Schema: there is a property φ and function δ such that (1) w = {x|φ(x)} exists, and (2) if y is a subset of w, then (i) δ(y) ∉ y, and (ii) δ(y) ∈ w. Thus, for example, in the case of Burali-Forti's Paradox, φ(x) is the property of being an ordinal, w is the set of all ordinals, and δ(y) is the least ordinal greater than every member of y. Priest spends the main part of his paper showing that th...

We investigate some well-known (and a few not-so-well-known)many-valued logics that have a small number (3 or 4) of truth values. For some of them we complain that they do not have any logical use (despite their perhaps having some intuitive semantic interest) and we look at ways to add features so as to make them useful, while retaining their intuitive appeal. At the end, we show some surprisi...

In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higherorder combinations of generalized truth values have been suggested to account for so-called hypercontradictions. In the present paper, Graham Priest’s treatment of generalized truth values is scrutinize...

Huntington (2007); argues that recent commentators (Robinson, 1957; Hayes, 1994; Tillemans, 1999; Garfield and Priest, 2002) err in attributing to Nāgārjuna and Candrakı̄rti a commitment to rationality and to the use of argument, and that these commentators do violence to the Madhyamaka project by using rational reconstruction in their interpretation of Nāgārjuna’s and Candrakı̄rti’s texts. Hunti...