Illicit Transposition

Also Known As: Converse Error Confusion of Converse

Formal Fallacy ID: illicit_transposition

Definition

A formal fallacy that confuses a conditional with its converse. The valid contrapositive of 'if A then B' is 'if not B then not A,' but illicit transposition instead derives 'if B then A,' which does not logically follow.

Examples

If it is raining, the ground is wet. Therefore, if the ground is wet, it is raining.

If someone is a licensed pilot, they have passed a flight test. Therefore, if someone has passed a flight test, they are a licensed pilot. (Ignores the fact that student pilots, military personnel, and others may pass flight tests without holding a commercial license.)

If a company is bankrupt, it cannot pay its employees. Therefore, if a company cannot pay its employees, it must be bankrupt. (Confuses the conditional with its converse — there are many reasons a company might fail to pay employees that have nothing to do with bankruptcy.)

Formal Logic Pattern

FOL Pattern

The First-Order Logic formula representing this reasoning pattern's logical structure.

FOL (First-Order Logic) uses quantifiers (∀ = for all, ∃ = there exists), connectives (∧ = and, ∨ = or, ⇒ = implies, ¬ = not), and predicates to capture the essential form of a reasoning pattern. For example, the Ad Hominem fallacy: Person(x) ∧ HasFlaw(x) ⇒ Invalid(Claim(x)). These patterns allow automated verification of logical validity.

View in glossary →

(A ⇒ B) ⇒ (B ⇒ A)

Formal Verification: Formally invalid

Verification Steps

Verification Steps

Binary yes/no questions that an AI must answer to detect a reasoning pattern in a text.

Each of the 452 aspects has verification steps — simple yes/no questions designed to systematically detect whether a pattern appears in a text. For ad hominem: "Does the argument attack a person rather than their claim?" For false dichotomy: "Are only two options presented when more exist?" This ensures consistent, reproducible analysis.

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Binary (yes/no) questions an LLM must answer to identify this aspect:

1

Does the argument involve a conditional statement (if A then B)?
Type: binary
2

Does the argument attempt to derive the converse (if B then A) without negation?
Type: binary
3

Is the converse treated as logically equivalent to the original conditional?
Type: binary