Individual choice sequences in the work of L. E. J. Brouwer

Joop Niekus

Philosophia Scientiae (2005)

  • Volume: 9, Issue: S2, page 217-232
  • ISSN: 1281-2463

Abstract

top
Choice sequences are sequences not completely determined by an algorithmic law. We maintain that the introduction of particular choice sequences by Brouwer in the late twenties was not recognised as such. We claim that their later use in the method of the creative subject was not traced back to this original usage and has been misinterpreted. We show where these particular choice sequences appear in the work of Brouwer and we show how they should be handled.

How to cite

top

Niekus, Joop. "Individual choice sequences in the work of L. E. J. Brouwer." Philosophia Scientiae 9.S2 (2005): 217-232. <http://eudml.org/doc/103769>.

@article{Niekus2005,
abstract = {Choice sequences are sequences not completely determined by an algorithmic law. We maintain that the introduction of particular choice sequences by Brouwer in the late twenties was not recognised as such. We claim that their later use in the method of the creative subject was not traced back to this original usage and has been misinterpreted. We show where these particular choice sequences appear in the work of Brouwer and we show how they should be handled.},
author = {Niekus, Joop},
journal = {Philosophia Scientiae},
language = {eng},
number = {S2},
pages = {217-232},
publisher = {Éditions Kimé},
title = {Individual choice sequences in the work of L. E. J. Brouwer},
url = {http://eudml.org/doc/103769},
volume = {9},
year = {2005},
}

TY - JOUR
AU - Niekus, Joop
TI - Individual choice sequences in the work of L. E. J. Brouwer
JO - Philosophia Scientiae
PY - 2005
PB - Éditions Kimé
VL - 9
IS - S2
SP - 217
EP - 232
AB - Choice sequences are sequences not completely determined by an algorithmic law. We maintain that the introduction of particular choice sequences by Brouwer in the late twenties was not recognised as such. We claim that their later use in the method of the creative subject was not traced back to this original usage and has been misinterpreted. We show where these particular choice sequences appear in the work of Brouwer and we show how they should be handled.
LA - eng
UR - http://eudml.org/doc/103769
ER -

