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Busting a myth about Leśniewski and definitions

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Abstract
A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Lesniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Lesniewski's published or unpublished work is known where the standard conditions are discussed. Second, Lesniewski's own logical theories allow for creative definitions. Third, Lesniewski's celebrated 'rules of definition' lay merely syntactical restrictions on the form of definitions: they do not provide definitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 1930s, a study of these meta-theoretical conditions is more readily found in the works of Lukasiewicz and Ajdukiewicz.
Keywords
definitions, Lesniewski, conservativeness of definitions, Ajdukiewicz, creativity of definitions, PRINCIPIA, SYSTEM, FREGE

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Please use this url to cite or link to this publication:

Chicago
Urbaniak, Rafal, and K Severi Hämäri. 2012. “Busting a Myth About Leśniewski and Definitions.” History and Philosophy of Logic 33 (2): 159–189.
APA
Urbaniak, R., & Hämäri, K. S. (2012). Busting a myth about Leśniewski and definitions. HISTORY AND PHILOSOPHY OF LOGIC, 33(2), 159–189.
Vancouver
1.
Urbaniak R, Hämäri KS. Busting a myth about Leśniewski and definitions. HISTORY AND PHILOSOPHY OF LOGIC. 2012;33(2):159–89.
MLA
Urbaniak, Rafal, and K Severi Hämäri. “Busting a Myth About Leśniewski and Definitions.” HISTORY AND PHILOSOPHY OF LOGIC 33.2 (2012): 159–189. Print.
@article{3148393,
  abstract     = {A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Lesniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Lesniewski's published or unpublished work is known where the standard conditions are discussed. Second, Lesniewski's own logical theories allow for creative definitions. Third, Lesniewski's celebrated 'rules of definition' lay merely syntactical restrictions on the form of definitions: they do not provide definitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 1930s, a study of these meta-theoretical conditions is more readily found in the works of Lukasiewicz and Ajdukiewicz.},
  author       = {Urbaniak, Rafal and H{\"a}m{\"a}ri, K Severi},
  issn         = {0144-5340},
  journal      = {HISTORY AND PHILOSOPHY OF LOGIC},
  keyword      = {definitions,Lesniewski,conservativeness of definitions,Ajdukiewicz,creativity of definitions,PRINCIPIA,SYSTEM,FREGE},
  language     = {eng},
  number       = {2},
  pages        = {159--189},
  title        = {Busting a myth about Le\'{s}niewski and definitions},
  url          = {http://dx.doi.org/10.1080/01445340.2011.583771},
  volume       = {33},
  year         = {2012},
}

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