sophistry and illusion. As the component parts of quantity and number
are entirely similar, their relations become intricate and involved; and
nothing can be more curious, as well as useful, than to trace, by a
variety of mediums, their equality or inequality, through their
different appearances. But as all other ideas are clearly distinct and
different from each other, we can never advance farther, by our utmost
scrutiny, than to observe this diversity, and, by an obvious reflection,
pronounce one thing not to be another. Or if there be any difficulty in
these decisions, it proceeds entirely from the undeterminate meaning of
words, which is corrected by juster definitions. That _the square of the
hypothenuse is equal to the squares of the other two sides_, cannot be
known, let the terms be ever so exactly defined, without a train of
reasoning and enquiry. But to convince us of this proposition, _that
where there is no property, there can be no injustice_, it is only
necessary to define the terms, and explain injustice to be a violation
of property. This proposition is, indeed, nothing but a more imperfect
definition. It is the same case with all those pretended syllogistical
reasonings, which may be found in every other branch of learning, except
the sciences of quantity and number; and these may safely, I think, be
pronounced the only proper objects of knowledge and demonstration.

132. All other enquiries of men regard only matter of fact and
existence; and these are evidently incapable of demonstration. Whatever
_is_ may _not be_. No negation of a fact can involve a contradiction.
The non-existence of any being, without exception, is as clear and
distinct an idea as its existence. The proposition, which affirms it not
to be, however false, is no less conceivable and intelligible, than that
which affirms it to be. The case is different with the sciences,
properly so called. Every proposition, which is not true, is there
confused and unintelligible. That the cube root of 64 is equal to the