as well as the dd, &c., wch are allowed to be something, & consequently
may be magnify’d by glasses into inches, feet, &c., as well as the
quantities next below the M.?
Big, little, and number are the works of the mind. How therefore can ye
extension you suppose in Matter be big or little? How can it consist of
any number of points?
(M416) Mem. Strictly to remark L[ocke], b. 2. c. 8. s. 8.
Schoolmen compar’d with the mathematicians.
Extension is blended wth tangible or visible ideas, & by the mind
præscinded therefrom.
Mathematiques made easy—the scale does almost all. The scale can tell us
the subtangent in ye parabola is double the abscisse.
Wt need of the utmost accuracy wn the mathematicians own _in rerum natura_
they cannot find anything corresponding wth their nice ideas.
One should endeavour to find a progression by trying wth the scale.
Newton’s fluxions needless. Anything below an M might serve for Leibnitz’s
Differential Calculus.
How can they hang together so well, since there are in them (I mean the
mathematiques) so many _contradictoriæ argutiæ_. V. Barrow, Lect.
A man may read a book of Conics with ease, knowing how to try if they are
right. He may take ’em on the credit of the author.
Where’s the need of certainty in such trifles? The thing that makes it so
much esteem’d in them is that we are thought not capable of getting it
elsewhere. But we may in ethiques and metaphysiques.
The not leading men into mistakes no argument for the truth of the
infinitesimals. They being nothings may perhaps do neither good nor harm,
except wn they are taken for something, & then the contradiction begets a
contradiction.
a + 500 nothings = a + 50 nothings—an innocent silly truth.
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(M417) My doctrine excellently corresponds wth the creation. I suppose no
matter, no stars, sun, &c. to have existed before(247).
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It seems all circles are not similar figures, there not being the same
proportion betwixt all circumferences & their diameters.
When a small line upon paper represents a mile, the mathematicians do not
calculate the 1/10000 of the paper line, they calculate the 1/10000 of the
mile. ’Tis to this they have regard, ’tis of this they think; if they
think or have any idea at all. The inch perhaps might represent to their
imaginations the mile, but ye 1/10000 of the inch cannot be made to
represent anything, it not being imaginable.
But the 1/10000 of a mile being somewhat, they think the 1/10000 inch is
somewhat: wn they think of yt they imagine they think on this.
3 faults occur in the arguments of the mathematicians for divisibility _ad
infinitum_—
1. They suppose extension to exist without the mind, or not
perceived.
2. They suppose that we have an idea of length without
breadth(248), or that length without breadth does exist.
3. That unity is divisible _ad infinitum_.
To suppose a M. S. divisible is to say there are distinguishable ideas
where there are no distinguishable ideas.
The M. S. is not near so inconceivable as the _signum in magnitudine
individuum_.
Mem. To examine the math, about their _point_—what it is—something or
nothing; and how it differs from the M. S.
All might be demonstrated by a new method of indivisibles, easier perhaps
and juster than that of Cavalierius(249).
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(M418) Unperceivable perception a contradiction.
(M419) 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 excuse(250) may hurt Transubstantiation, but not the
Trinity.
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We need not strain our imaginations to conceive such little things. Bigger
may do as well for infinitesimals, since the integer must be an infinite.
Evident yt wch has an infinite number of parts must be infinite.
Qu. Whether extension be resoluble into points it does not consist of?
Nor can it be objected that we reason about numbers, wch are only words &
not ideas(251); 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.
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(M420) Our eyes and senses inform us not of the existence of matter or
ideas existing without the mind(252). They are not to be blam’d for the
mistake.
I defy any man to assign a right line equal to a paraboloid, but wn look’d
at thro’ a microscope they may appear unequall.
(M421) 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.
(M422) Men allow colours, sounds, &c.(253) not to exist without the mind,
tho’ they have no demonstration they do not. Why may they not allow my
Principle with a demonstration?
(M423) Qu. Whether I had not better allow colours to exist without the
mind; taking the mind for the active thing wch I call “I,” “myself”—yt
seems to be distinct from the understanding(254)?
