The Works of George Berkeley. Vol. 1 of 4

Volume 4 — Commonplace Book (continued 2)

Reading edition

One eternity greater than another of the same kind.

In what sense eternity may be limited.

G. T.

Whether succession of ideas in the Divine intellect?

Time is the train of ideas succeeding each other.

Duration not distinguish'd from existence.

Succession explain'd by before, between, after, & numbering.

Why time in pain longer than time in pleasure?

Duration infinitely divisible, time not so.

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The same τὸ νῦν not common to all intelligences.

Time thought infinitely divisible on account of its measure.

Extension not infinitely divisible in one sense.

Revolutions immediately measure train of ideas, mediately duration.

Time a sensation; therefore onely in ye mind.

Eternity is onely a train of innumerable ideas. Hence the immortality of ye soul easily conceiv'd, or rather the immortality of the person, that of ye soul not being necessary for ought we can see.

Swiftness of ideas compar'd with yt of motions shews the wisdom of God.

Wt if succession of ideas were swifter, wt if slower?

Fall of Adam, use of idolatry, use of Epicurism & Hobbism, dispute about divisibility of matter, &c. expounded by material substances.

Extension a sensation, therefore not without the mind.

In the immaterial hypothesis, the wall is white, fire hot, &c.

Primary ideas prov'd not to exist in matter; after the same manner yt secondary ones are prov'd not to exist therein.

Demonstrations of the infinite divisibility of extension suppose length without breadth, or invisible length, wch is absurd.

World wthout thought is nec quid, nec quantum, nec quale, &c.

'Tis wondrous to contemplate ye World empty'd of all intelligences.

Nothing properly but Persons, i.e. conscious things, do exist. All other things are not so much existences as manners of ye existence of persons198.

Qu. about the soul, or rather person, whether it be not compleatly known?

Infinite divisibility of extension does suppose the external existence of extension; but the later is false, ergo ye former also.

Qu. Blind man made to see, would he know motion at 1st sight?

Motion, figure, and extension perceivable by sight are [pg 060] different from those ideas perceived by touch wch goe by the same name.

Diagonal incommensurable wth ye side. Quære how this can be in my doctrine?

Qu. how to reconcile Newton's 2 sorts of motion with my doctrine?

Terminations of surfaces & lines not imaginable per se.

Molyneux's blind man would not know the sphere or cube to be bodies or extended at first sight199.

Extension so far from being incompatible wth, yt 'tis impossible it should exist without thought.

M. S.

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.

Wn we imagine 2 bowls v. g. moving in vacuo, 'tis only conceiving a person affected with these sensations.

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?

In some dreams succession of ideas swifter than at other times.

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?

Qu. Whether, on the supposition of external bodies, it be possible for us to know that any body is absolutely [pg 061] at rest, since that supposing ideas much slower than at present, bodies now apparently moving wd then be apparently at rest?

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?

The age of a fly, for ought that we know, may be as long as yt of a man200.

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 him201.

Nothing but ideas perceivable202.

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 being203.

Succession a simple idea, [succession is an abstract, i.e. an inconceivable idea,] Locke says204.

Visible extension is [proportional to tangible extension, also is] encreated & diminish'd by parts. Hence taken for the same.

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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 eye205. 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.

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.

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?

Each particle of matter if extended must be infinitely extended, or have an infinite series of extension.

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.

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M. N.

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.

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 impressions206.

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.

Any subject can have of each sort of primary qualities but one particular at once. Locke, b. 4. c. 3. s. 15.

Qu. whether we have clear ideas of large numbers themselves, or onely of their relations?

Of solidity see L. b. 2. c. 4. s. 1, 5, 6. If any one ask wt 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?

Mem. That I take notice that I do not fall in wth sceptics, Fardella207, &c., in that I make bodies to exist certainly, wch they doubt of.

I am more certain of ye existence & reality of bodies than Mr. Locke; since he pretends onely to wt he calls sensitive knowledge208, whereas I think I have demonstrative [pg 064] knowledge of their existence—by them meaning combinations of powers in an unknown substratum209.

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.

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.

Material substance banter'd by Locke, b. 2. c. 13. s. 19.

In my doctrine all absurdities from infinite space &c. cease210.

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?

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.

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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 mind211?

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.

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, & motion—and not visible212.

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.

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Depth or solidity now perceived by sight213.

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 all214.

Length perceivable by hearing—length & breadth by sight—length, breadth, & depth by touch.

