The 8 Axes of the Logic Spectrum

A detailed model adding dimensions of quantification and modality. Axis 1: Formal-Informal. Axis 2: Classical-Nonclassical. Axis 3: Deductive-Inductive. Axis 4: Monotonic-Nonmonotonic. Axis 5: Bivalent-Many-Valued. Axis 6: Truth-Preserving-Information-Preserving. Axis 7: First-Order-Higher-Order (quantification over individuals vs. over properties/functions). Axis 8: Extensional-Intensional (logic of truth values vs. logic of meanings/possibilities). These eight axes create 256 logical positions. Modal logic (necessity/possibility) is formal, nonclassical (in some classifications), deductive, monotonic, bivalent typically, truth-preserving, can be higher-order, intensional (deals with meanings across possible worlds). The 8 Axes demonstrate that the explosion of logical systems in the 20th century reflects different choices on these fundamental dimensions.

The 8 Axes of the Logic Spectrum "You think logic is just propositional calculus. The 8 Axes show that's one tiny point: formal, classical, deductive, monotonic, bivalent, truth-preserving, first-order, extensional. Modal logic changes intensional. Fuzzy logic changes many-valued. Nonmonotonic logic changes monotonic. The axes map the entire universe of logic—and you're still in the first galaxy."

by Dumu The Void February 25, 2026

The 8 Axes of the Knowledge Spectrum

A detailed model adding dimensions of subject matter and value. Axis 1: A Priori-A Posteriori. Axis 2: Propositional-Procedural. Axis 3: Personal-Communal. Axis 4: Explicit-Tacit. Axis 5: Certain-Fallible. Axis 6: Direct-Inferential. Axis 7: Empirical-Conceptual (knowledge of facts vs. knowledge of concepts/meanings). Axis 8: Instrumental-Intrinsic (knowledge for use vs. knowledge for its own sake). These eight axes create 256 knowledge positions. Scientific knowledge is a posteriori, propositional, communal, explicit, fallible, inferential, empirical, both instrumental and intrinsic. Philosophical knowledge is often a priori, propositional, personal (though debated), explicit, fallible (or certain in some views), inferential, conceptual, intrinsic. The 8 Axes demonstrate that knowledge isn't just about truth—it's about purpose, subject, and value.

The 8 Axes of the Knowledge Spectrum "You say knowledge is just facts. The 8 Axes ask: facts about what? Empirical facts (science) or conceptual facts (philosophy)? Facts for use (engineering) or for understanding (pure math)? The axes show that 'facts' are as varied as knowledge itself. Treating all knowledge as empirical facts for use is like treating all food as protein bars—nutritionally reductive and spiritually empty."

by Dumu The Void February 25, 2026