Illicit major

The textbook case

All roses are flowers. No tulips are roses. So no tulips are flowers.

Both premises are true and the conclusion is false. The first premise is about every rose, not every flower, so it leaves room for flowers that aren’t roses. Tulips can fill that room. Saying tulips aren’t roses removes them from one part of the flower group, not from all of it.

The kids’ menu

A parent asks a server which soups are gluten-free. The server checks the menu and says, “Every dish on the kids’ menu is gluten-free, and none of the soups are on the kids’ menu, so none of the soups are gluten-free.”

The first statement is a promise about every kids’-menu dish. It says nothing about gluten-free dishes elsewhere on the menu. A soup can be gluten-free without being on the kids’ menu, so the server has no grounds to rule them all out. The conclusion might happen to be true; the reasoning doesn’t show it.

A cautious-sounding “some”

All the certified lifeguards at the camp are strong swimmers. Some of the counselors aren’t certified lifeguards. So some of the counselors aren’t strong swimmers.

This one is harder to catch, because the conclusion is modest and quite plausible. But “some counselors aren’t strong swimmers” still says those counselors fall outside the whole group of strong swimmers, and the first premise only described the lifeguards among them. Uncertified counselors might all swim well.

In a syllogism (two premises, a conclusion, three terms), the major term (R, “flowers”) is the predicate of the conclusion, the minor term (P, “tulips”) is its subject, and the middle term (Q, “roses”) links them in the premises. The major premise is the one containing the major term.

A term is distributed in a statement when the statement says something about every member of that group. “All roses are flowers” says something about every rose but not every flower. “No tulips are flowers” says something about every flower (none is a tulip). “Some counselors aren’t strong swimmers” also counts as distributing its predicate, because it places those counselors outside the whole group of strong swimmers. (The Undistributed middle page explains distribution in more detail.)

The rule broken: a term distributed in the conclusion must be distributed in its premise. Hurley’s explanation is that the conclusion “makes an assertion about every member” of the major term’s group while the premise covered only some of it, so the conclusion “contains information not contained in the premises.”

The valid column swaps the major premise around. “All R are Q” (every flower is a rose, say) is about every R, and the same conclusion then follows, though that particular premise would be false.

With a single thing as the subject, the pattern is Denying the antecedent in categorical dress: “If it’s a rose, it’s a flower. This isn’t a rose. So it isn’t a flower.”

The name. Hurley’s textbook says “illicit major” is short for “illicit process of the major term”; Hamblin gives the same long name. Illicit process is the umbrella term for breaking this rule with either term: with the conclusion’s subject instead, the fallacy is Illicit minor. The SEP entry on fallacies reports that Richard Whately counted undistributed middle and illicit process among the “purely logical” fallacies.

• When the premise really does cover all of the major term’s group. “All flowers here are roses”, “Only kids’-menu dishes are gluten-free”, or “Every gluten-free dish is marked with a leaf” each say something about every member, and a negative conclusion can follow.
• As a clue rather than a proof. If most strong swimmers at the camp are there because they are certified lifeguards, knowing someone isn’t certified is some evidence about their swimming. The error is presenting that as settled.

The test: does the premise that mentions the conclusion’s predicate say something about every member of that group?

A mark that every member carries

Every gluten-free dish on the menu is marked with a green leaf. None of the soups have a green leaf. So none of the soups are gluten-free.

This has the same ingredients as the kids’-menu example: an “all” premise, a “none” premise, and a “none” conclusion about gluten-free dishes. The difference is which way the “all” runs. Here it is about every gluten-free dish, so any gluten-free soup would carry the leaf, and the conclusion follows. Whether the menu is marked reliably is a question about the premise’s truth.

“Only”

Only the dishes on the kids’ menu are gluten-free. None of the soups are on the kids’ menu. So none of the soups are gluten-free.

One word changed from the fallacy. “Only kids’-menu dishes are gluten-free” means every gluten-free dish is on the kids’ menu, a statement about the whole gluten-free group. That meets the first condition under “When it isn’t an error”, so the argument is valid.

“All roses are flowers” is easy to hear as a two-way link between roses and flowers, and “only” and “all” are easily blurred in conversation. Once the link feels two-way, being outside one group seems to mean being outside the other.

A plausible conclusion also hides the gap. When the conclusion is probably true anyway, as with the counselors, nothing prompts a check on whether the premises actually reached it.

Ask whether anything outside the middle group could still belong to the conclusion’s group: a gluten-free dish not on the kids’ menu, a strong swimmer who isn’t a lifeguard. If so, the premises don’t rule it out. That shows the argument is invalid, not that its conclusion is false (see Valid vs. true).