Part 12

Herein mathematiques have the advantage over metaphysiques and morality. Their definitions, being of words not yet known to ye learner, are not disputed; but words in metaphysiques & morality, being mostly known to all, the definitions of them may chance to be contraverted.

(M376) The short jejune way in mathematiques will not do in metaphysiques & ethiques: for yt about mathematical propositions men have no prejudices, no anticipated opinions to be encounter’d; they not having yet thought on such matters. ’Tis not so in the other 2 mentioned sciences. A man must [there] not onely demonstrate the truth, he must also vindicate it against scruples and established opinions which contradict it. In short, the dry, strigose(221), rigid way will not suffice. He must be more ample & copious, else his demonstration, tho’ never so exact, will not go down with most.

Extension seems to consist in variety of homogeneal thoughts co-existing without mixture.

Or rather visible extension seems to be the co-existence of colour in the mind.

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(M377) Enquiring and judging are actions which depend on the operative faculties, wch depend on the Will, wch is determin’d by some uneasiness; ergo &c. Suppose an agent wch is finite perfectly indifferent, and as to desiring not determin’d by any prospect or consideration of good, I say, this agent cannot do an action morally good. Hence ’tis evident the suppositions of A. B. are insignificant.

Extension, motion, time, number are no simple ideas, but include succession to them, which seems to be a simple idea.

Mem. To enquire into the angle of contact, & into fluxions, &c.

The sphere of vision is equal whether I look onely in my hand or on the open firmament, for 1st, in both cases the retina is full; 2d, the radius’s of both spheres are equall or rather nothing at all to the sight; 3dly, equal numbers of points in one & t’other.

In the Barrovian case purblind would judge aright.

Why the horizontal moon greater?

Why objects seen erect?

(M378) To what purpose certain figure and texture connected wth other perceptions?

Men estimate magnitudes both by angles and distance. Blind at 1st could not know distance; or by pure sight, abstracting from experience of connexion of sight and tangible ideas, we can’t perceive distance. Therefore by pure sight we cannot perceive or judge of extension.

Qu. Whether it be possible to enlarge our sight or make us see at once more, or more points, than we do, by diminishing the _punctum visibile_ below 30 minutes?

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(M379) Speech metaphorical more than we imagine; insensible things, & their modes, circumstances, &c. being exprest for the most part by words borrow’d from things sensible. Hence manyfold mistakes.

(M380) The grand mistake is that we think we have _ideas_ of the operations of our minds(222). Certainly this metaphorical dress is an argument we have not.

Qu. How can our idea of God be complex & compounded, when his essence is simple & uncompounded? V. Locke, b. 2. c. 23. s. 35(223).

(M381) The impossibility of defining or discoursing clearly of such things proceeds from the fault & scantiness of language, as much perhaps as from obscurity & confusion of thought. Hence I may clearly and fully understand my own soul, extension, &c., and not be able to define them(224).

(M382) The substance _wood_ a collection of simple ideas. See Locke, b. 2. c. 26. s. 1.

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Mem. concerning strait lines seen to look at them through an orbicular lattice.

Qu. Whether possible that those visible ideas wch are now connected with greater tangible extensions could have been connected with lesser tangible extensions,—there seeming to be no _necessary_ connexion between those thoughts?

Speculums seem to diminish or enlarge objects not by altering the optique angle, but by altering the apparent distance.

Hence Qu. if blind would think things diminish’d by convexes, or enlarg’d by concaves?

(M383) Motion not one idea. It cannot be perceived at once.

(M384) Mem. To allow existence to colours in the dark, persons not thinking, &c.—but not an actual existence. ’Tis prudent to correct men’s mistakes without altering their language. This makes truth glide into their souls insensibly(225).

(M385) Colours in ye dark do exist really, i.e. were there light; or as soon as light comes, we shall see them, provided we open our eyes; and that whether we will or no.

How the retina is fill’d by a looking-glass?

Convex speculums have the same effect wth concave glasses.

Qu. Whether concave speculums have the same effect wth convex glasses?

The reason why convex speculums diminish & concave magnify not yet fully assign’d by any writer I know.

Qu. Why not objects seen confus’d when that they seem inverted through a convex lens?

Qu. How to make a glass or speculum which shall magnify or diminish by altering the distance without altering the angle?

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No identity (other than perfect likeness) in any individuals besides persons(226).

(M386) As well make tastes, smells, fear, shame, wit, virtue, vice, & all thoughts move wth local motion as immaterial spirit.

On account of my doctrine, the identity of finite substances must consist in something else than continued existence, or relation to determined time & place of beginning to exist—the existence of our thoughts (which being combined make all substances) being frequently interrupted, & they having divers beginnings & endings.

