal kuni tänapäevani ning selgitada uue grammatika kirjutamisega seotud ülesandeid. Kuigi liivi keele süntaksi uurimine on hoogus tunud alles viimastel aastakümnetel, on süntaksi põhiküsimusi varemalt käsitletud vähemalt põgusalt. On nii teemasid, mis on alles hiljuti tähelepanu keskmesse tõusnud (nt tuleviku, modaalsuse, eituse väljendamine), kuid on ka teemasid, mida on viimati käsitletud üle 150 aasta tagasi (nt sõnajärg) või mida pole üldse uuritud (nt osaöeldistäide, sõnajärg kõrvallauses). Peamiste eesseisvate ülesannetena nähaksegi varasemate uurimistulemuste koondamist uude grammatikasse; vajadusel nende ühtlustamist ja kontrollimist, kuna uurimused on kirjutatud eri aegadel ning traditsioonis; ning varasemas uurimuses esinevate lünkade täitmist.Märksõnad: liivi keel, süntaks, grammatika, predikaat, nominaalsed argumendid, lausetüübidKubbõvõttõks. Miina Norvik: Līvõ kīel sintaks tuņšlimi: jedlõmizt rezultātõd ja tulbizt ilzandõkst. Kēra võttõksõks um līvõ kīel sintaks tuņšlimiz pǟmizt rezultātõd klīerimi ežmiz tieudliz grammatik ulzõ āndamizõst 1861. āigastõn tämpiz sǭņõ ja seļțõ tulbiži ilzandõkši ūd grammatik kēratimiz pierāst. Koks kil līvõ kīel sintaks tuņšlimi um võttõn jūontõ set perrizt āigastkimmõd āigal, sintaks pūojkizzimiži um vaņțõltõd jõvā vaŗīmõld, amā veitõm lītõld. Nei ātõ tematõd, mis ātõ perīst kõrdõ vaņțõltõd jemīņ ku 150 āigastõ tāgižpēḑõn (ngț. sõnākȭrda) agā ka seļļizt, mis äb ūotõ vaņțõltõd. Nei siz pǟmizt tulbizt ilzandõd ātõ vaŗīmõd tuņšlimiz rezultātõd kubtimi ūd grammatik pierāst, nänt lebbõ vaņțlimi, ītiztimi ja vaŗīmiz tuņšlimiz ōkõd tǟtami.


1996 ◽  
Vol 46 (1) ◽  
pp. 207-216 ◽  
Author(s):  
Gianpiero Rosati

Of all the works attributed to Ovid but of disputed authenticity, the epistle of Sappho to Phaon is notoriously the one which has most perplexed scholars. Most philologists at the end of the 19th century asserted the Ovidian paternity of the epistle; but in recent years the discussion has flared up once again, especially following an important contribution, tending in the opposite direction, by R. J. Tarrant, and today, above all in Anglo-American studies, the pendulum seems to be swinging more in the direction of inauthenticity, according to the movement typical in debates of this kind. The present article obviously does not intend to discuss the whole question once again nor to reaffirm tout court the attribution to Ovid, but brings to the attention of scholars certain arguments which should not be neglected in the discussion (and which point in the direction of authenticity). I do not mean to underestimate the linguistic, stylistic, and metrical anomalies which scholars up to Tarrant and beyond have imputed to the epistula Sapphus, but rather to indicate some characteristics, above all of compositional technique, which have not been considered but which I think have a not insignificant weight in the debate on authenticity.


2009 ◽  
Vol 63 (5) ◽  
pp. 480-492
Author(s):  
Christoph Joest

AbstractSince Jerome's Latin translation of the monastic rules attributed to Pachomius (287-347) these have never vanished from the memory and the tradition of Western monasticism. This contrasts strongly with a cluster of rules written in Coptic. These were not published until the 19th century, and in accordance with the edition of Louis-Théophile Lefort they are usually called the 'règlements' (regulations) of Horsiese. This attribution has, however, been questioned. The present article aims to offer a sound basis for the view that Horsiese is indeed the author of these rules.


Author(s):  
C.H. van Rhee

AbstractThe present article discusses the powers of the judge in civil litigation in three jurisdictions that have been influenced by the French Code of Civil Procedure (1806). It shows that in the 19th century these jurisdictions adopted French law but at the same time tried to reduce party autonomy by increasing the judge's directive powers. This approach was most successful in Geneva. In The Netherlands, changes in the judge's position were less pronounced, whereas a 19th century Belgian draft code, which contained a number of measures that would have increased the judge's case-management powers, was not adopted in practice.


