Re: Model != World? - 01-04-2010 , 04:33 PM
On 4 jan, 22:44, Tegiri Nenashi <tegirinena... (AT) gmail (DOT) com> wrote:
define the truth value of a formula. In conventional logic this is
usually a model of the particular world we assume we are in. However,
in modal logic this includes the complete set of possible worlds plus
the particular world we assume we are in. Both are needed since for
basic propositions we need to inspect the actual world and the modal
operators refer also to the other possible worlds.
-- Jan Hidders
Re: Model != World? - 01-04-2010 , 04:34 PM
Tegiri Nenashi says...
works. (Although there may need to be certain constraints on what models of a
theory are under consideration). But the philosophical discussion of what's
possible, and what's necessary, and alternative possible worlds predates modern
One thing that is different about modal logics is that ability to refer to
multiple possible worlds (any time you say that something is possible, you are
implicitly quantifying over possible worlds). It's not usual in model theory to
allow quantification over models in the object language (although such
quantification may take place in the metalanguage). When you consider
propositions involving modal operators, a single "possible world" is not a model
for such propositions. It's the entire structure of all possible worlds that is
being referred to by statements such as: "It is necessarily the case that X".
There is a discussion of the various uses of possible worlds here:
but there is no mention of the fact that a possible world is a model of a
Re: Model != World? - 01-04-2010 , 07:56 PM
On Jan 4, 1:44*pm, Tegiri Nenashi <tegirinena... (AT) gmail (DOT) com> wrote:
signature, and interpretation function>. Now, assuming "universe =
world" we have "world != model". QED.
Re: Model != World? - 01-04-2010 , 08:59 PM
On Jan 4, 10:44*pm, Tegiri Nenashi <tegirinena... (AT) gmail (DOT) com> wrote:
and for Higher-order modal logic:
Definition for model for classical logic is:
A model is every structure S = ( A, F, R, C), where A is a non-empty
set, (A, F, C) is an algebra and R is set of relations over A.
Re: Fitch's paradox and OWA - 01-05-2010 , 01:40 AM
On 4 jan, 17:56, stevendaryl3... (AT) yahoo (DOT) com (Daryl McCullough) wrote:
explain this to me. I'm afraid I can only give a short reply now
because life and work are getting busier again.
I think I see now better your point about the fact that in different
worlds we might use the same description to refer to things that are
actually different facts. Your example being "it rains" which refers
to something different if the different worlds correspond to different
days. But I would argue that this is from the perspective of someone
who is outside the model and has some way to identify the different
worlds independent of what facts hold in them. When you are inside the
model and in a certain world the only way to distinguish them is by
looking which facts hold in them. For the rain example it could be
that in your vocabulary you can express what day it is, and then you
can distinguish the different days, but then you could have formulated
the fact that you had in mind as "it rains and it is today 5 January
2010". If the date in your world is not in your vocabulary then you
have no way of describing the differences between the "it rains"
proposition in different worlds.
For me the meaning of a proposition is in its pragmatics. If "it
rains" means that I will get wet when I go outside and I need to take
my umbrella with me, then I don't care what day it is, so it will in
that respect be the same proposition each day. Another example might
be "all mushrooms are edible" which might mean something different
when I'm in different forests, but if I have no way of knowing in
which forest I am, and if the pragmatics are the same for me (I will
eat them), then from my perspective these are the same facts.
I think I now understand also better how you want to distinguish in
your model theory between modal and nonmodal facts, and why you want
to restrict the K operator to nonmodal facts. Briefly put, since p &
~Kp is a modal fact, we then simply cannot formulate K(p & ~Kp) and
get the contradiction. Although I may not fully agree with the
philosophy behind this restriction, I agree now that this strategy,
when executed properly, could indeed avoid the contradiction.
That's it for now. As I said, it is possible that I will not be able
to reply quickly in the future, but I will certainly try to follow the
-- Jan Hidders
Re: Fitch's paradox and OWA - 01-05-2010 , 06:28 AM
Jan Hidders says...
don't explicitly talk about *specific* other worlds. However,
I think that for some uses of modal talk, we *do* have an
explicit way to characterize the other possible worlds. For
example, in a deterministic physical theory (such as Newtonian
physics), the various possible worlds are characterized by
initial conditions, which are determined by a point in phase
language of "possible, necessary" even though there is no
way for us to know what is possible and what is necessary
(without knowledge of other possible worlds). So if you just
stick to what we can know in *this* world, it seems to me
that the only notion of "possibility" is logical consistency.
That's a very uninteresting notion of possibility.
To go beyond logical consistency, we have to have some theory
about what the other possible worlds are.
language, the "possibilities" are actually found with one
physical world (or the history of that world).