A Freeper's Introduction to Rhetoric (Part 11, Fallacies of Composition and Division)

Introduction to Logic | Irving M. Copi & Carl Cohen

[general_re]

Composition

The term "fallacy of composition" is applied to both of two closely related types of invalid argument. The first may be described as reasoning fallaciously from the attributes of the parts of a whole to the attributes of the whole itself. A particularly flagrant example would be to argue that, since every part of a certain machine is light in weight, the machine "as a whole" is light in weight. The error here is manifest when we recognize that a very heavy machine may consist of a very large number of lightweight parts. Not all examples of this kind of fallacious composition are so obvious, however. Some are misleading. One may hear it seriously argued that, since each scene of a certain play is a model of artistic perfection, the play as a whole is artistically perfect. But this is as much a fallacy of composition as it would be to argue that, since every ship is ready for battle, the whole fleet must be ready for battle.

The other type of composition fallacy is strictly parallel to that just described. Here, the fallacious reasoning is from attributes of the individual elements or members of a collection to attributes of the collection or totality of those elements. For example, it would be fallacious to argue that because a bus uses more gasoline than an automobile, therefore all buses use more gasoline than all automobiles. This version of the fallacy of composition turns on a confusion between the "distributive" and the "collective" use of general terms. Thus, although college students may enroll in no more than six different classes each semester, it is also true that college students enroll in hundreds of different classes each semester. This verbal conflict is easily resolved. It may be true of college students, distributively, that each of them may enroll in no more than six classes each semester. This is a distributive use of the term "college students," in that we are speaking of college students taken singly. But it is true of college students, taken collectively, that they enroll in hundreds of different classes each semester. This is a collective use of the term "college students" in that we are speaking of college students all together, as a totality. Thus, buses use more gasoline than automobiles, distributively, but collectively automobiles use more gasoline than buses, because there are so many more of them.

This second kind of composition fallacy may be defined as "the invalid inference that what may truly be predicated of a term distributively may also be truly predicated of the term collectively. " Thus the atomic bombs dropped during World War II did more damage than did the ordinary bombs dropped — but only distributively. The matter is exactly reversed when the two kinds of bombs are considered collectively, because there were so many more conventional bombs dropped than atomic ones. Ignoring this distinction in an argument would permit the fallacy of composition.

These two varieties of composition, although parallel, are really distinct because of the difference between a mere collection of elements and a whole constructed out of those elements. Thus a mere collection of parts is no machine; a mere collection of bricks is neither a house nor a wall. A whole such as a machine, a house, or a wall has its parts organized or arranged in certain definite ways. And since organized wholes and mere collections are distinct, so are the two versions of the composition fallacy, one proceeding invalidly to wholes from their parts, the other proceeding invalidly to collections from their members or elements.

Division

The fallacy of division is simply the reverse of the fallacy of composition. In it the same confusion is present, but the inference proceeds in the opposite direction. As in the case of composition, two varieties of the fallacy of division may be distinguished. The first kind of division consists in arguing fallaciously that what is true of a whole must also be true of its parts. To argue that, since a certain corporation is very important and Mr. Doe is an official of that corporation, therefore Mr. Doe is very important, is to commit the fallacy of division. This first variety of the division fallacy would be committed in any such argument, as in moving from the premiss that a certain machine is heavy, or complicated, or valuable, to the conclusion that this or any other part of the machine must be heavy, or complicated, or valuable. To argue that a student must have a large room because it is located in a large dormitory would be still another instance of the first kind of fallacy of division.

The second type of division fallacy is committed when one argues from the attributes of a collection of elements to the attributes of the elements themselves. To argue that, since university students study medicine, law, engineering, dentistry, and architecture, therefore each, or even any, university student studies medicine, law, engineering, dentistry, and architecture would be to commit the second kind of division fallacy. It is true that university students, collectively, study all these various subjects, but it is false that university students, distributively, do so. Instances of this variety of the fallacy of division often look like valid arguments, for what is true of a class distributively is certainly true of each and every member. Thus the argument

Dogs are carnivorous.
Afghan hounds are dogs.
Therefore Afghan hounds are carnivorous.

is perfectly valid. Closely resembling this argument is another,

Dogs are frequently encountered in the streets.
Afghan hounds are dogs.
Therefore Afghan hounds are frequently encountered in the streets.

which is invalid, committing the fallacy of division. Some instances of division are obviously jokes, as when the classical example of valid argumentation

Humans are mortal.
Socrates is a human.
Therefore Socrates is mortal.

is parodied by the fallacious

American Indians are disappearing.
That man is an American Indian.
Therefore that man is disappearing.

The old riddle "Why do white sheep eat more than black ones?" turns on the confusion involved in the fallacy of division, for the answer, "Because there are more of them," treats collectively what seemed to be referred to distributively in the question. The fallacy of division, which springs from a kind of ambiguity, resembles the fallacy of accident (discussed previously) which springs from unwarranted presumption. Likewise, the fallacy of composition, also flowing from ambiguity, resembles the hasty generalization we call "converse accident." But these likenesses are superficial. An explanation of the differences between the two pairs of fallacies will be helpful in grasping the errors committed in all four.