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 pleases215.

Mem. Quære whether extension be equally a sensation with colour? The mob use not the word extension. 'Tis an abstract term of the Schools.

Round figure a perception or sensation in the mind, but in the body is a power. L[ocke], b. 2. c. 8. s. 8.

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.

“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?

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.

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.

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All visible concentric circles whereof the eye is the centre are absolutely equal.

Infinite number—why absurd—not rightly solv'd by Locke216.

Qu. how 'tis possible we should see flats or right lines?

Qu. why the moon appears greatest in the horizon217?

Qu. why we see things erect when painted inverted218?

Question put by Mr. Deering touching the thief and paradise.

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.

No active power but the Will: therefore Matter, if it exists, affects us not219.

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.

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.

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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.

Mo. S.

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.

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.

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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.

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 faculties220.

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.

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, strigose221, rigid way will not suffice. He must be more ample & copious, else his demonstration, tho' never so exact, will not go down with most.

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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.

S. Mo.

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?

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?

I. S.

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.

The grand mistake is that we think we have ideas of the [pg 071] operations of our minds222. 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. 35223.

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 them224.

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?

P.N.

Motion not one idea. It cannot be perceived at once.

M. P.

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 insensibly225.

M. P.

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.

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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 persons226.

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.

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 [pg 073] 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 confusion227.

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 [pg 074] 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 [pg 075] 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 extension229?

All our ideas are adæquate: our knowledge of the laws of nature is not perfect & adæquate230.

M. P.

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 head231?

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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.

Absurd that men should know the soul by idea—ideas being inert, thoughtless. Hence Malbranch confuted232.

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?

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?

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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 faintness233?

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 therefrom234.

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 [pg 078] not exist, cannot be imagin'd, or have an idea framed thereof,—no more than meer colour without extension235.

Mem. A great difference between considering length wthout breadth, & having an idea of, or imagining, length without breadth236.

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 [pg 079] 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.

M. P.

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 doctrines237.

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.

M. P.

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

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

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.

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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 down238?

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.

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.

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.

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.

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.

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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.

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.

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.

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.

M. P.

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.

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.

The great danger of making extension exist without the mind is, that if it does it must be acknowledg'd infinite, immutable, eternal, &c.;—wch will be to make either God extended (wch I think dangerous), or an eternal, immutable, infinite, increate Being beside God.

Finiteness of our minds no excuse for the geometers.

The Principle easily proved by plenty of arguments ad absurdum.

The twofold signification of Bodies, viz.

1. Combinations of thoughts239;

2. Combinations of powers to raise thoughts.

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These, I say, in conjunction with homogeneous particles, may solve much better the objections from the creation than the supposition that Matter does exist. Upon wch supposition I think they cannot be solv'd.

Bodies taken for powers do exist wn not perceiv'd; but this existence is not actual240. Wn I say a power exists, no more is meant than that if in the light I open my eyes, and look that way, I shall see it, i.e. the body, &c.

Qu. whether blind before sight may not have an idea of light and colours & visible extension, after the same manner as we perceive them wth eyes shut, or in the dark—not imagining, but seeing after a sort?

Visible extension cannot be conceiv'd added to tangible extension. Visible and tangible points can't make one sum. Therefore these extensions are heterogeneous.

A probable method propos'd whereby one may judge whether in near vision there is a greater distance between the crystalline & fund than usual, or whether the crystalline be onely render'd more convex. If the former, then the v. s. is enlarg'd, & the m. v. corresponds to less than 30 minutes, or wtever it us'd to correspond to.

Stated measures, inches, feet, &c., are tangible not visible extensions.

Locke, More, Raphson, &c. seem to make God extended. 'Tis nevertheless of great use to religion to take extension out of our idea of God, & put a power in its place. It seems dangerous to suppose extension, wch is manifestly inert, in God.

But, say you, The thought or perception I call extension is not itself in an unthinking thing or Matter—but it is like something wch is in Matter. Well, say I, Do you apprehend or conceive wt you say extension is like unto, or do you not? If the later, how know you they are alike? How can you compare any things besides your own ideas? If the former, it must be an idea, i.e. perception, thought, [pg 083] or sensation—wch to be in an unperceiving thing is a contradiction241.

I abstain from all flourish & powers of words & figures, using a great plainness & simplicity of simile, having oft found it difficult to understand those that use the lofty & Platonic, or subtil & scholastique strain242.