References

top
  1. [1] Atten, Mark van2004.— On Brouwer, Wadsworth Philosophers Series, London: Thomson Learning, 2004. Zbl1072.03005MR2054116
  2. [2] Borwein, Jonathan M.1998.— Brouwer-Heyting Sequences converge, The Mathematical Intellencer, 20, 14-15. Zbl0921.00003MR1601815
  3. [3] Brouwer, Luitzen, Egbert, Jan1975.— Collected Works I, Philosophy and Foundations of Mathematics, editor A. Heyting, Amsterdam: North Holland Publishing Company, 1975. Zbl0311.01021
  4. [4] Brouwer, Luitzen, Egbert, Jan1907.— Over de grondslagen van de wiskunde, D. van Dalen, Amsterdam: Mathematisch Centrum 1981; English translation [Brouwer 1975, 13-101]. 
  5. [5] Brouwer, Luitzen, Egbert, Jan1908.— De onbetrouwbaarheid der logische principes, Tijdschrift voor Wijsbegeerte, 2 (1908), 152-158; English translation: The Unreliability of the logical Principles; [Brouwer 1975, 107-111]. 
  6. [6] Brouwer, Luitzen, Egbert, Jan1918.— Begründung der Mengenlehre unabhängig der Satz vom ausgeschlossenen Dritten; Erster Teil: Allgemeine Mengenlehre, Verhandelingen der Koninklijke Akademie van Wetenschappen te Amsterdam, 5 (1918), 1-43; [Brouwer 1975, 150-221]. JFM46.0310.06
  7. [7] Brouwer, Luitzen, Egbert, Jan1919.— Begründung der Mengenlehre unabhängig der Satz vom ausgeschlossenen Dritte; Zweiter Teil: Theorie der Punktmengen, Verhandelingen der Koninklijke Akademie van Wetenschappen te Amsterdam, 7 (1919), 1-33; [Brouwer 1975, 191-221]. JFM47.0171.03
  8. [8] Brouwer, Luitzen, Egbert, Jan1927.— Über Definitionsbereiche von Funktionen, Mathematische Annalen, 97 (1927), 60-75; [Brouwer, 390-406]. Zbl52.0239.01MR1512354JFM52.0239.01
  9. [9] Brouwer, Luitzen, Egbert, Jan1929.— Mathematik, Wissenschaft und Sprache, Monatshefte für Mathematik und Physik, 36 (1929) 153-164; [Brouwer 1975, 417-428]. MR1549679JFM55.0028.04
  10. [10] Brouwer, Luitzen, Egbert, Jan1930.— Die Struktur des Kontinuums, Vienna: Gottlieb Gistel, 1930; [Brouwer 1975, 429-440]. 
  11. [11] Brouwer, Luitzen, Egbert, Jan1948.— Essentieel negatieve eigenschappen, Proceedings Koninklijke Nederlandse Akademie van Wetenschappen te Amsterdam, 51 (1948), 963-964; English translation: Essentially negative Properties, Indagationes Math, 10:322-323; [Brouwer, 1975, 478-479]. 
  12. [12] Brouwer, Luitzen, Egbert, Jan1981.— Brouwer’s Cambridge Lectures on Intuitionism, editor D. van Dalen, Cambridge: Cambridge University Press, 1981. Zbl0476.03056
  13. [13] Brouwer, Luitzen, Egbert, Jan1991.— Intuitionismus, Editor D. van Dalen, Mannheim: B.I.-Wissenschaftsverlag, 1991. Zbl0761.03001MR1189793
  14. [14] Dalen, Dirk van1999.— From Brouwerian Counterexamples to the creating Subject Studia Logica, 62 (1999), 305-314. Zbl0922.03083MR1696005
  15. [15] Dalen, Dirk van and Troelstra, Anne S.1988.— Constructivity in Mathematics Volume I and II, Amsterdam: North Holland Publishing Company, 1988. 
  16. [16] Kreisel, Georg1963.— Stanford report of the seminar on the foundations of analysis, section IV, Stanford University, 1963. 
  17. [17] Kreisel, Georg1968.— Lawless Sequences of natural Numbers, Compositio Math, 20 (1968), 222-248. Zbl0157.33401MR226992
  18. [18] Kreisel, Georg and Troelstra, Anne S.1970.— Formal Systems for some Branches of intuitionistic Analysis, Annals of Mathematical Logic, 1 (1970), 229-387. Zbl0211.01101MR263609
  19. [19] Martino, Enrico1985.— On the Brouwerian Concept of negative Continuity, Journal of Philosophical Logic, 14 (1985), 379-398. Zbl0631.03046MR816242
  20. [20] Niekus, Joop M.1987.— The Method of the creative Cubject, Proceedings of the Koninklijke Akademie van Wetenschappen te Amsterdam, Series A, 4 (1987), 431-443. Zbl0644.03034MR922447
  21. [21] Niekus, Joop M.2002.— Individual choice sequences in the work of L.E.J.Brouwer, ILLS Scientific Series, PP-2002-05. 
  22. [22] Posy, Carl1976.— Varieties of Indeterminacy in the Theory of general Choice Sequences, Journal of Philosophical Logic, 5 (1976), 91-132. Zbl0349.02027MR437315
  23. [23] Troelstra, Anne S.1977.— Choice Sequences, Oxford: Clarendon Press, 1977. MR476415
  24. [24] Troelstra, Anne S.1982.— On the Origin and Development of Brouwer’s Concept of Choice Sequences, L.E.J.Brouwer Centenary Symposium, editors A.S.Troelstra and D.van Dalen, Amsterdam, North Holland Publishing Company, 1982: 465-486. Zbl0522.03049MR717261

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.