| This thesis focuses on the so-called paracomplete theories of truth,which consistently characterize naive principles of truth in the first order theory by dropping the law of Excluded Middle.Among them,we specially pick the two most celebrated works as our research sources:one is the Saul Kripke's essay "The Outline Theory of Truth",the another is Hartry Field's book "Saving Truth from Paradox".By illustrating the relationship of these two theories,we aim to show what major problems this approach currently faces and accordingly contribute our explorations on them.Firstly,we clarify how Field understands Kripke's theory of truth.He argued that the concept of truth should not.coincide with the concept of "having semantic value 1"both in unrestrict,ed and restricted language,that the latter defined in ZFC obeys the classical logic while the former expressed by primitive predicate does not.Thus,in Field's view,Kripke's construction and its fixed points are simply model-theoretic tools,which can be used to(i)prove the consistency of a group of principles about truth(Intersubstitutivity Principle plus Kleene logic)and its conservativeness relative to the ground theory,(ii)understand the logic of the non-classical theory of truth.However,the paracomplete theory(KFS)generated by Kripke's construction falls short of Field's desires.Specifically,(i)there are no laws in KFS,(ii)KFS fails to express linguistic T-schema and(iii)the indeterminacy of paradoxical sentences.Secondly,we illustrate how Field managed to combine Kripke's construction with revision semantics to obtain his paracomplete theory equipped with a new conditional.Specifically,we show the logic of Field's theory from the view of algebraic semantics,where we see that Field's theory fully retained Kleene logic invoked by the Kripke's,while the former additionally invoked a conditional that satisfies some classical principles.Basing on this,we continue to show Field's achievements on expressive power,that his theory has not only maintained IP and Kleene logic;but also(i)saved quite amounts of classical principles for conditionals and(ii)consistently expressed the defectiveness of paradoxical sentences.Hence,Field's work has restored the expressive defects of Kripke's theory to a great extent.Last but not least,Field's paracomplete theory was also called into questioned from different aspects.Specifically,this thesis focuses on the puzzle of philosophical justification of Field's condit.ional and gives an elaborate analysis to it.We point out that the non-truth-functional interpretation on conditional adopted by Field brought high complexity to his semantics,which results in the difficulties of giving a satisfying philosophical justification of his conditional.In order to explore a semantics of theory of truth whose conditional has a philosophical significance besides for the relative strong expressive power,we further generalize Lorenzo Rossi's work(2016)to a hierarchy of languages.On one hand,we adopt the truth-functional monotonic interpretation on conditional to gain the conciseness.On the other hand,we persistently introduce new conditionals and semantic values to gain the expressive power.And we eventually obtain a sequence of fixed points relative to the hierarchy of languages,where the conditionals receive good philosophical interpretations.However,the expressive power of such semantics with fragmented conditionals is weaker than Field's,which reveals a tension between the attempt to strengthen the expressive power via introducing a conditional and the requirement of providing a good philosophical justification to it in paracomplete theories of truth. |
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