Illicit minor

The textbook case

All sparrows are birds. All birds lay eggs. So everything that lays eggs is a sparrow.

The premises are true and the conclusion is false: turtles and bees lay eggs. “All birds lay eggs” is about every bird, and tells us nothing about egg-layers that aren’t birds. The conclusion speaks for all of them anyway.

From some seeds to all of them

All the seeds in tray A sprouted. Some of the tomato seeds were planted in tray A. So all the tomato seeds sprouted.

The premise about tomato seeds is a “some” statement: it covers the tomato seeds in tray A and says nothing about the others. The conclusion is about every tomato seed, including the ones in trays nobody has checked. What does follow is smaller: some tomato seeds sprouted.

A group that quietly changes places

A teacher notices, “Everyone on the chess team is in honors math, and everyone on the chess team is a sophomore. So every sophomore is in honors math.”

Here the error is hidden in ordinary phrasing. “Everyone on the chess team is a sophomore” is about every chess player, not every sophomore, yet the conclusion makes “sophomores” its subject and speaks for all of them. The sophomores who aren’t on the chess team were never described. The premises support only “some sophomores are in honors math”, and even that relies on the chess team having members (see Existential fallacy).

In a syllogism (two premises, a conclusion, three terms), the minor term (P, “egg-layers”) is the subject of the conclusion, the major term (R, “sparrows”) is its predicate, and the middle term (Q, “birds”) links them in the premises. The minor premise is the one containing the minor term. Here the major premise is listed first, as textbooks do.

A term is distributed in a statement when the statement says something about every member of that group. “All birds lay eggs” says something about every bird, but not every egg-layer. “Some tomato seeds were in tray A” says something about neither group as a whole. An “all” or “no” conclusion distributes its subject. (The Undistributed middle page explains distribution in more detail.)

The rule broken: a term distributed in the conclusion must be distributed in its premise. The conclusion makes a claim about every P while the premise described only some P’s, so the conclusion carries information the premises don’t.

The valid column is the familiar pattern “All birds lay eggs; all sparrows are birds; so all sparrows lay eggs”, with sparrows now as P and egg-layers as R. Its minor premise is about every sparrow, which is what the conclusion needs.

The name. Hurley’s textbook says “illicit minor” is short for “illicit process of the minor term”, and Hamblin gives the same long name. Illicit process is the umbrella term for breaking this rule with either term: when the term in question is the conclusion’s predicate, the fallacy is Illicit major.

• When the premise really does cover all of the minor term’s group. “All sparrows are birds”, “every tomato seed was planted in tray A” or “every sophomore is on the chess team” is about every member, and an “all” conclusion can follow.
• When the conclusion is only “some”. From the seed premises, “some tomato seeds sprouted” follows. This doesn’t always work: a “some” conclusion from two “all” premises also needs the groups to have members, which is the Existential fallacy‘s territory.
• As an inductive generalization, labeled as one. If the tomato seeds in tray A were a fair sample, their sprouting is evidence about the rest. That’s a question of sample quality (see Hasty generalization), and the conclusion should be stated as probable, not as following from the premises.

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

The same terms, the right way round

All birds lay eggs. All sparrows are birds. So all sparrows lay eggs.

This uses the same three groups as the textbook case, with “all” statements throughout. But the conclusion’s subject is now sparrows, and “All sparrows are birds” is about every sparrow. The premise covers the whole group the conclusion talks about, so the argument is valid.

A “some” conclusion from a “some” premise

All the seeds in tray A sprouted. Some of the tomato seeds were planted in tray A. So some of the tomato seeds sprouted.

A reader primed by the seed example might flag this too, since it reasons from one tray to the tomato seeds. But the conclusion is now about some tomato seeds, which distributes nothing, and the “some” premise already says those seeds exist. That’s the second condition under “When it isn’t an error”.

The illicit minor often rides on quietly flipping an “all” statement. “Everyone on the chess team is a sophomore” slides into “the sophomores are the chess team”. Hurley names that reversal, “All A are B, so all B are A”, as its own formal fallacy, illicit conversion.

It also borrows the feel of a generalization. Seeing a pattern hold across one part of a group invites the thought that it holds for the group as a whole. The syllogism looks like it proves that, when at most it supplies a sample.

Ask about the members of the conclusion’s group that the premises never mentioned: the egg-layers that aren’t birds, the seeds in other trays, the sophomores not on the chess team. If the premises say nothing about them, the “all” conclusion outruns its support. That shows the argument is invalid, not that the conclusion is false (see Valid vs. true).