Molyneux’s blind man would not know the sphere or cube to be bodies or extended at first sight(199).
Extension so far from being incompatible wth, yt ’tis impossible it should exist without thought.
(M336) Extension itself or anything extended cannot think—these being meer ideas or sensations, whose essence we thoroughly know.
No extension but surface perceivable by sight.
(M337) Wn we imagine 2 bowls v. g. moving in vacuo, ’tis only conceiving a person affected with these sensations.
(M338) Extension to exist in a thoughtless thing [or rather in a thing void of perception—thought seeming to imply action], is a contradiction.
Qu. if visible motion be proportional to tangible motion?
(M339) In some dreams succession of ideas swifter than at other times.
(M340) If a piece of matter have extension, that must be determined to a particular bigness & figure, but &c.
Nothing wthout corresponds to our primary ideas but powers. Hence a direct & brief demonstration of an active powerfull Being, distinct from us, on whom we depend.
The name of colours actually given to tangible qualities, by the relation of ye story of the German Count.
Qu. How came visible & tangible qualities by the same name in all languages?
Qu. Whether Being might not be the substance of the soul, or (otherwise thus) whether Being, added to ye faculties, compleat the real essence and adequate definition of the soul?
(M341) Qu. Whether, on the supposition of external bodies, it be possible for us to know that any body is absolutely at rest, since that supposing ideas much slower than at present, bodies now apparently moving wd then be apparently at rest?
(M342) Qu. What can be like a sensation but a sensation?
Qu. Did ever any man see any other things besides his own ideas, that he should compare them to these, and make these like unto them?
(M343) The age of a fly, for ought that we know, may be as long as yt of a man(200).
Visible distance heterogeneous from tangible distance demonstrated 3 several ways:— 1st. If a tangible inch be equal or in any other reason to a visible inch, thence it will follow yt unequals are equals, wch is absurd: for at what distance would the visible inch be placed to make it equal to the tangible inch?
2d. One made to see that had not yet seen his own limbs, or any thing he touched, upon sight of a foot length would know it to be a foot length, if tangible foot & visible foot were the same idea—sed falsum id, ergo et hoc.
3dly. From Molyneux’s problem, wch otherwise is falsely solv’d by Locke and him(201).
(M344) Nothing but ideas perceivable(202).
A man cannot compare 2 things together without perceiving them each. Ergo, he cannot say anything wch is not an idea is like or unlike an idea.
Bodies &c. do exist even wn not perceived—they being powers in the active being(203).
Succession a simple idea, [succession is an abstract, i.e. an inconceivable idea,] Locke says(204).
Visible extension is [proportional to tangible extension, also is] encreated & diminish’d by parts. Hence taken for the same.
If extension be without the mind in bodies. Qu. whether tangible or visible, or both?
Mathematical propositions about extension & motion true in a double sense.
Extension thought peculiarly inert, because not accompany’d wth pleasure & pain: hence thought to exist in matter; as also for that it was conceiv’d common to 2 senses, [as also the constant perception of ’em].
Blind at 1st sight could not tell how near what he saw was to him, nor even whether it be wthout him or in his eye(205). Qu. Would he not think the later?
Blind at 1st sight could not know yt wt he saw was extended, until he had seen and touched some one self-same thing—not knowing how _minimum tangibile_ would look in vision.
(M345) Mem. That homogeneous particles be brought in to answer the objection of God’s creating sun, plants, &c. before animals.
In every bodie two infinite series of extension—the one of tangible, the other of visible.
All things to a blind [man] at first seen in a point.
Ignorance of glasses made men think extension to be in bodies.
(M346) Homogeneous portions of matter—useful to contemplate them.
Extension if in matter changes its relation wth _minimum visibile_, wch seems to be fixt.
Qu. whether m.v. be fix’d?
(M347) Each particle of matter if extended must be infinitely extended, or have an infinite series of extension.
(M348) If the world be granted to consist of Matter, ’tis the mind gives it beauty and proportion.
Wt I have said onely proves there is no proportion at all times and in all men between a visible & tangible inch.
Tangible and visible extension heterogeneous, because they have no common measure; also because their simplest constituent parts or elements are specifically different, viz. _punctum visibile & tangibile_. N. B. The former seems to be no good reason.
(M349) By immateriality is solv’d the cohesion of bodies, or rather the dispute ceases.
Our idea we call extension neither way capable of infinity, i.e. neither infinitely small or great.
Greatest possible extension seen under an angle wch will be less than 180 degrees, the legs of wch angle proceed from the ends of the extension.
