In ‘A Consistent Way with Paradox’, Laurence Goldstein (2009) clarifies his solution to the liar, which he touts as revenge immune . In addition, he (Ibid.) responds to one of the objections that Armour-Garb and Woodbridge (2006) raise against certain solutions to the open pair and argues that his proffered solution to the liar family of paradoxes undermines what they (Ibid.) call the dialetheic conjecture . In this paper, after critically evaluating Goldstein’s response to A-G&W, I turn to his proposed (...) solution to the liar paradox, where I show that it is difficult to see how it manages to avoid that conjecture. (shrink)

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

A common objection to hierarchical approaches to truth is that they fragment the concept of truth. This paper defends hierarchical approaches in general against the objection of fragmentation. It argues that the fragmentation required is familiar and unprob-lematic, via a comparison with mathematical proof. Furthermore, it offers an explanation of the source and nature of the fragmentation of truth. Fragmentation arises because the concept exhibits a kind of failure of closure under reflection. This paper offers a more precise characterization of (...) the reflection involved, first in the setting of formal theories of truth, and then in a more general setting. (shrink)

When ordinary people--mathematicians among them--take something to follow from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, as it were, of our reasoning. This (...) point is illustrated with a close analysis of a paradigmatic case of ordinary reasoning: mathematical proof. (shrink)

When ordinary people - mathematicians among them - take something to follow from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, as it were, (...) of our reasoning. This point is illustrated with a close analysis of a paradigmatic case of ordinary reasoning: mathematical proof. (shrink)

If we try to evaluate the sentence on line 1 we ¯nd ourselves going in an unending cycle. For this reason alone we may conclude that the sentence is not true. Moreover we are driven to this conclusion by an elementary argument: If the sentence is true then what it asserts is true, but what it asserts is that the sentence on line 1 is not true. Consequently the sentence on line 1 is not true. But when we write this (...) true conclusion on line 2 we ¯nd ourselves repeating the very same sentence. It seems that we are unable to deny the truth of the sentence on line 1 without asserting it at the same time. (shrink)

Key words: liar paradoxes, propositions, definite descriptions A Liar would be a sentence or sentence-token that expresses a proposition that is both true and not true. A Liar Paradox is reasoning that would do the impossible and demonstrate the reality of a Liar. It is sufficient, fully to resolve a Liar Paradox, to turn its purported demonstration that some sentence or sentence-token expresses a proposition that is both true and not true into a reductio of the existence of the proposition (...) that would be expressed, while ‘explaining away’ the particular tricks and charm of the purported demonstration of paradox. The interest of these exercises lies in the seductiveness of the would be demonstration of a Liar Paradox, and in the depth and subtlety of logical/grammatical resources that can be tapped and fashioned to dispel it. The Liar taken on in this paper occasions especially seductive reasoning that exploits ‘scope-ambiguities’ of definite descriptions that, not incidentally, survive unscathed when its argument is symbolized in a Fregean description theory in which scopes of definite descriptions are not discriminated. Symbolizing this argument in a Russellian description theory in which scopes are discriminated makes unavoidable that its scope-ambiguities be settled one way or another, and reveals that however the scope ambiguity of a certain premise is settled the resultant unambiguous argument is unsound, either because it is invalid, though this premise comes out true, or because, though it is valid, this premise comes out not true. These results of Russellian analysis pave the way to a formal demonstration, from premises to which a monger of the paradox would be committed, that contrary to his case the Liar of this paper does not express a proposition. This conclusion is confirmed in the Appendix to this paper by a demonstration from a single empirical premise that no one can deny, in a Russellian calculus enhanced for truth of propositions expressed by tokens of sentences.. (shrink)