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.M.I wonder how men cannot see a truth so obvious, as that extension cannot exist without a thinking substance.M.Species of all sensible things made by the mind. This prov'd either by turning men's eyes into magnifyers or diminishers.Yrm. v. is, suppose, less than mine. Let a 3rdperson 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.[pg 080]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 yeeyes of a child, & continu'd to the years of manhood—when he looks up, or turns up his head, he shall behold wtwe callunder. Qu. What would he think ofupanddown238?M.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.M.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.M.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.M.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' perhapsa parte reiit 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.[pg 081]The ideas we have by a successive, curious inspection of yeminute 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 yeperson 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 ytobey not the acts of volition, and in wchthe mind is passive, are more properly call'd sensations or perceptions. But ytis 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.P.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.M.Tho' matter be extended wthan 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.M.The great danger of making extension exist without the mind is, that if it does it must be acknowledg'd infinite, immutable, eternal, &c.;—wchwill be to make either God extended (wchI think dangerous), or an eternal, immutable, infinite, increate Being beside God.I.Finiteness of our minds no excuse for the geometers.M.The Principle easily proved by plenty of argumentsad absurdum.The twofold signification of Bodies, viz.1. Combinations of thoughts239;2. Combinations of powers to raise thoughts.[pg 082]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 wchsupposition I think they cannot be solv'd.Bodies taken for powers do exist wnnot perceiv'd; but this existence is not actual240. WnI 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 wtheyes 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.M.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, wchis manifestly inert, in God.M.But, say you, The thought or perception I call extension is not itself in an unthinking thing or Matter—but it is like something wchis in Matter. Well, say I, Do you apprehend or conceive wtyou 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—wchto be in an unperceiving thing is a contradiction241.I.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.M.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 wchalters the appearance of the horizontal moon, rather proceeds from the quantity or grossness of the intermediate atmosphere, than from any change of distance, wchis 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 (wchis the same thing) according as they appear higher or lower. Those wchseem higher are farther off.Qu. why we see objects greater in yedark? whether this can be solv'd by any but my Principles?M.The reverse of yePrinciple introduced scepticism.M.N. B. On my Principles there is a reality: there are things: there is arerum 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 wtwe think so positively of the situation of objects.Hays's, Keill's243, &c. method of proving the infinitesimals of the 3dorder absurd, & perfectly contradictions.[pg 084]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 wthrelation to themselves.M.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 divisiblead infinitum.M.Difficulties about concentric circles.N.Mem. To examine & accurately discuss the scholium of the 8thdefinition of Mr. Newton's245Principia.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.[pg 085]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 ytthe 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., wchare 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 yeextension you suppose in Matter be big or little? How can it consist of any number of points?P.Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8.Schoolmen compar'd with the mathematicians.Extension is blended wthtangible or visible ideas, & by the mind præscinded therefrom.Mathematiques made easy—the scale does almost all. The scale can tell us the subtangent in yeparabola is double the abscisse.Wtneed of the utmost accuracy wnthe mathematicians ownin rerum naturathey cannot find anything corresponding wththeir nice ideas.One should endeavour to find a progression by trying wththe 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 manycontradictoriæ 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.[pg 086]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 wnthey are taken for something, & then the contradiction begets a contradiction.a + 500 nothings = a + 50 nothings—an innocent silly truth.M.My doctrine excellently corresponds wththe 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 ye1/10000 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: wnthey think of ytthey imagine they think on this.3 faults occur in the arguments of the mathematicians for divisibilityad 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 divisiblead infinitum.To suppose a M. S. divisible is to say there are distinguishable ideas where there are no distinguishable ideas.[pg 087]The M. S. is not near so inconceivable as thesignum in magnitudine individuum.Mem. To examine the math, about theirpoint—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.M.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 excuse250may 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 ytwchhas 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, wchare 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.[pg 088]I defy any man to assign a right line equal to a paraboloid, but wnlook'd at thro' a microscope they may appear unequall.M.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.P.Men allow colours, sounds, &c.253not 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.