Argumentation Fallacies & Inference

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Abstractions about the validity and failure modes of reasoning patterns, spanning circular and question-begging arguments, inference fallacies and paradoxes (Hempel's paradox, naturalistic and moralistic fallacies, belief bias), logical validity results (Peirce's law, Lewis's triviality result), and legal and moral argument schemas (legal syllogism, Golden Rule).

15 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Begging the Question — Detect an argument whose premises presuppose the very conclusion they are offered to support — valid, even sound, yet dialectically empty — by testing whether the premises would survive an interlocutor who denies the conclusion.
• Belief Bias — The tendency to judge an argument's logical validity by the believability of its conclusion rather than its form — a cheap plausibility check displacing an effortful logical-form check — exposed by crossing validity against believability in a 2×2.
• Circular Reasoning — Diagnose an argument whose conclusion already appears among its premises by tracing its justification graph for a cycle that never touches a node the audience grants independently.
• Golden Rule — An interpersonal moral heuristic asks agents to guide their treatment of others by how they would wish or accept corresponding treatment themselves.
• Hempel's Paradox — Expose that treating confirmation as yes/no forces the absurd conclusion that a white shoe confirms 'all ravens are black' via the contrapositive — dissolved by grading confirmation, so a non-black non-raven confirms only by a vanishing likelihood ratio.
• Is-Ought Problem — Hume's principle that no purely descriptive premises can by themselves deductively entail a normative conclusion — so any move from 'is' to 'ought' requires an explicit, defensible bridging value premise, and its absence marks a category error.
• Legal Syllogism — A deductive legal-argument schema deriving a case-specific legal consequence from an accepted general legal rule and a case characterized under its conditions.
• Lewis's Triviality Result — An impossibility argument showing that a fixed conditional proposition cannot generally have probability equal to conditional probability throughout a nontrivial class closed under relevant conditioning.
• Material Inference — An inference licensed by the nonlogical conceptual content of its premises and conclusion rather than by logical form alone.
• Moralistic fallacy — Detect the inference that runs from normative undesirability straight to empirical falsity — 'this would be bad if true, therefore it is not so' — foreclosing a factual question on a moral ground without any evidence being weighed, the mirror of the naturalistic fallacy.
• Moving the goalposts — An argumentative pattern in which, on being shown evidence that meets a previously stipulated standard, one party revises the standard upward to block the conclusion rather than accept it — repeated so that no finite evidence can settle the question.
• Naturalistic Fallacy — The metaethical error of identifying goodness with a natural property, exposed by the open-question argument — for any proposed good = N, 'but is N good?' stays a meaningful question, so goodness cannot be identical with any natural property it merely co-occurs with.
• Paradigm-Case Argument — Answer a sweeping skeptical denial by identifying an actual central case through which the disputed expression is ordinarily taught or applied, while keeping the argument’s semantic premises distinct from stronger metaphysical claims.
• Peirce's Law — An implication-only formula valid in classical logic but not intuitionistic logic: if (P→Q) implies P, then P.
• Underdeterminacy (Law) — Diagnose a legal text as underdeterminate when its recovered communicative content constrains a dispute but does not uniquely fix the doctrine or outcome, leaving a construction choice among compatible options.