(M24) 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 1/4_d 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.
Mem. To remark Cheyne(64) & 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 B(65)?
Barrow"s arguing against indivisibles, lect. i. p. 16, is a pet.i.tio principii, for the Demonstration of Archimedes supposeth the circ.u.mference 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 contradiction(66).
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, nothing(67).
(M25) 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.
(M26) 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 a.s.sign"d in numbers. Say you a.s.sign 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 a.s.signable.
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 about the usefull & practical mathematiques, what advantage had it brought to mankind!
(M27) 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.
(M28) But, say you, then a chimaera 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.
(M29) [(69)According 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.]
You ask me whether there can be an infinite idea? I answer, in one sense there may. Thus the visual sphere, tho" ever so small, is infinite, i.e.
has no end. But if by infinite you mean an extension consisting of innumerable points, then I ask yr pardon. Points, tho" never so many, may be numbered. The mult.i.tude of points, or feet, inches, &c., hinders not their numbrableness (i.e. hinders not their being numerable) in the least.
Many or most are numerable, as well as few or least. Also, if by infinite idea you mean an _idea_ too great to be comprehended or perceiv"d all at once, you must excuse me. I think such an infinite is no less than a contradiction(70).
(M30) The sillyness of the current doctrine makes much for me. They commonly suppose a material world-figures, motions, bulks of various sizes, &c.-according to their own confession to no purpose. All our sensations may be, and sometimes actually are, without them; nor can men so much as conceive it possible they should concur in any wise to the production of them.
(M31) Ask a man, I mean a philosopher, why he supposes this vast structure, this compages of bodies? he shall be at a stand; he"ll not have one word to say. Wch sufficiently shews the folly of the hypothesis.
(M32) Or rather why he supposes all ys Matter? For bodies and their qualities I do allow to exist independently of _our_ mind.
(M33) Qu. How is the soul distinguish"d from its ideas? Certainly if there were no sensible ideas there could be no soul, no perception, remembrance, love, fear, &c.; no faculty could be exerted(71).
(M34) The soul is the Will, properly speaking, and as it is distinct from ideas.
(M35) The grand puzzling question, whether I sleep or wake, easily solv"d.
Qu. Whether minima or meer minima may not be compar"d by their sooner or later evanescence, as well as by more or less points, so that one sensible may be greater than another, though it exceeds it not by one point?
Circles on several radius"s are not similar figures, they having neither all nor any an infinite number of sides. Hence in vain to enquire after 2 terms of one and ye same proportion that should constantly express the reason of the _d_ to the _p_ in all circles.
Mem. To remark Wallis"s harangue, that the aforesaid proportion can neither be expressed by rational numbers nor surds.
We can no more have an idea of length without breadth or visibility, than of a general figure.
One idea may be like another idea, tho" they contain no common simple idea(72). Thus the simple idea red is in some sense like the simple idea blue; "tis liker it than sweet or shrill. But then those ideas wch are so said to be alike, agree both in their connexion with another simple idea, viz. extension, & in their being receiv"d by one & the same sense. But, after all, nothing can be like an idea but an idea.
No sharing betwixt G.o.d & Nature or second causes in my doctrine.
(M36) Materialists must allow the earth to be actually mov"d by the attractive power of every stone that falls from the air, with many other the like absurditys.
Enquire concerning the pendulum clock, &c.; whether those inventions of Huygens, &c. be attained to by my doctrine.
The ... & ... & ... &c. of time are to be cast away and neglected, as so many noughts or nothings.
Mem. To make experiments concerning minimums and their colours, whether they have any or no, & whether they can be of that green wch seems to be compounded of yellow and blue.
(M37) Qu. Whether it were not better _not_ to call the operations of the mind ideas-confining this term to things sensible(73)?
(M38) Mem. diligently to set forth how that many of the ancient philosophers run into so great absurditys as even to deny the existence of motion, and of those other things they perceiv"d actually by their senses.
This sprung from their not knowing wt Existence was, and wherein it consisted. This the source of all their folly. "Tis on the discovering of the nature and meaning and import of Existence that I chiefly insist. This puts a wide difference betwixt the sceptics &c. & me. This I think wholly new. I am sure this is new to me(74).