MENTAL MODEL · M0571

Berkeley's Ghosts of Departed Quantities

StructureHigh supportLogic

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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

Bishop Berkeley criticized the concept of $dx$ (infinitesimal) in Newton's calculus as logically unclear: it is neither zero nor non-zero, like 'ghosts of departed quantities'. This prompted the later rigorous development of limit theory.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

Scrutinize vague concepts. In business plans, be wary of concepts like $dx$ (e.g., 'potential users', 'private domain traffic'): they are treated as real numbers when calculating market size, but ignored as zero when discussing conversion rates. Must demand precise definitions to dispel 'logical ghosts'.

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Anchor fast decisions

Berkeley ridiculed Newton's infinitesimal dx as 'neither zero nor non-zero' as 'ghosts of departed quantities', exposing logical flaws in early calculus and promoting rigorous limit theory.

MINIMUM ACTION

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Practice this model in one real situation:

When encountering vague quantities like dx in business or arguments (e.g., 'potential users', 'private domain traffic'), demand precise definitions
do not let them be treated as real numbers in calculations and as zero in conversions.

Check to track your progress (stored locally)

Learning progress0%

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Source support: Explicit

link
baike.baidu.comhttps://baike.baidu.com/item/%E8%B4%9D%E5%85%8B%E8%8E%B1%E6%82%96%E8%AE%BA/2482725ZH · Explicit
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