On 17 Dec 2012, at 22:31, meekerdb wrote:

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On 12/17/2012 1:15 PM, Quentin Anciaux wrote:ISTM that consistency is the fact that you can't have contradiction.In some logics you're allowed to have contradictions, but the rulesof inference don't permit you to prove everything from acontradiction. I think they are then called 'para-consistent'.

`But that can have some uses in natural language studies, but be`

`misleading in the ideal case needed fro physics.`

`In particular it is important to understand that PA + "PA is`

`inconsistent" is a consistent theory.`

`Indeed if from PA + "PA is inconsistent" you can get a contradiction`

`in PA, then you have prove correctly, by absurdum, the consistency of`

`PA in PA, violating the second incompleteness theorem.`

Dt -> ~BDt is equivalent with Dt -> DBf. Bruno

Incompletness that you can't prove every proposition.No, incompleteness is you can't prove every true proposition. Whichimplies there is some measure of 'true' other than 'provable'.Brent --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.