Fallacy of Division and Composition

by Thomas Howe

posted by Southern Evangelical Seminary

Fallacy of Division

 

Definition of the Fallacy

The FALLACY OF DIVISION is the reverse of the fallacy of Composition (see below). Someone commits the fallacy of Division when he assumes that what is true of the whole is true of a part. There are two kinds of fallacy of Division. First, one argues that what is true of the whole is true of all of the parts. The second instance is to argue from the attributes of a collection of elements to the attributes of each of the elements.

Example of the Fallacy

An example of the first kind would be to argue that because a machine is heavy, or complicated, or valuable, that each of its parts must be heavy, or complicated, or valuable. An example of the second kind is to argue that because SES students study philosophy, theology, hermeneutics, Greek, Hebrew, missions, evangelism, and preaching, that every SES student studies philosophy, theology, hermeneutics, Greek, Hebrew, missions, evangelism, and preaching.

Attacking the Fallacy

Attacking either form of the fallacy involves showing that what is true of the whole is not necessarily true of the parts. One way to do this is by a counter-example. Just because a mosaic on the wall of the county courthouse is rectangular does not mean that each piece of the mosaic is rectangular. You must challenge your opponent to demonstrate why or how what is true of the whole is necessarily true of the parts. This is not as easy as it sounds, however. Take the following example:

The wall of the county courthouse is yellow.

This tile is a tile in the wall of the courthouse.

Therefore, this tile is yellow.

It would seem to be the case that if the whole wall is yellow, that every part of the wall is yellow. But, think about a computer screen. The analog computer screen is composed of pixels that are excited by the beam of an electron gun. The electron gun shoots out beams that excite certain pixels on the screen. These pixels correspond to the colors red, green, and blue. That is why they are often referred to as RGB monitors. But, it is possible to make the entire screen yellow. But, because the entire screen is yellow, does that mean that each of the pixels is yellow? Apparently not. Apparently, it is the exciting of the appropriate pixels at the appropriate intensity that makes the screen appear yellow. How then do we distinguish between valid and invalid division? Consider the following examples.

Dogs are carnivorous.

Afgans are dogs.

Therefore, Afgans are carnivorous.

Is this a valid argument? If so, how does it differ from the following argument?

Dogs are frequently seen in people’s back yards.

Afgans are dogs.

Therefore, Afgans are frequently seen in people’s back yards.

The above argument is obviously not valid. Just because dogs are often found in someone’s backyard does not mean, necessarily, that Afgans are so found. Valid from invalid division can be distinguished by distinguishing an accidental property from that which constitutes the essence of anything. For example, it is part of the essence of a dog that it be carnivorous. Consequently, what is true of the essence of dogs is true of any particular dog. However, although it is true of the essence of a dog that it be located in some place, it is not essential that the dog be in this specific place.

Native Americans are disappearing.

That man is an Native Americans.

Therefore, that man is disappearing.

The relationship of parts to whole depends upon how a substance actuates its potency. If a substance actuates its potency by means of the individual accidents of which it is composed, then the character of the individual accidents will constitute the character of the whole. If the substance actuates its potency by means of all of the accidents as a whole, then the individual characteristic of the accident may not be the characteristic of the whole. A color inheres in a substance, and the actuation of the potency to be a certain color adds a form to the substance, or by virtue of actuating a potency of the accident, a potency of the substance is actuated. So, if all the accidental parts of a thing are green, then the whole is green. However, other kinds of accidents do not add any form or alter in any way the form of a substance. For example, the color of a wall is intrinsic to the wall as a wall. In other words, a wall must have some color, but it is not a necessary characteristic of a wall to be a certain color, say, blue. But, the shape of individual parts of the wall are extrinsic to the wall as a wall, in the same way the location of the wall is extrinsic to the wall as a wall. Being here or being there does not change the form of the wall. But, being green or being non-green does change the form of the wall. The color of the individual parts actuates the form of the wall. The shape of the individual parts does not actuate the shape of the wall. Rather, the shape of all of the parts together actuates the shape of the wall.

Fallacy of Composition

Definition of the Fallacy

The FALLACY OF COMPOSITION consists of assuming that what is true of the parts of a whole is necessarily true of the whole.

Example of the Fallacy

There are instances in which an argument of this type does not commit the fallacy of composition. It is not accurately identified as an exception, however. Rather, it is simply an argument that does not commit this fallacy. The question is this: on the basis of what principle is it possible to distinguish between an argument that does and one that does not commit this fallacy. A general rule might be that if the characteristic of the parts to which the argument refers are characteristics that constitute not only an essential characteristic of the part, but an essential characteristic of the whole, then the argument is not a fallacy.

For example, to say that every part of a mosaic is green, therefore the whole mosaic is green, we are referring to an essential characteristic of both the parts and the whole. It is of the essence of a mosaic that it be some color. A mosaic would not be a mosaic except it be colored in some way. Even white is a color. If all of the parts have the same color, then the resulting whole will have that color. However, if someone argues that every part of a mosaic is triangular in shape, therefore the whole mosaic is triangular is a fallacy of composition. It is true that in order for a mosaic to be a mosaic it must have a shape. But whereas it is the color of the individual parts that necessarily constitutes the essential attribute of the color of the whole, it is not the case that the shape of the individual parts necessarily constitutes the essential attribute of the shape of the whole. The relationship between the whole and its parts is different in the two instances. In the instance of color, the color of the whole derives from the color of its parts individually because that is the nature of the characteristic itself. However, the characteristic of the shape of the whole does not derive from the characteristic of the shape of the parts individually. The shape of the whole does not directly derive from the shape of individual parts because that is the nature of the characteristic. With regard to some attributes, there is an emergent quality in the whole that is the result of the combination of parts. But, if every part of the universe is finite, then an infinite quality does not emerge from the combination of finite parts because one cannot get an infinite by adding finite parts together. Color is a characteristic that derives from the nature of the parts. Shape is a characteristic that derives from the nature of the whole.

Attacking the Fallacy

To attack this fallacy one must show that the individual characteristics either do not constitute that characteristic of the whole or that the characteristics of the parts do not provide an exhaustive explanation of the whole. If all the parts of the garden are flowers, then the whole garden will be flowers because the kind of thing the garden is is derived from the kind of thing its parts are. However, simply because all the parts of the garden are flowers, does not mean the garden is only flowers because the fact that the individual flowers are arranged in an interrelated pattern is what makes this group of flowers into a garden. The gardenness of the garden is a characteristic that derives from the nature of the whole, not solely from the nature of the parts.

The views and opinions expressed in this article are those of the author and do not necessarily reflect the position of Southern Evangelical Seminary.

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