A conception is _correct_; a judgment is _true_; a body is _real_; and a
relation is _evident_. A proposition of immediate certainty is an _axiom_.
Only the fundamental principles of logic, and those of mathematics drawn
_a priori_ from intuition or perception, and finally also the law of
causality, have immediate certainty. A proposition of indirect certainty
is a maxim, and that by means of which it obtains its certainty is the
proof. If immediate certainty is attributed to a proposition which has no
such certainty, this is a _petitio principii_. A proposition which appeals
directly to the empirical perception is an _assertion_: to confront it
with such perception demands judgment. Empirical perception can primarily
afford us only _particular_, not universal truths. Through manifold
repetition and confirmation such truths indeed obtain a certain
universality also, but it is only comparative and precarious, because it
is still always open to attack. But if a proposition has absolute
universality, the perception to which it appeals is not empirical but _a
priori_. Thus Logic and Mathematics alone are absolutely certain sciences;
but they really teach us only what we already knew beforehand. For they
are merely explanations of that of which we are conscious _a priori_, the
forms of our own knowledge, the one being concerned with the forms of
thinking, the other with those of perceiving. Therefore we spin them
entirely out of ourselves. All other scientific knowledge is empirical.
A proof proves _too much_ if it extends to things or cases of which that
which is to be proved clearly does not hold good; therefore it is refuted
apagogically by these. The _deductio ad absurdum_ properly consists in
this, that we take a false assertion which has been made as the major
proposition of a syllogism, then add to it a correct minor, and arrive at
a conclusion which clearly contradicts facts of experience or
unquestionable truths. But by some round-about way such a refutation must
be possible of every false doctrine. For the defender of this will yet
certainly recognise and admit some truth or other, and then the
consequences of this, and on the other hand those of the false assertion,
must be followed out until we arrive at two propositions which directly
contradict each other. We find many examples in Plato of this beautiful
artifice of genuine dialectic.
A _correct hypothesis_ is nothing more than the true and complete
expression of the present fact, which the originator of the hypothesis has
intuitively apprehended in its real nature and inner connection. For it
tells us only what really takes place here.