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Recipe

Check a syllogism with the five rules

Use when: an argument has two premises and a conclusion, each an all, no, or some statement, sharing exactly three groups

Goal: a verdict, valid or invalid, and for an invalid one the name of the rule it breaks

Taught in Syllogisms, mood, figure, and distribution

Quick recipe

  1. Put it in standard form and order
  2. Mark every distributed term
  3. Rules 1 and 2, distribution
  4. Rules 3 and 4, negatives
  5. Rule 5, existence
  6. Give the verdict
  1. 1

    Rewrite each sentence in standard form. Read S and P off the conclusion, find M, and put the major premise first.

    Example

    "Some of today's returns need a receipt, because all refunds need one and some of today's returns are refunds": conclusion S = today's returns, P = things needing a receipt, M = refunds.

    Why: the rules talk about the major term, minor term, and middle term, so you need to know which is which.

  2. 2

    In each statement, mark the distributed terms: A its subject, E both, I neither, O its predicate.

    Example

    "All refunds are things needing a receipt": refunds distributed. "Some returns are refunds": nothing distributed. "Some returns are things needing a receipt": nothing distributed.

    Why: rules 1 and 2 are both about distribution.

  3. 3

    Is M distributed in at least one premise? Is every term that is distributed in the conclusion also distributed in its premise?

    • M never distributed — invalid, undistributed middle.
    • P or S distributed in the conclusion only — invalid, illicit major or illicit minor.

    Why: the middle term has to cover its whole class to link S and P, and a conclusion can't cover more of a class than its premise did.

  4. 4

    Count the negative statements (E and O).

    • both premises negative — invalid, exclusive premises.
    • one negative premise but an affirmative conclusion, or a negative conclusion with no negative premise — invalid, rule 4 (affirmative conclusion from a negative premise, or negative conclusion from affirmative premises).

    Why: exclusions alone link nothing, and negatives in the premises and the conclusion have to match.

  5. 5

    If both premises are A or E and the conclusion is I or O, it is invalid: the existential fallacy.

    Why: on the Boolean reading, universal premises never promise that anything exists, and a particular conclusion does.

  6. 6

    Passing all five rules means valid. Otherwise name the first rule broken.

    Why: the five rules are both necessary and sufficient for Boolean validity, as the rules card states.

Common mistakes

  • Reading S and P from the premises instead of the conclusion.
  • Treating the predicate of an A-statement as distributed.
  • Forgetting rule 5 because the argument "obviously" talks about real things.