Whatsoever has any of our ideas in it must perceive; it being that very having, that passive recognition of ideas, that denominates the mind perceiving—that being the very essence of perception, or that wherein perception consists.

The faintness wch alters the appearance of the horizontal moon, rather proceeds from the quantity or grossness of the intermediate atmosphere, than from any change of distance, wch is perhaps not considerable enough to be a total cause, but may be a partial of the phenomenon. N. B. The visual angle is less in cause the horizon.

We judge of the distance of bodies, as by other things, so also by the situation of their pictures in the eye, or (wch is the same thing) according as they appear higher or lower. Those wch seem higher are farther off.

Qu. why we see objects greater in ye dark? whether this can be solv'd by any but my Principles?

The reverse of ye Principle introduced scepticism.

N. B. On my Principles there is a reality: there are things: there is a rerum natura.

Mem. The surds, doubling the cube, &c.

We think that if just made to see we should judge of the distance & magnitude of things as we do now; but this is false. So also wt we think so positively of the situation of objects.

Hays's, Keill's243, &c. method of proving the infinitesimals of the 3d order absurd, & perfectly contradictions.

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Angles of contact, & verily all angles comprehended by a right line & a curve, cannot be measur'd, the arches intercepted not being similar.

The danger of expounding the H. Trinity by extension.

M. P.

Qu. Why should the magnitude seen at a near distance be deem'd the true one rather than that seen at a farther distance? Why should the sun be thought many 1000 miles rather than one foot in diameter—both being equally apparent diameters? Certainly men judg'd of the sun not in himself, but wth relation to themselves.

4 Principles whereby to answer objections, viz.

1. Bodies do really exist, tho' not perceiv'd by us.

2. There is a law or course of nature.

3. Language & knowledge are all about ideas; words stand for nothing else.

4. Nothing can be a proof against one side of a contradiction that bears equally hard upon the other244.

What shall I say? Dare I pronounce the admired ἀκρίβεια mathematica, that darling of the age, a trifle?

Most certainly no finite extension divisible ad infinitum.

Difficulties about concentric circles.

Mem. To examine & accurately discuss the scholium of the 8th definition of Mr. Newton's245 Principia.

Ridiculous in the mathematicians to despise Sense.

Qu. Is it not impossible there should be abstract general ideas?

All ideas come from without. They are all particular. The mind, 'tis true, can consider one thing wthout another; but then, considered asunder, they make not 2 ideas. Both together can make but one, as for instance colour & visible extension246.

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The end of a mathematical line is nothing. Locke's argument that the end of his pen is black or white concludes nothing here.

Mem. Take care how you pretend to define extension, for fear of the geometers.

Qu. Why difficult to imagine a minimum? Ans. Because we are not used to take notice of 'em singly; they not being able singly to pleasure or hurt us, thereby to deserve our regard.

Mem. To prove against Keill yt the infinite divisibility of matter makes the half have an equal number of equal parts with the whole.

Mem. To examine how far the not comprehending infinites may be admitted as a plea.

Qu. Why may not the mathematicians reject all the extensions below the M. as well as the dd, &c., wch are allowed to be something, & consequently may be magnify'd by glasses into inches, feet, &c., as well as the quantities next below the M.?

Big, little, and number are the works of the mind. How therefore can ye extension you suppose in Matter be big or little? How can it consist of any number of points?

Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8.

Schoolmen compar'd with the mathematicians.

Extension is blended wth tangible or visible ideas, & by the mind præscinded therefrom.

Mathematiques made easy—the scale does almost all. The scale can tell us the subtangent in ye parabola is double the abscisse.

Wt need of the utmost accuracy wn the mathematicians own in rerum natura they cannot find anything corresponding wth their nice ideas.

One should endeavour to find a progression by trying wth the scale.

Newton's fluxions needless. Anything below an M might serve for Leibnitz's Differential Calculus.

How can they hang together so well, since there are in them (I mean the mathematiques) so many contradictoriæ argutiæ. V. Barrow, Lect.

A man may read a book of Conics with ease, knowing how to try if they are right. He may take 'em on the credit of the author.

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Where's the need of certainty in such trifles? The thing that makes it so much esteem'd in them is that we are thought not capable of getting it elsewhere. But we may in ethiques and metaphysiques.

The not leading men into mistakes no argument for the truth of the infinitesimals. They being nothings may perhaps do neither good nor harm, except wn they are taken for something, & then the contradiction begets a contradiction.

a + 500 nothings = a + 50 nothings—an innocent silly truth.

