Hannes Leitgeb

Carnapian Logicism and Semantic Analyticity

Introduction

Carnapian logicism and semantic analyticity. Explore a Carnapian logicism for mathematics, defining terms logically and showing theorems are semantically analytic within a conceptual framework. Understand math's conceptual nature.

Abstract

This article argues for a (quasi-)Carnapian version of logicism about mathematics: there is a logicist conceptual framework in which (i) all standard mathematical terms are defined by logical terms, and (ii) all standard mathematical theorems are (likely to be) analytic. Along the way, the article explains the historical-philosophical background, how the definitions in (i) are to proceed, what the framework and the semantic notion of analyticity-in-a-framework are like, and why the probabilistic qualification ‘likely to be’ is used in (ii). The upshot is not some logicist epistemic foundationalism about mathematics but the insight that mathematics can be rationally reconstructed as being conceptual, i.e., as coming along with a conceptual framework.

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