(M424) The taking extension to be distinct from all other tangible &
visible qualities, & to make an idea by itself, has made men take it to be
without the mind.
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I see no wit in any of them but Newton. The rest are meer triflers, mere
Nihilarians.
The folly of the mathematicians in not judging of sensations by their
senses. Reason was given us for nobler uses.
(M425) Keill’s filling the world with a mite(255). This follows from the
divisibility of extension _ad infinitum_.
Extension, or length without breadth, seems to be nothing save the number
of points that lie betwixt any 2 points(256). It seems to consist in meer
proportion—meer reference of the mind.
To what purpose is it to determine the forms of glasses geometrically?
Sir Isaac(257) owns his book could have been demonstrated on the
supposition of indivisibles.
(M426) Innumerable vessels of matter. V. Cheyne.
I’ll not admire the mathematicians. ’Tis wt any one of common sense might
attain to by repeated acts. I prove it by experience. I am but one of
human sense, and I &c.
Mathematicians have some of them good parts—the more is the pity. Had they
not been mathematicians they had been good for nothing. They were such
fools they knew not how to employ their parts.
The mathematicians could not so much as tell wherein truth & certainty
consisted, till Locke told ’em(258). I see the best of ’em talk of light
and colours as if wthout the mind.
By _thing_ I either mean ideas or that wch has ideas(259).
Nullum præclarum ingenium unquam fuit magnus mathematicus. Scaliger(260).
A great genius cannot stoop to such trifles & minutenesses as they
consider.
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1. (261)All significant words stand for ideas(262).
2. All knowledge about our ideas.
3. All ideas come from without or from within.
4. If from without it must be by the senses, & they are call’d
sensations(263).
5. If from within they are the operations of the mind, & are called
thoughts.
6. No sensation can be in a senseless thing.
7. No thought can be in a thoughtless thing.
8. All our ideas are either sensations or thoughts(264), by 3, 4, 5.
9. None of our ideas can be in a thing wch is both thoughtless &
senseless(265), by 6, 7, 8.
10. The bare passive recognition or having of ideas is called perception.
11. Whatever has in it an idea, tho’ it be never so passive, tho’ it exert
no manner of act about it, yet it must perceive. 10.
12. All ideas either are simple ideas, or made up of simple ideas.
13. That thing wch is like unto another thing must agree wth it in one or
more simple ideas.
14. Whatever is like a simple idea must either be another simple idea of
the same sort, or contain a simple idea of the same sort. 13.
15. Nothing like an idea can be in an unperceiving thing. 11, 14. Another
demonstration of the same thing.
16. Two things cannot be said to be alike or unlike till they have been
compar’d.
17. Comparing is the viewing two ideas together, & marking wt they agree
in and wt they disagree in.
18. The mind can compare nothing but its own ideas. 17.
19. Nothing like an idea can be in an unperceiving thing. 11, 16, 18.
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N. B. Other arguments innumerable, both _a priori_ & _a posteriori_, drawn
from all the sciences, from the clearest, plainest, most obvious truths,
whereby to demonstrate the Principle, i.e. that neither our ideas, nor
anything like our ideas, can possibly be in an unperceiving thing(266).
N. B. Not one argument of any kind wtsoever, certain or probable, _a
priori_ or _a posteriori_, from any art or science, from either sense or
reason, against it.
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Mathematicians have no right idea of angles. Hence angles of contact
wrongly apply’d to prove extension divisible _ad infinitum_.
We have got the Algebra of pure intelligences.
We can prove Newton’s propositions more accurately, more easily, & upon
truer principles than himself(267).
Barrow owns the downfall of geometry. However I’ll endeavour to rescue
it—so far as it is useful, or real, or imaginable, or intelligible. But
for _the nothings_, I’ll leave them to their admirers.
I’ll teach any one the whole course of mathematiques in 1/100 part the
time that another will.
Much banter got from the prefaces of the mathematicians.
