But, since the manner wherein the mind apprehends by sight the motion of
tangible objects, with the various degrees thereof, may be easily
collected from what has been said concerning the manner wherein that sense
doth suggest their various distances, magnitudes, and situations, I shall
not enlarge any farther on this subject, but proceed to inquire what may
be alleged, with greatest appearance of reason, against the proposition we
have demonstrated to be true; for, where there is so much prejudice to be
encountered, a bare and naked demonstration of the truth will scarce
suffice. We must also satisfy the scruples that men may start in favour of
their preconceived notions, shew whence the mistake arises, how it came to
spread, and carefully disclose and root out those false persuasions that
an early prejudice might have implanted in the mind.
139. _First_, therefore, it will be demanded how visible extension and
figures come to be called by the same name with tangible extension and
figures, if they are not of the same kind with them? It must be something
more than humour or accident that could occasion a custom so constant and
universal as this, which has obtained in all ages and nations of the
world, and amongst all ranks of men, the learned as well as the
illiterate.
140. To which I answer, we can no more argue a visible and tangible square
to be of the same species, from their being called by the same name, than
we can that a tangible square, and the monosyllable consisting of six
letters whereby it is marked, are of the same species, because they are
both called by the same name. It is customary to call written words, and
the things they signify, by the same name: for, words not being regarded
in their own nature, or otherwise than as they are marks of things, it had
been superfluous, and beside the design of language, to have given them
names distinct from those of the things marked by them. The same reason
holds here also. Visible figures are the marks of tangible figures; and,
from sect. 59, it is plain that in themselves they are little regarded, or
upon any other score than for their connexion with tangible figures, which
by nature they are ordained to signify. And, because this language of
nature(445) does not vary in different ages or nations, hence it is that
in all times and places visible figures are called by the same names as
the respective tangible figures suggested by them; and not because they
are alike, or of the same sort with them.
141. But, say you, surely a tangible square is liker to a visible square
than to a visible circle: it has four angles, and as many sides; so also
has the visible square—but the visible circle has no such thing, being
bounded by one uniform curve, without right lines or angles, which makes
it unfit to represent the tangible square, but very fit to represent the
tangible circle. Whence it clearly follows, that visible figures are
patterns of, or of the same species with, the respective tangible figures
represented by them; that they are like unto them, and of their own nature
fitted to represent them, as being of the same sort; and that they are in
no respect arbitrary signs, as words.
142. I answer, it must be acknowledged the visible square is fitter than
the visible circle to represent the tangible square, but then it is not
because it is liker, or more of a species with it; but, because the
visible square contains in it several distinct parts, whereby to mark the
several distinct corresponding parts of a tangible square, whereas the
visible circle doth not. The square perceived by touch hath four distinct
equal sides, so also hath it four distinct equal angles. It is therefore
necessary that the visible figure which shall be most proper to mark it
contain four distinct equal parts, corresponding to the four sides of the
tangible square; as likewise four other distinct and equal parts, whereby
to denote the four equal angles of the tangible square. And accordingly we
see the visible figures contain in them distinct visible parts, answering
to the distinct tangible parts of the figures signified or suggested by
them.
143. But, it will not hence follow that any visible figure is like unto or
of the same species with its corresponding tangible figure—unless it be
also shewn that not only the number, but also the kind of the parts be the
same in both. To illustrate this, I observe that visible figures represent
tangible figures much after the same manner that written words do sounds.
Now, in this respect, words are not arbitrary; it not being indifferent
what written word stands for any sound. But, it is requisite that each
word contain in it as many distinct characters as there are variations in
the sound it stands for. Thus, the single letter _a_ is proper to mark one
simple uniform sound; and the word _adultery_ is accommodated to represent
the sound annexed to it—in the formation whereof there being eight
different collisions or modifications of the air by the organs of speech,
each of which produces a difference of sound, it was fit the word
representing it should consist of as many distinct characters, thereby to
mark each particular difference or part of the whole sound. And yet
nobody, I presume, will say the single letter _a_, or the word _adultery_,
are alike unto or of the same species with the respective sounds by them
represented. It is indeed arbitrary that, in general, letters of any
language represent sounds at all; but, when that is once agreed, it is not
arbitrary what combination of letters shall represent this or that
particular sound. I leave this with the reader to pursue, and apply it in
his own thoughts.
