Division
Jason Waller
You hated this casserole made of onions, carrots, and beef that I cooked for you, so I’ll make sure to never buy onions, carrots, or beef for you to eat again.
The typical mom
The fallacy of division occurs when one incorrectly infers that the characteristics, attributes, or features of the group as a whole will also be found in the individuals comprising the group.
Consider the following:
(1) The Cleveland Orchestra can play the full-orchestrated version of Beethoven’s Symphony No. 7.
(2) Therefore, Mary Kay Fink (the piccolo player) can play the full- orchestrated version of Beethoven’s Symphony No. 7.
From the fact that the entire orchestra can do something, it does not follow that each part can do that same thing. Mary Kay Fink can certainly play her part of the symphony, but she cannot play the whole thing. She could never play all of the different instruments at the same time. So even if the whole orchestra can play a certain piece of music, we cannot infer that Mary Kay Fink can play the same piece of music. Similarly, the following argument makes the same mistake:
(1) Beethoven’s Symphony No. 7 takes around 35 minutes to perform.
(2) Therefore, the second movement of Beethoven’s Symphony No. 7 takes around 35 minutes to perform.
Clearly, because the whole symphony performance has some particular property (namely, that of taking 35 minutes to perform), it does not follow that the parts of the symphony have the same property. In fact, the time it takes to perform each movement must be much shorter than the time it takes to perform the whole. To consider another set of examples, consider the case of Congress:
(1) The laws passed by the Congress were radical.
(2) Jones is a member of Congress.
(3) Therefore, Jones is radical.
If the laws that Congress passed were radical and Jones were a member of that Congress, it may be tempting to infer that Jones himself must be a radical. But a moment’s reflection reveals that this inference is invalid.
Perhaps Jones was outvoted by many other radicals in the Congress. Perhaps the laws were compromises, which no one in the Congress particularly wanted. Perhaps the Congress members did not understand the laws they were passing. There are many possible ways for both Premise 1 and Premise 2 to be true but Premise 3 false. Thus, this argument is clearly invalid. We cannot infer that the parts of something have a property just because the whole of something has that property.The easiest way to avoid this fallacy is never to assume that the characteristics, attributes, or features of the group as a whole will also be found in the individuals comprising the group. One must inspect and evaluate the characteristics, attributes, or features of the whole separately from the parts of which the whole is comprised. Inferences from a whole to a part can be made, however, if additional assumptions are added to the argument that link together the property had by the whole with the property had by the part. For example, if may be inferred from the claim that a book is made of paper that each chapter of the book is made of paper. But this inference can only be made if the additional assumption is added that the entire book is made of only one kind of material (i.e., paper). Similar arguments can be made about a wall made only from bricks. If the wall is made only of bricks, then we can infer that half of the wall is made entirely of bricks also. This inference is possible only because we added information about the composition of the wall to the premises so that we avoid the fallacy of division.