How well does Hansen’s theory model truth and avoid paradox? - A reply to Casper S. Hansen, “Grounded Ungroundedness”
Summary
In 2014 Inquiry published Casper Storm Hansen’s paper “Grounded Ungroundedness”, which proposed a theory of truth in formal logic, based on Saul Kripke’s 1975 paper “Outline of a Theory of Truth”. Theories of truth in formal logic, as long as they have existed, have been complicated by the existence of the Liar Paradox, the proposition that claims of itself that it is not true. The challenge is to construct a theory that satisfies our basic intuitions concerning truth but does not trivialise the system through the Liar Paradox. Kripke suggested that some sentences, like the Liar, should not receive a truth value (true or false) and remain undefined. Hansen proposes to explicitly declare sentences undefined when it becomes clear they will never become true or false.
This thesis analyses Hansen’s system and its description in “Grounded Ungroundedness”. After a first, introductory chapter, the second chapter summarises Hansen’s theory, shows the evaluation process for a number of different sentences, and points out a flaw in the definition of the system. The third chapter compares Hansen’s system with Kripke’s. It is shown Hansen’s theory shares some important merits with Kripke’s theory, but it also shares some of its flaws. Chapter 4 shows a critical view on Hansen’s system, discussing among other things the failing of the Leibniz law, the definition of quantifiers, the possibility of adapting the system to define satisfaction instead of truth and an adaptation for one of the rules of the system. The final chapter forms the conclusion, where it is argued that Hansen’s theory provides many desirable results but also exhibits some flaws which may be hard to address without compromising the merits.