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.