Hodges’ Theorem Does not Account for Determinacy of Translation. A Reply to Werning

Werning applies a theorem by Hodges in order to put forward an argument against Quine’s thesis of the indeterminacy of translation (understood as a thesis on meaning, not on reference) and in favour of what Werning calls ‘semantic realism’. We show that the argument rests on two critical premises both of which are false. The reasons for these failures are explained and the actual place of this application of Hodges’ theorem within Quine’s philosophy of language is outlined.     

Truth as Translation – Part A

According to Tarski's Convention T, the adequacy of a truth definition is (implicitly) defined relatively to a translation mapping from the object language to the metalanguage; the translation mapping itself is left unspecified. This paper restates Convention T in a form in which the relativity to translation is made explicit. The notion of an interpreted language is introduced, and a corresponding notion of a translation between interpreted languages is defined. The latter definition is stated both in an algebraic version, and in an equivalent possible worlds version. It is a consequence of our definition that translation is indeterminate in certain cases. Finally, we give an application of our revised version of Convention T and show that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate. This is possible if only truth is based on a nonstandard translation mapping by which, e.g., the Liar sentence is translated to its own negation. In this part of the paper this existence result is proved only for languages without quantifiers; in Part B the result will be extended to first-order languages.     

Finitistic and Frequentistic Approximation of Probability Measures with or without <Emphasis Type="Italic">σ</Emphasis>-Additivity

In this paper a theory of finitistic and frequentistic approximations — in short: f-approximations — of probability measures P over a countably infinite outcome space N is developed. The family of subsets of N for which f-approximations converge to a frequency limit forms a pre-Dynkin system . The limiting probability measure over D can always be extended to a probability measure over , but this measure is not always σ-additive. We conclude that probability measures can be regarded as idealizations of limiting frequencies if and only if σ-additivity is not assumed as a necessary axiom for probabilities. We prove that σ-additive probability measures can be characterized in terms of so-called canonical and in terms of so-called full f-approximations. We also show that every non-σ-additive probability measure is f-approximable, though neither canonically nor fully f-approximable. Finally, we transfer our results to probability measures on open or closed formulas of first-order languages.     

Time sharing and dichotic listening asymmetry in normal and learning-disabled children

Time-sharing and dichotic listening techniques were used to examine cerebral lateralization for language function in 48 normal and 48 learning-disabled children. All subjects were matched according to age, sex, and handedness. An analysis of results indicated that both nornal and learning-disabled children demonstrated left hemisphere lateralization of language function on the time-sharing and dichotic listening tasks. However, no developmental trends were evident for either group. Differences observed in the performance of the normal and learning-disabled children may relate to how each group utilizes “verbal strategies” and processes simultaneous information in the left hemisphere. The results strongly question the notion that attributes learning disabilities to incomplete or delayed language lateralization and lend support to the notion that cerebral lateralization is not a developmental phenomena.