In a recent paper, Philip Kremer proposes a formal and theory-relative desideratum for theories of truth that is spelled out in terms of the notion of ‘no vicious reference’. Kremer’s Modified Gupta-Belnap Desideratum (MGBD) reads as follows: if theory of truth T dictates that there is no vicious reference in ground model M, then T should dictate that truth behaves like a classical concept in M. In this paper, we suggest an alternative desideratum (AD): if theory of truth T dictates (...) that there is no vicious reference in ground model M, then T should dictate that all T-biconditionals are (strongly) assertible in M. We illustrate that MGBD and AD are not equivalent by means of a Generalized Strong Kleene theory of truth and we argue that AD is preferable over MGBD as a desideratum for theories of truth. (shrink)

This article is a lecture note I wrote for my philosophy of mathematics course. Its main task is to explain the main ideas of Gupta's acceptable model proposed in his paper [J. Philos. Logic 11(1), 1–60, 1982]. I aim to provide detailed information on a result established by Gupta. On the one hand, I hope this explanation can be helpful for those who are learning Gupta's acceptable model, and on the other hand, I also hope to provide a guide for (...) beginners to interpret literature. (shrink)

Kremer presented three approaches of comparing fixed-point and revision theories of truth in Kremer, 363–403, 2009). Using these approaches, he established the relationships among ten fixed-point theories suggested by Kripke in, 690–716, 1975) and three revision theories presented by Gupta and Belnap in. This paper continues Kremer’s work. We add five other revision theories to the comparisons, including the theory proposed by Gupta in, 1–60, 1982), the theory proposed by Herzberger in, 61–102, 1982), the theory based on fully-varied revision sequences (...) proposed by Gupta and Belnap in, the theory proposed by Yaqūb in, and the theory based on weakly consistent revision sequences. We show that, the notion of Thomason model defined by Belnap’s limit rule is not equivalent to the one defined by Gupta’s limit rule, and that the theory based on fully-varied revision sequences is ≤2-equivalent to the one based on the greatest intrinsic fixed point of σ. (shrink)

We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field.