(M427) Newton says colour is in the subtil matter. Hence Malbranch proves
nothing, or is mistaken, in asserting there is onely figure & motion.
I can square the circle, &c.; they cannot. Wch goes on the best
principles?
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The Billys(268) use a finite visible line for an 1/m.
(M428) Marsilius Ficinus—his appearing the moment he died solv’d by my
idea of time(269).
(M429) The philosophers lose their abstract or unperceived Matter. The
mathematicians lose their insensible sensations. The profane [lose] their
extended Deity. Pray wt do the rest of mankind lose? As for bodies, &c.,
we have them still(270).
N. B. The future nat. philosoph. & mathem. get vastly by the bargain(271).
(M430) There are men who say there are insensible extensions. There are
others who say the wall is not white, the fire is not hot, &c. We Irishmen
cannot attain to these truths.
The mathematicians think there are insensible lines. About these they
harangue: these cut in a point at all angles: these are divisible _ad
infinitum_. We Irishmen can conceive no such lines.
The mathematicians talk of wt they call a point. This, they say, is not
altogether nothing, nor is it downright something. Now we Irishmen are apt
to think something(272) & nothing are next neighbours.
Engagements to P.(273) on account of ye Treatise that grew up under his
eye; on account also of his approving my harangue. Glorious for P. to be
the protector of usefull tho’ newly discover’d truths.
How could I venture thoughts into the world before I knew they would be of
use to the world? and how could I know that till I had try’d how they
suited other men’s ideas?
I publish not this so much for anything else as to know whether other men
have the same ideas as we Irishmen. This is my end, & not to be inform’d
as to my own particular.
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My speculations have the same effect as visiting foreign countries: in the
end I return where I was before, but my heart at ease, and enjoying life
with new satisfaction.
Passing through all the sciences, though false for the most part, yet it
gives us the better insight and greater knowledge of the truth.
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He that would bring another over to his opinion, must seem to harmonize
with him at first, and humour him in his own way of talking(274).
From my childhood I had an unaccountable turn of thought that way.
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It doth not argue a dwarf to have greater strength than a giant, because
he can throw off the molehill which is upon him, while the other struggles
beneath a mountain.
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The whole directed to practise and morality—as appears 1st, from making
manifest the nearness and omnipresence of God; 2dly, from cutting off the
useless labour of sciences, and so forth.
AN ESSAY TOWARDS A NEW THEORY OF VISION
_First published in 1709_
Editor’s Preface To The Essay Towards A New Theory Of Vision
Berkeley’s _Essay towards a New Theory of Vision_ was meant to prepare the
way for the exposition and defence of the new theory of the material
world, its natural order, and its relation to Spirit, that is contained in
his book of _Principles_ and in the relative _Dialogues_, which speedily
followed. The _Essay_ was the firstfruits of his early philosophical
studies at Dublin. It was also the first attempt to show that our
apparently immediate Vision of Space and of bodies extended in
three-dimensioned space, is either tacit or conscious inference,
occasioned by constant association of the phenomena of which alone we are
visually percipient with assumed realities of our tactual and locomotive
experience.
The first edition of the _Essay_ appeared early in 1709, when its author
was about twenty-four years of age. A second edition, with a few verbal
changes and an Appendix, followed before the end of that year. Both were
issued in Dublin, “printed by Aaron Rhames, at the back of Dick’s
Coffeehouse, for Jeremy Pepyat, bookseller in Skinner Row.” In March,
1732, a third edition, without the Appendix, was annexed to _Alciphron,_
on account of its relation to the Fourth Dialogue in that book. This was
the author’s last revision.
In the present edition the text of this last edition is adopted, after
collation with those preceding. The Appendix has been restored, and also
the Dedication to Sir John Percival, which appeared only in the first
edition.
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A due appreciation of Berkeley’s theory of seeing, and his conception of
the visible world, involves a study, not merely of this tentative juvenile
_Essay_, but also of its fuller development and application in his more
matured works. This has been commonly forgotten by his critics.
