Part to Whole — Cheat Sheet

The pattern

The argument moves a property from a part up to the whole, or from the whole down to a part, as if it automatically carries over.

Parts and wholes can differ. The transfer has to be earned.

PremiseThe English department went over budget.

ConclusionTherefore the Education department went over budget.

The gapSeems reasonable, but one part going over does not mean the whole did.

The whole may be on budget even if the part went over. Two ways in:

Another part offset itMath came in under budget, covering for English.

The whole had bufferEducation has reserve funds outside the sub-department allocations.

The argument is assuming:

No other part offsetNo sub-department had a surplus to cover for English.

The whole has no bufferEducation's budget is exactly the sum of its sub-budgets, no reserves.

Listing these out strengthens the argument. Negate either and it collapses.

Same idea, rotated: "The Education department went over budget. Therefore the English department went over budget."

The flawThe whole's property does not necessarily distribute to every part.

Weakens itAny reason the part may be on budget even though the whole went over.

Strengthens / NAThe argument assumes the part is representative of the whole.

Same framework, just rotated.

When the property genuinely distributes, the inference holds.

Part to whole"Every word in this book is written in Arabic. Therefore this book is written in Arabic." Valid.

Whole to part"This region is entirely in California. Therefore every town in the region is in California." Valid.

Pattern

A property moved between part and whole without earning the transfer.

Strategy

Ask if the property actually carries over. Look for an offset or a buffer, or, flipped, whether the part is representative.