Truth And Paradox: From Deflationism To Dialetheism

Truth theory and paradox studies are the attractive topics in contemporary philosophy, especially in the philosophies of logic and language. Deflationism and dialetheism are the frontier theories. My thesis is focus on truth and paradox in the sight of deflationism and dialetheism.The logical starting point of this thesis is deflationism about truth. Firstly, the deflationary theory is investigated from the perspective of the ’meta-theory of truth’. The so-called ’meta-theory of truth’ is a sort of second order theory, which takes ’theories of truth’ rather than ’truth’ as the research objects. Susan Haack’s ’family tree’ and Richard Kirkham’s ’projects’ is the representative for the empirical approach. The review of this approach is useful to confirm the position of deflationism in the history of truth theory and the relationships between deflationary theory and the other theories of truth. Scott Soames, Michael Devitt, Mi Jianguo and Michael Lynch’s work is the representative for the a priori approach. The meta-theories of truth to a priori approach usually focus on the ambiguity of the word ’truth’; analyze ’truth’ as word and concept, concept and property, as well as the linguistic and metaphysical dimension to reveal the ’deflation of truth’is necessary consequence of the abovementioned distinctions. The thesis then turns to the inner examination of ’deflation of truth’, but without discussing every version of deflationism, instead, taking Frege and Ramsey’s redundancy theory and Paul Horwich’s minimalism as examples, comparing deflationism between fore-Tarski and post-Tarski period to understand the ’deflation’ from naive intuition to delicate formulation. The thesis emphases the role of Equivalence Schema (E) and analyzes the relationship between deflationism and Tarski’s semantic theory and the relation between deflationism and Quinean disquotationism, in terms of explaining the implications of Truth Schema (T) and (E). What of importance is thesis connects deflationism and truth-theoretic paradox in terms of the resemblance of (E) and (T). Next, the thesis summarizes Horwich’s analysis on deducing paradox from the minimalism theory, but rejects Horwich’s solution to paradox, because the elimination of some instances of (E) betrays the standpoint of deflationism. Subsequently, the thesis turns to Jc Beall’s analysis on paradox from a standpoint of deflationism about truth. In Beall’s theory, the semantic paradoxes are considered as ’spandrels’ of truth. Although in the sight of deflationists, ’is true’ is transparent for it says nothing when predicating a declarative sentence, truth predicate could not be eliminated for its transparency, because without it ’blind ascription’ and the generalization could not be expressed. Therefore, the deflationist prefers the tolerance of paradoxes rather than eliminating paradoxes by breaking the deflationist principle. Deflationists tolerating the paradoxes thus become the dialetheists claiming the existence of dialetheias or true contradictions.For the sake of deflation, the thesis takes the ’moderate dialetheism’ as the theoretic partner of deflationism to deal with paradoxes. Although dialetheism is not a logic theory, the contemporary dialetheists need a logic that is beyond the consistency of classical logic for inconsistent language, because what they claim is conflict with the non-contradiction law. The thesis examines paraconsistent logic ’logic of paradox’ (LP), which is employed by the dialetheists. The three-valued semantics of LP can assign the paradoxical sentence intuitively and invalidate ECQ in classical logic. Therefore, LP is a logic that is not only can deal with reasoning in inconsistent language, but also is non-trivial. However, the shortage of LP is the invalidity of modus ponens (MP). The thesis discusses dialetheists’ responses to this problem in the following two kinds of strategy. One is so called the ’positive strategy’, that is finding MP for LP. The extensional approach is adding a detachable conditional, but it could not avoid Curry’s paradox. The intension approach is to introduce the ’normal world’ and ’abnormal word’, and to let MP validates in normal world but avoid Curry’s Paradox in the abnormal world. However, this approach also fails for the difficulties to satisfy. The other strategy is the ’positive’ one, that is, the project ’logic without detachment’(LWD) developed by Jc Beall. The thesis examines Beall’s LP+, which is the multi-conclusion logic of LP. In LP+, all LP-valid inferences remain valid. Moreover, the multi-conclusion forms of some LP-invalid inferences, like MP, are valid. LP+ demonstrates, logic provides two conclusions as the consequence for the MP-like reasoning:one is the expected resulted from the use of MP; the other is a contradiction. What determines the choice is extra-logical principles, for instance,’reject inconsistency’. Although Beall’s work explains why MP-like reasoning is rational in spite of the invalidity of MP, he has not provided an explanation for why dialetheists take ’reject inconsistency’ as their ’rationality principle’. Therefore, the thesis tries to give a better explanation for Beall’s work. The idea is to make distinctions between Aristotelian/Anti-Aristotelian logic based on Aristotle’s realistic philosophy. Next, taking ’choice’ as the boundary, to differentiate and analyze the ’logic shift’ from the Aristotelian to the Anti-Aristotelian. Thus, on one hand, to defend the practicability of classical logic governing reality world, on the other hand, to distinguish various logics for various objects as well as to defend the rationality of LP+.The happy marriage of deflationism and dialetheism and the improvement from LP to LP+ illustrate:although its characteristic claims could result in paradox, deflationism should not only be falsified by the existence of contradictions, but also meet the requirements from rationality to the greatest extent possible.