David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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This original and enticing book provides a fresh, unifying perspective on many old and new logico-philosophical conundrums. Its basic thesis is that many concepts central in ordinary and philosophical discourse are inherently circular and thus cannot be fully understood as long as one remains within the conﬁnes of a standard theory of deﬁnitions. As an alternative, the authors develop a revision theory of deﬁnitions, which allows deﬁnitions to be circular without this giving rise to contradiction (but, at worst, to “vacuous” uses of deﬁnienda). The theory is applied with varying levels of detail to a circular analysis of concepts as diverse as truth, predication, necessity, physical object, etc. The focus is on truth, and hope is expressed that a deeper understanding of the Liar and related paradoxes has been provided: “We have tried to show that once the circularity of truth is recognized, a great deal of its behavior begins to make sense. In particular, from this viewpoint, the existence of the paradoxes seems as natural as the existence of the eclipses” (p. 142). We think that this hope is fully justiﬁed, although some problems remain that future research in this ﬁeld should take into account. The following assumptions constitute the typical background in which the truth paradoxes arise: (i) classical ﬁrst-order logic, (ii) a language allowing for self-reference, and (iii) the “semantic” Tarskian schema: (TS) T ‘A’ ↔ A (where ‘T’ is the truth predicate, and the single quotes are a nominalization device applicable to sentences; for simplicity, we only consider homophonic versions of TS). This background can be seen as somehow part of our ordinary linguistic and conceptual background and yet, to avoid inconsistency, one or more of these assumptions must be suitably weakened. The classical, Tarskian strategy is to forbid self-reference, whereas the ﬁxed-point approaches stemming from the work of Saul Kripke (1975) and Robert Martin and Peter Woodruff (1975) weaken the logic..
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