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         Heyting Arend:     more detail
  1. Intuitionism, An Introduction: Third Revised Edition by Arend Heyting, 2011-01-20
  2. Constructivity in mathematics: Proceedings of the colloquium held at Amsterdam, 1957 (Studies in logic and the foundations of mathematics) by Arend Heyting, 1959
  3. Kolmogorov, Heyting and Gentzen on the intuitionistic logical constants *.: An article from: Crítica by Gustavo Fernandez Diez, 2000-12-01
  4. Semantical Investigations in Heyting's Intuitionistic Logic (Synthese Library) by Dov M. Gabbay, 1981-03-31
  5. ERKENNTNIS, Zugleich Annalen der Philosophie... BAND 2, HEFT 2-3, 1931; Bericht über die 2. Tagung für Erkenntnishlehre der exakten Wissenschaften Königsberg 1930 by Rudolf & Hans Reichenbach, eds. Arend Heyting, Johann von Neumann, Otto Carnap, 1931
  6. Mathematische Grundlagenforschung Intuitionismus-Beweistheorie by A. [Arend] HEYTING, 1980

41. Sobre El Axioma X De Heyting
Translate this page En la formalización que presenta arend heyting. para la lógica intuicionista estaexpresión heyting, arend Intuitionism. North Holland Amsterdam, 1956.
http://galileo.fcien.edu.uy/sobre_el_axioma_x_de_heyting.htm
SOBRE EL AXIOMA X DE HEYTING
Robert Calabria La ley de Scoto o ex falso quodlibet , esto es ØA®(A®B) fue considerada desde siempre una paradoja para la Lógica Clásica al menos en el débil sentido de “resultado chocante”; así que uno no puede menos de preguntarse cómo en un sistema intuicionista llega a tener la dignidad de un axioma. En la formalización que presenta Arend Heyting para la lógica intuicionista esta expresión corresponde al axioma X . Ciertamente, el mismo Heyting se siente obligado a dar una especie de justificación del mismo-y, como anota Susan Haack en , p.109, es significativo que considerara que sólo este axioma requiriese justificación-, ofreciéndola en , p.102, como sigue: Axiom X may not seem intuitively clear. As a matter of fact, it adds to the precision of the definition of implication. You remember that A®B can be asserted if and only if we possess a construction which , joined to the construction A , would prove B Now suppose that A that is, we have deduced a contradiction from the supposition that

42. Logician's Year
9 May, *, heyting, arend, (* 1898). 13 May, +, Wang, Hao, (+ 1995). 18 May, *,Russell, Bertrand Arthur William, (* 1872). 20 May, *, Wang, Hao, (* 1921)
http://www.volny.cz/logici/vyroci/english.html
The Logician's Year
January February March April ... December
January
5 Jan Kleene, Stephen Cole 6 Jan Cantor, Georg 12 Jan Hintikka, Jaakko 14 Jan Carroll, Lewis Tarski, Alfred Gödel, Kurt 19 Jan Ramsey, Frank Plumpton 23 Jan Hilbert, David 26 Jan Kleene, Stephen Cole 27 Jan Carroll, Lewis
February
2 Feb Russell, Bertrand Artur William 3 Feb Lewis, Clarence Irving 6 Feb Arnauld, Antoine 8 Feb von Neumann, Johannes 11 Feb Post, Emil Leon 12 Feb Herbrand, Jean Dedekind, Richard 13 Feb £ukasiewicz, Jan 14 Feb Hilbert, David 15 Feb Whitehead, Alfred North 16 Feb Nicod, Jean 17 Feb Fraenkel, Adolf Abraham 22 Feb Ramsey, Frank Plumpton 27 Feb Brouwer, Luitzgen Egbertus Jan
March
3 Mar Cantor, Georg 5 Mar Barwise, Jon 6 Mar Davidson, Donald 7 Mar Montague, Richard 18 Mar de Morgan, Augustus Carnap Rudolf 23 Mar Skolem, Thoralf 24 Mar Lorenzen, Paul 25 Mar Ackermann, Wilhelm
April
2 Apr Vaught, Robert Lawson 4 Apr Venn, John Vaught, Robert Lawson 12 Apr Lewis, Clarence Irving 19 Apr Peirce, Charles Sanders 20 Apr Peano, Giuseppe 21 Apr Post, Emil Leon 26 Apr Wittgenstein, Ludwig 28 Apr Gödel, Kurt

