A Treatise of Human Nature · Chapter
Section IV: Objections Answered explained
Hume addresses objections to his theory of space and time, defending the finite divisibility of extension and the rejection of vacuum.
What happens
Hume addresses objections to his theory of space and time, defending the finite divisibility of extension and the rejection of vacuum. He argues that mathematical points, when conceived as colored or solid, avoid the absurdity of nonentity and penetration. He also critiques the notion of an imaginary standard of equality, showing that our ideas of equality and right lines are based on sensory appearances and corrections, not on any perfect standard. Hume concludes that geometrical demonstrations for infinite divisibility are sophistical, as they rely on ideas that are themselves finite and indivisible.
Themes in this chapter
Skepticism About the External World
Hume questions the certainty of geometrical and mathematical knowledge, suggesting that our standards of equality and perfection are imaginary fictions.
Custom and General Rules
The mind forms fictions of perfect equality and right lines through custom, even when reason has ceased to support them.
Characters to notice
- David Hume
Author and narrator, presenting arguments against objections to his system.
Key passages
“This standard is plainly imaginary. For as the very idea of equality is that of such a particular appearance corrected by juxtaposition or a common measure. The notion of any correction beyond what we have instruments and art to make, is a mere fiction of the mind, and useless as well as incomprehensible.”
The standard of perfect equality is a fiction of the mind, since our actual idea of equality is based on sensory appearances corrected by measurement, and any correction beyond that is imaginary and useless.
Hume argues that our notion of perfect equality is an imaginary standard, not derived from experience.
“The original standard of a right line is in reality nothing but a certain general appearance; and it is evident right lines may be made to concur with each other, and yet correspond to this standard, though corrected by all the means either practicable or imaginable.”
Our idea of a right line is based on a general sensory appearance, and even with all possible corrections, lines can still appear right while actually meeting, showing the standard is not precise.
Hume challenges the mathematical notion of a perfect right line, asserting it is based on appearance rather than exact definition.