144. It must be confessed that we are not so apt to confound other signs
with the things signified, or to think them of the same species, as we are
visible and tangible ideas. But, a little consideration will shew us how
this may well be, without our supposing them of a like nature. These signs
are constant and universal; their connexion with tangible ideas has been
learnt at our first entrance into the world; and ever since, almost every
moment of our lives, it has been occurring to our thoughts, and fastening
and striking deeper on our minds. When we observe that signs are variable,
and of human institution; when we remember there was a time they were not
connected in our minds with those things they now so readily suggest, but
that their signification was learned by the slow steps of experience: this
preserves us from confounding them. But, when we find the same signs
suggest the same things all over the world; when we know they are not of
human institution, and cannot remember that we ever learned their
signification, but think that at first sight they would have suggested to
us the same things they do now: all this persuades us they are of the same
species as the things respectively represented by them, and that it is by
a natural resemblance they suggest them to our minds.
145. Add to this that whenever we make a nice survey of any object,
successively directing the optic axis to each point thereof, there are
certain lines and figures, described by the motion of the head or eye,
which, being in truth perceived by feeling(446), do nevertheless so mix
themselves, as it were, with the ideas of sight that we can scarce think
but they appertain to that sense. Again, the ideas of sight enter into the
mind several at once, more distinct and unmingled than is usual in the
other senses beside the touch. Sounds, for example, perceived at the same
instant, are apt to coalesce, if I may so say, into one sound: but we can
perceive, at the same time, great variety of visible objects, very
separate and distinct from each other. Now, tangible(447) extension being
made up of several distinct coexistent parts, we may hence gather another
reason that may dispose us to imagine a likeness or analogy between the
immediate objects of sight and touch. But nothing, certainly, does more
contribute to blend and confound them together, than the strict and close
connexion(448) they have with each other. We cannot open our eyes but the
ideas of distance, bodies, and tangible figures are suggested by them. So
swift, and sudden, and unperceived is the transit from visible to tangible
ideas that we can scarce forbear thinking them equally the immediate
object of vision.
146. The prejudice(449) which is grounded on these, and whatever other
causes may be assigned thereof, sticks so fast on our understandings, that
it is impossible, without obstinate striving and labour of the mind, to
get entirely clear of it. But then the reluctancy we find in rejecting any
opinion can be no argument of its truth, to whoever considers what has
been already shewn with regard to the prejudices we entertain concerning
the distance, magnitude, and situation of objects; prejudices so familiar
to our minds, so confirmed and inveterate, as they will hardly give way to
the clearest demonstration.
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147. Upon the whole, I think we may fairly conclude(450) that the proper
objects of Vision constitute the Universal Language of Nature; whereby we
are instructed how to regulate our actions, in order to attain those
things that are necessary to the preservation and well-being of our
bodies, as also to avoid whatever may be hurtful and destructive of them.
It is by their information that we are principally guided in all the
transactions and concerns of life. And the manner wherein they signify and
mark out unto us the objects which are at a distance is the same with that
of languages and signs of human appointment; which do not suggest the
things signified by any likeness or identity of nature, but only by an
habitual connexion that experience has made us to observe between
them(451).
148. Suppose one who had always continued blind be told by his guide that
after he has advanced so many steps he shall come to the brink of a
precipice, or be stopped by a wall; must not this to him seem very
admirable and surprising? He cannot conceive how it is possible for
mortals to frame such predictions as these, which to him would seem as
strange and unaccountable as prophecy does to others. Even they who are
blessed with the visive faculty may (though familiarity make it less
observed) find therein sufficient cause of admiration. The wonderful art
and contrivance wherewith it is adjusted to those ends and purposes for
which it was apparently designed; the vast extent, number, and variety of
objects that are at once, with so much ease, and quickness, and pleasure,
suggested by it—all these afford subject for much and pleasing
speculation, and may, if anything, give us some glimmering analogous
prænotion of things, that are placed beyond the certain discovery and
comprehension of our present state(452).
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149. I do not design to trouble myself much with drawing corollaries from
the doctrine I have hitherto laid down. If it bears the test, others may,
so far as they shall think convenient, employ their thoughts in extending
it farther, and applying it to whatever purposes it may be subservient to.
Only, I cannot forbear making some inquiry concerning the object of
geometry, which the subject we have been upon does naturally lead one to.
We have shewn there is no such idea as that of extension in abstract(453);
and that there are two kinds of sensible extension and figures, which are
entirely distinct and heterogeneous from each other(454). Now, it is
natural to inquire which of these is the object of geometry(455).
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150. Some things there are which, at first sight, incline one to think
geometry conversant about visible extension. The constant use of the eyes,
both in the practical and speculative parts of that science, doth very
much induce us thereto. It would, without doubt, seem odd to a
mathematician to go about to convince him the diagrams he saw upon paper
were not the figures, or even the likeness of the figures, which make the
subject of the demonstration—the contrary being held an unquestionable
truth, not only by mathematicians, but also by those who apply themselves
more particularly to the study of logic; I mean who consider the nature of
science, certainty, and demonstration; it being by them assigned as one
reason of the extraordinary clearness and evidence of geometry, that in
that science the reasonings are free from those inconveniences which
attend the use of arbitrary signs, the very ideas themselves being copied
out, and exposed to view upon paper. But, by the bye, how well this agrees
with what they likewise assert of abstract ideas being the object of
geometrical demonstration I leave to be considered.
