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Re: [ontolog-forum] intangibles (was RE: Why most classifications are fu

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "AzamatAbdoullaev" <abdoul@xxxxxxxxxxxxxx>
Date: Thu, 21 Jul 2011 22:01:46 +0300
Message-id: <55B3AAA74A12453283B2BC042BABB571@personalpc>

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 cross-section 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: [ontolog-forum] 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 space-time 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 space-time 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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