“A line is composed of points. Points have no length. Therefore a line has no…

Concept

An argument commits a fallacy of composition when it assumes that a property of each individual part must also be a property of the whole. Properties do not always transfer from parts to the structure they collectively form.

Application

The premises say that every point has zero length. The conclusion then transfers that property of the points to the line composed of them, treating the whole as if it must share the property of each part.

Contrast

• Equivocation requires a key expression to change meaning during the argument; no such meaning shift occurs here.

• Hasty generalisation infers a broad claim from an insufficient sample; the argument does not reason from a sample.

• A slippery slope predicts a chain of escalating consequences; the statement predicts no such chain.

Cross-check

The defining pattern is “each part has property P, so the whole has property P.” That pattern is exactly the fallacy of composition.

Result

The committed informal fallacy is the fallacy of composition.