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Moving the Logicpost

When, after an opponent successfully engages within a prescribed logical framework, the arguer changes the rules of what constitutes “valid logic.” This can mean switching logical systems (from deductive to inductive), redefining fallacies on the fly, or declaring that a formally valid syllogism is now invalid because it’s “based on a false premise” they previously accepted.
Moving the Logicpost Example:
You use their preferred deductive logic to build a sound argument.
They respond: “Deduction is limited. Real-world problems require fuzzy logic, which your binary reasoning fails. Your point is logically simplistic.”
They’ve moved the logicpost from formal deduction to an amorphous alternative to evade your conclusion.
Moving the Logicpost by Dumuabzu February 8, 2026

The 4 Axes of the Logic Spectrum

An expanded model adding two crucial dimensions to the basic framework. Axis 1: Formal-Informal (form vs. content). Axis 2: Classical-Nonclassical (standard vs. alternatives). Axis 3: Deductive-Inductive (certain inference vs. probabilistic inference). Axis 4: Monotonic-Nonmonotonic (adding premises never invalidates conclusions vs. conclusions can be defeated by new information). These four axes create sixteen logical positions. Mathematical logic is formal, classical, deductive, monotonic. Legal reasoning is informal, classical (mostly), inductive (evidence weighs), nonmonotonic (new evidence changes everything). AI reasoning is often formal, nonclassical (fuzzy, probabilistic), inductive, nonmonotonic. The 4 Axes reveal that different domains require different logics—using monotonic deductive logic for legal reasoning would be disastrous.
The 4 Axes of the Logic Spectrum "You think logic is universal. The 4 Axes show otherwise: math logic is monotonic—once proven, always proven. Legal logic is nonmonotonic—new evidence overturns verdicts. Same logic label, completely different behavior. The axes help you see why your 'logical' argument fails in court: you're using the wrong logic for the domain."

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."

The 6 Axes of the Logic Spectrum

A comprehensive model adding dimensions of truth and inference. Axis 1: Formal-Informal. Axis 2: Classical-Nonclassical. Axis 3: Deductive-Inductive. Axis 4: Monotonic-Nonmonotonic. Axis 5: Bivalent-Many-Valued (two truth values vs. many). Axis 6: Truth-Preserving-Information-Preserving (logic keeps truth vs. logic keeps information). These six axes generate sixty-four logical positions. Relevance logic is formal, nonclassical, deductive, monotonic, bivalent, but demands relevance between premises and conclusion—it preserves relevance, not just truth. Fuzzy logic is formal, nonclassical, can be deductive or inductive, monotonic typically, many-valued (degrees of truth), truth-preserving (of degrees). The 6 Axes reveal that logical systems are designed for different goals—some prioritize certainty, others nuance, others relevance.
The 6 Axes of the Logic Spectrum "You want a logic that handles uncertainty. The 6 Axes ask: uncertainty as degrees of truth (fuzzy) or as probability (inductive)? Many-valued or probabilistic? Both are nonclassical, but they're different nonclassical. The axes help you choose the right tool, not just any tool labeled 'logic for uncertainty.'"

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."

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."
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