61. Er Uendelighed Aktuel Eller Potentiel? På den anden side er der intuitionisterne, som i denne opgave repræsenteresaf LEJ.Brouwer (18811966) og arend heyting (1898-1980). http://www.filosofi.net/Afhandlinger/Html/uendelighed.htm

Uendelighed, aktuel eller potentiel? er et BA-projekt ved: Center for Filosofi, Filosofisk Institut Odense Universitet, Syddansk Universitet Af Lisbeth Jørgensen lisbeth_jorgensen@yahoo.com Vejleder: Cynthia M. Grund Forside: Georg Cantor og L.E.J.Brouwer set med uendelighedens brilleglas Afleveret d. 8/1 2001 Indholdsfortegnelse Problemformulering Indledning Uendelighedens paradokser Baggrundshistorien for distinktionen mellem aktuel og potentiel uendelighed ... Litteraturliste Problemformulering Er uendelighed aktuel eller potentiel? Hvad er argumenterne for at uendelighed er aktuel henholdsvis potentiel? Hvilke nye problemer udløser disse argumenter? Indledning Hvad er uendelighed? Findes uendelighed, er der noget uendeligt i verden? Eller er uendelighed bare noget vi bruger som begreb, en slags grænse som egentlig ikke er der. I det overordnede spørgsmål om hvad uendelighed er, ligger også en undersøgelse af tid og rum, men jeg vil i denne opgave begrænse mig til den matematiske uendelighed. Således hører denne opgave ind under matematikkens filosofi. Min filosofiske indgangsvinkel til dette emne er at tage udgangspunkt i de paradokser der opstår ved nærmere betragtning af uendelighed. Man kan så spørge hvilken opfattelse af uendelighed der har betydning for at de forskellige paradokser opstår. Kan de forskellige forklaringer af matematisk uendelighed give en løsning på paradokserne, uden at nye opstår? Uendelighed optræder i matematikken bl.a. i mængdelære og i geometri. Mængden af naturlige tal er uendelig stor; uanset hvor langt man tæller, er det altid muligt at tælle én til. Der er således ikke noget største naturligt tal – enhver kandidat til et sådant kan med det samme blive større ved at lægge én til. I geometriens studie af rummet kan en linje deles uendeligt mange gange, og ethvert interval kan blive underinddelt i flere underinddelinger. Den tanke at en proces kan fortsættes i det uendelige, introducerer uendelighed som potentiel; uendelighed er aldrig noget der kan nås. I vores standard aritmetik (tallære) opfattes uendelighed på den anden side også som aktuel: Mængden af naturlige tal opfattes som

62. Full Alphabetical Index Translate this page 2275) Herschel, Caroline (1760*) Herschel, John (2821*) Herstein, Yitz (295*) Hesse,Otto (165*) Heuraet, Hendrik van (170) heyting, arend (62*) Higman, Graham http://www.maththinking.com/boat/mathematicians.html

Full Alphabetical Index Click below to go to one of the separate alphabetical indexes A B C D ... XYZ The number of words in the biography is given in brackets. A * indicates that there is a portrait. A Abbe , Ernst (602*) Abel , Niels Henrik (2899*) Abraham bar Hiyya (641) Abraham, Max Abu Kamil Shuja (1012) Abu Jafar Abu'l-Wafa al-Buzjani (1115) Ackermann , Wilhelm (205) Adams, John Couch Adams, J Frank Adelard of Bath (1008) Adler , August (114) Adrain , Robert (79*) Adrianus , Romanus (419) Aepinus , Franz (124) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (313*) Aitken , Alec (825*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (861) al-Nasawi , Abu (681) al-Nayrizi , Abu'l (621) al-Qalasadi , Abu'l (1247) al-Quhi , Abu (1146) al-Samarqandi , Shams (202) al-Samawal , Ibn (1569) al-Sijzi , Abu (708) al-Tusi , Nasir (1912) al-Tusi , Sharaf (1138) al-Umawi , Abu (1014) al-Uqlidisi , Abu'l (1028) Albanese , Giacomo (282) Albategnius (al-Battani) (1333*)

