The 2 Axes of the Logic Spectrum

A foundational model for understanding logical systems along two fundamental dimensions. The first axis runs from Formal Logic (concerned with pure form, syntax, validity regardless of content—math-like reasoning) to Informal Logic (concerned with real-world arguments, fallacies, natural language—how people actually reason). The second axis runs from Classical Logic (bivalent, law of excluded middle, truth-functional—Aristotle to Frege) to Non-Classical Logic (deviations: many-valued, paraconsistent, intuitionistic, fuzzy). These two axes create four basic logical orientations: formal-classical (standard mathematical logic), formal-nonclassical (modal logic, fuzzy logic), informal-classical (critical thinking textbooks, fallacy studies), informal-nonclassical (practical reasoning with uncertainty, everyday fuzzy logic). The model reveals that "logic" isn't one thing—it's a family of tools for different purposes, from pure mathematics to everyday argument evaluation.

The 2 Axes of the Logic Spectrum "You say someone's argument is illogical. The 2 Axes ask: by which logic? Classical formal logic might call it invalid. Informal logic might see it as reasonable in context. Fuzzy logic might give it .73 truth. Same argument, three different verdicts. The axes help you see that 'logic' isn't a single judge—it's a panel, and they don't always agree."

by Dumu The Void February 25, 2026