Schindler, Thomas (2015): Typefree truth. Dissertation, LMU München: Faculty of Philosophy, Philosophy of Science and the Study of Religion 

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Abstract
This book is a contribution to the flourishing field of formal and philosophical work on truth and the semantic paradoxes. Our aim is to present several theories of truth, to investigate some of their modeltheoretic, recursiontheoretic and prooftheoretic aspects, and to evaluate their philosophical significance. In Part I we first outline some motivations for studying formal theories of truth, fix some terminology, provide some background on Tarski’s and Kripke’s theories of truth, and then discuss the prospects of classical typefree truth. In Chapter 4 we discuss some minimal adequacy conditions on a satisfactory theory of truth based on the function that the truth predicate is intended to fulfil on the deflationist account. We cast doubt on the adequacy of some nonclassical theories of truth and argue in favor of classical theories of truth. Part II is devoted to grounded truth. In chapter 5 we introduce a gametheoretic semantics for Kripke’s theory of truth. Strategies in these games can be interpreted as referencegraphs (or dependencygraphs) of the sentences in question. Using that framework, we give a graphtheoretic analysis of the Kripkeparadoxical sentences. In chapter 6 we provide simultaneous axiomatizations of groundedness and truth, and analyze the prooftheoretic strength of the resulting theories. These range from conservative extensions of Peano arithmetic to theories that have the full strength of the impredicative system ID1. Part III investigates the relationship between truth and settheoretic comprehen sion. In chapter 7 we canonically associate extensions of the truth predicate with Henkinmodels of secondorder arithmetic. This relationship will be employed to determine the recursiontheoretic complexity of several theories of grounded truth and to show the consistency of the latter with principles of generalized induction. In chapter 8 it is shown that the sets definable over the standard model of the Tarskian hierarchy are exactly the hyperarithmetical sets. Finally, we try to apply a certain solution to the settheoretic paradoxes to the case of truth, namely Quine’s idea of stratification. This will yield classical disquotational theories that interpret full secondorder arithmetic without set parameters, Z2 (chapter 9). We also indicate a method to recover the parameters. An appendix provides some background on ordinal notations, recursion theory and graph theory.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  truth, semantic paradoxes, grounding, deflationism 
Subjects:  100 Philosophy and Psychology 100 Philosophy and Psychology > 160 Logic 
Faculties:  Faculty of Philosophy, Philosophy of Science and the Study of Religion 
Language:  English 
Date Accepted:  29. January 2015 
1. Referee:  Leitgeb, Hannes 
Persistent Identifier (URN):  urn:nbn:de:bvb:19183351 
MD5 Checksum of the PDFfile:  e99955396473435aff468ab7ce84996c 
Signature of the printed copy:  0001/UMC 23029 
ID Code:  18335 
Deposited On:  29. Jun 2015 13:17 
Last Modified:  20. Jul 2016 10:39 