adhere to the received opinions.

118. THE ERRORS ARISING FROM THE DOCTRINES OF ABSTRACTION AND EXTERNAL
MATERIAL EXISTENCES, INFLUENCE MATHEMATICAL REASONINGS.--Hitherto of
Natural Philosophy: we come now to make some inquiry concerning
that other great branch of speculative knowledge, to wit, Mathematics.
These, how celebrated soever they may be for their clearness and
certainty of demonstration, which is hardly anywhere else to be
found, cannot nevertheless be supposed altogether free from mistakes, if
in their principles there lurks some secret error which is common to the
professors of those sciences with the rest of mankind. Mathematicians,
though they deduce their theorems from a great height of evidence, yet
their first principles are limited by the consideration of quantity: and
they do not ascend into any inquiry concerning those transcendental
maxims which influence all the particular sciences, each part whereof,
Mathematics not excepted, does consequently participate of the errors
involved in them. That the principles laid down by mathematicians are
true, and their way of deduction from those principles clear and
incontestible, we do not deny; but, we hold there may be certain
erroneous maxims of greater extent than the object of Mathematics, and
for that reason not expressly mentioned, though tacitly supposed
throughout the whole progress of that science; and that the ill effects
of those secret unexamined errors are diffused through all the branches
thereof. To be plain, we suspect the mathematicians are as well as other
men concerned in the errors arising from the doctrine of abstract general
ideas, and the existence of objects without the mind.

119. Arithmetic has been thought to have for its object abstract ideas of
Number; of which to understand the properties and mutual habitudes, is
supposed no mean part of speculative knowledge. The opinion of the pure