This book, provides a critical approach to all major logical paradoxes: from ancient to contemporary ones. There are four key aims of the book: 1. Providing systematic and historical survey of different approaches – solutions of the most prominent paradoxes discussed in the logical and philosophical literature. 2. Introducing original solutions of major paradoxes like: Liar paradox, Protagoras paradox, an unexpected examination paradox, stone paradox, crocodile, Newcomb paradox. 3. Explaining the far-reaching significance of paradoxes of vagueness and change for philosophy (...) and ontology. 4. Proposing a novel, well justified and, as it seems, natural classification of paradoxes. (shrink)

Sorensen has argued that one can exploit the vagueness of an ordinary predicate like ‘small’ to induce a sort of vagueness in ‘vague’, by constructing a series of predicates of the form ‘n-small’, where x is n- small if and only if x is small or x n. The resulting ‘Sorensen’ed’ predicates present a Sorites case for ‘vague’ ; hence the vagueness of ‘vague’. Hyde argues that this demonstrates that all vague predicates are higher-order vague. Others doubt whether Sorensen’s series (...) really delivers such a result, claiming Hyde’s argument to be either: unsound, because it misidentifies the true source of vagueness in Sorensen’s Sorites ; invalid, because it fails to generalize to all vague predicates ; or circular, because it presupposes the very thing it tries to prove, namely, higher-order vagueness. This paper contributes to the Sorensen-Hyde vs. Tye-Deas-Hull-Varzi debate by clarifying the relations between vague vagueness and higher-order vagueness. I show how claims of higher-order vagueness are derivable from claims of vague vagueness. This is the missing piece needed to complete Hyde’s argument and overcome the objections presented by Deas, Hull, Tye, and Varzi. I then show how Sorensen’s considerations, once properly generalized, pose more far-reaching consequences about the vagueness of ‘vague’ than either defenders or critics of Hyde’s argument have appreciated. (shrink)

Varzi has recently joined a thread of arguments originating in an attempt by Sorensen (1985) to demonstrate that the predicate ‘vague’ is itself vague. Sorensen's conclusion is significant in that it has provided the basis for a subsequent effort by Hyde (1994) to defend the legitimacy of supposing higher-order vagueness. Varzi's contribution to this debate is twofold. First, contra earlier criticism by Deas (1989), he claims that Sorensen's result is sound so far as it goes. Second, he argues that despite (...) this it cannot be used as Hyde wishes on pain of circularity. I am not interested in the latter argument—it is examined in Hyde (2003)—but rather wish to defend and elaborate Deas's criticism of Sorensen against Varzi's repudiation. (shrink)

The purpose of this paper is to challenge some widespread assumptions about the role of the modal axiom 4 in a theory of vagueness. In the context of vagueness, axiom 4 usually appears as the principle ‘If it is clear (determinate, definite) that A, then it is clear (determinate, definite) that it is clear (determinate, definite) that A’, or, more formally, CA → CCA. We show how in the debate over axiom 4 two different notions of clarity are in play (...) (Williamson-style "luminosity" or self-revealing clarity and concealeable clarity) and what their respective functions are in accounts of higher-order vagueness. On this basis, we argue first that, contrary to common opinion, higher-order vagueness and S4 are perfectly compatible. This is in response to claims like that by Williamson that, if vagueness is defined with the help of a clarity operator that obeys axiom 4, higher-order vagueness disappears. Second, we argue that, contrary to common opinion, (i) bivalence-preservers (e.g. epistemicists) can without contradiction condone axiom 4 (by adopting what elsewhere we call columnar higher-order vagueness), and (ii) bivalence-discarders (e.g. open-texture theorists, supervaluationists) can without contradiction reject axiom 4. Third, we rebut a number of arguments that have been produced by opponents of axiom 4, in particular those by Williamson. (The paper is pitched towards graduate students with basic knowledge of modal logic.). (shrink)