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The Fallacies of Composition and Division
Sandra LaFave
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.”[1]
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
member
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. Try it! 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.
Do
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.
Emergent
Properties
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. [1] 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.
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