43. Logikùv Rok
Translate this page Svìtlé pivo, heyting, arend, (* 1898). 13. 5. Èerné pivo, Wang, Hao, (+ 1995).18. 5. Svìtlé pivo, Russell, Bertrand Arthur William, (* 1872)
http://www.volny.cz/logici/vyroci/
Logikùv rok
Leden Únor Bøezen Duben ... Prosinec
Leden
Kleene, Stephen Cole Cantor, Georg Hintikka, Jaakko Carroll, Lewis Tarski, Alfred Gödel, Kurt Ramsey, Frank Plumpton Hilbert, David Kleene, Stephen Cole Carroll, Lewis
Únor
Russell, Bertrand Artur William Lewis, Clarence Irving Arnauld, Antoine von Neumann, Johannes Post, Emil Leon Herbrand, Jean Dedekind, Richard £ukasiewicz, Jan Hilbert, David Whitehead, Alfred North Nicod, Jean Fraenkel, Adolf Abraham Ramsey, Frank Plumpton Brouwer, Luitzgen Egbertus Jan
Bøezen
Cantor, Georg Barwise, Jon Davidson, Donald Montague, Richard de Morgan, Augustus Carnap Rudolf Skolem, Thoralf Lorenzen, Paul Ackermann, Wilhelm
Duben
Vaught, Robert Lawson Venn, John Vaught, Robert Lawson Lewis, Clarence Irving Peirce, Charles Sanders Peano, Giuseppe Post, Emil Leon Wittgenstein, Ludwig Gödel, Kurt Wittgenstein, Ludwig
Kvìten
Löwenheim, Leopold Heyting, Arend Wang, Hao Russell, Bertrand Arthur William Wang, Hao Zermelo, Ernst Skolem, Thoralf
Èerven
Turing, Alan Mathison Church, Alonzo von Wright, Georg Henrik von Wright, Georg Henrik Turing, Alan Mathison

44. IPM - Homepage
In 1930, Brouwer s student arend heyting gave the first axiomatization ofintuitionistic logic. Kripke semantics for intuitionistic logic was invented by
http://www.ipm.ac.ir/IPM/activities/ViewProgramInfo.jsp?PTID=206

45. Luitzen Egbertus Jan Brouwer
Brouwer s principal students were Maurits Belinfante and arend heyting; thelatter, in turn, was the teacher of Anne Troelstra and Dirk van Dalen.
http://plato.stanford.edu/entries/brouwer/
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Luitzen Egbertus Jan Brouwer
In classical mathematics, he founded modern topology by establishing, for example, the topological invariance of dimension and the fixpoint theorem. He also gave the first correct definition of dimension. In philosophy, his brainchild is intuitionism, a revisionist foundation of mathematics. Intuitionism views mathematics as a free activity of the mind, independent of any language or Platonic realm of objects, and therefore bases mathematics on a philosophy of mind. The implications are twofold. First, it leads to a form of constructive mathematics, in which large parts of classical mathematics are rejected. Second, the reliance on a philosophy of mind introduces features that are absent from classical mathematics as well as from other forms of constructive mathematics: unlike those, intuitionistic mathematics is not a proper part of classical mathematics.

