The Fallacies of Composition and Division
We begin with some review.
Terms are words or phrases that designate classes.
General terms designate classes with more than one member, e.g., common nouns such as “book” or “tree.”
Singular terms designate individuals, e.g., proper nouns (“The Taj Mahal”), or proper names (“Princess Diana”).
Non-denoting terms refer to the empty class (also known as the “null set”), e.g., “mermaid.”
The denotation of a term is, for general terms, the class of things in the world to which the term correctly applies. Philosophical synonyms for “denotation” are “reference” and “extension.” For example, the denotation (or “reference” or “extension”) of the term “book” is all books. Of course, as discussed in the handout “Open and Closed Concepts and the Continuum Fallacy,” for most terms, strictly-defined classes of things to which terms refer (strictly-defined denotations) don’t really exist, since most concepts are open. For example, most of the time we can say whether or not something is a book (the things on shelves in libraries are, the things in cages in zoos are not); yet we are still puzzled about whether a text existing entirely online should be called a book. It’s okay that most concepts are open and denotations can be fuzzy; that’s how language works.
The connotation of a term is the list of membership conditions for the denotation. Philosophical synonyms for “connotation” are “sense,” “intension,” and “real definition.” Note this sense of “connotation” differs from the literary sense. Again, as language and thought evolves, connotations get modified.
The connotation of the general term “square” is “rectangular and equilateral.” The denotation of the general term “square” is all squares.
Now let’s focus on general terms only.
We often use general terms as the subjects of statements. (A statement is a kind of sentence – the kind of sentence that states that something is so, as opposed to questions or exclamations or commands, which don’t explicitly claim anything. Statements are also called assertions or claims. A statement has a subject and a predicate. The subject of the statement is what it’s about. The predicate of a statement is what’s said about the subject.)
Here are some examples of statements whose subjects are general terms. The subjects of the statements are in italics; the predicates of the statements are the non-italicized parts.
In the first statement above, the predicate is “are mammals”. Note that the noun “mammals” in the predicate is also a general term denoting a class. The statement “Cats are mammals” says that the class of cats is a subclass of the class of mammals. Or, all the members of the denotation of “cats” are also members of the denotation of “mammals.”
The fallacies of composition and division arise from ambiguity in the denotation of general terms in cases like (1) – (4) above, where the general term functions as the subject of a statement.
When a general term is the subject of a statement, the predicate of the statement can apply to it collectively or distributively .
Consider the following two statements:
1. Passengers on this airline fly millions of miles a year.
2. Passengers on this airline have their choice of three meals.
These statements have the same subject term (“passengers on this airline”). But notice that the predicates apply to this subject differently. In the first sentence, the predicate “fly millions of miles a year” is true of passengers on this airline considered as a group, but it is not true of each passenger, since many airline passengers do not fly millions of miles a year. However, the collective mileage of all the passengers considered as a group does amount to millions of miles a year, so in that sense the statement is true.
In the second sentence, the predicate “have their choice of three meals” is true of each passenger, but it is not true of the passengers considered as a group. (It’s not like there are only three meals that all the passengers have to share, so each passenger gets only a few molecules – no, each passenger can choose among three whole meals.)
A predicate applies to a general-term subject collectively
if and only if the statement is true of the denotation of the subject term
considered as a whole unit, but the statement is not necessarily true of each
of the denotation. In statement (1) above, the predicate applies collectively.
A predicate applies to a general-term subject distributively if and only if the statement is true of each member of the denotation, but not necessarily true of the denotation considered as a whole. In statement (2) above, the predicate applies distributively.
Here is a simple rule to remember the difference. Ask yourself, “Could I rephrase this statement beginning with the word “each” and preserve truth value?” If yes, the predicate applies distributively. If no, the predicate applies collectively. This simple rule works well in many cases.
1. Cats are mammals.
2. Animals have roamed the earth longer than humans.
In (1) the predicate applies distributively, since it’s true that each cat is a mammal. So you could reasonably argue:
Cats are mammals.
Fluffy is a cat.
So Fluffy is a mammal.
