T 1.2.4.33
SBN 53 · cited directly by 2 papers, reached by 3 more through page or section ranges
I might give as instances those arguments for infinite divisibility, which are deriv'd from the point of contact. I know there is no mathematician, who will not refuse to be judg'd by the diagrams he describes upon paper, these being loose draughts, as he will tell us, and serving only to convey with greater facility certain ideas, which are the true foundation of all our reasoning. This I am satisfy'd with, and am willing to rest the controversy merely upon these ideas. I desire therefore our mathematician to form, as accurately as possible, the ideas of a circle and a right line; and I then ask, if upon the conception of their contact he can conceive them as touching in a mathematical point, or if he must necessarily imagine them to concur for some space. Whichever side he chuses, he runs himself into equal difficulties. If he affirms, that in tracing these figures in his imagination, he can imagine them to touch only in a point, he allows the possibility of that idea, and consequently of the thing. If he says, that in his conception of the contact of those lines he must make them concur, he thereby acknowledges the fallacy of geometrical demonstrations, when carry'd beyond a certain degree of minuteness; since 'tis certain he has such demonstrations against the concurrence of a circle and a right line; that is, in other words, he can prove an idea, viz. that of concurrence, to be incompatible with two other ideas, viz. those of a circle and right line; tho' at the same time he acknowledges these ideas to be inseparable.
Who cites it
2 of 5 papers cite this paragraph directly; the rest reach it through a page or section range. Snippets are the words around each citation.
| Paper | Cited as | Context |
|---|---|---|
| Ainslie 2003 | T 1.4.2.53 T 1.2.4.33 to T 1.2.5.1 (2 paragraphs) Citation pattern | …o be (T 1.4.7.14, SBN 273) 'leaves [his] closet, [and] mingles with the rest of mankind' (T 1.4.2.53, SBN 216), he will … |
| Strawson 2011 | 1.2.4.33 this paragraph Citation pattern | ….6; inexact,seee.g.45/1.2.4.17;merely'relative',seee.g.62/1.2.6.9;inaccura te, seee.g.53/1.2.4.33;unfixed,seee.g.189/… |
| 1.2.4.25,33 T 1.2.4 (2 paragraphs) Citation pattern | …;inadequate,seee.g.160/1. 3.14.10;imprecise,seee.g.50/1.2.4.27,67n/ 7.15n;loose,seee.g.49/1.2.4.25,33n/4.16n,77n/ 7.29n;u… | |
| Loeb 2009 | (pp. 16, 53) T 1.1.6.1 to T 1.2.5.1 (4 paragraphs) Checked by model | …eived rests on a propensity to mistake resembling but distinct objects for identical ones (pp. 16, 53). Philosophers recog… |
| Cottrell 2015 | T 1.4.2.46 - 55 T 1.2.4.20 to T 1.2.5.5 (19 paragraphs) Citation pattern | …uses of our sensory impressions and attributes the defining properties of a body to them (T 1.4.2.46 - 55; SBN 211 - 17). He … |
| Rocknak 2019 | 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'… |