On translating conditional statements into mathematical logic

TL;DR

This paper explores the fundamental differences between how conditional statements are expressed and understood in mathematical logic versus natural language, emphasizing implications for mathematical theorems.

Contribution

It clarifies the conceptual gap between natural language and formal logic conditionals, providing insights into their translation and interpretation.

Findings

Identifies key differences between natural language and logical conditionals

Highlights implications for mathematical theorem formulation

Suggests need for careful translation in mathematical logic

Abstract

In this paper, we highlight a profound difference between conditional statements in mathematical logic and natural languages. This difference exists even when the conditional statements are used in mathematical theorems.