46. Homepage Of Marc Staudacher - Endnote Library
Edited by heyting, arend / Robinson, Abraham / Suppes, Patrick / Mostowski, Andrzej.2 vols. Vol. 1, Studies in Logic and the foundations of mathematics.
http://wwwhomes.uni-bielefeld.de/mstaudacher/philo8.html
Endnote library (periodically updated) Home Presentations Papers and notes Endnote library ... Links
Achinstein, Peter. "Types of explanation." In The encyclopedia of philosophy; Supplement , edited by Edwards, Paul, 168-170. New York: Macmillan [u.a.], 1996. Aho, Alfred V. / Ullman, Jeffrey D. The theory of parsing, translation and compiling . Edited by Forsythe, George. 2 vols. Vol. 1, Series in automatic computation . Englewood Cliffs, NJ: Prentice Hall, 1972a. The theory of parsing, translation and compiling . Edited by Forsythe, George. 2 vols. Vol. 2, Series in automatic computation . Englewood Cliffs, NJ: Prentice Hall, 1972b. Aldrich, Virgil C. "On seeing bodily movements as actions." American Philosophical Quarterly 4, no. 3 (1967): 222-230. Alexander, H. G. "More about the paradigm-case argument." Analysis Angst, Walter. Das Ausdrucksverhalten des Javaneraffen Macaca fascicularis Raffles 1821: eine Einf¼hrung . Berlin [u.a.]: Parey, 1974. Anscombe, Gertrude E. M. Intention . 2 ed. Oxford: Basil Blackwell, 1963.

47. BIBLIOGRAPHY
heyting, arend. “The Intuitionist Foundations of Mathematics” In Philosophy ofMathematics. Eds. Paul Benacerraf and Hillary Putnam.
http://www.bdoghouse.com/Thesis/BIBLIO.html
BIBLIOGRAPHY Agassi, Joseph. “Leibniz's Place in the History of Physics.” Journal of the History of Ideas Alexander, Samuel. “Spinoza and Time.” In Studies in Spinoza: Critical and Interpretive Essays . Ed. S. Paul Kashap. Berkeley: University of California Press, 1972. Aristotle. Categorieae, De Interpretatione, Analytica Priora, Analytica Posteriora, Physica, De Caelo, and Metaphysica In The Basic Works of Aristotle Ed. Richard McKeon. New York: Random House, 1941. Benacerraf, Paul and Hilary Putnam, eds. Philosophy of Mathematics. Englewood Cliffs, N.J.: Prentice-Hall, 1964. Bennett, Jonathan. Kant's Analytic. Cambridge: Cambridge University Press, 1966. A Study of Spinoza's Ethics. Indianapolis: Hackett Publishing Co., 1984. Berkeley, George. A Treatise Concerning the Principles of Human Knowledge . LaSalle, Ill.: Open Court, 1963. Berkson, William. Fields of Force: The Development of a World View from Faraday to Einstein. New York: Bernoulli, Daniel. Hydrodynamica Trans. Thomas Carmody and Helmut Kobus. New York: Dover, 1968. Bohm, David.

48. Philosophy Of Mathematics Syllabus
heyting, arend (1931). “The intuitionist foundations of mathematics,” Symposiumon the Foundations of Mathematics, Erkenntnis (1931), translated by Erna
http://www.usiouxfalls.edu/~jadouma/WebDocs/390Philsyl.J05.htm
Truth and Beauty: Topics in the Philosophy of Mathematics MAT 390 University of Sioux Falls Interim, 2005 Instructor: Jason Douma Time: MTWRF 9:30 – 11:30 a.m. Office: Science Center 116 Place: Cleveland Center 106B Phone: (605) 331-6750 (office) email: jason.douma@USiouxFalls.edu (605) 362-4727 (home) jason douma (on local network) Webpage: www.usiouxfalls.edu/~jadouma Required Texts: Reuben Hersh, What is Mathematics, Really? , Oxford Press, 1997. Stewart Shapiro, Thinking About Mathematics , Oxford Press, 2000. Readings from other texts are found in the reading list. Office Hours: Monday 8:00 - 9:15 a.m. Tuesday 2:00 - 3:00 p.m. Wednesday 8:00 - 9:15 a.m. Thursday 1:00 - 3:00 p.m. I will also be happy to honor appointments you make. "Mathematics may rightly claim to be the most original creation of the human spirit." Alfred North Whitehead Course Description: When mathematicians say that something is ‘true,’ what do they really mean? In what sense—if at all—do mathematical objects actually exist? What does ‘beautiful mathematics’ look like? Are mathematical structures necessary or contingent?

