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.
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: Thursday, January 12, 2006 10:03 AM
Subject: Re: Paper+Exercises+Naming Issue-faith
Le 09-janv.-06, à 18:30, Benjamin Udell a écrit :
> By "ampliative induction" I mean, not mathematical induction.
Nice! I hope you will be patient enough to see that this is a good
description of G* \ G.
G characterises the self-referential discourse of the lobian machine,
which is fundamentally a machine capable of using mathematical
induction(+).
G* \ G will correspond to anything true that the machine can guess
without using mathematical induction.
Bruno
(+) IF a property is such that 1) it is true for 0, and 2) if true for
n it is true for n+1; THEN it will be true for all numbers.
More compactly: {P(0) & [for all n: P(n) -> P(n+1)]} -> for all n
P(n).
http://iridia.ulb.ac.be/~marchal/
Received on Thu Jan 12 2006 - 10:56:33 PST