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 12 Axes of the Logic Spectrum

An ultra-fine-grained model adding dimensions of paraconsistency, relevance, and computation. Building on the 8 Axes, we add: Axis 9: Explosive-Paraconsistent (contradiction entails everything vs. contradictions can be contained). Axis 10: Relevant-Irrelevant (premises must be relevant to conclusion vs. relevance not required). Axis 11: Computational-Noncomputational (logic has effective decision procedure vs. undecidable). Axis 12: Static-Dynamic (logic of static propositions vs. logic of change/action). These twelve axes generate 4096 logical positions. Paraconsistent logic is formal, nonclassical, deductive, monotonic or nonmonotonic, bivalent or many-valued, truth-preserving, any order, extensional or intensional, paraconsistent (non-explosive), can be relevant or not, often decidable, static typically. Dynamic logic is formal, nonclassical, deductive, monotonic, bivalent, truth-preserving, higher-order, intensional, explosive, relevant-ish, decidable often, dynamic (explicitly about change). The 12 Axes reveal that logical pluralism isn't optional—different problems require different logical tools, and the axes help you find the right one.

The 12 Axes of the Logic Spectrum "You want a logic for contradictions in legal reasoning. The 12 Axes ask: explosive (standard logic) would destroy everything. Paraconsistent contains them. Relevant ensures the contradiction matters. Dynamic handles changing laws. Twelve axes, twelve design choices. Your 'simple logic' is just the one you're used to—not the one you need."

by Dumu The Void February 25, 2026

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.

by Dumu The Void February 25, 2026