Demonstration. That absolute
proof, which shows not only that a thing is so, but that it cannot be
otherwise. It is of course confined to necessary matter, which belongs
only to mathematics and logic.
The laws and properties of pure space in
geometry are such, so the relations of numbers and abstract
quantity in algebra, and those between premisses
and their conclusion in logic. A syllogism is a demonstration, not
indeed of the truth of the conclusion, but of its necessarily following
from the premisses. All other proof amounts but to probability, although
the maximum of probability will always produce conviction of that on
behalf of which it is urged.