151. To come to a resolution in this point, we need only observe what has
been said in sect. 59, 60, 61, where it is shewn that visible extensions
in themselves are little regarded, and have no settled determinate
greatness, and that men measure altogether by the application of tangible
extension to tangible extension. All which makes it evident that visible
extension and figures are not the object of geometry.
152. It is therefore plain that visible figures are of the same use in
geometry that words are. And the one may as well be accounted the object
of that science as the other; neither of them being any otherwise
concerned therein than as they represent or suggest to the mind the
particular tangible figures connected with them. There is, indeed, this
difference betwixt the signification of tangible figures by visible
figures, and of ideas by words—that whereas the latter is variable and
uncertain, depending altogether on the arbitrary appointment of men, the
former is fixed, and immutably the same in all times and places. A visible
square, for instance, suggests to the mind the same tangible figure in
Europe that it doth in America. Hence it is, that the voice of nature,
which speaks to our eyes, is not liable to that misinterpretation and
ambiguity that languages of human contrivance are unavoidably subject
to(456). From which may, in some measure, be derived that peculiar
evidence and clearness of geometrical demonstrations.
153. Though what has been said may suffice to shew what ought to be
determined with relation to the object of geometry, I shall, nevertheless,
for the fuller illustration thereof, take into my thoughts the case of an
intelligence or unbodied spirit, which is supposed to see perfectly well,
i.e. to have a clear perception of the proper and immediate objects of
sight, but to have no sense of touch(457). Whether there be any such being
in nature or no, is beside my purpose to inquire; it suffices, that the
supposition contains no contradiction in it. Let us now examine what
proficiency such a one may be able to make in geometry. Which speculation
will lead us more clearly to see whether the ideas of sight can possibly
be the object of that science.
154. _First_, then, it is certain the aforesaid intelligence could have no
idea of a solid or quantity of three dimensions, which follows from its
not having any idea of distance. We, indeed, are prone to think that we
have by sight the ideas of space and solids; which arises from our
imagining that we do, strictly speaking, see distance, and some parts of
an object at a greater distance than others; which has been demonstrated
to be the effect of the experience we have had what ideas of touch are
connected with such and such ideas attending vision. But the intelligence
here spoken of is supposed to have no experience of touch. He would not,
therefore, judge as we do, nor have any idea of distance, outness, or
profundity, nor consequently of space or body, either immediately or by
suggestion. Whence it is plain he can have no notion of those parts of
geometry which relate to the mensuration of solids, and their convex or
concave surfaces, and contemplate the properties of lines generated by the
section of a solid. The conceiving of any part whereof is beyond the reach
of his faculties.
155. _Farther_, he cannot comprehend the manner wherein geometers describe
a right line or circle; the rule and compass, with their use, being things
of which it is impossible he should have any notion. Nor is it an easier
matter for him to conceive the placing of one plane or angle on another,
in order to prove their equality; since that supposes some idea of
distance, or external space. All which makes it evident our pure
intelligence could never attain to know so much as the first elements of
plain geometry. And perhaps, upon a nice inquiry, it will be found he
cannot even have an idea of plain figures any more than he can of solids;
since some idea of distance is necessary to form the idea of a geometrical
plane, as will appear to whoever shall reflect a little on it.
156. All that is properly perceived by the visive faculty amounts to no
more than colours with their variations, and different proportions of
light and shade—but the perpetual mutability and fleetingness of those
immediate objects of sight render them incapable of being managed after
the manner of geometrical figures; nor is it in any degree useful that
they should. It is true there be divers of them perceived at once; and
more of some, and less of others: but accurately to compute their
magnitude, and assign precise determinate proportions between things so
variable and inconstant, if we suppose it possible to be done, must yet be
a very trifling and insignificant labour.
157. I must confess, it seems to be the opinion of some very ingenious men
that flat or plane figures are immediate objects of sight, though they
acknowledge solids are not. And this opinion of theirs is grounded on what
is observed in painting, wherein (say they) the ideas immediately
imprinted in the mind are only of planes variously coloured, which, by a
sudden act of the judgment, are changed into solids: but, with a little
attention, we shall find the planes here mentioned as the immediate
objects of sight are not visible but tangible planes. For, when we say
that pictures are planes, we mean thereby that they appear to the touch
smooth and uniform. But then this smoothness and uniformity, or, in other
words, this planeness of the picture is not perceived immediately by
vision; for it appeareth to the eye various and multiform.
