Naslov
Gödel’s ontological system and justification logic

Autori
Kovač, Srećko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Trends in Logic XI: Advances in Philosophical Logic / - : Ruhr University Bochum, 2012, 34-34

Skup
Trends in Logic XI: Advances in Philosophical Logic

Mjesto i datum
Bochum, Njemačka, 03.06.2012. - 05.06.2012

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
axiomatization; ontology; justification logic; causality

Sažetak
Philosophical disciplines, including ontology, usually do not have standard axiomatizations. One of the candidates for the axiomatization of ontology is Gödel’s higher-order modal system (GO) (see [3]), which Gödel used in his ontological proof. System GO does not make explicit Gödel’s idea to base ontology on the causality as the “fundamental concept”. Moreover, the concept of causality presently lacks some well established logical formalism. It is natural to propose a transformation of Gödel’s ontological system into a sort of justification logic (G¨odel, Artemov, Fitting), where modal boxes are replaced by explicit reasons, interpreted in our proposal in a causal way. We propose axiomatic system CGO, which transforms Gödel’s GO into a secondorder system and is obtained as a modification and extension of the firstorder axiomatization given by Artemov ([1], for semantics see [2]). Beside causally interpreted usual justification terms, we introduce lamx(t) (“property maker”), exs(t) (affirmation of a cause t), and g (cause of “positivity” in one of the axioms: \forall X(PX -> g:_{; ; ; X}; ; ; PX)). We give causal versions of Gödel’s ontological theorems and prove some further theorems of CGO. A possible semantics for CGO with the soundness and completeness proofs is outlined.

Izvorni jezik
Engleski

Znanstvena područja
Filozofija

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