PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2017 | 46 | 3/4 |
Tytuł artykułu

Identity, Equality, Nameability and Completeness

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the first is a binary relation between objects while the second is a symbolic relation between terms. Owing to the central role the notion of identity plays in logic, you can be interested either in how to define it using other logical concepts or in the opposite scheme. In the first case, one investigates what kind of logic is required. In the second case, one is interested in the definition of the other logical concepts (connectives and quantifiers) in terms of the identity relation, using also abstraction. The present paper investigates whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic a reliable definition of identity is possible. However, the definition needs the standard semantics and we know that with this semantics completeness is lost. We have also studied the relationship of equality with comprehension and extensionality and pointed out the relevant role played by these two axioms in Henkin’s completeness method. We finish our paper with a section devoted to general semantics, where the role played by the nameable hierarchy of types is the key in Henkin’s completeness method.
Rocznik
Tom
46
Numer
3/4
Opis fizyczny
Daty
wydano
2017-12-30
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_46_3_4_02
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.