[Ben] >> Bruno, list,
>> If I understand you correctly, then you mean, more generally:
>> G* \ G will correspond to any true conclusion that the machine can draw by
>> other than deductive (= truth-preservative)inference.
[Bruno] > Yes. Except that if deduction are generally thought indeed as truth
preservative, truth preservation is far more general than deduction. If I get
the time and the patience of the lister, I could one day introduce you to some
typical lobian entity which are NOT machine for illustrating more concretely
such phenomena. The incompleteness phenomena itself illustrates that truth
preservation is much more general than deduction.
I'm wondering whether we mean the same thing by "truth preservation." I mean
the validity of such arguments as exemplified (in trivial forms) by "p, ergo p"
and "pq, ergo p" or whatever argument such that the conclusion is "contained"
in the premisses. Or maybe I've been using the word "deductive" in too broad a
sense? I tend to think, for instance, of the reductio ad absurdum as
"deductive" in a broad sense, because I'm trying to differentiate simply in
terms of truth-(non)preservativeness and falsity-(non)preservativeness of the
overall reasoning process in which such a piece of reasoning takes place.
How did you guess that I currently have patience and time on my hands? :-)
Best, Ben Udell