49. [Phil-logic] Re:Intuitionism-Heyting
quoted in AS Troelstra, arend heyting and His Contributions to Intuitionism ,Nieuw Archief Voor Wiskunde 29 (1981) 123. Also noted in Wim Ruitenberg,
http://philo.at/pipermail/phil-logic/2001-September/000031.html
[Phil-logic] Re:Intuitionism-Heyting
Graham Solomon gsolomon at wlu.ca
Wed Sep 26 18:48:37 CEST 2001 axioms, and deleted those which he thought are nonconstructive. That is hardly possible. Hilbert-Ackermann would seem a more likely source of inspiration. Yes, I likely misremembered the story. More information about the Phil-logic mailing list

50. FOM: Re: Constructive Mathematics
The following is an extract of what arend heyting wrote in his 1956 IntuitionismAn Introduction (This is part of an excellent dialogue,
http://www.cs.nyu.edu/pipermail/fom/2000-May/004002.html
FOM: Re: constructive mathematics
V. Sazonov V.Sazonov at doc.mmu.ac.uk
Tue May 30 12:33:33 EDT 2000 Ayan wrote on 27 May (17:40 on my clock): Goes *against* subjectivism? I don't understand. The following is an extract of what Arend Heyting wrote in his 1956: Intuitionism: An Introduction (This is part of an excellent dialogue, between the characters called "Class" (classical mathematician), "Form" (a formalist, seems to refer to a mixture of Hilbert and Carnap), "Int" (an intuitionist, seems to refer to Brouwer), "Letter" (a sort of finitist formalist), "Prag" (a pragmatist, seems a bit like Quine) and a mysterious character called "Sign"): mathematical theorem expresses a purely empirical fact, namely the The characteristic of mathematical thought is, that it does not convey truth about the external world, but is only concerned with mental In fact, mathematics, from the intuitionistic point of view, is a study

51. FOM: Re: Constructive Mathematics
The following is an extract of what arend heyting wrote in his 1956 IntuitionismAn Introduction (This is part of an excellent dialogue,
http://www.cs.nyu.edu/pipermail/fom/2000-May/003991.html
FOM: Re: constructive mathematics
Jeffrey Ketland ketland at ketland.fsnet.co.uk
Sat May 27 15:55:16 EDT 2000 One thing may be worth pointing out, that constructive mathematics (Bishop's style which I understand is the topic of current discussion) is currently seen as working with Intuitionistic logic. I guess this goes against any subjectivism in constructive mathematics. Jeffrey.Ketland at nottingham.ac.uk More information about the FOM mailing list

52. Learning-Org Jul 2000: Systematical Patterns In Boolean Logic L
his students (arend heyting) managed to create a model for this intuitionistic,constructivist logic of Brouwer. It is now called the
http://www.learning-org.com/00.07/0052.html
Systematical Patterns in Boolean Logic LO25063 [complex]
From: AM de Lange ( amdelange@gold.up.ac.za
Date: Replying to LO25047
Dear Organleaners,
Greetings to you all.
In my reply to the topic Efficiency and Emergence LO25047, I did
somethings so as to initiate this contribution. I wrote:
>philospher CS Peirce as "inclusive denials". .... It is often
>called among logicians as Peirce's "dagger" and can be
(snip)
>This "dagger" seems to be a self-destruction of truth in statements.
This "handle" gives me the opportunity to say something more on the relationship between logic and Learning Organisations. I specifically avoid calling this contribution "Systems Thinking and

53. Learning-Org May 1999: "Junk" Science LO21531
In the mean while one of Brouwer s students arend heyting created a logical systemto generate the intuitionistic theorems which Brouwer
http://www.learning-org.com/99.05/0074.html
"Junk" Science LO21531
AM de Lange ( amdelange@gold.up.ac.za
Fri, 7 May 1999 10:16:31 +0200
Replying to LO21521
Dear Organlearners,
jgunkler@sprintmail.com

Greetings John,
Thank you very much for explaining in more detail what you meant. When
you warned against fallicious thinking, I had the uneasy feeling that
you were using the shot gun with the sawn off barrel, spraying hail
all over the place, hoping to hit someone's thoughts. Now I know that
you had something much more clear in mind. Just two points on the name of the topic. If we are going to stay on