In (2), the predicate applies collectively but not distributively, since it’s not true that each animal has roamed the earth longer than humans. So you can’t reasonably argue:
Animals have roamed the earth longer than humans.
My dog Spot is an animal.
So Spot has roamed the earth longer than humans.
you see that collective and distributive predication matter, then? I hope so!
Now let’s look at some fallacious arguments, where the fallacy consists in confusion of collective and distributive predication. Many of these arguments are obviously bad, and funny. For example,
Twenty percent of the men who attend WVC are married.
Jack attends WVC.
So twenty percent of Jack is married.
What’s wrong exactly? It’s that the predicate “married” applies to the subject “twenty percent of the men who attend WVC” collectively; in other words, if you consider the whole group of guys who attend WVC, you’ll find that twenty percent of the whole group are married. The predicate is not true of each man (it doesn’t apply distributively; it’s true of some and false of others), but it does apply to the men considered as a whole.
Arguments like this are said to commit the fallacy of division. The fallacy of division consists in assuming (wrongly) that a predicate that applies collectively must also apply distributively.
Here’s another silly argument:
The atoms comprising this barrel of bricks are practically weightless.
So this barrel of bricks is practically weightless.
The predicate “practically weightless” is true of each atom; i.e., it is true of the barrel of bricks distributively, if you think of the barrel of bricks as a collection of atoms. Yet the predicate is clearly false when you think of the barrel of bricks as a whole; barrels of bricks have noticeable weight.
Arguments like this are said to commit the fallacy of composition. The fallacy of composition consists in assuming (wrongly) that a predicate that applies to a subject distributively must also apply collectively.
These examples have been silly, but they point to deep philosophical issues. For example, many people would agree with the following argument:
Everything in the universe has a cause.
So the universe as a whole must have a cause.
Now, the predicate “caused” is true of everything in the universe (nothing is uncaused); in other words, the predicate “caused” is true of the universe distributively. But from that, can we be certain it’s true collectively as well? No, because we know that predicates true distributively are not necessarily true collectively. This argument commits the fallacy of composition.
Here’s another, more complex and extremely common argument:
1. All the individual cells comprising my body lack consciousness (i.e., no individual cell is conscious).
2. Therefore, my body can’t be conscious.
3. But I am conscious.
4. Therefore, I must be more than a mere body. I must have a mysterious non-physical component to account for my consciousness.
I hope you see that the move from (1) to (2) is clearly a fallacy of composition. What’s true of my cells (me distributively) is not necessarily true of me (me collectively, i.e., as a person or body). So the argument consisting of statements (2) through (4), though of modus tollens form and valid, is still unsound.
Some properties emerge only after you combine things into wholes. Such properties are called, not surprisingly, emergent properties. That’s often why what’s true of the parts isn’t necessarily true of the wholes, and vice-versa. Using John Searle’s famous example, being wet is an emergent property of water. None of the water molecules are wet. But wetness happens when you put enough of those molecules together. Obviously, then, the following argument is silly:
1. All the individual molecules comprising this water lack wetness.
2. Therefore, this water can’t be wet.
3. But this water is wet.
4. Therefore, this water must be more than these mere molecules. This water must have a mysterious non-physical component to account for its wetness.
The move from (1) to (2) is an obvious fallacy of composition because wetness is an emergent property. Searle says consciousness is an emergent property of brains just like wetness is an emergent property of water. Neither wetness nor consciousness necessarily requires anything non-physical to explain it.
 Philosophers also like to think of predicates as properties. A property, in philosophy, means an attribute or characteristic. So when we say “Cats are mammals” we mean not only that the members of the denotation of the word “cats” are also members of the denotation of the word “mammals”; we also mean cats have the property or characteristic of being mammals.
Philosophers like to use the word “predicate” as a verb as well as a noun. When we use the word “predicate” as a verb, we pronounce the word with a long “a”: PRED-i-cayte. We predicate when we say that something has a certain property. Saying “Cats are mammals,” for example, assigns the property of “mammal-ness” to cats. In other words, in this sentence “mammal-ness” is predicated of cats.