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.M.I wonder how men cannot see a truth so obvious, as that extension cannot exist without a thinking substance.M.Species of all sensible things made by the mind. This prov'd either by turning men's eyes into magnifyers or diminishers.Yrm. v. is, suppose, less than mine. Let a 3rdperson 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.[pg 080]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 yeeyes of a child, & continu'd to the years of manhood—when he looks up, or turns up his head, he shall behold wtwe callunder. Qu. What would he think ofupanddown238?M.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.M.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.M.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.M.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' perhapsa parte reiit 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.[pg 081]The ideas we have by a successive, curious inspection of yeminute 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 yeperson 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 ytobey not the acts of volition, and in wchthe mind is passive, are more properly call'd sensations or perceptions. But ytis 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.P.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.M.Tho' matter be extended wthan 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.M.The great danger of making extension exist without the mind is, that if it does it must be acknowledg'd infinite, immutable, eternal, &c.;—wchwill be to make either God extended (wchI think dangerous), or an eternal, immutable, infinite, increate Being beside God.I.Finiteness of our minds no excuse for the geometers.M.The Principle easily proved by plenty of argumentsad absurdum.The twofold signification of Bodies, viz.1. Combinations of thoughts239;2. Combinations of powers to raise thoughts.[pg 082]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 wchsupposition I think they cannot be solv'd.Bodies taken for powers do exist wnnot perceiv'd; but this existence is not actual240. WnI 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 wtheyes 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.M.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, wchis manifestly inert, in God.M.But, say you, The thought or perception I call extension is not itself in an unthinking thing or Matter—but it is like something wchis in Matter. Well, say I, Do you apprehend or conceive wtyou 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—wchto be in an unperceiving thing is a contradiction241.I.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.M.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 wchalters the appearance of the horizontal moon, rather proceeds from the quantity or grossness of the intermediate atmosphere, than from any change of distance, wchis 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 (wchis the same thing) according as they appear higher or lower. Those wchseem higher are farther off.Qu. why we see objects greater in yedark? whether this can be solv'd by any but my Principles?M.The reverse of yePrinciple introduced scepticism.M.N. B. On my Principles there is a reality: there are things: there is arerum 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 wtwe think so positively of the situation of objects.Hays's, Keill's243, &c. method of proving the infinitesimals of the 3dorder absurd, & perfectly contradictions.[pg 084]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 wthrelation to themselves.M.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 divisiblead infinitum.M.Difficulties about concentric circles.N.Mem. To examine & accurately discuss the scholium of the 8thdefinition of Mr. Newton's245Principia.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.[pg 085]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 ytthe 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., wchare 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 yeextension you suppose in Matter be big or little? How can it consist of any number of points?P.Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8.Schoolmen compar'd with the mathematicians.Extension is blended wthtangible or visible ideas, & by the mind præscinded therefrom.Mathematiques made easy—the scale does almost all. The scale can tell us the subtangent in yeparabola is double the abscisse.Wtneed of the utmost accuracy wnthe mathematicians ownin rerum naturathey cannot find anything corresponding wththeir nice ideas.One should endeavour to find a progression by trying wththe 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 manycontradictoriæ 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.[pg 086]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 wnthey are taken for something, & then the contradiction begets a contradiction.a + 500 nothings = a + 50 nothings—an innocent silly truth.M.My doctrine excellently corresponds wththe 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 ye1/10000 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: wnthey think of ytthey imagine they think on this.3 faults occur in the arguments of the mathematicians for divisibilityad 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 divisiblead infinitum.To suppose a M. S. divisible is to say there are distinguishable ideas where there are no distinguishable ideas.[pg 087]The M. S. is not near so inconceivable as thesignum in magnitudine individuum.Mem. To examine the math, about theirpoint—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.M.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 excuse250may 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 ytwchhas 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, wchare 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.[pg 088]I defy any man to assign a right line equal to a paraboloid, but wnlook'd at thro' a microscope they may appear unequall.M.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.P.Men allow colours, sounds, &c.253not 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.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.M.I wonder how men cannot see a truth so obvious, as that extension cannot exist without a thinking substance.M.Species of all sensible things made by the mind. This prov'd either by turning men's eyes into magnifyers or diminishers.Yrm. v. is, suppose, less than mine. Let a 3rdperson 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.