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Illicit Minor

Also Known As: Illicit Process of the Minor Term
Formal Fallacy ID: illicit_minor

Definition

The illicit minor is a formal fallacy in categorical syllogisms where the minor term (the subject of the conclusion) is distributed in the conclusion but not in the minor premise. This means the conclusion makes a claim about all members of a category when the premises only established something about some members. It is the counterpart to the illicit major, involving the other end of the syllogism.

Examples

"All roses are flowers. All roses are plants. Therefore, all plants are flowers." (The minor term 'plants' is distributed in the conclusion but undistributed in the minor premise, where only some plants -- roses -- are discussed.)

'All senators are politicians. All senators are public figures. Therefore, all public figures are politicians.' (The minor term 'public figures' is distributed in the conclusion, but in the minor premise it refers only to the subset of public figures who are senators, not all public figures.)

'All jazz musicians are artists. All jazz musicians are improvisers. Therefore, all improvisers are artists.' (The minor term 'improvisers' is used universally in the conclusion, but the minor premise only tells us that jazz musicians — a specific subset of improvisers — are improvisers, not all improvisers.)

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.
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All M are P; All M are S; therefore All S are P [S undistributed in premise but distributed in conclusion]
Formal Verification:
Formal Verification
Checks whether a reasoning pattern is logically valid or invalid using an automated theorem prover.
Formal verification uses an SMT (Satisfiability Modulo Theories) solver — specifically Z3 — to mathematically check whether an argument's logical structure is valid. Each reasoning pattern is translated into First-Order Logic and tested: Can the premises be true while the conclusion is false? If yes, it's formally invalid. If no, it's formally valid. Many real-world patterns (analogies, heuristics) cannot be fully captured in formal logic — these are marked as not formally decidable, which doesn't mean they're wrong.
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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. 1

    Is the minor term distributed in the conclusion?

    Type: binary
  2. 2

    Is the minor term also distributed in the minor premise?

    Type: binary
  3. 3

    Does the distribution of the minor term match between premise and conclusion?

    Type: binary
Deep Dive
The expandable detail section on each aspect page with examples, psychology, and counter-strategies.
The Deep Dive section provides in-depth information about each aspect: a real-world example showing the pattern in action, an explanation of why it works psychologically, practical advice on how to counter it, alternative names, and links to related aspects.
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Hierarchical Context

→ is a Formal Fallacies

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