Description

• Tytuł:
  Pieces of mereology
• Twórca:
  Pietruszczak, Andrzej
• Opis:
  In this paper we will treat mereology as a theory of some structures that are not axiomatizable in an elementary language (one of the axioms will contain the predicate ‘belong’ (‘∈’) and we will use a variable ranging over the power set of the universe of the structure). A mereological structure is an ordered pair M = <M,⊑>, where M is a non-empty set and ⊑ is a binary relation in M, i.e., ⊑ is a subset of M × M. The relation ⊑ is a relation of being a mereological part (instead of ‘<x,y> ∈ ⊑’ we will write ‘x ⊑ y’ which will be read as “x is a part of y”). We formulate an axiomatization of mereological structures, different from Tarski’s axiomatization as presented in [10] (Tarski simplified Leśniewski’s axiomatization from [6]; cf. Remark 4). We prove that these axiomatizations are equivalent (see Theorem 1). Of course, these axiomatizations are definitionally equivalent to the very first axiomatization of mereology from [5], where the relation of being a proper part ⊏ is a primitive one.Moreover, we will show that Simons’ “Classical Extensional Mereology” from [9] is essentially weaker than Leśniewski’s mereology (cf. Remark 6).
• Dostępność obiektu:
  free access
• Prawa:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Data:
  2005.12.23
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Język:
  English
• Źródło:
  Logic and Logical Philosophy; Vol. 14 No. 2 (2005); 211-234;
  Logic and Logical Philosophy; Tom 14 Nr 2 (2005); 211-234;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Wydawca:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relacja: https://apcz.umk.pl/LLP/article/view/LLP.2005.014/1445
• Temat i słowa kluczowe:
  mereology;
  mereological structures;
  axioms of mereology;
  collective sets;
  mereological sets;
  mereological fusions;
  mereological parts
• Identyfikator: https://apcz.umk.pl/LLP/article/view/LLP.2005.014
• Dostawca danych:
  Akademicka Platforma Czasopism
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