63. Citations: Interpretation Of Analysis By Means Of Constructive Functionals Of Fi Interpretation of analysis by means of constructive functionals of finite types.In arend heyting, editor, Constructivity in mathematics, pp. 101128. http://citeseer.nj.nec.com/context/321/0

25 citations found. Retrieving documents... G. Kreisel, Interpretation of Analysis by means of constructive Functionals of finite Types , in: A. Heyting (ed.), Constructivity in Mathematics, North-Holland 1959, pp. 101-128 Home/Search Document Not in Database Summary Related Articles Check This paper is cited in the following contexts: The Modified Realizability Topos - van Oosten (1996) (1 citation) (Correct) ....logical consequences. Some important subcategories of Mod are described, and a general logical principle is derived, which holds in the larger topos and implies the well known Independence of Premiss principle. Introduction The notion of modified realizability originates with Kreisel s (see also [Kre62] While Kreisel intended to give a consistency proof for the system HA and, accordingly, defined a straightforward extension of Kleene s realizability to this typed system, today s meaning of the term modified realizability derives from Troelstra s collapse of this . G. Kreisel, Interpretation of Analysis by means of constructive Functionals of finite Types , in: A. Heyting (ed.), Constructivity in Mathematics, North-Holland 1959, pp. 101-128

64. Neue Seite 1 Translate this page van Heuraet, Hendrik (1633 - 1660). heyting, arend (1898 - 1980). Hilbert,David (23.1.1862 - 14.2.1943). Hill, George William (1838 - 1914). http://www.mathe-ecke.de/mathematiker.htm

Abbe, Ernst (1840 - 1909) Abel, Niels Henrik (5.8.1802 - 6.4.1829) Abraham bar Hiyya (1070 - 1130) Abraham, Max (1875 - 1922) Abu Kamil, Shuja (um 850 - um 930) Abu'l-Wafa al'Buzjani (940 - 998) Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843) Aepinus, Franz Ulrich Theodosius (13.12.1724 - 10.8.1802) Agnesi, Maria (1718 - 1799) Ahlfors, Lars (1907 - 1996) Ahmed ibn Yusuf (835 - 912) Ahmes (um 1680 - um 1620 v. Chr.) Aida Yasuaki (1747 - 1817) Aiken, Howard Hathaway (1900 - 1973) Airy, George Biddell (27.7.1801 - 2.1.1892) Aithoff, David (1854 - 1934) Aitken, Alexander (1895 - 1967) Ajima, Chokuyen (1732 - 1798) Akhiezer, Naum Il'ich (1901 - 1980) al'Battani, Abu Allah (um 850 - 929) al'Biruni, Abu Arrayhan (973 - 1048) al'Chaijami (? - 1123) al'Haitam, Abu Ali (965 - 1039) al'Kashi, Ghiyath (1390 - 1450) al'Khwarizmi, Abu Abd-Allah ibn Musa (um 790 - um 850) Albanese, Giacomo (1890 - 1948) Albert von Sachsen (1316 - 8.7.1390)

65. Practical Foundations Of Mathematics Collected Works Philosophy and Foundations of Mathematics, volume 1. NorthHolland,1975. Edited by arend heyting. Wiley, 1990. Hey56 arend heyting. http://www.dcs.qmul.ac.uk/~pt/Practical_Foundations/html/bib.html

Practical Foundations of Mathematics Paul Taylor Chapter 9 Bibliography Samson Abramsky and Achim Jung. Domain theory. In Samson Abramsky et al., editors, Handbook of Logic in Computer Science , volume 3, pages 1-168. Oxford University Press, 1994. Peter Aczel. Non-well-founded Sets . Number 14 in Lecture Notes. Center for the Study of Language and Information, Stanford University, 1988. Locally Presentable and Accessible Categories . Number 189 in London Mathematical Society Lecture Notes. Cambridge University Press, 1994. Pierre Ageron. The logic of structures. Journal of Pure and Applied Algebra Thorsten Altenkirch, Martin Hofmann, and Thomas Streicher. Categorical reconstruction of a reduction-free normalisation proof. In Peter Johnstone, David Pitt, and David Rydeheard, editors, Category Theory and Computer Science VI , number 953 in Lecture Notes in Computer Science, pages 182-199. Springer-Verlag, 1995. Roberto Amadio and Pierre-Louis Curien. Domains and Lambda-Calculi . Number 46 in Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, 1998.

