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" <[EMAIL PROTECTED]> To: "Benjamin Udell" <[EMAIL PROTECTED]> Cc: "Everything-List List" <everything-list@eskimo.com> 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/