Honoured Sir. --Between a
true and an
adequate idea, I
recognize no difference, except that the epithet
true only has
regard to the agreement between the idea and its object,
whereas the epithet adequate has regard to the nature of the
idea in itself; so that in reality there is no difference between a
true and an
adequate idea
beyond this extrinsic relation.
However, in order that I may know, from which idea out of
many all the properties of its object may be deduced, I pay
attention to one point only, namely, that the idea or
definition
should express the efficient cause of its object. For instance, in
inquiring into the properties of a circle, I ask, whether from the
idea of a circle, that it consists of infinite right angles, I can
deduce all its properties. I ask, I repeat, whether this idea
involves the efficient cause of a circle. If it does not, I look for
another, namely, that a circle is the space described by a line,
of which one point is fixed, and the other movable. As this
definition
explains the efficient cause, I know that I can
deduce from it all the properties of a circle. So, also, when
I define God
as a supremely perfect Being, then, since that
definition
does not express the efficient cause (I mean the
efficient cause internal as well as external) I shall not be able to
infer therefrom all the properties of
God; as I can, when I define
God as
a Being, &c. (see Ethics, E1D6).
As for your other
inquiries, namely, that concerning motion, and those
pertaining to method, my observations on them are not yet
written out in due order, so I will reserve them for another
occasion.
As regards your remark, that he "who considers lines applied
to curves makes many deductions with regard to the
measurement of curves, but does so with greater
facility from the consideration of tangents," &c., that
from the consideration of tangents many deductions will
be made with more difficulty, than from the
consideration of lines applied in succession; and I assert
absolutely, that from certain properties of any particular
thing (whatever idea be given) some things may be
discovered more readily, others with more difficulty,
though all are concerned with the nature of the thing. I
think it need only be observed, that an idea should be
sought for of such a kind, that all properties may be
inferred, as has been said above. He, who is about to
deduce all the properties of a
particular thing, knows
that the ultimate properties will necessarily be the most
difficult to discover, &c.
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