Commonplace

N. In physiques I have a vast view of things soluble hereby, but have not leisure.

N. Hyps and such like unaccountable things confirm my doctrine.

Angle not well defined. See Pardies’ Geometry, by Harris, &c. This one ground of trifling.

N. One idea not the cause of another—one power not the cause of another. The cause of all natural things is onely God. Hence trifling to enquire after second causes. This doctrine gives a most suitable idea of the Divinity56.

N. Absurd to study astronomy and other the like doctrines as speculative sciences.

N. The absurd account of memory by the brain, &c. makes for me.

How was light created before man? Even so were Bodies created before man57.

E. Impossible anything besides that wch thinks and is thought on should exist58.

That wch is visible cannot be made up of invisible things.

M.S. is that wherein there are not contain’d distinguishable sensible parts. Now how can that wch hath not sensible parts be divided into sensible parts? If you say it may be divided into insensible parts, I say these are nothings.

Extension abstract from sensible qualities is no sensation, I grant; but then there is no such idea, as any one may try59. There is onely a considering the number of points without the sort of them, & this makes more for me, since it must be in a considering thing.

Mem. Before I have shewn the distinction between visible & tangible extension, I must not mention them as distinct. I must not mention M. T. & M. V., but in general M. S., &c.60

Qu. whether a M. V. be of any colour? a M. T. of any tangible quality?

If visible extension be the object of geometry, ’tis that which is survey’d by the optique axis.

P. I may say the pain is in my finger, &c., according to my doctrine61.

Mem. Nicely to discuss wt is meant when we say a line consists of a certain number of inches or points, &c.; a circle of a certain number of square inches, points, &c. Certainly we may think of a circle, or have its idea in our mind, without thinking of points or square inches, &c.; whereas it should seem the idea of a circle is not made up of the ideas of points, square inches, &c.

Qu. Is any more than this meant by the foregoing expressions, viz. that squares or points may be perceived in or made out of a circle, &c., or that squares, points, &c. are actually in it, i.e. are perceivable in it?

A line in abstract, or Distance, is the number of points between two points. There is also distance between a slave & an emperor, between a peasant & philosopher, between a drachm & a pound, a farthing & a crown, &c.; in all which Distance signifies the number of intermediate ideas.

Halley’s doctrine about the proportion between infinitely great quantities vanishes. When men speak of infinite quantities, either they mean finite quantities, or else talk of [that whereof they have62] no idea; both which are absurd.

If the disputations of the Schoolmen are blam’d for intricacy, triflingness, & confusion, yet it must be acknowledg’d [pg 012]that in the main they treated of great & important subjects. If we admire the method & acuteness of the Math[ematicians]—the length, the subtilty, the exactness of their demonstrations—we must nevertheless be forced to grant that they are for the most part about trifling subjects, and perhaps mean nothing at all.

Motion on 2d thoughts seems to be a simple idea.

P. Motion distinct from ye thing moved is not conceivable.

N. Mem. To take notice of Newton for defining it [motion]; also of Locke’s wisdom in leaving it undefin’d63.

Ut ordo partium temporis est immutabilis, sin etiam ordo partium spatii. Moveantur hæ de locis suis, et movebuntur (ut ita dicam) de seipsis. Truly number is immensurable. That we will allow with Newton.

P. Ask a Cartesian whether he is wont to imagine his globules without colour. Pellucidness is a colour. The colour of ordinary light of the sun is white. Newton in the right in assigning colours to the rays of light.

A man born blind would not imagine Space as we do. We give it always some dilute, or duskish, or dark colour—in short, we imagine it as visible, or intromitted by the eye, wch he would not do.

N. Proinde vim inferunt sacris literis qui voces hasce (v. tempus, spatium, motus) de quantitatibus mensuratis ibi interpretantur. Newton, p. 10.

N. I differ from Newton, in that I think the recession ab axe motus is not the effect, or index, or measure of motion, but of the vis impressa. It sheweth not wt is truly moved, but wt has the force impressed on it, or rather that wch hath an impressed force.

D and P are not proportional in all circles. d d is to 1/4d p as d to p/4; but d and p/4 are not in the same proportion in all circles. Hence ’tis nonsense to seek the terms of one general proportion whereby to rectify all peripheries, or of another whereby to square all circles.