Various circumstances contribute to perplex and even repel the reader of
the _Essay_, making it less fit to be an easy avenue of approach to
Berkeley’s _Principles_.
Its occasion and design, and its connexion with his spiritual conception
of the material world, are suggested in Sections 43 and 44 of the
_Principles_. Those sections are a key to the _Essay_. They inform us that
in the _Essay_ the author intentionally uses language which seems to
attribute a reality independent of all percipient spirit to the ideas or
phenomena presented in Touch; it being beside his purpose, he says, to
“examine and refute” that “vulgar error” in “a work on Vision.” This
studied reticence of a verbally paradoxical conception of Matter, in
reasonings about vision which are fully intelligible only under that
conception, is one cause of a want of philosophical lucidity in the
_Essay_.
Another circumstance adds to the embarrassment of those who approach the
_Principles_ and the three _Dialogues_ through the _Essay on Vision_. The
_Essay_ offers no exception to the lax employment of equivocal words
familiar in the early literature of English philosophy, but which is
particularly inconvenient in the subtle discussions to which we are here
introduced. At the present day we are perhaps accustomed to more precision
and uniformity in the philosophical use of language; at any rate we
connect other meanings than those here intended with some of the leading
words. It is enough to refer to such terms as _idea_, _notion_,
_sensation_, _perception_, _touch_, _externality_, _distance_, and their
conjugates. It is difficult for the modern reader to revive and remember
the meanings which Berkeley intends by _idea_ and _notion_—so significant
in his vocabulary; and _touch_ with him connotes muscular and locomotive
experience as well as the pure sense of contact. Interchange of the terms
_outward_, _outness_, _externality_, _without the mind_, and _without the
eye_ is confusing, if we forget that Berkeley implies that percipient mind
is virtually coextensive with our bodily organism, so that being “without”
or “at a distance from” our bodies is being at a distance from the
percipient mind. I have tried in the annotations to relieve some of these
ambiguities, of which Berkeley himself warns us (cf. sect. 120).
The _Essay_ moreover abounds in repetitions, and interpolations of
antiquated optics and physiology, so that its logical structure and even
its supreme generalisation are not easily apprehended. I will try to
disentangle them.
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The reader must remember that this _Essay on Vision_ is professedly an
introspective appeal to human consciousness. It is an analysis of what
human beings are conscious of when they see, the results being here and
there applied, partly by way of verification, to solve some famous optical
or physiological puzzle. The aim is to present the facts, the whole facts,
and nothing but the facts of our internal visual experience, as
distinguished from supposed facts and empty abstractions, which an
irregular exercise of imagination, or abuse of words, had put in their
place. The investigation, moreover, is not concerned with Space in its
metaphysical infinity, but with finite sections of Space and their
relations, which concern the sciences, physical and mathematical, and with
real or tangible Distance, Magnitude, and Place, in their relation to
seeing.
From the second section onwards the _Essay_ naturally falls into six
Parts, devoted successively to the proof of the six following theses
regarding the relation of Sight to finite spaces and to things extended:—
I. (Sect. 2-51.) Distance, or outness from the eye in the line of vision,
is not seen: it is only suggested to the mind by visible phenomena and by
sensations felt in the eye, all which are somehow its arbitrarily
constituted and non-resembling Signs.
II. (Sect. 52-87.) Magnitude, or the amount of space that objects of sense
occupy, is really invisible: we only see a greater or less quantity of
colour, and colour depends upon percipient mind: our supposed visual
perceptions of real magnitude are only our own interpretations of the
tactual meaning of the colours we see, and of sensations felt in the eye,
which are its Signs.
III. (Sect. 88-120.) Situation of objects of sense, or their real relation
to one another in ambient space, is invisible: what we see is variety in
the relations of colours to one another: our supposed vision of real
tangible locality is only our interpretation of its visual non-resembling
Signs.
IV. (Sect. 121-46.) There is no object that is presented in common to
Sight and Touch: space or extension, which has the best claim to be their
common object, is specifically as well as numerically different in Sight
and in Touch.