66. Practical Foundations Of Mathematics REMARK 2.4.3 arend heyting and Andrei Kolmogorov independently gavethis interpretation of intuitionistic logic in 1934. To prove. http://www.dcs.qmul.ac.uk/~pt/Practical_Foundations/html/s24.html

Practical Foundations of Mathematics Paul Taylor Propositions as Types Although the predicate calculus underlies Zermelo type theory, it is always foolish to assert that one piece of mathematics is more basic than another, because a slight change of perspective overturns any such rigid orders. Indeed Jan Brouwer (1907) considered that logical steps rest on mathematical constructions. One of the most powerful ideas in logic and informatics in recent years has been the analogy between =0pt omitted tabular environment which puts propositions and types on a par. This is sometimes called the Curry-Howard isomorphism Formulae correspond to types and their deductions to terms. Crudely, a type gives rise to the proposition that the type has an element, and a proposition to the type whose elements are its proofs. Indeed, as soon as we take some care over it, we have no alternative but to treat the hypothesis for alongside the generic value of and the bound variable of l . Similarly Sections and show that midconditions go with program-variables. Other analogies with types

67. Collected Works Freudenthal. Subject Mathematics. Added Entry heyting, A. (arend), 1898CALL NO QA267 B79 1990 AUTHOR Buchi, J. Richard. TITLE Works. http://lib.nmsu.edu/subject/math/mbib.html

C OLLECTED W ORKS F M ATHEMATICIANS B IBLIOGRAPHY CALL NO: QA3 A14 1881 AUTHOR: Abel, Niels Henrik, 1802-1829. MAIN TITLE: OEuvres completes de Niels Henrik Abel. EDITION: Nouv. ed., publiee aux frais de l'etat norve-gien par L. Sylow PUBLISHER: Christiania [Sweden] Grondahl, 1881. LOCATION: Branson Material: 2 v. in 1. 28 cm. Contents: t. 1. Memoires publies par Abel.t. 2. Memoires posthumes d'Abel Subject: Mathematics. cm Added Entry: Sylow, Peter Ludvig Mejdel, 1832- Added Entry: Lie, Sophus, 1842-1899. CALL NO: QB3 A2 AUTHOR: Adams, John Couch, 1819-1892. MAIN TITLE: The scientific papers of John Adams Couch, edited by William Grylls Adams, with a memoir by J. W. L. Glaisher. PUBLISHER: Cambridge, University press, 1896-1900. LOCATION: Branson V.1 and V.2 Material: 2 v. front. (port.) fold. map, facsims., diagr. 30 cm. Contents: v. 1. Biographical notice, by J. W. L. Glaisher. [Original papers published by the author during his lifetime, 1844-1890, ed. by William Grylls Adams]v. 2. pt. 1. Extracts from unpublished manuscripts, ed. by Ralph Allen Simpson. pt. 2. Terrestial magnetism, ed. by William Grylls Adams. Subject: Geomagnetism.

68. Books Published In 1956 82, *****. Konrad Knopp, Infinite Sequences and Series, Mathematics,176, *****. arend heyting, Intuitionism, Mathematics, 50, *****.CS http://y-intercept.com/pub_l.html?year=1956

69. Einführung In Die Philosophie Der Mathematik Translate this page 52. Wiederabgedruckt in Benacerraf/Putnam (1983). heyting, arend (1956). IntuitionismAn Introduction. Amsterdam North-Holland. Hilbert, David (1899). http://www.ifi.unizh.ch/groups/ailab/teaching/NAISemi01/Presentations/Philosophi

