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From: JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it." data-scaytid="54">This email address is being protected from spambots. You need JavaScript enabled to view it.>
Subject: Re:'t Hooft on free will - Denial Logic DL, a system of justification logic that models an agent whose justified beliefs are false...
Date: March 5, 2012 4:51:29 PM PST
To: JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it." data-scaytid="62">This email address is being protected from spambots. You need JavaScript enabled to view it.>

On Mar 5, 2012, at 4:42 PM, Jonathan Post wrote:

Imagine an educated, intelligent person, who utterly flips out at the
suggestion that UFOs or interstellar flight or retrocausation MIGHT be
possible.  Now, model that in Mathematical Logic...


On Mon, Mar 5, 2012 at 3:34 PM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it." data-scaytid="63">This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
???

10-4
Oh like Gerardus 't Hooft? ;-)
See my comments on his free will paper attached.

On Mar 5, 2012, at 11:40 AM, Jonathan Post wrote:

Denial Logic
Authors: Florian Lengyel, Benoit St-Pierre
(Submitted on 2 Mar 2012)

  Abstract: We define Denial Logic DL, a system of justification
logic that models an agent whose justified beliefs are false, who
cannot avow his own propositional attitudes and who can believe
contradictions but not tautologies of classical propositional logic.
Using Artemov's natural semantics for justification logic JL, in which
justifications are interpreted as sets of formulas, we provide an
inductive construction of models of DL, and prove soundness and
completeness results for DL. Some logical notions developed for JL,
such as constant specifications and the internalization property, are
inconsistent with DL. This leads us to define negative constant
specifications for DL, which can be used to model agents with
justified false beliefs. Denial logic can therefore be relevant to
philosophical skepticism. We use DL with what we call coherent
negative constant specifications to model a Putnamian brain in a vat
with the justified false belief that it is not a brain in a vat, and
derive a model of JL in which "I am a brain in a vat" is false. We
define the fusion of Denial Logic with the Logic of Proofs to model an
agent who can justify and check tautologies and who can believe his
justified false beliefs. Denial Logic was inspired by the contemporary
debate over anthropogenic global warming
.

Comments:     18 pages
Subjects:     Logic (math.LO)
MSC classes:  03B42 (Primary) 03B62, 03A05, 03B80 (Secondary)
Cite as:      arXiv:1203.0389v1 [math.LO]
Submission history
From: Florian Lengyel [view email]
[v1] Fri, 2 Mar 2012 08:24:07 GMT (24kb)


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