54. Arend Heyting Université Montpellier II
Translate this page arend heyting (1898-1980). Cette image et la biographie complète en anglaisrésident sur le site de l’université de St Andrews Écosse
http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=1279

55. On Denoting
heyting Foundation- The arend heyting Foundation came into being as the resultof the last will of ms JF heyting-van Anrooij, who died in september 1998.
http://home.hccnet.nl/m.schraagen/ondenoting/zw/organisation3.html
Organisation
-VVL-
The Dutch Association for Logic and Philosophy of Sciences, commonly referred to as VvL (Dutch: Vereniging voor Logica), has become a true melting pot of logic adepts over the past years. The association does not just represent academic logic, but explicitly commits itself to bringing logic to the attention of the public at large. The association organizes a bi-annual event in the centre of the Netherlands, and furthermore lends their support to nationwide initiatives concerning logic. Beyond intention the association also serves as a society for Dutch logic alumni.
http://www.ai.rug.nl/orgs/vvl/

-Heyting Foundation-
The Arend Heyting Foundation came into being as the result of the last will of ms J.F. Heyting-van Anrooij, who died in september 1998. The aims of the Foundation are to support mathematical logic, and more specifically to organize every three years the Arend Heyting Lecture.

56. Intuitionism
special case of the last example cited above is the mathematical intuitionismof Luitzen Egbertus Jan Brouwer (18811966) and arend heyting (1898-1980),
http://www.philosophyprofessor.com/philosophies/intuitionism.php
@import url(http://www.philosophyprofessor.com/side/cssphp.css); HOME Philosophies Philosophers Library ... voluntarism web here SITE MAP
intuitionism
Any view holding that some of our knowledge is got by a direct process not depending on the senses and not open to rational assessment. The objects of such knowledge may include: moral principles (whether as the basis of duty or as ultimate values); particular moral duties on a particular occasion (sometimes called perceptual intuitionism); space and time and their contents, so far as these are presented to us independently of anything contributed by the understanding ( Immanuel Kant (1724-1804)), reality as it is itself, as opposed to reality processed by us for practical purposes (investigated by Henri Bergson (1859-1941)); things known by accumulated but forgotten experience or unconscious inference ('woman's intuition'; but this figures less prominently in philosophy); basic truths of logic and the principles of valid inference. An important special case of the last example cited above is the mathematical intuitionism of Luitzen Egbertus Jan Brouwer (1881-1966) and AREND HEYTING (1898-1980), a form of

57. Philosophy Of Mathematics - Phil 567/667 - Winter 05 - Richard Zach - University
Rudolf Carnap, arend heyting, and John von Neumann. 1931. Symposium on thefoundations of mathematics. Reprinted from Paul Benacerraf and Hilary Putnam,
http://www.ucalgary.ca/~rzach/567/
Richard Zach Home CV Teaching Publications ... Philosophy Department
PHILOSOPHY OF MATHEMATICS
(Phil 567.03/667.16, Winter 2005)
Richard Zach
Course Outline
A printable version of the outline is here
Contents
Instructor
Instructor Richard Zach Office: 1254 SS Email: rzach@ucalgary.ca Phone: Office Hours:
Lectures
Lectures 105 Social Sciences
Course Description
Prerequisites and Preparation
Two previous courses in Philosophy, one of which must be PHIL 367 or 467, and one of which must be a 400 or higher level course; or consent of the Department. Due to the nature of the course, I will be very open to waiving prerequisites, especially if you have advanced training in logic (such as PHIL 379 or 479) or in mathematics. Please email rzach@ucalgary.ca if you would like to take the course but do not have the listed prerequisites. Although Phil 279 (Logic I) and 379 (Logic II) are not formally prerequisites, you will have a hard time in this course if you have not at least taken Logic I. Obtaining a background in logic (at least Phil 279, preferably 379) is therefore highly recommended.
Required Text
Alexander George and Daniel J. Velleman

