A Reflection on Russell's Ramified Types and Kripke's Hierarchy of Truths

A Reflection on Russell's Ramified Types and Kripke's Hierarchy of Truths (1996)

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by Fairouz Kamareddine , Twan Laan

Venue:	Journal of the Interest Group in Pure and Applied Logic 4(2
Citations:	1 - 1 self

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Datum	Value	Source
TITLE	A Reflection on Russell's Ramified Types and Kripke's Hierarchy of Truths	user correction - Legacy Corrections
AUTHOR NAME	Fairouz Kamareddine	SVM HeaderParse 0.1
AUTHOR AFFIL	Department of Computing Science; University of Glasgow; 17 Lilybank Gardens	SVM HeaderParse 0.2
AUTHOR ADDR	Glasgow G12 8QQ, Scotland	SVM HeaderParse 0.1
AUTHOR NAME	Twan Laan	SVM HeaderParse 0.1
AUTHOR AFFIL	y; Department of Mathematics and Computing Science; Eindhoven University of Technology	SVM HeaderParse 0.2
AUTHOR ADDR	P.O.Box 513, 5600 MB Eindhoven, The Netherlands	SVM HeaderParse 0.1
ABSTRACT	Both in Kripke's Theory of Truth ktt [8] and Russell's Ramified Type Theory rtt [16, 9] we are confronted with some hierarchy. In rtt, we have a double hierarchy of orders and types. That is, the class of propositions is divided into different orders where a propositional function can only depend on objects of lower orders and types. Kripke on the other hand, has a ladder of languages where the truth of a proposition in language Ln can only be made in Lm where m ? n. Kripke finds a fixed point for his hierarchy (something Russell does not attempt to do). We investigate in this paper the similarities of both hierarchies: At level n of ktt the truth or falsehood of all order-n-propositions of rtt can be established. Moreover, there are order-n-propositions that get a truth value at an earlier stage in ktt. Furthermore, we show that rtt is more restrictive than ktt, as some type restrictions are not needed in ktt and more formulas can be expressed in the latter. Looking back at the dou...	user correction - Legacy Corrections
YEAR	1996	INFERENCE
VENUE	Journal of the Interest Group in Pure and Applied Logic 4(2	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
CITATIONS	16 found	ParsCit 1.0