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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: sowa@xxxxxxxxxxx
Date: Thu, 21 Jul 2011 13:40:31 -0400 (EDT)
Message-id: <20c070460e25d38ff7c077d62c2d9de9.squirrel@xxxxxxxxxxxxxxxxxxxx>

Dear Matthew,

I am using the term 'intensional' in the sense that was defined by Alonzo Church in the following excerpt from his book on lambda calculus:


I would also like to add the point that *every* intensional definition of possible worlds arises from some human intention to create some collection of possible worlds for some purpose.

That means that possible worlds are both intensional (with an S) and intentional (with a T).

As Church and many others have explained, the mapping from intensions to extensions is many to one:  For any given set S (in extension), there can be many different rules (intensions) that generate exactly the same elements of S.

That implies that an extensional set loses information. 
From any given set, there is no way to determine which of many (usually infinitely many) intensional rules could have generated that set.

Therefore, we have two many to one mappings: from many kinds of intentions to some intensional rule, and from many different intensional rules to some extension.  Trying to derive a unique intension from a given  extension is difficult or impossible, and trying to derive a unique intention from an  intension is difficult or impossible.

MW:  Lewis specifically asserts that possible worlds actually exist in the sense you mean.

Please note my reply to Chris M:  Lewis also said that a solution that did not assume the existence of possible worlds would be preferable if it could derive the same results.  Michael Dunn demonstrated such a solution, but Lewis was not aware of it.  As I said before, please, please, please read the following article:


MW: Talk about possible worlds might or might not correspond to something that really exists.

That is true.  But even if some claim about a possible world happened to be true, that does not refute my point that the claim was both intensional (with an S) and  intentional (with a T).

In general, I agree that looking at extensions is a useful exercise.  But further evidence and inferences are necessary to determine the intensions (with an S) that generated the extensions and the intentions (with a T) that led to the intensions.

Those inferences are often very difficult, and they may be mistaken.


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