Liar,Reducibility and Language

First, language and axioms of Church's paper 'Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski' are slightly modified and a version of the Liar paradox tentatively reconstructed. An obvious natural solution of the paradox leads to a hierarchy of truth predicates which is of a different kind from the one defined by Church: it depends on the enlargement of the semantical vocabulary and its levels do not differ in the ramified-type-theoretical sense. Second, two attempts are made in order to justify the Russellian, and perhaps Churchian, idea that language should not be fragmented beyond what is required by type distinctions. After all, because of reducibility, which seems to allow a semantics without propositions, this comes out to be possible only at the cost of resorting to two disputable theses. This revised version was published online in June 2006 with corrections to the Cover Date.     

Validity and Effectiveness of Ambiguity: A Famous Argument by Socrates

An argument can be superficially valid and rhetorically effective even if what is plausibly meant, what is derived from what, and how it is derived is not at all clear. An example of such an argument is provided by Socrates??s famous refutation of Euthyphro??s second definition of holy, which is generally regarded as clearly valid and successful. This paper provides a stricter logical analysis than the ones in the literature. In particular, it is shown that the argument contains a syntactically ambiguous expression, a passage that needs to be read charitably, and a previously unnoticed but crucial shift between two notions of unholy. Different analyses may be provided, depending on how these interpretation problems are solved. The conditions under which the refutation is valid and successful are far from obvious, and are here explicitly specified.