[FOM] origins of completeness in modal logic

Allen Hazen allenph at unimelb.edu.au
Thu Mar 5 05:11:30 EST 2009

By the way--
This is a bit off topic (Max Weiss was more interested in the philosophical
question of how to identify a "correct" notion of validity for modal logic,
so that the question of whether a formal system is complete in the INTUITIVE
sense could be asked), but there is an interesting historical discussion of
how possible worlds semantics came to notice by Jack Copeland in
Journal of Philosophical Logic, vol. 31, no. 2, (April 2002), pp. 99-137.
(In making allowances for possible bias: Copeland is a great admirer of

Allen Hazen
Philosophy (PASI)
University of Melbourne

On 3/3/09 5:07 AM, "Max Weiss" <30f0fn at gmail.com> wrote:

> For first-order logic, there is some intuitive notion of (classical)
> validity ...  However, for modal logic this
> seems not clearly to be the case: the question of an arbitrary modal
> formula "is it valid?" tout court, seems simply ill-posed.
> Roughly speaking, what I'm wondering is what sort of basis there might
> be for considering, say, Kripke (1959), as opposed to such earlier
> work, indeed to contain "a completeness theorem in modal logic".  

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