(M350) Allowing there be extended, solid, &c. substances without the mind, ’tis impossible the mind should know or perceive them; the mind, even according to the materialists, perceiving onely the impressions made upon its brain, or rather the ideas attending these impressions(206).
Unity _in abstracto_ not at all divisible, it being as it were a point, or with Barrow nothing at all; _in concreto_ not divisible _ad infinitum_, there being no one idea demonstrable _ad infinitum_.
(M351) Any subject can have of each sort of primary qualities but one Qu. whether we have clear ideas of large numbers themselves, or onely of their relations?
solidity is, let him put a flint between his hands and he will know.
Extension of body is continuity of solid, &c.; extension of space is continuity of unsolid, &c.
Why may not I say visible extension is a continuity of visible points, tangible extension is a continuity of tangible points?
(M353) Mem. That I take notice that I do not fall in wth sceptics, Fardella(207), &c., in that I make bodies to exist certainly, wch they doubt of.
(M354) I am more certain of ye existence & reality of bodies than Mr.
Locke; since he pretends onely to wt he calls sensitive knowledge(208), whereas I think I have demonstrative knowledge of their existence—by them meaning combinations of powers in an unknown substratum(209).
(M355) Our ideas we call figure & extension, not images of the figure and extension of matter; these (if such there be) being infinitely divisible, those not so.
’Tis impossible a material cube should exist, because the edges of a cube will appear broad to an acute sense.
Men die, or are in [a] state of annihilation, oft in a day.
(M356) Powers. Qu. whether more or one onely?
Lengths abstract from breadths are the work of the mind. Such do intersect in a point at all angles. After the same way colour is abstract from extension.
Every position alters the line.
Qu. whether ideas of extension are made up of other ideas, v.g. idea of a foot made up of general ideas of an inch?
The idea of an inch length not one determin’d idea. Hence enquire the reason why we are out in judging of extension by the sight; for which purpose ’tis meet also to consider the frequent & sudden changes of extension by position.
No stated ideas of length without a minimum.
(M358) In my doctrine all absurdities from infinite space &c. cease(210).
Qu. whether if (speaking grossly) the things we see were all of them at all times too small to be felt, we should have confounded tangible & visible extension and figure?
(M359) Qu. whether if succession of ideas in the Eternal Mind, a day does not seem to God a 1000 years, rather than a 1000 years a day?
But one only colour & its degrees.
Enquiry about a grand mistake in writers of dioptricks in assigning the cause of microscopes magnifying objects.
Qu. whether a born-blind [man] made to see would at 1st give the name of distance to any idea intromitted by sight; since he would take distance yt that he had perceived by _touch_ to be something existing without his mind, but he would certainly think that nothing _seen_ was without his mind(211)?
(M360) Space without any bodies existing _in rerum natura_ would not be extended, as not having parts—in that parts are assigned to it wth respect to body; from whence also the notion of distance is taken. Now without either parts or distance or mind, how can there be Space, or anything beside one uniform Nothing?
Two demonstrations that blind made to see would not take all things he saw to be without his mind, or not in a point—the one from microscopic eyes, the other from not perceiving distance, i.e. radius of the visual sphere.
(M361) The trees are in the park, i.e. whether I will or no, whether I imagine anything about them or no. Let me but go thither and open my eyes by day, & I shall not avoid seeing them.
By extension blind [man] would mean either the perception caused in his touch by something he calls extended, or else the power of raising that perception; wch power is without, in the thing termed extended. Now he could not know either of these to be in things visible till he had try’d.
Geometry seems to have for its object tangible extension, figures, & A man will say a body will seem as big as before, tho’ the visible idea it yields be less than wt it was; therefore the bigness or tangible extension of the body is different from the visible extension.
Extension or space no simple idea—length, breadth, & solidity being three several ideas.
Depth or solidity _now_ perceived by sight(213).
Strange impotence of men. Man without God wretcheder than a stone or tree; he having onely the power to be miserable by his unperformed wills, these having no power at all(214).
Length perceivable by hearing—length & breadth by sight—length, breadth, & depth by touch.
(M362) Wt affects us must be a thinking thing, for wt thinks not cannot subsist.
Number not in bodies, it being the creature of the mind, depending entirely on its consideration, & being more or less as the mind pleases(215).
Mem. Quære whether extension be equally a sensation with colour? The mob use not the word extension. ’Tis an abstract term of the Schools.
(M363) Round figure a perception or sensation in the mind, but in the body Mem. Mark well the later part of the last cited section.
Solids, or any other tangible things, are no otherwise seen than colours felt by the German Count.
(M364) “Of” and “thing” causes of mistake.
The visible point of he who has microscopical eyes will not be greater or less than mine.
