Finitism, intuitionism, constructivism, formalism, predicativism, structuralism, objectivism, platonism; foundationalism, anti-foundationalism, first orderism; constructive type theory, Cantorian set theory, proof theory; top down principles or building up from below—framework commitments, that is, ideology, permeates the logician’s mathematical life. Such commitments set ∗This paper is based o...

This paper is a review of the influence that lógos has had on ancient Greek, Jewish, and Christian writings. During the philosophical era known as Middle Platonism, the concept/ontology of the lógos played a unique role in enabling Pagan, Jewish, and Christian intellectuals to communicate on a small space of common ground.

The aim of this paper is to reveal the tacit assumptions of the logicist and structuralist theories on the nature of cardinal numbers. The privileged background theory is the representational theory of language with its main conjecture about necessary correspondence between metaphysical structure of reality and logical structure of language. In such a theory of language we meet a number of thes...