V. (Sect. 147-48.) The explanation of the tactual significance of the
visible and visual Signs, upon which human experience proceeds, is offered
in the Theory that all visible phenomena are arbitrary signs in what is
virtually the Language of Nature, addressed by God to the senses and
intelligence of Man.
VI. (Sect. 149-60.) The true object studied in Geometry is the kind of
Extension given in Touch, not that given in Sight: real Extension in all
its phases is tangible, not visible: colour is the only immediate object
of Sight, and colour being mind-dependent sensation, cannot be realised
without percipient mind. These concluding sections are supplementary to
the main argument.
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The fact that distance or outness is invisible is sometimes regarded as
Berkeley’s contribution to the theory of seeing. It is rather the
assumption on which the _Essay_ proceeds (sect. 2). The _Essay_ does not
prove this invisibility, but seeks to shew how, notwithstanding, we learn
to find outness through seeing. That the relation between the visual signs
of outness, on the one hand, and the real distance which they signify, on
the other, is in all cases arbitrary, and discovered through experience,
is the burden of sect. 2-40. The previously recognised signs of
“considerably remote” distances, are mentioned (sect. 3). But _near_
distance was supposed to be inferred by a visual geometry—and to be
“suggested,” not signified by arbitrary signs. The determination of the
visual signs which suggest outness, near and remote, is Berkeley’s
professed discovery regarding vision.
An induction of the visual signs which “suggest” distance, is followed
(sect. 43) by an assertion of the wholly sensuous reality of _colour_,
which is acknowledged to be the only immediate object of sight. Hence
_visible_ extension, consisting in colour, must be dependent for its
realisation upon sentient or percipient mind. It is then argued (sect. 44)
that this mind-dependent visible outness has no resemblance to the
tangible reality (sect. 45). This is the first passage in the _Essay_ in
which Touch and its data are formally brought into view. Tactual or
locomotive experience, it is implied, is needed to infuse true reality
into our conceptions of distance or outness. This cannot be got from
seeing any more than from hearing, or tasting, or smelling. It is as
impossible to see and touch the same object as it is to hear and touch the
same object. Visible objects and ocular sensations can only be _ideal
signs_ of _real things_.
The sections in which Touch is thus introduced are among the most
important in the _Essay_. They represent the outness given in hearing as
wholly sensuous, ideal, or mind-dependent: they recognise as more truly
real that got by contact and locomotion. But if this is all that man can
see, it follows that his _visible_ world, at any rate, becomes real only
in and through percipient mind. The problem of an _Essay on Vision_ is
thus, to explain _how_ the visible world of extended colour can inform us
of tangible realities, which it does not in the least resemble, and with
which it has no _necessary_ connexion. That visible phenomena, or else
certain organic sensations involved in seeing (sect. 3, 16, 21, 27),
gradually _suggest_ the real or tangible outness with which they are
connected in the divinely constituted system of nature, is the explanation
which now begins to dawn upon us.
Here an ambiguity in the _Essay_ appears. It concludes that the _visible_
world cannot be real without percipient realising mind, i.e. not otherwise
than ideally: yet the argument seems to take for granted that we are
percipient of a _tangible_ world that is independent of percipient
realising mind. The reader is apt to say that the tangible world must be
as dependent on percipient mind for its reality as the visible world is
concluded to be, and for the same reason. This difficulty was soon
afterwards encountered in the book of _Principles_, where the worlds of
sight and touch are put on the same level; and the possibility of
unperceived reality in both cases is denied; on the ground that a material
world cannot be realised in the total absence of Spirit—human and divine.
The term “external” may still be applied to tactual and locomotive
phenomena alone, if men choose; but this not because of the ideal
character of what is seen, and the unideal reality of what is touched, but
only because tactual perceptions are found to be more firm and steady than
visual. Berkeley preferred in this way to _insinuate_ his new conception
of the material world by degrees, at the risk of exposing this juvenile
and tentative _Essay on Vision_ to a charge of incoherence.
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