On the Fourfold Root of the Principle of Sufficient Reason, and On the Will in Nature: Two Essays (revised edition)
Schopenhauer · en
A judgment may have for its reason another judgment; in this case it
has _logical_ or _formal_ truth. Whether it has material truth also,
remains an open question and depends on whether the judgment on which
it rests has material truth, or whether the series of judgments on
which it is founded leads to a judgment which has material truth,
or not. This founding of a judgment upon another judgment always
originates in a comparison between them which takes place either
directly, by mere conversion or contraposition, or by adding a third
judgment, and then the truth of the judgment we are founding becomes
evident through their mutual relation. This operation is the complete
_syllogism_. It is brought about either by the opposition or by the
subsumption of conceptions. As the syllogism, which is the founding
of one judgment upon another by means of a third, never has to do
with anything but judgments; and as judgments are only combinations
of conceptions, and conceptions again are the exclusive object of our
Reason: syllogizing has been rightly called Reason's special function.
The whole syllogistic science, in fact, is nothing but the sum-total of
the rules for applying the principle of sufficient reason to the mutual
relations of judgments; consequently it is the canon of _logical truth_.
Judgments, whose truth becomes evident through the four well-known laws
of thinking, must likewise be regarded as based upon other judgments;
for these four laws are themselves precisely judgments, from which
follows the truth of those other judgments. For instance, the judgment:
"A triangle is a space enclosed within three lines," has for its last
reason the Principle of Identity, that is to say, the thought expressed
by that principle. The judgment, "No body is without extension,"
has for its last reason the Principle of Contradiction. This again,
"Every judgment is either true or untrue," has for its last reason
the Principle of the Excluded Middle; and finally, "No one can admit
anything to be true without knowing why," has for its last reason the
Principle of Sufficient Reason of Knowing. In the general employment
of our Reason, we do not, it is true, before admitting them to be true,
reduce judgments which follow from the four laws of thinking to their
last reasons, as premisses; for most men are even ignorant of the very
existence of these abstract laws. The dependence of such judgments upon
them, as their premisses, is however no more diminished by this, than
the dependence of the first judgment upon the second, as its premiss,
is diminished by the fact, that it is not at all necessary for the
principle, "all bodies incline towards the centre of the earth," to
be present in the consciousness of any one who says, "this body will
fall if its support is removed." That in Logic, therefore, _intrinsic
truth_ should hitherto have been attributed to all judgments founded
exclusively on the four laws of thinking: that is to say, that these