The 16 Axes of the Logic Spectrum

The ultimate model, adding the final dimensions of context, psychology, and metaphysics. Building on the 12 Axes, we add: Axis 13: Context-Independent-Context-Dependent (logic applies everywhere vs. context matters). Axis 14: Psychological-Ideal (logic describes how people think vs. how they should think). Axis 15: Ontologically-Neutral-Committed (logic assumes nothing about reality vs. logic has metaphysical implications). Axis 16: Unitary-Pluralist (one true logic vs. many logics for many purposes). These sixteen axes generate 65,536 potential positions—enough to capture every logical system ever conceived. The 16 Axes of the Logic Spectrum reveal that logic is not a single discipline but a multidimensional space of choices about how to reason, what reasoning is for, and what reasoning assumes. The 16 Axes don't tell you which logic is correct—they give you a language for understanding what any logic claims, what it's good for, and where it might fail. They are the map of the space of valid inference—the periodic table of reason itself.

The 16 Axes of the Logic Spectrum "You want the one true logic. The 16 Axes ask: which one? The one that's formal or informal? Classical or nonclassical? Deductive or inductive? Monotonic or nonmonotonic? Bivalent or many-valued? Truth-preserving or information-preserving? First-order or higher-order? Extensional or intensional? Explosive or paraconsistent? Relevant or irrelevant? Computational or noncomputational? Static or dynamic? Context-independent or context-dependent? Psychological or ideal? Ontologically neutral or committed? Unitary or pluralist? Sixteen questions, and until you answer them, 'one true logic' is just a slogan. The axes don't give you the answer—they force you to ask the questions that any real logic must answer. And that's the most logical thing of all."

Classical logic chooses formal, classical, deductive, monotonic, bivalent, truth-preserving, first-order, extensional, explosive, irrelevant (classical doesn't require relevance), computational (for propositional), static, context-independent, ideal, ontologically-neutral (claims to be), unitary (claims to be the one true logic). Relevance logic disagrees on relevance and maybe paraconsistency. Fuzzy logic disagrees on bivalence. Nonmonotonic logic disagrees on monotonicity.

The 16 Axes of the Logic Spectrum by Dumu The Void February 25, 2026