In the last post, we
saw Hoffmann deal with various types of deduction or proof and the
emphasis was on the question what type of formal properties make for
an acceptable demonstration. He is still well aware that formal
validity is not enough for a good demonstration. The premisses must
obviously be true, but this is something that must be justified
through further proofs and demonstrations and does not therefore
suggest any new line of investigation.
There is still
something other than mere truth in the premisses that is important
for the goodness of demonstrations, Hoffmann says: premisses must be
suitable for use in demonstrating these conclusions. What Hoffmann is
against here becomes evident through a simple example: petitio
principii. In cases where the chain of reasoning is somehow circular,
the premisses might well be true and the form of reasoning quite
valid, but some of the premisses still are improper as justifications
of these particular conclusions.
Another, more
important element in this propriateness is that premisses must be at
least as substantial as conclusions. In other words, one cannot use
mere nominal definitions as justification of conclusions stating the
existence of something. Hoffmann is once again pointing to Cartesian
proof of God's existence, which confuses the necessity of linking
thought of existence with thought of God and the actual necessary
existence of God.
The notion of
propriateness in reasoning is also of importance for Hoffmann, when
he is considering conflicts in demonstrations. Lewis White Beck, the grand old
scholar of pre-Kantian German philosophy, congratulates Hoffmann as
introducing to German philosophical culture the notion that we must
sometimes evaluate between demonstrations of seemingly equal
validity, which appear to have contrary conclusions – to Beck, this
is one way in which Hoffmann laid ground for Kant. Unfortunately,
Beck is exaggerating, since even Wolff's logical works contained
chapters dedicated to this very topic. Still, Hoffmann is at least
unusually thorough in this matter.
Hoffmann notes that
often these seeming conflicts, especially in metaphysical matters,
can be solved by noting that one demonstration is based on mere ideal
premisses – that is, it doesn't describe reality, but only the
manner in which we link our ideas. The trick is then to know which of
the demonstrations fits the bill better. A sure sign is when one
demonstration is based on the second or third basic rule of deduction
(the necessary linking or separating of ideas according to our
understanding), while the conflicting demonstration is based on mere
principle of non-contradiction. In such cases one must believe the
latter demonstration, because first rule of deduction trumps the
second and the third. Thus, although we cannot understand how God
could exist everywhere at once, if denying this would land us in
contradiction, we would have to accept the omnipresence of God.
In case of apparent
conflicts in physical matters, it has often happened that one
demonstration supposes that only a single force works in the
situation, while the other demonstration supposes that only another,
quite opposed force works in the situation. The apparent conflict of
demonstrations is then explained by this opposition of forces, and to
truly determine which force wins the contest, one must check which
force is the strongest.
A special case
consists of moral conflicts, in which different laws and maxims are
used in deciding the goodness of certain actions. Here the crux of
the matter is to balance and measure the various laws and maxims that
might motivate us to act in certain manner.
So much for
demonstrations, next time I shall investigate what Hoffmann has to
say about probabilities.
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