On Fri, Sep 20, 2013 at 3:58 PM, Bruno Marchal <[email protected]> wrote: > > On 19 Sep 2013, at 16:51, Telmo Menezes wrote: > >> On Thu, Sep 19, 2013 at 4:31 PM, Bruno Marchal <[email protected]> wrote: >>> >>> >>> On 18 Sep 2013, at 21:45, Telmo Menezes wrote: >>> >>>> On Wed, Sep 18, 2013 at 6:13 PM, Bruno Marchal <[email protected]> >>>> wrote: >>>>> >>>>> >>>>> >>>>> On 18 Sep 2013, at 11:43, Telmo Menezes wrote: >>>>> >>>>>> <snip> >>>>>> >>>>>> >>>>>> But maybe it doesn't. At least some week form of solipsism, where >>>>>> there is in fact only me, but the notion of "I" is extended. No? >>>>> >>>>> >>>>> >>>>> >>>>> I would say that there are as many notion of "I", that there are >>>>> intensional >>>>> nuances. >>>>> >>>>> The most basic is the 3-I, like when the machine says I have two arms, >>>>> (Bp), >>>>> then there is the 1-I, when the machine says that she has two arms, and >>>>> it >>>>> is the case that she has two arms (Bp & p), then there is the observer >>>>> I, >>>>> when the machine says that she has two arms, and it is possible, not >>>>> contradictory, for that machine that she has two arms, or equivalently >>>>> that >>>>> 0=0 is not a contradiction, Bp & Dp, >>>> >>>> >>>> >>>>> equivalent with Bp & Dt. Then the >>>>> "feeler" whioch combines both Dt and "& p". >>>> >>>> >>>> >>>> Bruno, I don't understand these last two lines. What's Dt? What's a >>>> feeler? >>> >>> >>> >>> A feeler is someone who feels. My automated spelling verifier does not >>> complain, but perhaps he get tired with me :) >> >> >> Ok. No, it's right. I just thought there was something more to it. > > > Nice! > > > > >> >>> D is for diamond. Dp, in modal logic, often written <>p is an >>> abbreviation >>> of ~B~p. >> >> >> I know, I meant Dt vs. Dp. Was it a typo? Otherwise what's Dt as opposed >> to Dp? > > > OK, sorry. "t" is for the logical constant true. In arithmetic you can > interpret it by "1=1". I use for the logical constant false. > > As the modal logic G has a Kripke semantics (it is a so-called normal modal > logic), The intensional nuance Bp & Dp is equivalent with Bp & Dt. "Dt" will > just means that there is an accessible world, and by Bp, p will be true in > that world.
Ok, thanks. If there is one or more accessible worlds, why not say []t? (I'm using [] for the necessity operator) Is there any conceivable world where D~t? If so, can't we say ~D~t and thus []t? Isn't the only situation where ~Dt the one where this is no world? > > > >> >>> For example (possible p) is the same as (not necessarily not p). Like "it >>> exists x such that p(x)" is the same as not for all x do e have not p(x). >>> >>> Bp & Dp, really means that p is true in all worlds (that I can access) >>> and >>> Dp really means that there is such a world (if not, classically Bp can be >>> vacuously true). Normally there will be some explanations of modal logic >>> (on >>> FOAR). Older explanations on this list exists also, may be by searching >>> on >>> "modal" (hmm... you will probably get too many posts ...). >> >> >> I've been slowly going through Chellas. > > > It is a very good book. Boolos 1979 (and 1993) sum up very well Modal Logic > too. > >> >> Thanks! > > > Welcome! > > > Bruno > > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
