Illicit Conversion

Also Known As: Converse Error of Categorical Propositions Simple Conversion Error

Formal Fallacy ID: illicit_conversion

Definition

Illicit conversion is a formal fallacy that involves invalidly converting a categorical statement by switching its subject and predicate. While 'No A are B' validly converts to 'No B are A,' and 'Some A are B' converts to 'Some B are A,' the statement 'All A are B' does not validly convert to 'All B are A.' This asymmetry is frequently overlooked in everyday reasoning.

Examples

"All terrorists are extremists. Therefore, all extremists are terrorists." (Being a terrorist implies being an extremist, but being an extremist does not imply being a terrorist.)

'All vaccines are medical interventions' is incorrectly converted to 'All medical interventions are vaccines.' Being a vaccine guarantees being a medical intervention, but surgeries, antibiotics, and therapies are also medical interventions without being vaccines.

A social media post reads: 'All convicted fraudsters lied to their victims, so everyone who has ever lied is a convicted fraudster.' The original relationship runs one way only — lying is a component of fraud, but lying alone does not make someone a convicted fraudster.

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 →

ALL x: A(x) -> B(x); therefore ALL x: B(x) -> A(x) [invalid]

Formal Verification: Not formally decidable

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

Has the subject and predicate of a categorical statement been switched?
Type: binary
2

Is the original statement a universal affirmative (All A are B)?
Type: binary
3

Does the conversion preserve the logical validity of the original proposition?
Type: binary

Description

Why It Works

Symmetric phrasing feels natural -- if A relates to B, B should relate to A in the same way. This intuition is correct for some logical forms but incorrect for universal affirmatives.

How to Counter

Test the conversion with a clear counterexample. Visualize with sets: all terrorists fall within extremists, but extremists is a larger set containing many non-terrorists.

Also Known As

Converse Error of Categorical Propositions Simple Conversion Error

Real-World Context

Pervasive in security profiling ('all terrorists are X, therefore all X are potential terrorists'), medical reasoning, and everyday categorical judgments that conflate subset with identity.

Related Aspects

Affirming the Consequent Denying the Antecedent Fallacy of Four Terms (Quaternio Terminorum) Hasty Generalization

Hierarchical Context

→ is a Formal Fallacies

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