COMMONPLACE BOOK. MATHEMATICAL, ETHICAL, PHYSICAL, AND METAPHYSICAL Written At Trinity College, Dublin, In 1705-8 _First published in 1871_ Editor’s Preface To The Commonplace Book Berkeley’s juvenile _Commonplace Book_ is a small quarto volume, in his handwriting, found among the Berkeley manuscripts in possession of the late Archdeacon Rose. It was first published in 1871, in my edition of Berkeley’s Works. It consists of occasional thoughts, mathematical, physical, ethical, and metaphysical, set down in miscellaneous fashion, for private use, as they arose in the course of his studies at Trinity College, Dublin. They are full of the fervid enthusiasm that was natural to him, and of sanguine expectations of the issue of the prospective authorship for which they record preparations. On the title-page is written, “G. B. Trin. Dub. alum.,” with the date 1705, when he was twenty years of age. The entries are the gradual accumulation of the next three years, in one of which the _Arithmetica_ and the _Miscellanea Mathematica_ made their appearance. The _New Theory of Vision_, given to the world in 1709, was evidently much in his mind, as well as the sublime conception of the material world in its necessary subordination to the spiritual world, of which he delivered himself in his book of _Principles_, in 1710.
This disclosure of Berkeley’s thoughts about things, in the years preceding the publication of his first essays, is indeed a precious record of the initial struggles of ardent philosophical genius. It places the reader in intimate companionship with him when he was beginning to awake into intellectual and spiritual life. We hear him soliloquising. We see him trying to translate into reasonableness our crude inherited beliefs about the material world and the natural order of the universe, self-conscious personality, and the Universal Power or Providence—all under the sway of a new determining Principle which was taking profound possession of his soul. He finds that he has only to look at the concrete things of sense in the light of this great discovery to see the artificially induced perplexities of the old philosophers disappear, along with their imposing abstractions, which turn out empty words. The thinking is throughout fresh and sincere; sometimes impetuous and one-sided; the outcome of a mind indisposed to take things upon trust, resolved to inquire freely, a rebel against the tyranny of language, morally burdened with the consciousness of a new world-transforming conception, which duty to mankind obliged him to reveal, although his message was sure to offend.
Men like to regard things as they have been wont. This new conception of the surrounding world—the impotence of Matter, and its subordinate office in the Supreme Economy must, he foresees, disturb those accustomed to treat outward things as the only realities, and who do not care to ask what constitutes reality. Notwithstanding the ridicule and ill-will that his transformed material world was sure to meet with, amongst the many who accept empty words instead of genuine insight, he was resolved to deliver himself of his thoughts through the press, but with the politic conciliation of a persuasive Irish pleader.
The _Commonplace Book_ steadily recognises the adverse influence of one insidious foe. Its world-transforming-Principle has been obscured by “the mist and veil of words.” The abstractions of metaphysicians, which poison human language, had to be driven out of the author’s mind before he could see the light, and must be driven out of the minds of others before they could be got to see it along with him: the concrete world as realisable only in percipient mind is with difficulty introduced into the vacant place. “The chief thing I pretend to is only to remove the mist and veil of words.” He exults in the transformed mental scene that then spontaneously rises before him. “My speculations have had the same effect upon me as visiting foreign countries,—in the end I return where I was before, get my heart at ease, and enjoy myself with more satisfaction. The philosophers lose their abstract matter; the materialists lose their abstract extension; the profane lose their extended deity. Pray what do the rest of mankind lose?” This beneficent revolution seemed to be the issue of a simple recognition of the fact, that the true way of regarding the world we see and touch is to regard it as consisting of ideas or phenomena that are presented to human senses, somehow regularly ordered, and the occasions of pleasure or pain to us as we conform to or rebel against their natural order. This is the surrounding universe—at least in its relations to us, and that is all in it that we have to do with. “I know not,” he says, “what is meant by things considered in themselves, i.e. in abstraction. This is nonsense. Thing and idea are words of much about the same extent and meaning. Existence is not conceivable without perception and volition. I only declare the meaning of the word _existence_, as far as I can comprehend it.”
