To found or not to found: that is the question

TL;DR

This paper examines Schröder's foundational views, arguing he relied on Dedekind's work for mathematics and that his pasigraphy was a personal, lifelong passion rooted in his childhood and love for languages.

Contribution

It clarifies Schröder's actual foundational stance and explores the personal origins of his pasigraphy, challenging previous misconceptions.

Findings

Schröder considered the problem of founding mathematics already solved by Dedekind.

He translated Chain Theory into the language of relatives.

His pasigraphy was deeply personal and rooted in his childhood and language interests.

Abstract

Aim of this paper is to confute two views, the first about Schr\"oder's presumptive foundationalism, according to he founded mathematics on the calculus of relatives; the second one mantaining that Schr\"oder only in his last years (from 1890 onwards) focused on an universal and symbolic language (by him called pasigraphy). We will argue that, on the one hand Schr\"oder considered the problem of founding mathematics already solved by Dedekind, limiting himself in a mere translation of the Chain Theory in the language of the relatives. On the other hand, we will show that Schr\"oder's pasigraphy was connaturate to himself and that it roots in his very childhood and in his love for foreign languages.