Bruno, list,
Thank your for clarifying with regard to semantics and truth-preservation, enough for me to do a little homework.
I searched around the Internet and see that you're quite right, I've wandered into semantic-vs.-syntactic issues with my talk of truth preservation in inference.
How did I get into this? For what it's worth, here's how:
Here and elsewhere I've started mentioning truth preservation and falsity preservation because it has seemed a concise and striking way to sum up (in terms of formal implicational relations between premisses and conclusion) a four-way distinction among kinds of inference. So in a sense it was my choices in rhetoric that got me into this. My argument is with some who see three basic kinds of inference -- deductive, inductive, and "abductive," and not so much with people who count two, since they'll probably grant at the very least some importance, albeit smaller, to a further subdivision.
Basically, I've wanted to moot, by resolving in a simple and systematic way, the excessively chewed-over issue of _formal_ reducibility of certain kinds of inferences to others, and to do so while pointing out that such definitions don't at all completely capture what's interesting or valuable about the thereby defined kinds of inference, not in _only some_ cases (surmise and inductive generalization, regarding which the objections may be anticipated) but instead in _all_ cases (i.e., also "strict" aka "reversible" deduction and "equipollential" aka "reversible" deduction (which includes the mathematical induction step in its usual application, i.e., to a set whose well-orderedness has already been granted)).
This sort of thing, taken further, would lead to why I joined the Everything-List -- correlations between families of research and the four Levels.
Best, Ben Udell
----- Original Message -----
From: "Bruno Marchal" <marchal.domain.name.hidden>
To: "Benjamin Udell" <budell.domain.name.hidden>
Cc: "Everything-List List" <everything-list.domain.name.hidden>
Sent: Saturday, January 14, 2006 8:43 AM
Subject: Re: Paper+Exercises+Naming Issue-faith
Le 13-janv.-06, à 19:13, Benjamin Udell wrote in part:
> 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?
Actually it is the contrary. What you describe is classical truth
preservation, which occurs with the classical deductive rules (so that
they are sound and complete). In general "truth preservation" is a
semantics dependant concept, where semantics can sometimes be given by
some mathematical structures. I don't want to be too technical at this
point.
(Mathematically a semantics is a subspaces' classifier)
> How did you guess that I currently have patience and time on my hands?
> :-)
Thanks for witnessing the interest. I wish only I would have more time
for now. I have the patience I think :-)
http://iridia.ulb.ac.be/~marchal/
Received on Sat Jan 14 2006 - 12:32:52 PST