Intension

Core claim: The intension of a term is the set of associated meanings, connotations, and contextual information that come with how it refers to its extension; errors arise when an argument treats two different descriptions as interchangeable while ignoring their distinct intensions.

• Two terms or descriptions refer to the same object (same extension) but carry different connotations or framing – e.g., “morning star” vs. “evening star” (both Venus), or “horse” vs. “steed” vs. “nag” – and an argument treats them as fully interchangeable without acknowledging this difference.
• A person's knowledge, belief, or emotional response is attributed based on one description while the reasoning actually depends on a different description of the same referent.
• The intensional context (how something is described) changes what can be validly inferred, but the argument ignores this shift.

• Intension and extension are two sides of the same coin: extension = what objects a term covers; intension = which meanings/properties come with it. They can diverge (same extension, different intensions) or converge differently (different extensions, overlapping intensions).
• An equivocation is when one term can refer to multiple extensions. An intensional ambiguity is when different terms refer to the same extension, albeit in different ways.

• Two terms with different intensions are used where only their shared extension matters (e.g., in formal logic, “horse”, “steed” or “nag” are all seen to refer to the same extension – intension does not matter here).
• The speaker explicitly acknowledges the difference in framing or connotation.
• The argument is about the linguistic or rhetorical effect of a term (e.g., discussing euphemisms) rather than making an inference that depends on treating different intensions as identical.

• Extension (MD) – the referent set side of a term. Ask: is the confusion about what objects the term covers (→ extension), or about which meanings/connotations come with it (→ intension)?
• Equivocation (MD) – the broader fallacy of shifting a term's meaning. Ask: is this specifically about ignoring different intensions of co-referential terms (→ intension), or about a more general shift in meaning/extension?

Input: “John doesn't know that the masked man in the park is his father. But the masked man in the park IS his father. Therefore, John knows that his father is in the park.”
Output: The intension of “the masked man in the park” (an unknown stranger) differs from “his father” (a known family member), even though both refer to the same person. Knowledge attributions are indexed to a specific description; you cannot substitute a co-referential term with a different intension inside them without preserving truth.

Input: “The terms 'morning star' and 'evening star' both refer to the same object (the planet Venus). So one should be able to say: 'the morning star appears in the evening.'”
Output: While 'morning star' and 'evening star' share the same extension (Venus), they carry different intensions, each implying a different time of day. Substituting one for the other in this way produces a statement that, while technically true, contradicts what the term connotes – avoid mixing the intensional content of two distinct descriptions.

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