Translation, Quotation and Truth :: Mathematical Mathematics Math Essays

Translation, Quotation and TruthABSTRACT If logical truth is truth due solely to syntactic form, because mathematics is distinct from logic, even if all mathematical truths are derivable from definitions and logical principles. This is often obscured by the plausibility of the Synonymy Substitution Principle that is unstated in the Fregean conception of analyticity viz., that synonyms are intersubstitutable without altering sentence sense. Now, unlike logical truth, mathematical truth is not due to syntax, so synonym interchange in mathematical truths preserves sentence syntax, sense, and mathematical necessity. Mathematical necessity, therefore, differs from both logical and lexical necessity. Alonzo Churchs Translation Test is supposed to evaluate alleged necessary equivalences. The canonic idea is that (correct) variation is meaning preserving, so if some disparity between the alleged equivalents appears under translation, the sentences are inequivalent. The Test translations are essentially synonym substitutions. The translation sentence is to have the syntax of the superior, and to differ only morphemically, by synonym subbing. Supposedly, whether the translations are inter-language or intra-language has no logical import. Either way, the underlying and seemingly untouchable principle is that synonym subbing transmits sentence sense. This Synonym Substitution Principle extends to subbing of coreferring proper names by taking their meaning to be their reference.The Tests deriving from this Principle should spark suspicions for two reasons. First, the Principle seems to entail the Tests inutility, for, presumably, any disparity appearing under translation but not appearing in the original must be a discrepancy in and of the translation. If the Principle is platitudinous, the Test should be profitless. This isnt the old Paradox of Analysis. Synonymies arent analyses. Genuine analyses are translanguistic necessary truths knowable a priori synonymies are contingent notational equivalences knowable only a posteriori. Unlike analysis, the assumption that translation can be informative for a competent bilingual of necessity justification.The Tests pet targets are peculiarly Carnapian theses e.g., that belief attributions like Mother believes Roger is nearby are semantic equivalents of speech attributions like Mother accepts Roger is nearby. The Tests plausibility and popularity may owe much to its confirming incredulity about independently refutable theses. We knew pre-Church that my dog Mothers believing her master is nearby doesnt entail any wagging at an face sentence.Another curiosity in the Test is that translation seems to reveal disparities not otherwise evident solely with talk about talk and thought, in the affinity between direct and indirect discourse. The Test gets touted only with instantiations of alleged logical or analytical principles wherein, allegedly, a quotation embedding sentence mutually entails a quotationle ss sentence.