Virittäjä ◽  
2017 ◽  
Vol 121 (3) ◽  
Author(s):  
Aila Mielikäinen

Suomalaisen murteentutkimuksen alku sijoittuu 1800-luvulla ajankohtaan, jolloin tieteellistä suomen kieltä ei vielä ollut olemassa. Kielestäkin oli kirjoitettu suomeksi vähän, ja kieliopit olivat suurimmaksi osaksi muunkielisiä. Suomenkielisistä kieliopeista saatu terminologia ei riittänyt murteiden äänneopin käsittelyyn, eli suomeksi kirjoittavilta tutkijoilta puuttuivat sopivat metakielen mallit. Tässä artikkelissa tarkastellaan, miten eri murteiden tyypillisiä piirteitä nimettiin ja kuvailtiin murteentutkimuksen ensimmäisinä vuosikymmeninä. Aineistona ovat 1860‒1890-luvuilla julkaistut tutkimukset, jotka edustavat vertailevaa, deskriptiivistä tutkimussuuntaa. Euroopassa 1870-luvulla tapahtunut paradigman muutos deskriptiivisestä historioivaan tutkimukseen (nuorgrammaattinen tutkimussuunta) saavutti suomalaisen murteentutkimuksen vasta 1890-luvulla. Sitä ennen murteita verrattiin kieliopeissa esitettyyn kirjakieleen. Tutkijat tunsivat hyvin suomen kielen rakenteen, mutta he pystyivät jossain määrin selittämään myös murrevarianttien taustoja ja syntyä. Analyysit eivät siten ole niin synkronisia kuin käytetyn metodin perusteella voisi olettaa. Artikkelissa tarkastellaan metakieltä myös tutkimusajankohdan kielellisessä kontekstissa. 1800-luvun kielenuudistuksessa oli yhtenä tavoitteena uudissanaston oma­peräisyys, ja tieteellisille termeillekin pyrittiin luomaan suomenkieliset vastineet. Murre­tutkimusten terminologia sisältää sekä vierasperäistä että omaa sanastoa, ja osa siitä on säilynyt dialektologiassa nykypäivään asti. Ennestään tutuille sanoille annettiin kieli­tieteellisessä kontekstissa uusi merkitys, ja lisäksi luotiin tarpeen mukaan uusia johdoksia. Sananvalinnat saattavat joskus kuulostaa kansanomaisilta ja muistuttaa jopa nykyistä kansanlingvististä metakieltä. On kuitenkin otettava huomioon, että sanojen tyylisävyt ovat muuttuneet ja että nykykielen ekspressiivisillä ja affektiivisilla sanoilla on voinut olla 1800-luvulla neutraalimpi merkitys. The metalanguage of the first Finnish-language studies in dialectology The roots of Finnish dialectology go back to a point in the 19th century when scholarly Finnish did not yet exist. Little had been written on linguistics in Finnish, and grammars were often in languages other than Finnish. The terminology gleaned from grammars written in Finnish for the treatment of dialectal phonology was insufficient, i.e., scholars writing in Finnish lacked suitable metalinguistic models. The present article examines the terminology used to describe typical features of a variety of dialects during the first decades of dialectology. The primary corpus of data consists of studies, published from 1860 until the 1890s and which represent a comparative descriptive approach. The paradigmatic change from descriptive to historical dialectology in Europe (during the 1870s) did not reach Finland until two decades later. Prior to this, dialects were compared to the literary language presented in grammars. While scholars were well acquainted with the structure of the Finnish language, they could also explain, to some degree, the background and birth of dialectal variations. For this reason, analyses are not as synchronic as the method used might suggest. The article also studies metalanguage in the linguistic context of the specific point of time in question. One of the aims of the language reforms of the 19th century was a Finnish-language-based collection of neologisms, an attempt to create Finnish equivalents for scholarly terms. Dialectological terminology employs both foreign and Finnish vocabulary, and some of these terms persist to this day. Familiar words were given a new meaning in a linguistic context, and new derivatives were created. The choice of words was sometimes popular in tone, occasionally reminiscent of a modern folk linguistic metalanguage. It is, nevertheless, to be noted, that the stylistics of words has changed, and that the stylistic values of expressive and affective words could have had a more neutral shade during the 19th century.


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