Translation, Quotation and Truth :: Mathematical Mathematics Math Essays

Translation, Quotation and TruthABSTRACT If arranged justness is truth due solely to syntactic form, then mathematics is pellucid from logic, even if all numeral truths be derivable from definitions and logical principles. This is a lot obscured by the plausibility of the Synonymy Substitution Principle that is implicit in the Fregean conception of analyticity viz., that synonyms are intersubstitutable without altering condemnation 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 mental test is supposed to evaluate alleged infallible equivalences. The basic idea is that (correct) rendition is meaning preserving, so if some variation between the alleged equivalents appears under variation, the sentences are inequivalent. The Test i nterlingual renditions are basically synonym substitutions. The translation sentence is to have the syntax of the original, and to differ save morphemically, by synonym subbing. Supposedly, whether the translations are inter-language or intra-language has no logical import. all way, the underlying and seemingly unassailable 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 derivation from this Principle should spark suspicions for ii reasons. First, the Principle seems to entail the Tests inutility, for, presumably, whatsoever 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 hoary 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 take 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 close individually refutable theses. We knew pre-Church that my dog Mothers believing her master is nearby doesnt entail any wagging at an English 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 relation between direct and indirect discourse. The Test gets touted only with instantiations of alleged logical or analytical principles wherein, allegedly, a deferred payment embedding sente nce mutually entails a quotationless sentence.