title: On Constructive Axiomatic Method
metadata.name: dc.contributor.author
metadata.value: Rodin, A. V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2015-08-28T06:51:25Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2015-08-28T06:51:25Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2014-08-14
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/1722
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The received notion of axiomatic method stemming from Hilbe
  rt is not fully
  adequate to the recent successful practice of axiomatizing
  mathematical theories. The
  axiomatic architecture of Homotopy type theory (HoTT) does
  not fit the pattern of
  formal axiomatic theory in the standard sense of the word.  Ho
  wever this theory falls
  under a more general and in some respects more traditional no
  tion of axiomatic theory,
  which I call after Hilbert and Bernays
  constructive
  and demonstrate using the Classical
  example of the First Book of Euclid’s
  Elements
  . I also argue that HoTT is not unique
  in the respect but represents a wider trend in today’s mathem
  atics, which also includes
  Topos theory and some other developments. On the basis of the
  se modern and ancient
  examples I claim that the received semantic-oriented forma
  l axiomatic method defended
  recently by Hintikka is not self-sustained but requires a su
  pport of constructive method.
  Finally I provide an epistemological argument showing that
  the constructive axiomatic
  method is more apt to present scientific theories than the rec
  eived axiomatic method.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On Constructive Axiomatic Method
metadata.lang: en_GB
resources.filename: 1408.3591v3.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/1722/1/1408.3591v3.pdf
resources.format: Adobe PDF
resources.size: 269,93 kB