 Looking to the rationalist traditions of Descartes and Leibniz, Jean van Heijenoort and Jaakko Hintikka have distinguished between two views of language that are relevant to the new linguistic turn (Mormann 1999): language as calculus (LC) and language as universal medium (LUM). The LC tradition, illustrated by Tarski’s views, aligned itself with the Cartesian ideal of a transparent language, with clear and distinctive meaning and explicit, mechanical combination and rule-following that extended to its use in reasoning. There are many possible constructed languages and each is an interpreted calculus with different possible semantics. The LUM tradition adopted the idea of a single actual or ideal language and one semantic or interpretation, to be elucidated, with no possibility of representing its relation to the world from outside. Views by Frege, who pointed to Leibniz on language and reasoning, and Wittgenstein illustrate this tradition, which in turn accommodates two versions, a Cartesian one (Frege and Russell) and a non-Cartesian one (Wittgenstein). Carnap’s conversion to semantics in the early 1930s took him to the LC Cartesian tradition seeking a universal language of rational reconstruction he had previously recognized in the language of physics. Neurath, by contrast, modeled his unification of the sciences in the LUM tradition, on a universal mixed language he called a universal jargon, with descriptions of spatio-temporal arrangements and connections he called physicalism, historically contingent use of vague and ordinary terms (see below). In this context Neurath adopted a militant syntacticism that opposed Carnap’s defense of semantics as metaphysical (Anderson 2019) and engaged in heated terminological disputes that ignored Carnap’s commitment to ontological neutrality (Carus 2019).