In the _Commonplace Book_ we see the youth at Trinity College forging the weapons which he was soon to direct against the materialism and scepticism of the generation into which he was born. Here are rough drafts, crude hints of intended arguments, probing of unphilosophical mathematicians—even Newton and Descartes, memoranda of facts, more or less relevant, on their way into the _Essay on Vision_ and the treatise on _Principles_—seeds of the philosophy that was to be gradually unfolded in his life and in his books. We watch the intrepid thinker, notwithstanding the inexperience of youth, more disposed to give battle to mathematicians and metaphysicians than to submit even provisionally to any human authority. It does not seem that his scholarship or philosophical learning was extensive. Descartes, Malebranche, and Locke were his intimates; Hobbes and Spinoza were not unknown to him; Newton and some lesser lights among the mathematicians are often confronted. He is more rarely in company with the ancients or the mediaevalists. No deep study of Aristotle appears, and there is even a disposition to disparage Plato. He seeks for his home in the “new philosophy” of experience; without anticipations of Kant, as the critic of what is presupposed in the scientific reliability of any experience, against whom his almost blind zeal against abstractions would have set him at this early stage. “Pure intellect I understand not at all,” is one of his entries. He asks himself, “What becomes of the _aeternae veritates_?” and his reply is, “They vanish.” When he tells himself that “we must with the mob place certainty in the senses,” the words are apt to suggest that the senses are our only source of knowledge, but I suppose his meaning is that the senses must be trustworthy, as ’the mob’ assume. Yet occasionally he uses language which looks like an anticipation of David Hume, as when he calls mind “a congeries of perceptions. Take away perceptions,” he adds, “and you take away mind. Put the perceptions and you put the mind. The understanding seemeth not to differ from its perceptions and ideas.” He seems unconscious of the total scepticism which such expressions, when strictly interpreted, are found to involve. But after all, the reader must not apply rigorous rules of interpretation to random entries or provisional memoranda, meant only for private use, by an enthusiastic student who was preparing to produce books.
I have followed the manuscript of the _Commonplace Book_, omitting a few repetitions of thought in the same words. Here and there Berkeley’s writing is almost obliterated and difficult to decipher, apparently through accident by water in the course of his travels, when, as he mentions long after in one of his letters, several of his manuscripts were lost and others were injured.
The letters of the alphabet which are interpreted on the first page, and prefixed on the margin to some of the entries, may so far help to bring the apparent chaos of entries under a few articulate heads.
I have added some annotations here and there as they happened to occur, and these might have been multiplied indefinitely had space permitted.
Commonplace Book I. = Introduction.
M. = Matter.
P. = Primary and Secondary qualities.
E. = Existence.
T. = Time.
S. = Soul—Spirit.
G. = God.
Mo. = Moral Philosophy.
N. = Natural Philosophy.
Qu. If there be not two kinds of visible extension—one perceiv’d by a confus’d view, the other by a distinct successive direction of the optique axis to each point?
(M1) No general ideas(46). The contrary a cause of mistake or confusion in mathematiques, &c. This to be intimated in ye Introduction(47).
The Principle may be apply’d to the difficulties of conservation, co-operation, &c.
(M2) Trifling for the [natural] philosophers to enquire the cause of magnetical attractions, &c. They onely search after co-existing ideas(48).
(M3) Quæcunque in Scriptura militant adversus Copernicum, militant pro me.
(M4) All things in the Scripture wch side with the vulgar against the learned, side with me also. I side in all things with the mob.
(M5) I know there is a mighty sect of men will oppose me, but yet I may expect to be supported by those whose minds are not so far overgrown wth madness. These are far the greatest part of mankind—especially Moralists, Divines, Politicians; in a word, all but Mathematicians and Natural Philosophers. I mean only the hypothetical gentlemen. Experimental philosophers have nothing whereat to be offended in me.
Newton begs his Principles; I demonstrate mine(49).
(M6) I must be very particular in explaining wt is meant by things existing—in houses, chambers, fields, caves, &c.—wn not perceiv’d as well as wn perceived; and shew how the vulgar notion agrees with mine, when we narrowly inspect into the meaning and definition of the word _existence_, wh is no simple idea, distinct from perceiving and being perceived(50).
The Schoolmen have noble subjects, but handle them ill. The mathematicians have trifling subjects, but reason admirably about them. Certainly their method and arguing are excellent.
God knows how far our knowledge of intellectual beings may be enlarg’d from the Principles.
(M7) The reverse of the Principle I take to have been the chief source of all that scepticism and folly, all those contradictions and inextricable puzzling absurdities, that have in all ages been a reproach to human reason, as well as of that idolatry, whether of images or of gold, that blinds the greatest part of the world, and that shamefull immorality that turns us into beasts.
(M8) היה Vixit & fuit.
οὐσία, the name for substance, used by Aristotle, the Fathers, &c.
If at the same time we shall make the Mathematiques much more easie and much more accurate, wt can be objected to us(51)?
