Open AccessGoedel's Property Abstraction and Possibilism
Author(s) -
Randoph Rubens Goldman
Publication year - 2014
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v11i2.2145
Subject(s) - s5 , modal logic , modal operator , property (philosophy) , ontological argument , possible world , epistemology , argument (complex analysis) , computer science , semantics (computer science) , modal , philosophy , accessibility relation , multimodal logic , programming language , description logic , philosophy of religion , chemistry , biochemistry , polymer chemistry
Gödel’s Ontological argument is distinctive because it is the most sophisticated and formal of ontological arguments and relies heavily on the notion of positive property. Gödel uses a third-order modal logic with a property abstraction operator and property quantification into modal contexts. Gödel describes positive property as "independent of the accidental structure of the world"; "pure attribution," as opposed to privation; "positive in the 'moral aesthetic sense.'" Pure attribution seems likely to be related to the Leibnizian concept of perfection.By a careful examination of the formal semantics of third-order modal logic with property abstraction together with a Completeness result for third-order modal logic with property abstraction for faithful models that I previously developed in 2000 in my work, Gödel’s Ontological Argument, I argue that it is not possible to develop a sufficient applied third-order modal semantics for Gödel’s ontological argument. As I explore possible approaches for an applied semantics including anti-Realist accounts of the semantics of modal logic compatible with Actualism, I argue that Gödel makes implicit philosophical assumptions which commit him to both possibilism (the belief in merely possible objects) and modal realism (the belief in possible worlds).