Wt I see is onely variety of colours & light. Wt I feel is hard or soft, hot or cold, rough or smooth, &c. Wt resemblance have these thoughts with those?
A picture painted wth great variety of colours affects the touch in one uniform manner. I cannot therefore conclude that because I see 2, I shall feel 2; because I see angles or inequalities, I shall feel angles or inequalities. How therefore can I-before experience teaches me-know that the visible leggs are (because 2) connected wth the tangible ones, or the visible head (because one) connected wth the tangible head(231)?
(M389) All things by us conceivable are-
1st, thoughts;
2ndly, powers to receive thoughts;
3rdly, powers to cause thoughts; neither of all wch can possibly exist in an inert, senseless thing.
An object wthout a gla.s.s may be seen under as great an angle as wth a gla.s.s. A gla.s.s therefore does not magnify the appearance by the angle.
(M390) Absurd that men should know the soul by idea-ideas being inert, thoughtless. Hence Malbranch confuted(232).
I saw gladness in his looks. I saw shame in his face. So I see figure or distance.
Qu. Why things seen confusedly thro" a convex gla.s.s are not magnify"d?
Tho" we should judge the horizontal moon to be more distant, why should we therefore judge her to be greater? What connexion betwixt the same angle, further distant, and greaterness?
(M391) My doctrine affects the essences of the Corpuscularians.
Perfect circles, &c. exist not without (for none can so exist, whether perfect or no), but in the mind.
Lines thought divisible _ad infinitum_, because they are suppos"d to exist without. Also because they are thought the same when view"d by the naked eye, & wn view"d thro" magnifying gla.s.ses.
They who knew not gla.s.ses had not so fair a pretence for the divisibility _ad infinitum_.
No idea of circle, &c. in abstract.
Metaphysiques as capable of certainty as ethiques, but not so capable to be demonstrated in a geometrical way; because men see clearer & have not so many prejudices in ethiques.
Visible ideas come into the mind very distinct. So do tangible ideas.
Hence extension seen & felt. Sounds, tastes, &c. are more blended.
Qu. Why not extension intromitted by the taste in conjunction with the smell-seeing tastes & smells are very distinct ideas?
Blew and yellow particles mixt, while they exhibit an uniform green, their extension is not perceiv"d; but as soon as they exhibit distinct sensations of blew and yellow, then their extension is perceiv"d.
Distinct perception of visible ideas not so perfect as of tangible-tangible ideas being many at once equally vivid. Hence heterogeneous extension.
Object. Why a mist increases not the apparent magnitude of an object, in proportion to the faintness(233)?
Mem. To enquire touching the squaring of the circle, &c.
That wch seems smooth & round to the touch may to sight seem quite otherwise. Hence no _necessary_ connexion betwixt visible ideas and tangible ones.
In geometry it is not prov"d that an inch is divisible _ad infinitum_.
Geometry not conversant about our compleat determined ideas of figures, for these are not divisible _ad infinitum_.
Particular circles may be squar"d, for the circ.u.mference being given a diameter may be found betwixt wch & the true there is not any perceivable difference. Therefore there is no difference-extension being a perception; & a perception not perceivd is contradiction, nonsense, nothing. In vain to alledge the difference may be seen by magnifying-gla.s.ses, for in yt case there is ("tis true) a difference perceiv"d, but not between the same ideas, but others much greater, entirely different therefrom(234).
Any visible circle possibly perceivable of any man may be squar"d, by the common way, most accurately; or even perceivable by any other being, see he never so acute, i.e. never so small an arch of a circle; this being wt makes the distinction between acute & dull sight, and not the m.v., as men are perhaps apt to think.
The same is true of any tangible circle. Therefore further enquiry of accuracy in squaring or other curves is perfectly needless, & time thrown away.
Mem. To press wt last precedes more homely, & so think on"t again.
A meer line or distance is not made up of points, does not exist, cannot be imagin"d, or have an idea framed thereof,-no more than meer colour without extension(235).
Mem. A great difference between _considering_ length wthout breadth, & having an _idea_ of, or _imagining_, length without breadth(236).
Malbranch out touching the crystallines diminishing, L. 1. c. 6.
"Tis possible (& perhaps not very improbable, that is, is sometimes so) we may have the greatest pictures from the least objects. Therefore no necessary connexion betwixt visible & tangible ideas. These ideas, viz.
great relation to _sphaera visualis_, or to the m. v. (wch is all that I would have meant by having a greater picture) & faintness, might possibly have stood for or signify"d small tangible extensions. Certainly the greater relation to s. v. and m. v. does frequently, in that men view little objects near the eye.
Malbranch out in a.s.serting we cannot possibly know whether there are 2 men in the world that see a thing of the same bigness. V. L. 1. c. 6.
Diagonal of particular square commensurable wth its side, they both containing a certain number of m. v.
I do not think that surfaces consist of lines, i.e. meer distances. Hence perhaps may be solid that sophism wch would prove the oblique line equal to the perpendicular between 2 parallels.
Suppose an inch represent a mile. 1/1000 of an inch is nothing, but 1/1000 of ye mile represented is something: therefore 1/1000 an inch, tho"
nothing, is not to be neglected, because it represents something, i.e.
1/1000 of a mile.
Particular determin"d lines are not divisible _ad infinitum_, but lines as us"d by geometers are so, they not being determin"d to any particular finite number of points. Yet a geometer (he knows not why) will very readily say he can demonstrate an inch line is divisible _ad infinitum_.
A body moving in the optique axis not perceiv"d to move by sight merely, and without experience. There is ("tis true) a successive change of ideas,-it seems less and less. But, besides this, there is no visible change of place.
Mem. To enquire most diligently concerning the incommensurability of diagonale & side-whether it does not go on the supposition of units being divisible _ad infinitum_, i.e. of the extended thing spoken of being divisible _ad infinitum_ (unit being nothing; also v. Barrow, Lect.
Geom.), & so the infinite indivisibility deduced therefrom is a _pet.i.tio principii_?
The diagonal is commensurable with the side.
(M392) From Malbranch, Locke, & my first arguings it can"t be prov"d that extension is not in matter. From Locke"s arguings it can"t be proved that colours are not in bodies.
Mem. That I was distrustful at 8 years old; and consequently by nature disposed for these new doctrines(237).