If we were to infer, from looking at one or two parts of a large machine, that because they happen to be well designed, every one of its many parts is well designed, we would commit the fallacy of converse accident, for what is true about one or two surely may not be true of all. If we were to examine every single part and find each carefully made, and from that finding infer that the entire machine is carefully made, we would also reason fallaciously, because however carefully the parts were produced, they may have been assembled awkwardly or carelessly. But here the fallacy is one of composition. In converse accident, one argues that some atypical members of a class have a specified attribute, and therefore that all members of the class, distributively, have that attribute; in composition, one argues that, since each and every member of the class has that attribute, the class itself (collectively) has that attribute. The difference is great. In converse accident, all predications are distributive, whereas in the composition fallacy, the mistaken inference is from distributive to collective predication.

Similarly, division and accident are two distinct fallacies; their superficial resemblance hides the same kind of underlying difference. In division, we argue (mistakenly) that, since the class itself has a given attribute, each of its members also has it. Thus it is the fallacy of division to conclude that, because an army as a whole is nearly invincible, each of its units is nearly invincible. But in accident, we argue (also mistakenly) that, because some rule applies in general, there are no special circumstances in which it might not apply. Thus we commit the fallacy of accident when we insist that a person should be fined for ignoring a "No Swimming" sign when jumping into the water to rescue someone from drowning.

Accident and converse accident are fallacies of presumption, in which we assume what we have no warrant for. Composition and division are fallacies of ambiguity, resulting from the multiple meanings of terms. Wherever the words or phrases used may mean one thing in one part of the argument and another thing in another part, and those different meanings are deliberately or accidentally confounded, we may expect the argument to be bad.

[general_re]

Previous installments:

Part 1 - Introduction and the Argument From Ignorance
Part 2 - the Appeal to Inappropriate Authority
Part 3 - the Argument Ad Hominem
Part 4 - the Appeal to Force and the Appeal to Emotion
Part 5 - the Irrelevant Conclusion
Part 6 - Fallacies of Presumption and the Complex Question
Part 7 - False Cause and Begging the Question
Part 8 - Accident and Converse Accident
Part 9 - Fallacies of Ambiguity and Equivocation
Part 10 - Amphiboly and Accent

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[general_re]

Part 11. Apologies all round for the long delay, but my employer suddenly got hyperactive about this "work" thing. Sorry.

In any case, as a way of mea culpa-ing, I will post a special bonus Part 12 later today, which will consist of examples of fallacious arguments - identifying and understanding the fallacies presented will make an excellent test of the material presented in this series. And no, this is not for a grade, purely for self-improvement purposes ;)

[PatrickHenry]

PING. [This ping list is for the evolution side of evolution threads, and sometimes for other science topics. FReepmail me to be added or dropped.]

[PatrickHenry]

A particularly flagrant example [of the "fallacy of composition"] would be to argue that, since every part of a certain machine is light in weight, the machine "as a whole" is light in weight.

Because the parts of a living cell are lifeless atoms, the cell itself must be lifeless.

[general_re]

Or in reverse, one rediscovers the notion of vitalism via division - because the organism is alive, its component chemicals (molecules/atoms/quarks/et cetera) must also be "alive" in some sense.

[LiteKeeper]

read later

[general_re]

No. I'm going to read it now, and you can't stop me.

Fallacy of amphiboly, dontcha know... ;)

[PatrickHenry]

Damned fallacy of blasphemy.

[risk]

I find these very useful. Of course it makes it harder to post comments when one reviews ones statements against these standards, but so be it!

[general_re]

I'm glad you find it useful. But don't just think of it as a way of improving your own argumentation - although it is that, of course. Think of it as enhancing the tools in your BS detector kit, for when someone else is trying to slip one over on you ;)

[risk]

Thanks, I agree these tools are useful for analyzing media as well as improving my own writing. I think it works best for me when I think of it both ways.

It would be fun to start tagging articles with keywords indicating which of these failures of logic were applied (intentionally or not) and then discussing how the articles go awry. Maybe we need a "logic ping list."

If course you're familiar with http://www.freerepublic.com/forum/a360d496e0c97.htm - propaganda techniques posted by Give me Liberty.

[VadeRetro]

The second type of division fallacy is committed when one argues from the attributes of a collection of elements to the attributes of the elements themselves.

Strictly speaking, fallacies of decomposition.

[general_re]

Beethoven's gone, but his music lives on,
And Mozart don't go shopping no more.
You'll never meet Liszt or Brahms again,
And Elgar doesn't answer the door.

Schubert and Chopin used to chuckle and laugh,
Whilst composing a long symphony,
But one hundred and fifty years later,
There's very little of them left to see.

They're decomposing composers.
There's nothing much anyone can do.
You can still hear Beethoven,
But Beethoven cannot hear you.

Handel and Haydn and Rachmaninov
Enjoyed a nice drink with their meal,
But nowadays, no one will serve them,
And their gravy is left to congeal.

Verdi and Wagner delighted the crowds
With their highly original sound.
The pianos they played are still working,
But they're both six feet underground.

They're decomposing composers.
There's less of them every year.
You can say what you like to Debussy,
But there's not much of him left to hear.

[Give me Liberty]

Thanks, risk! I've been surprised at how many places ended up linking back to that post over the years. I'm glad I mirrored it here, the site I snagged it from is long since gone.

Drug War Propaganda
http://drugwarpropaganda.news-bot.net/

[Give me Liberty]

Oh dear, http://www.freerepublic.com/forum/a360d496e0c97.htm is gone. (It served us well.)

Preserved is the content, here:
http://drugpolicycentral.com/bot/pg/propaganda/proptech.htm