Extension (logic)

Core claim: The extension of a term is the totality of all objects it refers to; fallacious reasoning can arise when the same term's referent set silently shifts between contexts within an argument.

• A term is used in multiple premises or statements where its referent set (extension) differs – e.g., “horse” meaning the animal in one premise and the chess piece in another.
• The context does not make the intended extension unambiguous, allowing a listener to assume a different referent set than the speaker intends.
• A category term's boundary is unclear (e.g., does “small business” include sole traders? franchises?) and this ambiguity affects the validity of an inference.

• Extension is the referent side of a term; its opposite, intension (MD), is the definitional side (the set of properties that define it). Confusing both directions lead to fallacies.
• In most everyday use, extension is fixed by context and poses no problem. It becomes relevant for fallacy detection primarily when a term's referent set could plausibly be read more than one way within the same argument.

• The context (topic, domain, preceding sentences) makes the intended extension unambiguous – e.g., in a chess tutorial, “horse” clearly refers to a knight piece.
• A term is used consistently with the same referent set throughout an entire discussion.
• An apparent shift in extension is intentional and transparent (e.g., a flagged analogy or deliberate metaphor).

• Intension (MD) – Refers to the definitional aspect of a term: how the extension is referenced can change how it is understood (e.g. 'horse' vs. 'nag' vs. 'steed'). Ask: is it about what does a term refers to (→ extension), or how its meaning shifts depending on how it is referenced, e.g. through the choice of words (→ intension)?
• Equivocation (MD) – A situation in which the same word/expression is used to refer to multiple different extensions. Ask: is this a background concept to check for (→ extension), or have you already identified an actual equivocation in the argument?

Input: “The term 'horse' refers to all animals of the genus Equidae.”
Output: Depending on context, 'horse' can have different meanings, one of them being the riding animals, another the chess pieces also known as 'knights', furthermore frames used for sawing ('saw horse'), gymnastic aparatuses ('pommel horse'), and many more. Make sure that the term is consistently used to refer to the same extension.

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