My doctrine excellently corresponds wth the creation. I suppose no matter, no stars, sun, &c. to have existed before247.

It seems all circles are not similar figures, there not being the same proportion betwixt all circumferences & their diameters.

When a small line upon paper represents a mile, the mathematicians do not calculate the 1/10000 of the paper line, they calculate the 1/10000 of the mile. 'Tis to this they have regard, 'tis of this they think; if they think or have any idea at all. The inch perhaps might represent to their imaginations the mile, but ye 1/10000 of the inch cannot be made to represent anything, it not being imaginable.

But the 1/10000 of a mile being somewhat, they think the 1/10000 inch is somewhat: wn they think of yt they imagine they think on this.

3 faults occur in the arguments of the mathematicians for divisibility ad infinitum—

1. They suppose extension to exist without the mind, or not perceived.

2. They suppose that we have an idea of length without breadth248, or that length without breadth does exist.

3. That unity is divisible ad infinitum.

To suppose a M. S. divisible is to say there are distinguishable ideas where there are no distinguishable ideas.

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The M. S. is not near so inconceivable as the signum in magnitudine individuum.

Mem. To examine the math, about their point—what it is—something or nothing; and how it differs from the M. S.

All might be demonstrated by a new method of indivisibles, easier perhaps and juster than that of Cavalierius249.

Unperceivable perception a contradiction.

P. G.

Proprietates reales rerum omnium in Deo, tam corporum quum spirituum continentur. Clerici, Log. cap. 8.

Let my adversaries answer any one of mine, I'll yield. If I don't answer every one of theirs, I'll yield.

The loss of the excuse250 may hurt Transubstantiation, but not the Trinity.

We need not strain our imaginations to conceive such little things. Bigger may do as well for infinitesimals, since the integer must be an infinite.

Evident yt wch has an infinite number of parts must be infinite.

Qu. Whether extension be resoluble into points it does not consist of?

Nor can it be objected that we reason about numbers, wch are only words & not ideas251; for these infinitesimals are words of no use, if not supposed to stand for ideas.

Axiom. No reasoning about things whereof we have no idea. Therefore no reasoning about infinitesimals.

Much less infinitesimals of infinitesimals, &c.

Axiom. No word to be used without an idea.

M. P.

Our eyes and senses inform us not of the existence of matter or ideas existing without the mind252. They are not to be blam'd for the mistake.

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I defy any man to assign a right line equal to a paraboloid, but wn look'd at thro' a microscope they may appear unequall.

Newton's harangue amounts to no more than that gravity is proportional to gravity.

One can't imagine an extended thing without colour. V. Barrow, L. G.

Men allow colours, sounds, &c.253 not to exist without the mind, tho' they have no demonstration they do not. Why may they not allow my Principle with a demonstration?

M. P.

Qu. Whether I had not better allow colours to exist without the mind; taking the mind for the active thing wch I call “I,” “myself”—yt seems to be distinct from the understanding254?

The taking extension to be distinct from all other tangible & visible qualities, & to make an idea by itself, has made men take it to be without the mind.

I see no wit in any of them but Newton. The rest are meer triflers, mere Nihilarians.

The folly of the mathematicians in not judging of sensations by their senses. Reason was given us for nobler uses.

Keill's filling the world with a mite255. This follows from the divisibility of extension ad infinitum.

Extension, or length without breadth, seems to be nothing save the number of points that lie betwixt any 2 points256. It seems to consist in meer proportion—meer reference of the mind.

To what purpose is it to determine the forms of glasses geometrically?

Sir Isaac257 owns his book could have been demonstrated on the supposition of indivisibles.

Innumerable vessels of matter. V. Cheyne.

I'll not admire the mathematicians. 'Tis wt any one of [pg 089] common sense might attain to by repeated acts. I prove it by experience. I am but one of human sense, and I &c.

Mathematicians have some of them good parts—the more is the pity. Had they not been mathematicians they had been good for nothing. They were such fools they knew not how to employ their parts.

The mathematicians could not so much as tell wherein truth & certainty consisted, till Locke told 'em258. I see the best of 'em talk of light and colours as if wthout the mind.

By thing I either mean ideas or that wch has ideas259.

Nullum præclarum ingenium unquam fuit magnus mathematicus. Scaliger260.

A great genius cannot stoop to such trifles & minutenesses as they consider.

1. 261All significant words stand for ideas262.