(M387) Qu. Whether identity of person consists not in the Will?

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No necessary connexion between great or little optique angles and great or little extension.

Distance is not perceived: optique angles are not perceived. How then is extension perceiv’d by sight?

Apparent magnitude of a line is not simply as the optique angle, but directly as the optique angle, & reciprocally as the confusion, &c. (i.e. the other sensations, or want of sensation, that attend near vision). Hence great mistakes in assigning the magnifying power of glasses. Vid. Moly[neux], p. 182.

Glasses or speculums may perhaps magnify or lessen without altering the optique angle, but to no purpose.

Qu. Whether purblind would think objects so much diminished by a convex speculum as another?

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Qu. Wherein consists identity of person? Not in actual consciousness; for then I’m not the same person I was this day twelvemonth but while I think of wt I then did. Not in potential; for then all persons may be the same, for ought we know.

Mem. Story of Mr. Deering’s aunt.

Two sorts of potential consciousness—natural & præternatural. In the last § but one, I mean the latter.

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If by magnitude be meant the proportion anything bears to a determined tangible extension, as inch, foot, &c., this, ’tis plain, cannot be properly & _per se_ perceived by sight; & as for determin’d visible inches, feet, &c., there can be no such thing obtain’d by the meer act of seeing—abstracted from experience, &c.

The greatness _per se_ perceivable by the sight is onely the proportion any visible appearance bears to the others seen at the same time; or (which is the same thing) the proportion of any particular part of the visual orb to the whole. But mark that we perceive not it is an orb, any more than a plain, but by reasoning.

This is all the greatness the pictures have _per se_.

Hereby meere seeing cannot at all judge of the extension of any object, it not availing to know the object makes such a part of a sphærical surface except we also know the greatness of the sphærical surface; for a point may subtend the same angle wth a mile, & so create as great an image in the retina, i.e. take up as much of the orb.

Men judge of magnitude by faintness and vigorousness, by distinctness and confusion, with some other circumstances, by great & little angles.

Hence ’tis plain the ideas of sight which are now connected with greatness might have been connected wth smallness, and vice versâ: there being no necessary reason why great angles, faintness, and distinctness without straining, should stand for great extension, any more than a great angle, vigorousness, and confusion(227).

My end is not to deliver metaphysiques altogether in a general scholastic way, but in some measure to accommodate them to the sciences, and shew how they may be useful in optiques, geometry, &c.(228)

Qu. Whether _per se_ proportion of visible magnitudes be perceivable by sight? This is put on account of distinctness and confusedness, the act of perception seeming to be as great in viewing any point of the visual orb distinctly, as in viewing the whole confusedly.

Mem. To correct my language & make it as philosophically nice as possible—to avoid giving handle.

If men could without straining alter the convexity of their crystallines, they might magnify or diminish the apparent diameters of objects, the same optic angle remaining.

The bigness in one sense of the pictures in the fund is not determin’d; for the nearer a man views them, the images of them (as well as other objects) will take up the greater room in the fund of his eye.

Mem. Introduction to contain the design of the whole, the nature and manner of demonstrating, &c.

Two sorts of bigness accurately to be distinguished, they being perfectly and _toto cælo_ different—the one the proportion that any one appearance has to the sum of appearances perceived at the same time wth it, wch is proportional to angles, or, if a surface, to segments of sphærical surfaces;—the other is tangible bigness.

Qu. wt would happen if the sphæræ of the retina were enlarged or diminish’d?

We think by the meer act of vision we perceive distance from us, yet we do not; also that we perceive solids, yet we do not; also the inequality of things seen under the same angle, yet we do not.

Why may I not add, We think we see extension by meer vision? Yet we do not.

Extension seems to be perceived by the eye, as thought by the ear.

As long as the same angle determines the _minimum visibile_ to two persons, no different conformation of the eye can make a different appearance of magnitude in the same thing. But, it being possible to try the angle, we may certainly know whether the same thing appears differently big to two persons on account of their eyes.

If a man could see ... objects would appear larger to him than to another; hence there is another sort of purely visible magnitude beside the proportion any appearance bears to the visual sphere, viz. its proportion to the M. V.

Were there but one and the same language in the world, and did children speak it naturally as soon as born, and were it not in the power of men to conceal their thoughts or deceive others, but that there were an inseparable connexion between words & thoughts, so yt _posito uno, ponitur alterum_ by the laws of nature; Qu. would not men think they heard thoughts as much as that they see extension(229)?

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All our ideas are adæquate: our knowledge of the laws of nature is not perfect & adæquate(230).

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(M388) Men are in the right in judging their simple ideas to be in the things themselves. Certainly heat & colour is as much without the mind as figure, motion, time, &c.

