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

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

The 4 Axes of the Knowledge Spectrum

An expanded model adding two crucial dimensions to the basic framework. Axis 1: A Priori-A Posteriori (reason vs. experience). Axis 2: Propositional-Procedural (that vs. how). Axis 3: Personal-Communal (knowledge held by individuals vs. knowledge stored in communities). Axis 4: Explicit-Tacit (knowledge you can state vs. knowledge you can't articulate). These four axes create sixteen knowledge types. Scientific knowledge is a posteriori, propositional, communal (scientific community knows), explicit (published). Cultural knowledge is a posteriori, procedural (knowing how to navigate a culture), communal, tacit (you just know how things work). The 4 Axes reveal that debates about knowledge often confuse these dimensions—dismissing tacit knowledge because it's not explicit, or communal knowledge because it's not personal.

The 4 Axes of the Knowledge Spectrum "You say you can't prove what you know. The 4 Axes ask: what kind of knowledge? Tacit knowledge can't be proved—that's its nature. Procedural knowledge is shown, not stated. Communal knowledge is distributed, not owned. The axes help you see that demanding explicit propositional proof for all knowledge is like demanding a fish to climb a tree."

by Dumu The Void February 25, 2026

The 6 Axes of the Knowledge Spectrum

A comprehensive model adding dimensions of certainty and access. Axis 1: A Priori-A Posteriori. Axis 2: Propositional-Procedural. Axis 3: Personal-Communal. Axis 4: Explicit-Tacit. Axis 5: Certain-Fallible (knowledge that can't be wrong vs. knowledge that might be mistaken). Axis 6: Direct-Inferential (known directly vs. known through reasoning). These six axes generate sixty-four knowledge positions. Mathematical knowledge is a priori, propositional, personal (when learned), explicit, certain (in ideal), inferential (proved). Perceptual knowledge is a posteriori, propositional, personal, explicit (usually), fallible, direct. The 6 Axes reveal that different kinds of knowledge have different epistemic statuses—certainty isn't the same for all.

The 6 Axes of the Knowledge Spectrum "You demand certainty. The 6 Axes ask: what kind of knowledge? Math can be certain (maybe). Perceptual knowledge can't—that's not its function. Certainty is a feature of some knowledge types, not a requirement for all. The axes help you see that demanding certainty from empirical knowledge is asking for the wrong thing."

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

The 12 Axes of the Knowledge Spectrum

An ultra-fine-grained model adding dimensions of justification, reliability, and social context. Building on the 8 Axes, we add: Axis 9: Justified-Unjustified (knowledge requires justification vs. reliable process suffices). Axis 10: Internalist-Externalist (justification depends on internal reasons vs. external reliability). Axis 11: Individualist-Social (knowledge is individual achievement vs. fundamentally social). Axis 12: Universal-Particular (knowledge of general truths vs. knowledge of specific facts). These twelve axes generate 4096 knowledge positions. Traditional epistemology (Plato's justified true belief) is internalist (reasons matter), individualist (the knower knows), and applies to both universal and particular. Reliabilist epistemology is externalist (reliable process suffices), individualist, universal and particular. Social epistemology is social (knowledge is communal achievement), externalist often, universal and particular. The 12 Axes reveal that debates about what knowledge is—justified true belief? reliable process? social achievement?—are debates about which axes matter most.

The 12 Axes of the Knowledge Spectrum "You think knowledge is justified true belief. The 12 Axes ask: justified internally (by reasons) or externally (by reliability)? Individually or socially? Universal or particular? Plato's definition assumes answers—internalist, individualist, both universal and particular. But externalists and social epistemologists disagree. The axes show that 'knowledge' is contested because different epistemologists make different choices on these axes—not because they're confused, but because knowledge itself is multidimensional."

by Dumu The Void February 25, 2026