158. From all which we may conclude that planes are no more the immediate
object of sight than solids. What we strictly see are not solids, nor yet
planes variously coloured—they are only diversity of colours. And some of
these suggest to the mind solids, and others plane figures; just as they
have been experienced to be connected with the one or the other: so that
we see planes in the same way that we see solids—both being equally
suggested by the immediate objects of sight, which accordingly are
themselves denominated planes and solids. But, though they are called by
the same names with the things marked by them, they are, nevertheless, of
a nature entirely different, as hath been demonstrated(458).
159. What has been said is, if I mistake not, sufficient to decide the
question we proposed to examine, concerning the ability of a pure spirit,
such as we have described, to know geometry. It is, indeed, no easy matter
for us to enter precisely into the thoughts of such an intelligence;
because we cannot, without great pains, cleverly separate and disentangle
in our thoughts the proper objects of sight from those of touch which are
connected with them. This, indeed, in a complete degree seems scarce
possible to be performed; which will not seem strange to us, if we
consider how hard it is for any one to hear the words of his native
language, which is familiar to him, pronounced in his ears without
understanding them. Though he endeavour to disunite the meaning from the
sound, it will nevertheless intrude into his thoughts, and he shall find
it extreme difficult, if not impossible, to put himself exactly in the
posture of a foreigner that never learnt the language, so as to be
affected barely with the sounds themselves, and not perceive the
signification annexed to them.
160. By this time, I suppose, it is clear that neither abstract nor
visible extension makes the object of geometry; the not discerning of
which may, perhaps, have created some difficulty and useless labour in
mathematics. [(459)Sure I am that somewhat relating thereto has occurred
to my thoughts; which, though after the most anxious and repeated
examination I am forced to think it true, doth, nevertheless, seem so far
out of the common road of geometry, that I know not whether it may not be
thought presumption if I should make it public, in an age wherein that
science hath received such mighty improvements by new methods; great part
whereof, as well as of the ancient discoveries, may perhaps lose their
reputation, and much of that ardour with which men study the abstruse and
fine geometry be abated, if what to me, and those few to whom I have
imparted it, seems evidently true, should really prove to be so.]
An Appendix To The Essay On Vision
[_This Appendix is contained only in the second edition._]
The censures which, I am informed, have been made on the foregoing _Essay_
inclined me to think I had not been clear and express enough in some
points; and, to prevent being misunderstood for the future, I was willing
to make any necessary alterations or additions in what I had written. But
that was impracticable, the present edition having been almost finished
before I received this information. Wherefore, I think it proper to
consider in this place the principal objections that are come to my
notice.
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In the _first_ place, it is objected, that in the beginning of the Essay I
argue either against all use of lines and angles in optics, and then what
I say is false; or against those writers only who will have it that we can
perceive by sense the optic axes, angles, &c., and then it is
insignificant, this being an absurdity which no one ever held. To which I
answer that I argue only against those who are of opinion that we perceive
the distance of objects by lines and angles, or, as they term it, by a
kind of innate geometry. And, to shew that this is not fighting with my
own shadow, I shall here set down a passage from the celebrated Des
Cartes(460):—
[Illustration]
“Distantiam præterea discimus, per mutuam quandam conspirationem oculorum.
Ut enim cæcus noster duo bacilla tenens, _A E_ et _C E_, de quorum
longitudine incertus, solumque intervallum manuum _A_ et _C_, cum
magnitudine angulorum _A C E_, et _C A E_ exploratum habens, inde, ut ex
Geometria quadam omnibus innata, scire potest ubi sit punctum _E_. Sic
quum nostri oculi _R S T_ et _r s t_ ambo, vertuntur ad _X_, magnitudo
lineæ _S s_, et angulorum _X S s_ et _X s S_, certos nos reddunt ubi sit
punctum _X_. Et idem opera alterutrius possumus indagare, loco illum
movendo, ut si versus _X_ illum semper dirigentes, prime sistamus in
puncto _S_, et statim post in puncto _s_, hoc sufficiet ut magnitudo lineæ
_S s_, et duorum angulorum _X S s_ et _X s S_ nostræ imaginationi simul
occurrant, et distantiam puncti _X_ nos edoceant: idque per actionem
mentis, quæ licet simplex judicium esse videatur, ratiocinationem tamen
quandam involutam habet, similem illi, qua Geometræ per duas stationes
diversas, loca inaccessa dimetiuntur.”
[Illustration]
I might amass together citations from several authors to the same purpose,
but, this being so clear in the point, and from an author of so great
note, I shall not trouble the reader with any more. What I have said on
this head was not for the sake of rinding fault with other men; but,
because I judged it necessary to demonstrate in the first place that we
neither see distance _immediately_, nor yet perceive it by the mediation
of anything that hath (as lines and angles) a _necessary_ connexion with
it. For on the demonstration of this point the whole theory depends(461).