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12. Fallacy of Division

 

Wireless Philosophy, Fallacies, 4:52. Original title: CRITICAL THINKING - Fallacies: Fallacy of Division

Summary​

Paul Henne (Duke University) turns to the mirror image of the previous fallacy: the fallacy of division, the error of inferring that what is true of a whole must also be true of its parts.

Definition and general form​

The fallacy of division is committed when someone infers that what is true of something must also be true of that thing's parts. Henne compares it to arguing that because a university has certain qualities overall, every one of its departments must have those qualities too, even though a generally good university need not have a good taxidermy programme.

Premise 1: Whole A has properties A, B and C.
Premise 2: P is a part of A.
Conclusion: Therefore, P must have properties A, B and C.

Two examples​

A red, fast car does not make its muffler red and fast: obviously no one would make that argument, but it shows where the inference fails. A more realistic case: a friend argues that because a computer is indestructible, and the hard drive is part of that computer, the hard drive must be indestructible too. If she then tries to transfer the hard drive into a different computer, she may discover that it was only indestructible while connected to the original computer's other components; she committed the fallacy of division.

When the inference still works​

Henne notes the reasoning does not always produce a false conclusion. If a house is painted pink, and the front door is part of the house, then the front door is pink too, because every part of the house happens to have been painted. The fallacy lies in assuming this without justification, not in the conclusion necessarily being wrong.

He adds that the fallacy of division is the converse of the fallacy of composition, which infers that what is true of the parts must be true of the whole.

Key takeaway​

Just because water is wet does not mean water molecules are wet: what holds for a whole need not hold for its parts, and the inference from whole to part needs its own justification each time.