[pg 080]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 yeeyes of a child, & continu'd to the years of manhood—when he looks up, or turns up his head, he shall behold wtwe callunder. Qu. What would he think ofupanddown238?M.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.M.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.M.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.M.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' perhapsa parte reiit 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.[pg 081]The ideas we have by a successive, curious inspection of yeminute 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 yeperson 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 ytobey not the acts of volition, and in wchthe mind is passive, are more properly call'd sensations or perceptions. But ytis 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.P.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.M.Tho' matter be extended wthan 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.M.The great danger of making extension exist without the mind is, that if it does it must be acknowledg'd infinite, immutable, eternal, &c.;—wchwill be to make either God extended (wchI think dangerous), or an eternal, immutable, infinite, increate Being beside God.I.Finiteness of our minds no excuse for the geometers.M.The Principle easily proved by plenty of argumentsad absurdum.The twofold signification of Bodies, viz.1. Combinations of thoughts239;2. Combinations of powers to raise thoughts.[pg 082]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 wchsupposition I think they cannot be solv'd.Bodies taken for powers do exist wnnot perceiv'd; but this existence is not actual240. WnI 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 wtheyes 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.M.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, wchis manifestly inert, in God.M.But, say you, The thought or perception I call extension is not itself in an unthinking thing or Matter—but it is like something wchis in Matter. Well, say I, Do you apprehend or conceive wtyou 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—wchto be in an unperceiving thing is a contradiction241.I.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.M.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 wchalters the appearance of the horizontal moon, rather proceeds from the quantity or grossness of the intermediate atmosphere, than from any change of distance, wchis 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 (wchis the same thing) according as they appear higher or lower. Those wchseem higher are farther off.Qu. why we see objects greater in yedark? whether this can be solv'd by any but my Principles?M.The reverse of yePrinciple introduced scepticism.M.N. B. On my Principles there is a reality: there are things: there is arerum 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 wtwe think so positively of the situation of objects.Hays's, Keill's243, &c. method of proving the infinitesimals of the 3dorder absurd, & perfectly contradictions.[pg 084]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 wthrelation to themselves.M.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 divisiblead infinitum.M.Difficulties about concentric circles.N.Mem. To examine & accurately discuss the scholium of the 8thdefinition of Mr. Newton's245Principia.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.[pg 085]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 ytthe 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., wchare 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 yeextension you suppose in Matter be big or little? How can it consist of any number of points?P.Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8.Schoolmen compar'd with the mathematicians.Extension is blended wthtangible or visible ideas, & by the mind præscinded therefrom.Mathematiques made easy—the scale does almost all. The scale can tell us the subtangent in yeparabola is double the abscisse.Wtneed of the utmost accuracy wnthe mathematicians ownin rerum naturathey cannot find anything corresponding wththeir nice ideas.One should endeavour to find a progression by trying wththe 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 manycontradictoriæ 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.[pg 086]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 wnthey are taken for something, & then the contradiction begets a contradiction.a + 500 nothings = a + 50 nothings—an innocent silly truth.M.My doctrine excellently corresponds wththe 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 ye1/10000 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: wnthey think of ytthey imagine they think on this.3 faults occur in the arguments of the mathematicians for divisibilityad 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 divisiblead infinitum.To suppose a M. S. divisible is to say there are distinguishable ideas where there are no distinguishable ideas.[pg 087]The M. S. is not near so inconceivable as thesignum in magnitudine individuum.Mem. To examine the math, about theirpoint—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.M.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 excuse250may 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 ytwchhas 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, wchare 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.[pg 088]I defy any man to assign a right line equal to a paraboloid, but wnlook'd at thro' a microscope they may appear unequall.M.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.P.Men allow colours, sounds, &c.253not 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.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.M.I wonder how men cannot see a truth so obvious, as that extension cannot exist without a thinking substance.M.Species of all sensible things made by the mind. This prov'd either by turning men's eyes into magnifyers or diminishers.Yrm. v. is, suppose, less than mine. Let a 3rdperson 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.[pg 080]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 yeeyes of a child, & continu'd to the years of manhood—when he looks up, or turns up his head, he shall behold wtwe callunder. Qu. What would he think ofupanddown238?M.