On 19 Sep 2013, at 16:51, Telmo Menezes wrote:

On Thu, Sep 19, 2013 at 4:31 PM, Bruno Marchal <marc...@ulb.ac.be> wrote:

On 18 Sep 2013, at 21:45, Telmo Menezes wrote:

On Wed, Sep 18, 2013 at 6:13 PM, Bruno Marchal <marc...@ulb.ac.be> 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.




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/



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