On the "Logic without Borders" Point of View

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 on a series of conversations with Jouko Vaananen.

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