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

The 2 Axes of the Knowledge Spectrum

A foundational model for understanding the nature of knowledge along two fundamental dimensions. The first axis runs from A Priori Knowledge (knowledge independent of experience—math, logic, conceptual truths) to A Posteriori Knowledge (knowledge dependent on experience—empirical facts, scientific observations). The second axis runs from Propositional Knowledge (knowing that—facts, information) to Procedural Knowledge (knowing how—skills, abilities, practices). These two axes create four basic knowledge types: a priori-propositional (mathematical truths), a priori-procedural (knowing how to reason), a posteriori-propositional (scientific facts), a posteriori-procedural (knowing how to ride a bike). The model reveals that "knowledge" isn't one thing—it's a family of cognitive achievements with different sources and different forms.

The 2 Axes of the Knowledge Spectrum "You say you know it. The 2 Axes ask: know that or know how? Know from reason or from experience? Knowing that 2+2=4 is very different from knowing how to ride a bike. Same word, different kinds. The axes help you see that 'knowledge' covers a lot of territory—and treating all knowledge like math is a category error."

by Dumu The Void February 25, 2026