Begin forwarded message:

From: JACK SARFATTI <

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 <

*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...

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 <

???

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.

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)