---
- title: Fallacies of distribution
- categories: [logic]
- synonyms: []
- related: [logic/formal_fallacies/fallacies_of_distribution/undistributed_middle, logic/formal_fallacies/fallacies_of_distribution/illicit_process]
- main_article: <https://fallacies.online/wiki/logic/formal_fallacies/fallacies_of_distribution/index>
- main_article_de: <https://denkfehler.online/wiki/logik/verteilungsfehler/hauptseite>
---

# Fallacies of distribution

**Core claim:** A categorical (syllogistic) inference is invalid because the *distribution* of its terms is not taken into account – a term is used in the conclusion with a different scope than in its premise(s), or the middle term never refers to the whole class it names. This is an umbrella entry for two specific rules: *undistributed middle* and *illicit process*.

## Applies when
- The argument is a formal categorical (syllogistic) inference, or is presented as representing such a form.
- At least one term is used with a different scope in the conclusion than in its premise(s), or the middle term never refers to the whole class it names – i.e., at least one of the two distribution rules below is violated.

## Notes
- **Routing:** if exactly one rule is clearly violated, use the specific page instead:
  - Middle term undistributed in all its occurrences → [Undistributed middle](logic/formal_fallacies/fallacies_of_distribution/undistributed_middle) ([MD](logic/formal_fallacies/fallacies_of_distribution/undistributed_middle.md))
  - A major/minor term overextended in the conclusion vs. its premise → [Illicit process](logic/formal_fallacies/fallacies_of_distribution/illicit_process) ([MD](logic/formal_fallacies/fallacies_of_distribution/illicit_process.md))
- This entry applies when several rules are violated at once, or when the form is non-standard (multi-premise derivations, unclear term roles) and the specific rule cannot be determined immediately.
- Distribution by statement type – *distributed* means the term refers to its entire class:
  - “All S are P”: subject distributed, predicate not
  - “No S is P”: both distributed
  - “Some S are P”: neither distributed
  - “Some S are not P”: subject not, predicate distributed
- An invalid syllogism often violates multiple rules simultaneously; report each one specifically rather than stopping at the first found.

## Does NOT apply when
- All distribution rules are satisfied – e.g., “All mammals are animals; All dogs are mammals → ∴ All dogs are animals” is valid: the middle term is distributed (as subject of the second premise), and no conclusion term is overextended.
- The inference is statistical, empirical, or inductive rather than a formal categorical deduction (unless it is presented as logically necessary).

## Commonly confused with
- **[Undistributed middle](logic/formal_fallacies/fallacies_of_distribution/undistributed_middle)** ([MD](logic/formal_fallacies/fallacies_of_distribution/undistributed_middle.md)) – the *middle* term fails to connect because it is undistributed in all its occurrences. Ask: which term is at fault?
- **[Illicit process](logic/formal_fallacies/fallacies_of_distribution/illicit_process)** ([MD](logic/formal_fallacies/fallacies_of_distribution/illicit_process.md)) – a *major or minor* term is overextended in the conclusion vs. its premise. Ask: which term is at fault?
- **[Fallacies of ambiguity](ambiguity/index)** ([MD](ambiguity/index.md)) – a term or statement is *ambiguous* (e.g., equivocation: the same word means different things in different premises), which can look like an inconsistent scope. Ask: does the term keep one consistent meaning but get a wider scope in the conclusion (→ fallacy of distribution, or one of its sub-types), or does its *meaning* shift, or is the ambiguity elsewhere (→ fallacies of ambiguity)?

## Examples
> **Input:** “All rectangles are polygons; all hexagons are polygons; therefore, all rectangles are hexagons.”    
> **Output:** The middle term ‘polygons’ refers only to parts of its class in both premises (the polygon-rectangles and the polygon-hexagons), so it cannot connect the other terms. This specific pattern is the *undistributed middle*; see that page for details.

> **Input:** “Some animals are cats; all dogs are animals; therefore, no dogs are cats.”    
> **Output:** This syllogism violates two distribution rules at once: ‘animals’ is undistributed in both premises (→ undistributed middle), and ‘cats’ is broader in the conclusion than in its premise (→ illicit process). Report both – the argument fails for either reason alone, even though the conclusion happens to be true.

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