[FOM] A minor issue in modal logic

[Richard Heck]

On 07/05/2010 12:53 AM, Michael Carroll wrote:
> Richard Heck wrote:
>
>    
>> Of course, one might sensibly argue that any reasonable notion of
>> necessity must validate "N\phi -->  \phi" and so argue that any modal
>> logic modelling any reasonable notion of necessity must have only models
>> in which the accessibility relation is reflexive. But that is a
>> substantive---i.e., not purely logical---claim.
>>      
> I'm sorry but I fail to see how that differs from :
>
> "One might sensibly argue that any reasonable notion of conjunction must
> validate "((A&  B) ->  (B&  A))", so that any logic modeling any reasonable
> notion of conjunction must have only models in which conjunction is
> commutative. But that is a substantive -- i.e., not purely logical --
> claim."
>
>    
Since there are logics in which commutation fails for conjunction, I 
suppose I'm willing to agree, to some extent. I think something like:
     A & B |- A
is probably non-negotiable, however. What isn't clear to me is that:
     Np |- p
is similarly non-negotiable.

In any event, the issue concerned:
     NAp |- Np
so this was a side remark.

Richard


-- 
-----------------------
Richard G Heck Jr
Romeo Elton Professor of Natural Theology
Brown University