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.M.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.M.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.M.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' perhapsa parte reiit 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.[pg 081]The ideas we have by a successive, curious inspection of yeminute 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 yeperson 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 ytobey not the acts of volition, and in wchthe mind is passive, are more properly call'd sensations or perceptions. But ytis 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.P.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.M.Tho' matter be extended wthan 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.M.The great danger of making extension exist without the mind is, that if it does it must be acknowledg'd infinite, immutable, eternal, &c.;—wchwill be to make either God extended (wchI think dangerous), or an eternal, immutable, infinite, increate Being beside God.I.Finiteness of our minds no excuse for the geometers.M.The Principle easily proved by plenty of argumentsad absurdum.The twofold signification of Bodies, viz.1. Combinations of thoughts239;2. Combinations of powers to raise thoughts.[pg 082]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 wchsupposition I think they cannot be solv'd.Bodies taken for powers do exist wnnot perceiv'd; but this existence is not actual240. WnI 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 wtheyes 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.M.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, wchis manifestly inert, in God.M.But, say you, The thought or perception I call extension is not itself in an unthinking thing or Matter—but it is like something wchis in Matter. Well, say I, Do you apprehend or conceive wtyou 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—wchto be in an unperceiving thing is a contradiction241.I.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.M.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 wchalters the appearance of the horizontal moon, rather proceeds from the quantity or grossness of the intermediate atmosphere, than from any change of distance, wchis 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 (wchis the same thing) according as they appear higher or lower. Those wchseem higher are farther off.Qu. why we see objects greater in yedark? whether this can be solv'd by any but my Principles?M.The reverse of yePrinciple introduced scepticism.M.N. B. On my Principles there is a reality: there are things: there is arerum 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 wtwe think so positively of the situation of objects.Hays's, Keill's243, &c. method of proving the infinitesimals of the 3dorder absurd, & perfectly contradictions.[pg 084]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 wthrelation to themselves.M.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 divisiblead infinitum.M.Difficulties about concentric circles.N.Mem. To examine & accurately discuss the scholium of the 8thdefinition of Mr. Newton's245Principia.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.[pg 085]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 ytthe 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., wchare 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 yeextension you suppose in Matter be big or little? How can it consist of any number of points?P.Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8.Schoolmen compar'd with the mathematicians.Extension is blended wthtangible or visible ideas, & by the mind præscinded therefrom.Mathematiques made easy—the scale does almost all. The scale can tell us the subtangent in yeparabola is double the abscisse.Wtneed of the utmost accuracy wnthe mathematicians ownin rerum naturathey cannot find anything corresponding wththeir nice ideas.One should endeavour to find a progression by trying wththe 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 manycontradictoriæ 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.[pg 086]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 wnthey are taken for something, & then the contradiction begets a contradiction.a + 500 nothings = a + 50 nothings—an innocent silly truth.M.My doctrine excellently corresponds wththe 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 ye1/10000 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: wnthey think of ytthey imagine they think on this.3 faults occur in the arguments of the mathematicians for divisibilityad 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 divisiblead infinitum.To suppose a M. S. divisible is to say there are distinguishable ideas where there are no distinguishable ideas.[pg 087]The M. S. is not near so inconceivable as thesignum in magnitudine individuum.Mem. To examine the math, about theirpoint—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.M.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 excuse250may 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 ytwchhas 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, wchare 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.[pg 088]I defy any man to assign a right line equal to a paraboloid, but wnlook'd at thro' a microscope they may appear unequall.M.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.P.Men allow colours, sounds, &c.253not 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.
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.
M. P.
Allowing extensions to exist in matter, we cannot know even their proportions—contrary to Malbranch.
M.
M.
I wonder how men cannot see a truth so obvious, as that extension cannot exist without a thinking substance.
M.
M.
Species of all sensible things made by the mind. This prov'd either by turning men's eyes into magnifyers or diminishers.
Yrm. v. is, suppose, less than mine. Let a 3rdperson 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.
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 yeeyes of a child, & continu'd to the years of manhood—when he looks up, or turns up his head, he shall behold wtwe callunder. Qu. What would he think ofupanddown238?