58. Is Mathematics A Scientific Discipline?
Cf. Brouwer, arend heyting, RL Goodstein, Hao Wang, Jan Mycielski, arend heyting, The Intuitionist Foundations of Mathematics, Philosophy of
http://www.henryflynt.org/studies_sci/mathsci.html
Back to H.F. Philosophy contents
IS MATHEMATICS A SCIENTIFIC DISCIPLINE? Henry Flynt (c) 1996 Henry A. Flynt, Jr. Introduction For many years, my work has called for a reorientation of mathematics and logic which diverges from the way these disciplines have been directed since the ancient Egyptiansor the old stone age, for that matter. My campaign has proceeded on many fronts; this is not the place for a full inventory of my work. Because I advocate a reorientation of the entire historical direction of the disciplines, I do not consider the future of mathematics and logic to be primarily a professional question. The scientific community is deeply committed to a view of its own destiny which is well articulated by theoretical physicists. Historically, science is a series of commitments to mathematical apparatuses which, once they are established, are endlessly elaborated, but never discarded. One builds on Newton, Maxwell, etc., by recycling them; one never repudiates them. In pure mathematics, the equivalent to this stance is that nobody wants to change the decision for the infinity of primes or the irrationality of [root]2 which was made at the outset of rational mathematics. These tenets are held to be valid by the latest, "Left-wing" standardsand to be the source and guiding light for all that followed them in mathematical history. The profession does not want the Greekswho adopted the elementary theorems on the basis of

59. Information
heyting, arend 1898–1980 Nederländsk matematiker och filosof. Hilbert, David1862–1943 Tysk matematiker och logiker. Hildebrand, Dietrich von 1889–1977
http://www.thephilosophynet.com/h.htm

E-post
A B C ... Z
H
Tysk filosof och sociolog. Haeckel, Ernst 1834–1919
Tysk biolog och filosof. Hahn, Hans 1879–1934
Österrikisk matematiker. Hamann, Johan Georg 1730–1788
Tysk författare och filosof. Hamelin, Octave 1856–1907
Fransk filosof. Hamilton, William 1788–1856
Skotsk filosof. Hampshire, Stuart Newton 1914–2004
Engelsk filosof. Hannay, Alastair född 1932 Skotsk-Norsk filosof. Professor Emeritus vid Oslo universitet. Till Alastair Hannays sida vid Oslo universitet. Hanson, Norwood Russell 1924–1967 Amerikans k filosof. Hare, Richard Mervyn 1919–2002 Engelsk moralfilosof. Harnack, Adolf von 1851–1930

60. CONFERENCES, SUMMER SCHOOLS, TALKS, WORKSHOPS [1] Eindhoven 23
5 Amsterdam (The Netherlands) 1426 September 1998 arend heyting CentenaryPROGRAM heyting Lectures, heyting Symposium, Thematic Day
http://colibri.let.uu.nl/html/html.24-1998/logic.html
CONFERENCES, SUMMER SCHOOLS, TALKS, WORKSHOPS Eindhoven 23 June 1998 ZIC Colloquium on Logic and Theoretical Computer Science dr. ir. Hans de Nivelle: "Implementation of a resolution theorem prover" Montpellier (France) 10-12 August 1998 ICCS'98 6th International Conference on Conceptual Structures CALL FOR PARTICIPATION Saarbruecken (Germany) 14-16 August 1998 FHCG-98 Joint Conference on Formal Grammar, Head-driven Phrase Structure Grammar and Categorial Grammar PROGRAM Freiburg (Germany) 7-9 September 1998 LD'98 The First International Workshop on Labelled Deduction http://www.informatik.uni-freiburg.de/~ld98 CALL FOR PARTICIPATION Amsterdam (The Netherlands) 14-26 September 1998 Arend Heyting Centenary PROGRAM: Heyting Lectures, Heyting Symposium, Thematic Day Prague (Czech Republic) 9-20 November 1998 Vilem Mathesius Lecture Series 13 SECOND CALL FOR PARTICIPATION Grenoble (France) 14-16 December 1998 LACL98 Logical Aspects of Computational Linguistics SECOND CALL FOR PAPERS Deadline: 31 July 1998 Vienna (Austria) 17-19 February 1999 CIMCA'99 Conference on Computational Intelligence for Modelling, Control and Automation http://www-gscit.fcit.monash.edu.au/conferences/cimca99 CALL FOR PAPERS Deadline: 14 August 1998

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