6533b833fe1ef96bd129b5cc

RESEARCH PRODUCT

Is mathematics syntax of language?, II

Francisco Rodríguez-consuegra

subject

NominalismConventionalismmedia_common.quotation_subjectObject languageRealmDoctrineA priori and a posterioriCertaintyLinguisticsSyntax (logic)media_common

description

Around 1930 R. Carnap, H. Hahn and M. Schlick,1 largely under the influence of L. Wittgenstein, developed a conception of the nature of mathematics2 which can be characterized as being a combination of nominalism and conventionalism and which had been foreshadowed in Schlick’s doctrine about implicit definitions.3 Its main objective, according to Hahn and Schlick,4 was to conciliate strict empiricism5 with the a priori certainty of mathematics. According to this conception (which, in the sequel, I shall call the syntactical viewpoint) mathematics can completely be reduced to (or replaced by) syntax of language.6 I.e. the validity of mathematical propositions consists solely in their being consequences7 of certain syntactical conventions about the use of symbols,8 not in their describing states of affairs in some realm of things. Or, as Carnap puts it: Mathematics is a system of auxiliary propositions without content or object.9

yearjournalcountryeditionlanguage
1995-01-01
https://doi.org/10.1007/978-3-0348-9248-3_7