Sorry, had to make a few corrections.

1. [correction]  " definitions don't at all completely capture..."
[instead of vague]  "...such definitions don't at all completely capture..." 

2. [correction]  "...'strict' aka 'non-reversible' deduction..."
[instead of mistake]  "...'strict' aka 'reversible' deduction..." 

This is an after-second-cup-of-coffee post and should be more reliable. The 
corrections are incorporated below. Again, sorry.

- Best Ben Udell.

----- Original Message [corrected] ----- 
From: "Benjamin Udell" <[EMAIL PROTECTED]>
To: "Everything-List List" <>
Sent: Saturday, January 14, 2006 12:26 PM
Subject: Re: Paper+Exercises+Naming Issue-faith

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 

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 my 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 "non-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 

Best, Ben Udell

----- Original Message ----- 
From: "Bruno Marchal" <[EMAIL PROTECTED]>
To: "Benjamin Udell" <[EMAIL PROTECTED]>
Cc: "Everything-List List" <>
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 
(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 :-)

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