gwalti@access.unizh.ch ), Nov. 2001 Einleitung Immanuel Kants Philosophie der Mathematik Der Logizismus von Gottlob Frege und Bertrand Russell Der Formalismus von David Hilbert Der Intuitionismus von Luitzen E.J. Brouwer Der Konventionalismus der logischen Empiristen Der Naturalismus von Philip Kitcher Literaturangaben Einleitung 1. Immanuel Kants (1724-1804) Philosophie der Mathematik In seiner Erkenntnistheorie Eine analytisch wahre Aussage Synthetische Aussagen Eine Erkenntnis ist nach Kant a priori Rechtfertigung Im Gegensatz zu den apriorischen Erkenntnissen sind aposteriorische Erkenntnisse synthetische Aussagen a priori synthetische Aussagen a posteriori analytische Aussagen a priori analytische Aussagen a posteriori Zu (3) und (4) Zu (1) und (2) Kant geht in seiner Theorie der Mathematik davon aus, dass die Aussagen der reinen Mathematik synthetisch a priori sind. Wie kommt er dazu, dies anzunehmen? „Eben so wenig ist irgend ein Grundsatz der reinen Geometrie analytisch. Dass die gerade Linie zwischen zweien Punkten die kürzeste sei, ist ein synthetischer Satz. Denn mein Begriff vom Geraden enthält nichts von Grösse, sondern nur eine Qualität. Der Begriff des Kürzesten kommt also gänzlich hinzu, und kann durch keine Zergliederung aus dem Begriffe der geraden Linie gezogen werden. Anschauung muss also hier zu Hülfe genommen werden, vermittelst deren allein die Synthesis möglich ist." (B17) 2. Der Logizismus von Gottlob Frege (1848-1925) und Bertrand Russell (1872-1970)

70. # De Schakel - Theaterprogramma 2002-2003 - Niet Schieten! - Jubileert! # arend Edel, Maarten Hennis en Erik Jobben richtten cabaretgroep Niet Schieten! KwaadBloed regie Bruun Kuijt 20002002 Noodlot regie Hetty heyting 1998-1999 http://www.deschakel.a3hosting.nl/110103.htm

Sociaal Cultureel Centrum "De Schakel" Middenwaard 61 1703 SC Heerhugowaard Tel. (072) 571 68 79 Fax (072) 574 56 94 Vrijdag 11 januari 2003 20.15 uur cabaret KLIK HIER VOOR "KWAAD BLOED" UITVERKOCHT Niet Schieten! met "Niet schieten julbileert!" Arend Edel, Maarten Hennis en Erik Jobben richtten cabaretgroep Niet Schieten! op in 1992, als blijkt dat zij de basketballvereniging waar zij lid van Zijn in Weesp, beter weten te vermaken met grappen, dan met doelgerichte Shots. De naam van de groep komt dan niet voor niets uit de periode dat zij meer op de reservebankjes zaten dan op het veld rondliepen. In 1994 wonnen zij het Cameretten Festival . Sinds die tijd heeft de groep zeven theaterprogramma's en vier CD's gemaakt. Om hun tienjarige bestaan te vieren, maakt Niet Schieten! een compilatie uit alle voorstellingen, waarbij ze voor deze ene keer alleen de leuke liedjes en sketches zullen brengen. Deze jubileumvoorstelling is in slechts enkele theaters in Nederland te zien! THEATERPROGRAMMA'S 2002-2004 Kwaad Bloed regie: Bruun Kuijt 2000-2002 Noodlot regie: Hetty Heyting 1998-1999 Petrov regie: Hetty Heyting 1997-1999 Taboe regie: Hetty Heyting 1996-1997 Een vlucht regendruppels regie: Dick van den Heuvel 1994-1995 Natte Narren regie: Onno Rademaker 1993-1994 Natongen in de foyer FESTIVALS Postbank Kleinkunstfestival Amsterdam , finaleplaats Cameretten Rotterdam , Jury- en publieksprijs CD's 2002 Iets 1999 Navelstaren 1996 Liplezen 1993 Acapella (niet meer leverbaar) TV 10-1998 - 03.1999 Cabaretserie 5 Hoog, RTL 5

71. Diccionario De Autores Translate this page (1889-1971) HEYDE, JOHANNES ERICH. (nac. 1892) HEYMANS, GERARDUS. (1857-1930) heyting,arend. (nac. 1898) HIEROCLES DE ALEJANDRÍA. fl. 420 HIEROCLES EL ESTOICO. http://www.cibernous.com/colabora/comunes/diccionario.htm