Qu. Whether the propositions & even axioms of geometry do not divers of them suppose the existence of lines &c. without the mind?
(M365) Whether motion be the measure of duration? Locke, b. 2. c. 14. s.
19.
Lines & points conceiv’d as terminations different ideas from those conceiv’d absolutely.
Every position alters a line.
(M366) Blind man at 1st would not take colours to be without his mind; but colours would seem to be in the same place with the coloured extension: therefore extension wd not seem to be without the mind.
All visible concentric circles whereof the eye is the centre are absolutely equal.
Qu. how ’tis possible we should see flats or right lines?
Qu. why the moon appears greatest in the horizon(217)?
Qu. why we see things erect when painted inverted(218)?
(M367) Question put by Mr. Deering touching the thief and paradise.
(M368) Matter tho’ allowed to exist may be no greater than a pin’s head.
Motion is proportionable to space described in given time.
Velocity not proportionable to space describ’d in given time.
(M369) No active power but the Will: therefore Matter, if it exists, affects us not(219).
Magnitude when barely taken for the _ratio partium extra partes_, or rather for co-existence & succession, without considering the parts co-existing & succeeding, is infinitely, or rather indefinitely, or not at all perhaps, divisible, because it is itself infinite or indefinite. But definite, determined magnitudes, i.e. lines or surfaces consisting of points whereby (together wth distance & position) they are determin’d, are resoluble into those points.
Again. Magnitude taken for co-existence and succession is not all divisible, but is one simple idea.
Simple ideas include no parts nor relations—hardly separated and considered in themselves—nor yet rightly singled by any author. Instance in power, red, extension, &c.
(M370) Space not imaginable by any idea received from sight—not imaginable without body moving. Not even then necessarily existing (I speak of infinite space)—for wt the body has past may be conceiv’d annihilated.
(M371) Qu. What can we see beside colours? what can we feel beside hard, soft, cold, warm, pleasure, pain?
Qu. Why not taste & smell extension?
Qu. Why not tangible & visible extensions thought heterogeneous extensions, so well as gustable & olefactible perceptions thought heterogeneous perceptions? or at least why not as heterogeneous as blue & red?
Moon wn horizontal does not appear bigger as to visible extension than at other times; hence difficulties and disputes about things seen under equal angles &c. cease.
All _potentiæ_ alike indifferent.
A. B. Wt does he mean by his _potentia_? Is it the will, desire, person, or all or neither, or sometimes one, sometimes t’other?
No agent can be conceiv’d indifferent as to pain or pleasure.
_We_ do not, properly speaking, in a strict philosophical sense, make objects more or less pleasant; but the laws of nature do that.
(M372) A finite intelligence might have foreseen 4 thousand years agoe the place and circumstances, even the most minute & trivial, of my present existence. This true on supposition that uneasiness determines the will.
(M373) Doctrines of liberty, prescience, &c. explained by billiard balls.
Wt judgement would he make of uppermost and lowermost who had always seen through an inverting glass?
All lines subtending the same optic angle congruent (as is evident by an easy experiment); therefore they are equal.
We have not pure simple ideas of blue, red, or any other colour (except perhaps black) because all bodies reflect heterogeneal light.
Qu. Whether this be true as to sounds (& other sensations), there being, perhaps, rays of air wch will onely exhibit one particular sound, as rays of light one particular colour.
Colours not definable, not because they are pure unmixt thoughts, but because we cannot easily distinguish & separate the thoughts they include, or because we want names for their component ideas.
(M374) By Soul is meant onely a complex idea, made up of existence, willing, & perception in a large sense. Therefore it is known and it may be defined.
We cannot possibly conceive any active power but the Will.
(M375) In moral matters men think (’tis true) that they are free; but this freedom is only the freedom of doing as they please; wch freedom is consecutive to the Will, respecting only the operative faculties(220).
Men impute their actions to themselves because they will’d them, and that not out of ignorance, but whereas they have the consequences of them, whether good or bad.
This does not prove men to be indifferent in respect of desiring.
If anything is meant by the _potentia_ of A. B. it must be desire; but I appeal to any man if his desire be indifferent, or (to speak more to the purpose) whether he himself be indifferent in respect of wt he desires till after he has desired it; for as for desire itself, or the faculty of desiring, that is indifferent, as all other faculties are.
Actions leading to heaven are in my power if I will them: therefore I will will them.
Qu. concerning the procession of Wills _in infinitum_.
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.
(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?
(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 (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.
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?
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?
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?
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.
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)?
All our ideas are adæquate: our knowledge of the laws of nature is not (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.
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.
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.