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.

• 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.

• Routing: if exactly one rule is clearly violated, use the specific page instead:
  • Middle term undistributed in all its occurrences → Undistributed middle (MD)
  • A major/minor term overextended in the conclusion vs. its premise → 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.

• 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).

• 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 (MD) – a major or minor term is overextended in the conclusion vs. its premise. Ask: which term is at fault?
• Fallacies of ambiguity (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)?

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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