Weyl's Quantifiers

TL;DR

This paper reevaluates Weyl's interpretation of logical signs, emphasizing his correctness-first view and explaining his rejection of the law of excluded middle, with insights on nested quantifiers.

Contribution

It clarifies Weyl's reasons for rejecting the law of excluded middle and offers preliminary thoughts on conditional obligations from nested quantifiers.

Findings

Weyl's rejection of the law of excluded middle is based on correctness-first principles.

Quantified statements generate conditional obligations to expand correct judgments.

Preliminary ideas on understanding obligations from nested quantifiers are proposed.

Abstract

I argue against the predominant view of Weyl's interpretation of the logical signs. Drawing on his correctness-first account of mathematical knowledge, I point out that, according to him, quantified statements generate conditional obligations to act in ways that expand the repository of correct judgments. This clarifies Weyl's reasons for rejecting the law of excluded middle, which have nothing to do with what has been attributed to him by the predominant view. I also offer some preliminary thoughts on how to understand conditional obligations generated by statements with nested quantifiers.