DICCIONARIO DE AUTORES A B C D ... Z A AALL, ANATHON ABBAGNANO, NICOLA (nac. 1901) ABBT, THOMA ABELARDO (PEDRO) ABENALARIF ABENALSID ABENARABI ABENHAZAM ABENMASARRA ABENTOFAIL ABU SALT ACHILLUNI, ALESSANDRO ACKERMANN, WILHELM ACONCIO, GIACOMO [ACONZIO, CONCIO; ACONTIUS, JACOBUS] entre 1492-1520-ca. 1568 ADAMSON, ROBERT (fallecido 1181) ADELARDO DE BATH (fl. 1100) ADICKES, ERICH ADLER, ALFRED ADLER, MAX ADORNO, THEODOR W[IESENGRUND] AECIO fl. ca. 150 AGRIPPA DE NETTESHEIM, HEINRICH CORNELIUS [HENRICUS CORNELIUS] AHRENS, HEINRICH AJDUKIEWICZ, KAZIMIERZ ALANO DE LILLE (ca. 1128-1202) ALBERINI, CORIANO ALBERT, HANS (nac. 1921) ALBERTO (SAN) ALBINO fl. 180 ALBO, JOSEF [YOSEF] ca. 1380-ca. 1444 ALEJANDRO DE AFRODISIA ALEJANDRO DE HALES (ca. 1185-1245) fl. ca. 300 ALEMBERT, JEAN LE ROND D' ALEXANDER, SAMUEL ALFARABI ALGAZELLI (ALGAZEL) ALIOTTA, ANTONIO ALKINDI ALONSO DE LA VERACRUZ (nac. 1906) ALTHUSSER, LOUIS (nac. 1918) (fallecido 1206/7) AMBROSIO (SAN) ca. 340-397 AMELIO fl. 240 AMMNOIO HERMEIOU [AMMNONIO DE HERMIA] fl. 530

72. No Title 138 arend heyting. Disputation. 139 arend heyting. The intuitionist foundationof mathematics die intuinistische grundlegung der mathematik. http://hjem.get2net.dk/eir/Documents/References/BibTex.html

References A Theory of Objects . Springer, 1996. Alfred V. Aho, Ravi Sethi, and Jeffrey D. Ullman. Compilers - Principles, Techniques and Tools . Addison-Wesley, 1986. Christopher Alexander. Notes on the Synthesis of Form , chapter The Unselfconscious Process, The Selfconscious Process. Oxford University Press, New York, 1979. Christopher Alexander. The Timeless Way of Building , chapter A Pattern Language. Oxford University Press, New York, 1979. Henrik Reif Andersen. An introduction to binary decision diagrams. 1996. Department of Computer Science, Technical University of Denmark. D. M. Armstrong. Against 'ostrich' nominalism: A reply to michael devitt. In D.H.Mellor and Alex Oliver, editors, Properties , Oxford Readings in Philosophy. Oxford University Press, 1997. D. M. Armstrong. Properties. In D.H.Mellor and Alex Oliver, editors, Properties , Oxford Readings in Philosophy. Oxford University Press, 1997. Alessandro Artale, Enrico Franconi, Nicola Guarino, and Luca Pazzi. Part-whole relations in object-centered systems: An overview. ASP. An asp you can grasp: The abss of active server pages. ASP Tips.

73. Untitled Translate this page arend heyting (1898-1980) http//www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/heyting.html(Wie hierüber Brouwer) Informationen (in engl. http://www.kirstin-zeyer.de/nl.htm

Philosophie in den Niederlanden Philosphie = 'filosofie' (Disziplin) und = 'wijsbegeerte' (das 'Streben nach Weisheit'). Interessanterweise sind die Niederländer in bezug auf das Wort 'Philosophie' um einen Begriff reicher als wir. Die 'Einführung' dieser Rubrik setzt keine niederländischen Sprachkenntnisse voraus. Die Linksammlung ('Phil-Links') hingegen möchte ausdrücklich eine Hilfestellung geben bei der Suche nach (in vorwiegend niederländischer Sprache gehaltenen) Webseiten in den Niederlanden. Hinweise zum Studium der Niederländischen Philologie oder Niederlandistik in Deutschland ('Nl-Studium') sowie allgemein nützliche Links ('Links NL'), zum Beispiel zum Fremdenverkehr, Bücherbestellungen etc. finden Sie in dieser Rubrik ebenfalls. Gibt es typisch niederländische Philosophie? Dieser Frage ist Cornelis Verhoeven in einem Beitag für das Filosofie Magazine (s.u.) nachgegangen. Um das Ergebnis vorwegzunehmen: Verhoeven zufolge handelt es sich hierbei um eine geradezu unsinnige Auseinandersetzung, da Niederländische Philosophie seiner Meinung nach schlicht Philosophie auf Niederländisch sei, wie niederländische Poesie eben Poesie auf Niederländisch. "

