Illicit Major and Minor Terms

6 Illicit Major and Minor Terms

McNuggets are fast food, but Big Macs aren’t McNuggets, so Big Macs aren’t fast foo… Wait. That doesn't work.

John Doe, thinking through categorical logic for the first time

The categorical syllogism is the foundation of Aristotelian logic, and he defines it in Prior Analytics at 24a19–22:

A syllogism is a discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so. I mean by the last phrase that it follows because of them, and by this, that no further term is required from without in order to make the consequence necessary.

There are 15 valid syllogisms, of which these three are examples:

(1) All A are B	All cats are mammals.
(2) All B are C	All mammals are warm blooded.
(3) All A are C	All cats are warm blooded.

(1) All A are B	All Christians are monotheists.
(2) No B are C	No monotheists are polytheists.
(3) No A are C	No Christians are polytheists.

(1) All A are B	All wolves are canines.
(2) Some A are C	Some wolves are black-colored.
(3) Some C are B	Some black-colored things are canines.

The categorical logic fallacies are called formal fallacies because they are all violations of proper syllogistic form. This chapter deals with the illicit major and minor terms fallacies. Also see the other chapters on the exclusive premises fallacy (Chapter 4), the four terms fallacy (Chapter 5), and the fallacy of the undistributed middle term (Chapter 7).

The fallacies of illicit major term and illicit minor term have to do with distribution in syllogisms. The rule for making a good syllogism is that you can’t have a term distributed in the conclusion that’s not distributed in the premise. So if you are only talking about some of something, then you can’t go on to conclude something about all of that something. For example:

1. All cats are blue.
2. All cats are furry.
3. Therefore, all blue things are furry.

In the premise, we haven’t extended the whole class of blue things, so we can’t go on to make a claim about all blue things in the conclusion. This argument is an example of the illicit process of the minor term. An illicit major occurs when the conclusion distributes its predicate but the major premise does not:

1. All cats are blue.
2. No dogs are cats.
3. Therefore, no dogs are blue.

From the first example’s premises, we could conclude that some furry things are blue – all the ones that are cats. Then we are not distributing the term “furry things.” At least, according to Aristotle we could conclude that. Nowadays, those who follow Boolean logic would claim that’s an example of the existential fallacy.

Sometimes, our terms are so undistributed that we can’t even make a valid conclusion, and that’s when we get the rule for all syllogisms that you can’t make a valid one from two particular premises. For example:

1. Some cats are blue.
2. Some cats are furry.
3. …?

There’s no way to know if the same cats are both blue and furry, because none of the terms are distributed in that example. That is, we don’t know anything about cats in general, we don’t know anything about blue things in general, and we don’t know anything about furry things in general. We don’t even know if the cats that are blue are the same as the ones that are furry, because the middle term is also undistributed. Aristotle gives a ton of examples of arguments that fail due to mismatched distributions, and the medieval logicians formalized rules based on these observations.

In short, you can’t distribute anything in the conclusion that wasn’t distributed in the premises. But feel free not to distribute in the conclusion whatever was distributed in the premises. That’s just fine.