M.
M.
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.
M.
M.
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.
M.
M.
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.
M.
M.
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.
1. Collections of thoughts.
2. Collections of powers to cause those thoughts.
These later exist; tho' perhapsa parte reiit 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.
The ideas we have by a successive, curious inspection of yeminute 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 yeperson 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 ytobey not the acts of volition, and in wchthe mind is passive, are more properly call'd sensations or perceptions. But ytis 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.
P.
P.
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.
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.
M.
M.
Tho' matter be extended wthan 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.
M.
M.
The great danger of making extension exist without the mind is, that if it does it must be acknowledg'd infinite, immutable, eternal, &c.;—wchwill be to make either God extended (wchI think dangerous), or an eternal, immutable, infinite, increate Being beside God.
I.
I.
Finiteness of our minds no excuse for the geometers.
M.
M.
The Principle easily proved by plenty of argumentsad absurdum.
The twofold signification of Bodies, viz.
1. Combinations of thoughts239;2. Combinations of powers to raise thoughts.
1. Combinations of thoughts239;
2. Combinations of powers to raise thoughts.
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 wchsupposition I think they cannot be solv'd.
Bodies taken for powers do exist wnnot perceiv'd; but this existence is not actual240. WnI 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 wtheyes 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.
M.
M.
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, wchis manifestly inert, in God.
M.
M.
But, say you, The thought or perception I call extension is not itself in an unthinking thing or Matter—but it is like something wchis in Matter. Well, say I, Do you apprehend or conceive wtyou 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—wchto be in an unperceiving thing is a contradiction241.
I.
I.
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.
M.
M.
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 wchalters the appearance of the horizontal moon, rather proceeds from the quantity or grossness of the intermediate atmosphere, than from any change of distance, wchis 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 (wchis the same thing) according as they appear higher or lower. Those wchseem higher are farther off.
Qu. why we see objects greater in yedark? whether this can be solv'd by any but my Principles?
M.
M.
The reverse of yePrinciple introduced scepticism.
M.
M.
N. B. On my Principles there is a reality: there are things: there is arerum 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 wtwe think so positively of the situation of objects.
Hays's, Keill's243, &c. method of proving the infinitesimals of the 3dorder absurd, & perfectly contradictions.
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.
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 wthrelation to themselves.
M.
M.
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.
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 divisiblead infinitum.
M.
M.
Difficulties about concentric circles.
N.
N.
Mem. To examine & accurately discuss the scholium of the 8thdefinition of Mr. Newton's245Principia.
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.
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 ytthe 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., wchare 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 yeextension you suppose in Matter be big or little? How can it consist of any number of points?
P.
P.
Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8.
Schoolmen compar'd with the mathematicians.
Extension is blended wthtangible or visible ideas, & by the mind præscinded therefrom.
Mathematiques made easy—the scale does almost all. The scale can tell us the subtangent in yeparabola is double the abscisse.
Wtneed of the utmost accuracy wnthe mathematicians ownin rerum naturathey cannot find anything corresponding wththeir nice ideas.
One should endeavour to find a progression by trying wththe 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 manycontradictoriæ 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.
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 wnthey are taken for something, & then the contradiction begets a contradiction.
a + 500 nothings = a + 50 nothings—an innocent silly truth.
M.
M.
My doctrine excellently corresponds wththe 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 ye1/10000 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: wnthey think of ytthey imagine they think on this.
3 faults occur in the arguments of the mathematicians for divisibilityad 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 divisiblead 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 divisiblead infinitum.
To suppose a M. S. divisible is to say there are distinguishable ideas where there are no distinguishable ideas.
The M. S. is not near so inconceivable as thesignum in magnitudine individuum.
Mem. To examine the math, about theirpoint—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.
M.
M.
Unperceivable perception a contradiction.
P. G.
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 excuse250may 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 ytwchhas 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, wchare 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.
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.
I defy any man to assign a right line equal to a paraboloid, but wnlook'd at thro' a microscope they may appear unequall.
M.
M.
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.
P.
P.
Men allow colours, sounds, &c.253not to exist without the mind, tho' they have no demonstration they do not. Why may they not allow my Principle with a demonstration?