74. Www.math.niu.edu/~rusin/known-math/99/photos Hevner, Alan R. Hewish, Antony Hewitt, Edwin Hewitt, WT Hewlett, William Heyden,Anders heyting, arend Higman, DG Higman, Graham Hilands, Thomas W. Hilb, Emil http://www.math.niu.edu/~rusin/known-math/99/photos

75. Untitled The heyting Centenary (UvA) There will be several activities to commemoratethe fact that arend heyting (18981980) was born a hundred years ago. http://www.risc.uni-linz.ac.at/research/category/risc/conferences/past/heyting-c

The Heyting Centenary (UvA) There will be several activities to commemorate the fact that Arend Heyting (18981980) was born a hundred years ago. A regular update with information on the actitivities may be found at the following internet page: http://www.wins.uva.nl/research/illc/heyting.html For more information, when available, you can also mail ingridvl@wins.uva.nl . Symposium 25 september 1998, Amsterdam. place: Agnietenkapel Organized by the Institute for Logic, Language and Information Concept programme, with names of speakers only, no titles as yet. 9.3010.00 Opening and introduction. 10.0011.00 U. Berger 11.1512.15 Ghilardi 12.1513.30 lunch 13.3014.30 Moerdijk 14.4515.45 Visser/de Jongh 16.0017.00 Coquand. Thematic day, september 26, Utrecht Place: a location near the central station. Organized by the Dutch Logic Association. Opening, biographical introduction. 1. (Goran Sundholm) Early history of intuitionistic logic. 2. (Dennis Hesseling) The reactions to intuitionism before 1930. Lunch 3. (Miriam Franchella) Heyting's notes on solipsism. 4. (M.D.G. Swaen) Heyting's ideas on the teaching of mathematics.

76. Historical Notes kind during the existence of the sector was a Summer School and Conference on MathematicalLogic honourably dedicated to the 90th anniversary of arend heyting. http://www.fmi.uni-sofia.bg/fmi/logic/skordev/history.htm

Some short historical notes on Mathematical Logic in Sofia by Dimiter Skordev As well known, the foundations of mathematics have been and still are an important background and an object of study for Mathematical Logic. The interest in them has a long tradition at Sofia. For example, several competently written articles on the foundations of arithmetic were published in the Journal of the Physico-Mathematical Society in Sofia almost a century ago, in particular a series of articles by an author publishing under the alias "Uni". (Corresponding references can be found in the survey [ ]). Mention may here be made also of a lecture of the German mathematician Otto Blumenthal (1876-1944) which was held in Sofia in 1935. The title of this lecture was "The life and the scientific work of David Hilbert", and the contents of the lecture is known from its Bulgarian translation [ ]. A short description of Hilbert's work on the foundations of arithmetic and logic can be found on pp. 49-50 there, namely the idea of Hilbert's program is briefly explained (without using the term "Mathematical Logic" and, unfortunately, keeping off the then already known problems encountered by that program). One may be curious about the earliest occasions when Mathematical Logic was explicitly mentioned at Sofia in public. The first such occasion known to me is a lecture held in 1945 by the Bulgarian mathematician Yaroslav Tagamlitzki (1917-1983). An information about it can be found in [

77. Whither "intuitionistic"? the formalization of intuitionistic reasoning. Thereby he draw on earlierwork done by arend heyting. A good source to enhance the http://www.cis.upenn.edu/~bcpierce/types/archives/1997-98/msg00212.html