N. B. If the circle be squar’d arithmetically, ’tis squar’d geometrically, arithmetic or numbers being nothing but lines & proportions of lines when apply’d to geometry.

[pg 013] Mem. To remark Cheyne64 & his doctrine of infinites.

Extension, motion, time, do each of them include the idea of succession, & so far forth they seem to be of mathematical consideration. Number consisting in succession & distinct perception, wch also consists in succession; for things at once perceiv’d are jumbled and mixt together in the mind. Time and motion cannot be conceiv’d without succession; and extension, qua mathemat., cannot be conceiv’d but as consisting of parts wch may be distinctly & successively perceiv’d. Extension perceived at once & in confuso does not belong to math.

The simple idea call’d Power seems obscure, or rather none at all, but onely the relation ’twixt Cause and Effect. When I ask whether A can move B, if A be an intelligent thing, I mean no more than whether the volition of A that B move be attended with the motion of B? If A be senseless, whether the impulse of A against B be followed by ye motion of B65?

Barrow’s arguing against indivisibles, lect. i. p. 16, is a petitio principii, for the Demonstration of Archimedes supposeth the circumference to consist of more than 24 points. Moreover it may perhaps be necessary to suppose the divisibility ad infinitum, in order to demonstrate that the radius is equal to the side of the hexagon.

Shew me an argument against indivisibles that does not go on some false supposition.

A great number of insensibles—or thus, two invisibles, say you, put together become visible; therefore that M. V. contains or is made up of invisibles. I answer, the M. V. does not comprise, is not composed of, invisibles. All the matter amounts to this, viz. whereas I had no idea awhile agoe, I have an idea now. It remains for you to prove that I came by the present idea because there were two invisibles added together. I say the invisibles are nothings, cannot exist, include a contradiction66.

[pg 014] I am young, I am an upstart, I am a pretender, I am vain. Very well. I shall endeavour patiently to bear up under the most lessening, vilifying appellations the pride & rage of man can devise. But one thing I know I am not guilty of. I do not pin my faith on the sleeve of any great man. I act not out of prejudice or prepossession. I do not adhere to any opinion because it is an old one, a reviv’d one, a fashionable one, or one that I have spent much time in the study and cultivation of.

Sense rather than reason or demonstration ought to be employed about lines and figures, these being things sensible; for as for those you call insensible, we have proved them to be nonsense, nothing67.

I. If in some things I differ from a philosopher I profess to admire, ’tis for that very thing on account whereof I admire him, namely, the love of truth. This &c.

I. Whenever my reader finds me talk very positively, I desire he’d not take it ill. I see no reason why certainty should be confined to the mathematicians.

I say there are no incommensurables, no surds. I say the side of any square may be assign’d in numbers. Say you assign unto me the side of the square 10. I ask wt 10—10 feet, inches, &c., or 10 points? If the later, I deny there is any such square, ’tis impossible 10 points should compose a square. If the former, resolve yr 10 square inches, feet, &c. into points, & the number of points must necessarily be a square number whose side is easily assignable.

A mean proportional cannot be found betwixt any two given lines. It can onely be found betwixt those the numbers of whose points multiply’d together produce a square number. Thus betwixt a line of 2 inches & a line of 5 inches a mean geometrical cannot be found, except the number of points contained in 2 inches multiply’d by ye number of points contained in 5 inches make a square number.

If the wit and industry of the Nihilarians were employ’d [pg 015]about the usefull & practical mathematiques, what advantage had it brought to mankind!

M. E. You ask me whether the books are in the study now, when no one is there to see them? I answer, Yes. You ask me, Are we not in the wrong for imagining things to exist when they are not actually perceiv’d by the senses? I answer, No. The existence of our ideas consists in being perceiv’d, imagin’d, thought on. Whenever they are imagin’d or thought on they do exist. Whenever they are mentioned or discours’d of they are imagin’d & thought on. Therefore you can at no time ask me whether they exist or no, but by reason of yt very question they must necessarily exist.

E. But, say you, then a chimæra does exist? I answer, it doth in one sense, i.e. it is imagin’d. But it must be well noted that existence is vulgarly restrain’d to actuall perception, and that I use the word existence in a larger sense than ordinary.68

N. B.—According to my doctrine all things are entia rationis, i.e. solum habent esse in intellectum.

[69According to my doctrine all are not entia rationis. The distinction between ens rationis and ens reale is kept up by it as well as any other doctrine.]