perceptions; a notion so imperfect, that no sceptic will think it
worth while to contend against it.

                              PART II.

  124. It may seem a very extravagant attempt of the sceptics to
destroy reason by argument and ratiocination; yet is this the grand
scope of all their enquiries and disputes. They endeavour to find
objections, both to our abstract reasonings, and to those which regard
matter of fact and existence.

  The chief objection against all abstract reasonings is derived
from the ideas of space and time; ideas, which, in common life and
to a careless view, are very clear and intelligible, but when they
pass through the scrutiny of the profound sciences (and they are the
chief object of these sciences) afford principles, which seem full
of absurdity and contradiction. No priestly dogmas, invented on
purpose to tame and subdue the rebellious reason of mankind, ever
shocked common sense more than the doctrine of the infinitive
divisibility of extension, with its consequences; as they are
pompously displayed by all geometricians and metaphysicians, with a
kind of triumph and exultation. A real quantity, infinitely less
than any finite quantity, containing quantities infinitely less than
itself, and so on in infinitum; this is an edifice so bold and
prodigious, that it is too weighty for any pretended demonstration
to support, because it shocks the clearest and most natural principles
of human reason.* But what renders the matter more extraordinary,
is, that these seemingly absurd opinions are supported by a chain of
reasoning, the clearest and most natural; nor is it possible for us to
allow the premises without admitting the consequences. Nothing can
be more convincing and satisfactory than all the conclusions
concerning the properties of circles and triangles; and yet, when
these are once received, how can we deny, that the angle of contact
between a circle and its tangent is infinitely less than any
rectilineal angle, that as you may increase the diameter of the circle
in infinitum, this angle of contact becomes still less, even in
infinitum, and that the angle of contact between other curves and
their tangents may be infinitely less than those between any circle
and its tangent, and so on, in infinitum? The demonstration of these
principles seems as unexceptionable as that which proves the three
angles of a triangle to be equal to two right ones, though the
latter opinion be natural and easy, and the former big with
contradiction and absurdity. Reason here seems to be thrown into a
kind of amazement and suspence, which, without the suggestions of
any sceptic, gives her a diffidence of herself, and of the ground on
which she treads. She sees a full light, which illuminates certain
places; but that light borders upon the most profound darkness. And
between these she is so dazzled and confounded, that she scarcely
can pronounce with certainty and assurance concerning any one object.

  * Whatever disputes there may be about mathematical points, we
must allow that there are physical points; that is, parts of
extension, which cannot be divided or lessened, either by the eye or
imagination. These images, then, which are present to the fancy or
senses, are absolutely indivisible, and consequently must be allowed
by mathematicians to be infinitely less than any real part of
extension; and yet nothing appears more certain to reason, than that
an infinite number of them composes an infinite extension. How much
more an infinite number of those infinitely small parts of
extension, which are still supposed infinitely divisible.

  125. The absurdity of these bold determinations of the abstract
sciences seems to become, if possible, still more palpable with regard
to time than extension. An infinite number of real parts of time,
passing in succession, and exhausted one after another, appears so
evident a contradiction, that no man, one should think, whose
judgement is not corrupted, instead of being improved, by the
sciences, would ever be able to admit of it.

  Yet still reason must remain restless, and unquiet, even with regard
to that scepticism, to which she is driven by these seeming
absurdities and contradictions. How any clear, distinct idea can
contain circumstances, contradictory to itself, or to any other clear,
distinct idea, is absolutely incomprehensible; and is, perhaps, as
absurd as any proposition, which can be formed. So that nothing can be
more sceptical, or more full of doubt and hesitation, than this
scepticism itself, which arises from some of the paradoxical
conclusions of geometry or the science of quantity.*

  * It seems to me not impossible to avoid these absurdities and
contradictions, if it be admitted, that there is no such thing as
abstract or general ideas, properly speaking; but that all general
ideas are, in reality, particular ones, attached to a general term,
which recalls, upon occasion, other particular ones, that resemble, in
certain circumstances, the idea, present to the mind. Thus when the
term Horse is pronounced, we immediately figure to ourselves the
idea of a black or a white animal, of a particular size or figure: But
as that term is also usually applied to animals of other colours,
figures and sizes, these ideas, though not actually present to the
imagination, are easily recalled; and our reasoning and conclusion
proceed in the same way, as if they were actually present. If this
be admitted (as seems reasonable) it follows that all the ideas of
quantity, upon which mathematicians reason, are nothing but
particular, and such as are suggested by the senses and imagination,
and consequently, cannot be infinitely divisible. It is sufficient
to have dropped this hint at present, without prosecuting it any
farther. It certainly concerns all lovers of science not to expose
themselves to the ridicule and contempt of the ignorant by their
conclusions; and this seems the readiest solution of these
difficulties.