Description

• Tytuł:
  The critics of paraconsistency and of many-valuedness and the geometry of oppositions
• Twórca:
  Moretti, Alessio
• Opis:
  In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition theory (NOT) we analyse Beziau’s anti-Slater move and show both its right intuitions and its technical limits. Moreover, we suggest that Slater’s criticism is much akin to a well-known one by Suszko (1975) against the conceivability of many-valued logics. This last criticism has been addressed by Malinowski (1990) and Shramko and Wansing (2005), who developed a family of tenable logical counter-examples to it: trans-Suszkian systems are radically many-valued. This family of new logics has some strange logical features, essentially: each system has more than one consequence operator. We show that a new, deeper part of the aforementioned geometry of logical oppositions (NOT), the “logical poly-simplexes of dimension m”, generates new logical-geometrical structures, essentially many-valued, which could be a very natural (and intuitive) geometrical counterpart to the “strange”, new, non-Suszkian logics of Malinowski, Shramko and Wansing. By a similar move, the geometry of opposition therefore sheds light both on the foundations of paraconsistent logics and on those of many-valued logics.
• Dostępność obiektu:
  free access
• Prawa:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Data:
  2010.06.30
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Język:
  English
• Źródło:
  Logic and Logical Philosophy; Vol. 19 No. 1-2 (2010); 63-94;
  Logic and Logical Philosophy; Tom 19 Nr 1-2 (2010); 63-94;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Wydawca:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relacja: https://apcz.umk.pl/LLP/article/view/LLP.2010.004/956
• Temat i słowa kluczowe:
  n-opposition theory;
  logical poly-simplexes;
  paraconsistent logic;
  many-valued logic;
  trans-Suszkian logic;
  geometry of opposition;
  Slater;
  Priest;
  Béziau;
  Suszko;
  Shramko;
  Wansing
• Identyfikator: https://apcz.umk.pl/LLP/article/view/LLP.2010.004
• Dostawca danych:
  Akademicka Platforma Czasopism
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