2. All knowledge about our ideas.

3. All ideas come from without or from within.

4. If from without it must be by the senses, & they are call'd sensations263.

5. If from within they are the operations of the mind, & are called thoughts.

6. No sensation can be in a senseless thing.

7. No thought can be in a thoughtless thing.

8. All our ideas are either sensations or thoughts264, by 3, 4, 5.

9. None of our ideas can be in a thing wch is both thoughtless & senseless265, by 6, 7, 8.

10. The bare passive recognition or having of ideas is called perception.

11. Whatever has in it an idea, tho' it be never so passive, tho' it exert no manner of act about it, yet it must perceive. 10.

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12. All ideas either are simple ideas, or made up of simple ideas.

13. That thing wch is like unto another thing must agree wth it in one or more simple ideas.

14. Whatever is like a simple idea must either be another simple idea of the same sort, or contain a simple idea of the same sort. 13.

15. Nothing like an idea can be in an unperceiving thing. 11, 14. Another demonstration of the same thing.

16. Two things cannot be said to be alike or unlike till they have been compar'd.

17. Comparing is the viewing two ideas together, & marking wt they agree in and wt they disagree in.

18. The mind can compare nothing but its own ideas. 17.

19. Nothing like an idea can be in an unperceiving thing. 11, 16, 18.

N. B. Other arguments innumerable, both a priori & a posteriori, drawn from all the sciences, from the clearest, plainest, most obvious truths, whereby to demonstrate the Principle, i.e. that neither our ideas, nor anything like our ideas, can possibly be in an unperceiving thing266.

N. B. Not one argument of any kind wtsoever, certain or probable, a priori or a posteriori, from any art or science, from either sense or reason, against it.

Mathematicians have no right idea of angles. Hence angles of contact wrongly apply'd to prove extension divisible ad infinitum.

We have got the Algebra of pure intelligences.

We can prove Newton's propositions more accurately, more easily, & upon truer principles than himself267.

Barrow owns the downfall of geometry. However I'll endeavour to rescue it—so far as it is useful, or real, or imaginable, or intelligible. But for the nothings, I'll leave them to their admirers.

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I'll teach any one the whole course of mathematiques in 1/100 part the time that another will.

Much banter got from the prefaces of the mathematicians.

Newton says colour is in the subtil matter. Hence Malbranch proves nothing, or is mistaken, in asserting there is onely figure & motion.

I can square the circle, &c.; they cannot. Wch goes on the best principles?

The Billys268 use a finite visible line for an 1/m.

Marsilius Ficinus—his appearing the moment he died solv'd by my idea of time269.

The philosophers lose their abstract or unperceived Matter. The mathematicians lose their insensible sensations. The profane [lose] their extended Deity. Pray wt do the rest of mankind lose? As for bodies, &c., we have them still270.

N. B. The future nat. philosoph. & mathem. get vastly by the bargain271.

There are men who say there are insensible extensions. There are others who say the wall is not white, the fire is not hot, &c. We Irishmen cannot attain to these truths.

The mathematicians think there are insensible lines. About these they harangue: these cut in a point at all angles: these are divisible ad infinitum. We Irishmen can conceive no such lines.

The mathematicians talk of wt they call a point. This, they say, is not altogether nothing, nor is it downright something. Now we Irishmen are apt to think something272 & nothing are next neighbours.

Engagements to P.273 on account of ye Treatise that grew up under his eye; on account also of his approving my [pg 092] harangue. Glorious for P. to be the protector of usefull tho' newly discover'd truths.

How could I venture thoughts into the world before I knew they would be of use to the world? and how could I know that till I had try'd how they suited other men's ideas?

I publish not this so much for anything else as to know whether other men have the same ideas as we Irishmen. This is my end, & not to be inform'd as to my own particular.

My speculations have the same effect as visiting foreign countries: in the end I return where I was before, but my heart at ease, and enjoying life with new satisfaction.

Passing through all the sciences, though false for the most part, yet it gives us the better insight and greater knowledge of the truth.

He that would bring another over to his opinion, must seem to harmonize with him at first, and humour him in his own way of talking274.

From my childhood I had an unaccountable turn of thought that way.

It doth not argue a dwarf to have greater strength than a giant, because he can throw off the molehill which is upon him, while the other struggles beneath a mountain.

The whole directed to practise and morality—as appears 1st, from making manifest the nearness and omnipresence of God; 2dly, from cutting off the useless labour of sciences, and so forth.

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