We need not force our imagination to conceive such very small lines for infinitesimals. They may every whit as well be imagin’d big as little, since that the integer must be infinite.
Evident that wch has an infinite number of parts must be infinite.
We cannot imagine a line or space infinitely great—therefore absurd to talk or make propositions about it.
We cannot imagine a line, space, &c., quovis lato majus. Since yt what we imagine must be datum aliquod; a thing can’t be greater than itself.
If you call infinite that wch is greater than any assignable by another, then I say, in that sense there may be an infinite square, sphere, or any other figure, wch is absurd.
Qu. if extension be resoluble into points it does not consist of?
No reasoning about things whereof we have no ideas(52); therefore no reasoning about infinitesimals.
No word to be used without an idea.
(M9) If uneasiness be necessary to set the Will at work, Qu. how shall we will in heaven?
Bayle’s, Malbranch’s, &c. arguments do not seem to prove against Space, but onely against Bodies.
(M10) I agree in nothing wth the Cartesians as to ye existence of Bodies & Qualities(53).
Aristotle as good a man as Euclid, but he was allowed to have been mistaken.
Lines not proper for demonstration.
(M11) We see the house itself, the church itself; it being an idea and nothing more. The house itself, the church itself, is an idea, i.e. an Instead of injuring, our doctrine much benefits geometry.
(M12) Existence is percipi, or percipere, [or velle, i.e. agere(55)]. The horse is in the stable, the books are in the study as before.
(M13) In physiques I have a vast view of things soluble hereby, but have not leisure.
(M14) Hyps and such like unaccountable things confirm my doctrine.
Angle not well defined. See Pardies’ Geometry, by Harris, &c. This one ground of trifling.
(M15) 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 Divinity(56).
(M16) Absurd to study astronomy and other the like doctrines as speculative sciences.
(M17) The absurd account of memory by the brain, &c. makes for me.
How was light created before man? Even so were Bodies created before man(57).
(M18) Impossible anything besides that wch thinks and is thought on should exist(58).
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 try(59). 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. & 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.
(M19) I may say the pain is _in_ my finger, &c., according to my doctrine(61).
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 have(62)] 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 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.
(M20) Motion distinct from ye thing moved is not conceivable.
(M21) Mem. To take notice of Newton for defining it [motion]; also of Locke’s wisdom in leaving it undefin’d(63).
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.
(M22) 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.
(M23) Proinde vim inferunt sacris literis qui voces hasce (v. tempus, spatium, motus) de quantitatibus mensuratis ibi interpretantur. Newton, p.
10.
(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 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 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 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 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 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.
(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 multitude 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 God & 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).
We have learn’d from Mr. Locke that there may be, and that there are, several glib, coherent, methodical discourses, which nevertheless amount to just nothing. This by him intended with relation to the Scholemen. We may apply it to the Mathematicians.
Qu. How can all words be said to stand for ideas? The word blue stands for a colour without any extension, or abstract from extension. But we have not an idea of colour without extension. We cannot imagine colour without extension.
Locke seems wrongly to assign a double use of words: one for communicating & the other for recording our thoughts. ’Tis absurd to use words for recording our thoughts to ourselves, or in our private meditations(75).
No one abstract simple idea like another. Two simple ideas may be connected with one & the same 3d simple idea, or be intromitted by one & the same sense. But consider’d in themselves they can have nothing common, and consequently no likeness.
Qu. How can there be any abstract ideas of colours? It seems not so easily as of tastes or sounds. But then all ideas whatsoever are particular. I can by no means conceive an abstract general idea. ’Tis one thing to abstract one concrete idea from another of a different kind, & another thing to abstract an idea from all particulars of the same kind(76).
(M39) Mem. Much to recommend and approve of experimental philosophy.
(M40) What means Cause as distinguish’d from Occasion? Nothing but a being wch wills, when the effect follows the volition. Those things that happen from without we are not the cause of. Therefore there is some other Cause of them, i.e. there is a Being that wills these perceptions in us(77).
(M41) [(78)It should be said, nothing but a Will—a Being which wills being unintelligible.]
One square cannot be double of another. Hence the Pythagoric theorem is false.
Some writers of catoptrics absurd enough to place the apparent place of the object in the Barrovian case behind the eye.
Blew and yellow chequers still diminishing terminate in green. This may help to prove the composition of green.
There is in green 2 foundations of 2 relations of likeness to blew & yellow. Therefore green is compounded.
A mixt cause will produce a mixt effect. Therefore colours are all compounded that we see.
