'peculiar' properties.
Now, it has been shown that the positing of one thing-be it one
term or one premiss-never involves a necessary consequent: two
premisses constitute the first and smallest foundation for drawing a
conclusion at all and therefore a fortiori for the demonstrative
syllogism of science. If, then, A is implied in B and C, and B and C
are reciprocally implied in one another and in A, it is possible, as
has been shown in my writings on the syllogism, to prove all the
assumptions on which the original conclusion rested, by circular
demonstration in the first figure. But it has also been shown that
in the other figures either no conclusion is possible, or at least
none which proves both the original premisses. Propositions the
terms of which are not convertible cannot be circularly demonstrated
at all, and since convertible terms occur rarely in actual
demonstrations, it is clearly frivolous and impossible to say that
demonstration is reciprocal and that therefore everything can be
demonstrated.
4
Since the object of pure scientific knowledge cannot be other than
it is, the truth obtained by demonstrative knowledge will be
necessary.
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