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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.
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