Treatise Mapping
Map · Book 1: Of the Understanding · Part 2: Of the ideas of space and time · T 1.2.4 Objections answer'd

T 1.2.4.19

SBN 45 · cited directly by 6 papers, reached by 1 more through page or section ranges

There are few or no mathematicians, who defend the hypothesis of indivisible points; and yet these have the readiest and justest answer to the present question. They need only reply, that lines or surfaces are equal, when the numbers of points in each are equal; and that as the proportion of the numbers varies, the proportion of the lines and surfaces is also vary'd. But tho' this answer be just, as well as obvious; yet I may affirm, that this standard of equality is entirely useless, and that it never is from such a comparison we determine objects to be equal or unequal with respect to each other. For as the points, which enter into the composition of any line or surface, whether perceiv'd by the sight or touch, are so minute and so confounded with each other, that 'tis utterly impossible for the mind to compute their number, such a computation will never afford us a standard, by which we may judge of proportions. No one will ever be able to determine by an exact numeration, that an inch has fewer points than a foot, or a foot fewer than an ell or any greater measure; for which reason we seldom or never consider this as the standard of equality or inequality.

Who cites it

6 of 7 papers cite this paragraph directly; the rest reach it through a page or section range. Snippets are the words around each citation.

PaperCited asContext
Kail 2007
focused
T 1.4.2.45
T 1.2.4 (3 paragraphs)
Citation pattern
…ents' to convince us that 'our perceptions are not possest of any independent existence' (T 1.4.2.45; SBN 210), and that…
Hatfield 2009(Treatise, 45)
T 1.2.4 (3 paragraphs)
Citation pattern
… 'doctrine of indivisible points' that 'few or no mathematicians' hold, according to Hume (Treatise, 45)? What is the 'doctr…
Noonan 2012
focused
THN 1.4.2.45
T 1.2.4 (3 paragraphs)
Citation pattern
…riments familiar to philosophers (but apparently not known to the vulgar) establish this (THN 1.4.2.45 / 211). But even ph…
Pitson 2012T 1.4.2.45
T 1.2.4 (3 paragraphs)
Citation pattern
…iments' which enable us to infer that all or our perceptio fact depend on our physiology (T 1.4.2.45). This opens the p …
Pitson 2013T 1.4.2.45
T 1.2.4 (3 paragraphs)
Citation pattern
…ct, have no distinct or independent existence in so far as they depend on our physiology (T 1.4.2.45; SBN 210-11). This …
Rocknak 2019T 1.4.2.45
T 1.2.4 (3 paragraphs)
Citation pattern
… they summarily reject it by using simple logic (modus tollens) and a thought experiment (T 1.4.2.45; SBN 210-11). 14 I…
T 1.4.2.43-53
T 1.2.4.10 to T 1.2.5.1 (26 paragraphs)
Citation pattern
…to the senses," where he discusses the philosopher's rejection of the vulgar perspective (T 1.4.2.43-53; SBN 209-16). Hume'…
T 1.4.2.45
T 1.2.4 (3 paragraphs)
Citation pattern
… position we might view them from, and according to what state of health we are in, etc. (T 1.4.2.45; SBN 211). As a res…
Cottrell 2015T 1.4.2.44-45
T 1.2.4 (6 paragraphs)
Citation pattern
…r" conceive them, because none of our impressions have the defining properties of a body (T 1.4.2.44-45; SBN 210-11). But, …