Jone wrote: "Whatever extensional sets you
derive from them just support a well known fact about intensions and
extensions: you can always derive extensions from intensions, but the
mapping is many to one  you can't uniquely derive intensions from extensions."
The intension ... is a function mapping
possible worlds to truth values. In Ontology, Intension is coextensive with
Immanency, Inherency, Fundamental Reality, and Being. In logic, being
inversly proportional to extension, it's coextensive with "information",
"deductive power", "logical strength", "theory", or "context", the logical
relations in which the propositions are set.
Re how to formalize the possible worlds.
Roughly and briefly, for more see the Reality Book. Let O
be a universal theory about the possible worlds W and call
S (W) the collection of possible states (state space) of a specific world,
W. W is the totality of all things now. The union of all the state spaces
of all possible worlds W is marked as S (W).
Then O is to be a global mapping/representation of
W, so that there exists a universal function
F: S ÞO, assigning to every world's state
S an ontology/theory/model/law statements, O =F (S), which is accurate
when bijective and true for every specific world as a state of affairs.
The formalities aside, all depends on
how one defines the world:
the totality of all worlds (as a sequence
of worlds, or a hierarchy of worlds)
the totality of all worlds
now,
the totality of all things,
the totality of all things
now.
The world as the sum total of all
beings and events now, an actual world, a crosssection of all
existence at a certain point of time, is mostly popular perception nowadays.
Many think that the world is just all what is given at this moment, at the
certain locations. So while i write, there are individual disjoint events
across the world, the star's birth, the earthquake in China, the forest fire in
Russia, the quadruple bearing in France, the animals' killing in Africa, the
criminal attack in America, the wiretapping in UK, the marriage in
Europe, the cyberoffence on the Internet, and the power cut in
Cyprus. The real order of the world is hardly so extensional  a multitude
of disjoint individual things.
Azamat
 Original Message 
Sent: Thursday, July 21, 2011 7:16
PM
Subject: Re: [ontologforum] intangibles
(was RE: Why most classifications are fuzzy)
Jerry,
I am happy to agree with your statement  because it is another way of
making the same point I was trying to make.
JH > One concrete way of understanding possible worlds is that a
possible > world is a mapping from spacetime points to "states" (mass,
energy, > whatever) (e.g., hydrogen atom at (x,y,z,t), under certain
physical > constraints (which distinguish the possible from the
impossible). Under > this interpretation, a possible world is exactly as
real as any mapping, > e.g., the square root function.
As I said to Chris M, you can use Dunn's method to replace any possible
world w with a pair of propositions (L,F), which state the laws and facts of
w.
Your method replaces each possible world with mappings from spacetime
points to states of mass, energy or whatever. I certainly agree that
they are just as real as the square root function.
Those mappings are propositions that describe a world w  i.e., a subset
of the facts F about w. And the constraints you mention are a subset of
the laws L of w. If you generalize the notion of 'state' and
'constraint' sufficiently far, you could probably make your subset of L and F
equivalent to Michael Dunn's.
All those propositions and the square root function are real in the same
sense as any mathematical structure  i.e., you can put existential
quantifiers in front of the variables that refer to them. As a born and
bred mathematician, I am happy to talk that way.
But I would still claim that those propositions exist in a different sense
from the kinds of atoms that we and all the stuff we encounter are made
of. Unlike atoms, those propositions are figments of our
imagination.
That implies that any information you can get from those mappings could be
derived directly from whatever thoughts you had in mind when you defined the
mappings. Those thoughts or their formal statements in some logic are
intensional.
Whatever extensional sets you derive from them just support a well known
fact about intensions and extensions: you can always derive extensions
from intensions, but the mapping is many to one  you can't uniquely derive
intensions from extensions.
John
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