subservient to its existence than an exciting cause. For if scientific
conclusions are indubitable, if the truth of demonstration is necessary
and eternal, this universal is truly all, and not like that gained by
abstraction, limited to a certain number of particulars. Thus, the
proposition that the angles of every triangle are equal to two right, if
it is indubitably true, that is, if the term every in it really includes
all triangles, cannot be the result of any abstraction; for this, however
extended it may be, is limited, and falls far short of universal
comprehension. Whence is it then that the dianoetic power concludes thus
confidently that the Proposition is true of all triangles? For if it be
said that the mind, after having abstracted triangle from a certain
number of particulars, adds from itself what is wanting to complete the
all; in the first place, no man, I believe, will say that any such
operation as this took place in his mind when he first learnt this
proposition; and in the next place, if this should be granted, it would
follow that such proposition is a mere fiction, since it is uncertain
whether that which is added to complete the all is truly added; and thus
the conclusion will no longer be indubitably necessary.

In short, if the words all and every, with which every page of theoretic
mathematics is full, mean what they are conceived by all men to mean, and
if the universals which they signify are the proper objects of science,
such universals must subsist in the soul prior to the energies of sense.
Hence it will follow that induction is no otherwise subservient to
science, than as it produces credibility in axioms and petitions; and
this by exciting the universal conception of these latent in the soul.
The particulars, therefore, of which an induction is made in order to
produce science, must be so simple, that they may be immediately
apprehended, and that the universal may be predicated of them without
hesitation. The particulars of the experimentalists are not of this kind,