Mem. To consider Newton’s two sorts of green.
N. B. My abstract & general doctrines ought not to be condemn’d by the Royall Society. ’Tis wt their meeting did ultimately intend. V. Sprat’s History S. R.(79) Mem. To premise a definition of idea(80).
(M42) The 2 great principles of Morality—the being of a God & the freedom of man. Those to be handled in the beginning of the Second Book(81).
Subvertitur geometria ut non practica sed speculativa.
Archimedes’s proposition about squaring the circle has nothing to do with circumferences containing less than 96 points; & if the circumference contain 96 points it may be apply’d, but nothing will follow against indivisibles. V. Barrow.
Those curve lines that you can rectify geometrically. Compare them with their equal right lines & by a microscope you shall discover an inequality. Hence my squaring of the circle as good and exact as the best.
(M43) Qu. whether the substance of body or anything else be any more than the collection of concrete ideas included in that thing? Thus the substance of any particular body is extension, solidity, figure(82). Of general abstract body we can have no idea.
(M44) Mem. Most carefully to inculcate and set forth that the endeavouring to express abstract philosophic thoughts by words unavoidably runs a man into difficulties. This to be done in the Introduction(83).
Mem. To endeavour most accurately to understand what is meant by this axiom: Quæ sibi mutuo congruunt æqualia sunt.
Qu. what the geometers mean by equality of lines, & whether, according to their definition of equality, a curve line can possibly be equal to a right line?
If wth me you call those lines equal wch contain an equal number of points, then there will be no difficulty. That curve is equal to a right line wch contains the same points as the right one doth.
(M45) I take not away substances. I ought not to be accused of discarding substance out of the reasonable world(84). I onely reject the philosophic sense (wch in effect is no sense) of the word substance. Ask a man not tainted with their jargon wt he means by corporeal substance, or the substance of body. He shall answer, bulk, solidity, and such like sensible qualitys. These I retain. The philosophic nec quid, nec quantum, nec quale, whereof I have no idea, I discard; if a man may be said to discard that which never had any being, was never so much as imagin’d or conceiv’d.
(M46) In short, be not angry. You lose nothing, whether real or chimerical. Wtever you can in any wise conceive or imagine, be it never so wild, so extravagant, & absurd, much good may it do you. You may enjoy it for me. I’ll never deprive you of it.
N. B. I am more for reality than any other philosophers(85). They make a thousand doubts, & know not certainly but we may be deceiv’d. I assert the direct contrary.
A line in the sense of mathematicians is not meer distance. This evident in that there are curve lines.
Curves perfectly incomprehensible, inexplicable, absurd, except we allow points.
(M47) If men look for a thing where it’s not to be found, be they never so sagacious, it is lost labour. If a simple clumsy man knows where the game lies, he though a fool shall catch it sooner than the most fleet & dexterous that seek it elsewhere. Men choose to hunt for truth and knowledge anywhere rather than in their own understanding, where ’tis to be found.
(M48) All knowledge onely about ideas. Locke, B. 4. c. 1.
(M49) It seems improper, & liable to difficulties, to make the word person stand for an idea, or to make ourselves ideas, or thinking things ideas.
(M50) Abstract ideas cause of much trifling and mistake.
Mathematicians seem not to speak clearly and coherently of equality. They nowhere define wt they mean by that word when apply’d to lines.
Locke says the modes of simple ideas, besides extension and number, are counted by degrees. I deny there are any modes or degrees of simple ideas.
What he terms such are complex ideas, as I have proved.
Wt do the mathematicians mean by considering curves as polygons? Either they are polygons or they are not. If they are, why do they give them the name of curves? Why do not they constantly call them polygons, & treat them as such? If they are not polygons, I think it absurd to use polygons in their stead. Wt is this but to pervert language? to adapt an idea to a name that belongs not to it but to a different idea?
The mathematicians should look to their axiom, Quæ congruunt sunt æqualia.
I know not what they mean by bidding me put one triangle on another. The under triangle is no triangle—nothing at all, it not being perceiv’d. I ask, must sight be judge of this congruentia or not? If it must, then all lines seen under the same angle are equal, wch they will not acknowledge.
Must the touch be judge? But we cannot touch or feel lines and surfaces, such as triangles, &c., according to the mathematicians themselves. Much less can we touch a line or triangle that’s cover’d by another line or triangle.
Do you mean by saying one triangle is equall to another, that they both take up equal spaces? But then the question recurs, what mean you by equal spaces? If you mean _spatia congruentia_, answer the above difficulty truly.