Short answers, pulled from the story.
Aristotle wrote his Organon in the 4th century BCE, establishing term logic as the dominant system of reasoning for over two thousand years. His work introduced the hypothetical syllogism and temporal modal logic to Western thought.
Gottlob Frege published his Begriffsschrift in 1879, marking what many see as the birthplace of modern logic. This work introduced quantifiers and relational predicates using formal language instead of natural language.
Intuitionistic logic uses the same symbols as classical logic but excludes rules like double negation elimination because truth is established by verification using a proof. In this system, the inference that if a sentence is not not true then it is true becomes invalid.
Gongsun Long proposed the white horse paradox while defending the thesis that a white horse is not a horse. The Mohist school in China also acknowledged the importance of language for logic while relating ideas to ethics.
Set theory originated in Georg Cantor's study of the infinite during the late 19th century. His work generated challenging issues including Cantor's theorem and the status of the Axiom of Choice.