On 6/13/2012 12:14 AM, Bruno Marchal wrote:

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On 13 Jun 2012, at 00:38, Russell Standish wrote:On Tue, Jun 12, 2012 at 08:17:38PM +0200, Bruno Marchal wrote:On 12 Jun 2012, at 00:47, Russell Standish wrote:On Thu, Jun 07, 2012 at 01:33:48PM +0200, Bruno Marchal wrote:In fact we have p/p for any p. If you were correct we would have []p for any p.This is what I thought you said the "meta-axiom" stated? How else do we get p/[]p for Kripke semantics?Because if p is true in all worlds, then []p is true in all worlds OK?No. I didn't say that. p means p is true in a world. p true in all worlds would be written []p.But in logic, if p appears in a deduction, p is true in all worlds.

`You mean if p is a tautology. It may be a deduction from premises that are not true in`

`all worlds. Is Russell thinking of p="Socrates is mortal" while you're thinking of p="If`

`all men are mortal and Socrates is a man then Socrates is mortal."`

Take as example a formalization of classical propositional calculus. The axioms have tobe tautologies,

`An axiom is just a proposition taken to be true for purposes of inference. Why can't`

`"Socrates is a man" be an axiom?`

Brent

and so are true in all worlds (valuations, interpretation). The modus ponens concervestautologicalness, so all theorems (the formula appearing in the deduction) are true inall worlds.And p/[]p means that if p is true in all worlds (like if it is proved) then []p is truein all worlds.If you want to mean that p is true in a world, or the actual world, you can say it, butnot in deduction. Usually you will name that world, by saying that p is true in alpha,at some meta level.Bruno-- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- --You received this message because you are subscribed to the Google Groups "EverythingList" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email toeverything-list+unsubscr...@googlegroups.com.For more options, visit this group athttp://groups.google.com/group/everything-list?hl=en.http://iridia.ulb.ac.be/~marchal/

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