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

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: sowa@xxxxxxxxxxx
Date: Thu, 21 Jul 2011 12:16:24 -0400 (EDT)
Message-id: <1a4ed8541170d9790c16463badbae711.squirrel@xxxxxxxxxxxxxxxxxxxx>


I am happy to agree with your statement -- because it is another way of making the same point I was trying to make.

> 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.


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