[Prev] [Next] [Index] [Thread] Whither "intuitionistic"? To types@cs.indiana.edu Subject : Whither "intuitionistic"? From rf@rainer-fischbach.com Date : Mon, 20 Oct 1997 23:12:11 +0100 Delivery-Date : Mon, 20 Oct 1997 16:01:42 -0500 mailto:rf@rainer-fischbach.com http://www.rainer-fischbach.com http://www.ba-stuttgart.de/~rf Prev: Re: Whence "intuitionistic"? Next: Formal Methods Day at Royal Holloway Index(es): Main Thread

78. Www.eeng.dcu.ie/~tkpw/hoover/hoover.txt of the Paradox of the Liar, 1954 September 1. Speech, Association for Symbolic Logic,Amsterdam, Holland 16 General Correspondence 17 heyting, arend, 1954 18 http://www.eeng.dcu.ie/~tkpw/hoover/hoover.txt

79. Hoorcolleges (di. 11--13) latere wiskunde hoogleraar LEJ Brouwer. Twintig jaar later werd dezelogica geformaliseerd door zijn leerling en opvolger A. heyting. http://turing.wins.uva.nl/~jaspars/hc/hoorcolleges.html

Hoorcolleges (di. 1113) 1. Propositielogica 2 September. In dit college introduceren we de taal en de semantiek van propositielogica (hoofdstuk 2 van het boek). Daarbij gaan we nog wat uitgebreider in op alternatieve interpretaties van de propositielogica: proposities en (digitaal) rekenen en proposities en informatiegroei 9 September. Vandaag beginnen we het college met een overblijvertje van het vorige college digitaal rekenen en Boolese circuits . Daarna behandelen we het derde hoofdstuk van het boek. We gaan het begrip geldig gevolg semantische tableau's . Laat je hierbij niet misleiden door het predicaat "semantisch", het is een werkelijk afleidingssysteem, d.w.z. een systeem op basis van pure symbolische herschrijving. "Semantisch" refereert hier aan het feit dat de tableau's bedacht zijn op basis van semantiek. Met een semantisch tableau beschrijf je op een symbolisch structurele manier dat een tegenmodel voor een gegegeven propositie logische redenering uitgesloten is. In het vijfde college zullen we bewijzen zien voor de correctheid en volledigheid van deze methode. Voor dit college kan je al het materiaal vinden in hoofdstuk 3 van het boek en de handout van het vorige college.

80. Philosophy Of Mathematics Class Notes Philosophy of Mathematics Dr. Carl Posy Greg J. Badros Table of Contents Part I General Survey of Philosophy of Mathematics 1 I.1 Prehistory of numbers 1 I.2 Greek Development of Math 2 2.1 Flowering of the Pythagoreans 3 http://www.cs.washington.edu/homes/gjb/doc/philmath.htm

Philosophy of Mathematics Class Notes PHL-113 Dr. Carl Posy Duke University Fall 1992 Prepared by Greg J. Badros Table of Contents Part I: General Survey of Philosophy of Mathematics 1 I.1 Prehistory of numbers 1 I.2 Greek Development of Math 2 2.1 Flowering of the Pythagoreans 3 2.2 Downfall of the Pythagoreans 3 2.3 Greek Reaction to the Downfall 4 I.3 Road to Non-Euclidean Geometry 12 3.1 Hilbert's axiomatization of Geometry 12 3.2 The Evaluation of non-Euclidean Geometry 13 I.4 History of the concept of a number 16 I.5 Conceptual Foundations of Mathematics 22 5.0 General Overview of Reactions to Berkeley 23 5.0.1 Kant's Philosophy of Mathematics 24 5.1.1 Introduction of the Notion of a Limit 25 5.1.2 Arithmetization of Mathematics 26 5.2 Cantor 29 5.3.1 Peano 33 5.3.2 Frege 34 I.6 Two of the Three Reactions to the Third Crisis 37 6.1 Platonistic Reaction 37 6.2 Hilbert's Program 40 Part II: Intuitionism, A Third Direction 46 II.1 General Introduction to Intuitionism 46 II.2 Intuitionist's Construction of the Natural Numbers 47 II.3 Intuitionist's Construction of the Real Numbers 47

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