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We know many things wch we want words to express. Great things discoverable upon this principle. For want of considering wch divers men have run into sundry mistakes, endeavouring to set forth their knowledge by sounds; wch foundering them, they thought the defect was in their knowledge, while in truth it was in their language.

Qu. Whether the sensations of sight arising from a man’s head be liker the sensations of touch proceeding from thence or from his legs?

Or, Is it onely the constant & long association of ideas entirely different that makes me judge them the same?

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.

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An object wthout a glass may be seen under as great an angle as wth a glass. A glass 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 glass 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 glasses.

They who knew not glasses 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 circumference 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-glasses, 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 _sphæra 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 asserting 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 _petitio 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.

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Mem. That I was distrustful at 8 years old; and consequently by nature disposed for these new doctrines(237).

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Qu. How can a line consisting of an unequal number of points be divisible [_ad infinitum_] in two equals?

Mem. To discuss copiously how & why we do not see the pictures.

(M393) Allowing extensions to exist in matter, we cannot know even their proportions—contrary to Malbranch.

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(M394) I wonder how men cannot see a truth so obvious, as that extension cannot exist without a thinking substance.

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(M395) Species of all sensible things made by the mind. This prov’d either by turning men’s eyes into magnifyers or diminishers.

Yr m. v. is, suppose, less than mine. Let a 3rd person have perfect ideas of both our m. vs. His idea of my m. v. contains his idea of yours, & somewhat more. Therefore ’tis made up of parts: therefore his idea of my m. v. is not perfect or just, which diverts the hypothesis.

Qu. Whether a m. v. or t. be extended?

Mem. The strange errours men run into about the pictures. We think them small because should a man be suppos’d to see them their pictures would take up but little room in the fund of his eye.

It seems all lines can’t be bisected in 2 equall parts. Mem. To examine how the geometers prove the contrary.

’Tis impossible there should be a m. v. less than mine. If there be, mine may become equal to it (because they are homogeneous) by detraction of some part or parts. But it consists not of parts, ergo &c.

Suppose inverting perspectives bound to ye eyes of a child, & continu’d to the years of manhood—when he looks up, or turns up his head, he shall behold wt we call _under_. Qu. What would he think of _up_ and _down_(238)?

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(M396) I wonder not at my sagacity in discovering the obvious tho’ amazing truth. I rather wonder at my stupid inadvertency in not finding it out before—’tis no witchcraft to see.

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(M397) Our simple ideas are so many simple thoughts or perceptions; a perception cannot exist without a thing to perceive it, or any longer than it is perceiv’d; a thought cannot be in an unthinking thing; one uniform simple thought can be like to nothing but another uniform simple thought. Complex thoughts or ideas are onely an assemblage of simple ideas, and can be the image of nothing, or like unto nothing, but another assemblage of simple ideas, &c.

(M398) The Cartesian opinion of light & colours &c. is orthodox enough even in their eyes who think the Scripture expression may favour the common opinion. Why may not mine also? But there is nothing in Scripture that can possibly be wrested to make against me, but, perhaps, many things for me.

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(M399) Bodies &c. do exist whether we think of ’em or no, they being taken in a twofold sense—

1. Collections of thoughts.

2. Collections of powers to cause those thoughts.

These later exist; tho’ perhaps _a parte rei_ it may be one simple perfect power.

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Qu. whether the extension of a plain, look’d at straight and slantingly, survey’d minutely & distinctly, or in the bulk and confusedly at once, be the same? N. B. The plain is suppos’d to keep the same distance.

The ideas we have by a successive, curious inspection of ye minute parts of a plain do not seem to make up the extension of that plain view’d & consider’d all together.

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Ignorance in some sort requisite in ye person that should disown the Principle.

Thoughts do most properly signify, or are mostly taken for the interior operations of the mind, wherein the mind is active. Those yt obey not the acts of volition, and in wch the mind is passive, are more properly call’d sensations or perceptions. But yt is all a case of words.

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Extension being the collection or distinct co-existence of minimums, i.e. of perceptions intromitted by sight or touch, it cannot be conceiv’d without a perceiving substance.

(M400) Malbranch does not prove that the figures & extensions exist not when they are not perceiv’d. Consequently he does not prove, nor can it be prov’d on his principles, that the sorts are the work of the mind, and onely in the mind.

(M401) The great argument to prove that extension cannot be in an unthinking substance is, that it cannot be conceiv’d distinct from or without all tangible or visible quality.

(M402) Tho’ matter be extended wth an indefinite extension, yet the mind makes the sorts. They were not before the mind perceiving them, & even now they are not without the mind. Houses, trees, &c., tho’ indefinitely extended matter do exist, are not without the mind.