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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: Mon, 25 Jul 2011 05:37:37 -0400 (EDT)
Message-id: <cb22000853dce29a4a921afb8e2b51e5.squirrel@xxxxxxxxxxxxxxxxxxxx>


Whenever I discuss intensions, I always cite the definition by Alonzo Church, which is very close to what I mean.  I've cited it repeatedly on this list, but here's another copy:


See Section 2 of that excerpt for Church's distinction between an intensional definition of function vs. an extensional definition.  In general, intensions are defined by some rule or specification.  Church defined his specifications by means of the lambda calculus, but he allowed an open-ended number of ways of defining intensionss.

The general principle that Church states is that multiple intensional specifications can determine exactly the same extensions.  That means that the intensions have more content (i.e. more information) than the extensions.

Peirce didn't use the terms intension and extension, but he made similar points repeatedly.  The basic point is that intensional specifications have more meaning (or content or information), which cannot be derived from the extensions.  As many philosophers have observed, you cannot derive 'ought' from 'is' -- i.e., extensions don't contain any information about values or intentions (with a T).

> I don't have any idea what you mean by his "intensional specications of
> worlds". Could you give an example?

I did.  Following is an example from my previous note:
>> In Dunn's terminology, the laws that determine whatever modality lurks
>> in Lewis's worlds come from his own imagination in conjuring them up.

> Lewis would dispute the claim that he is conjuring them up. He provides
> principles (notably his principle of Recombination) that entail their
> existence and that have no more to do with conjuring than the set
> theoretic principles of pairing and infinity.

Every magician or alchemist uses principles that are as formal as anything that Lewis specified.  If you prefer a less loaded term, you can replace 'conjure up' with 'generate',  But in any case, Lewis's principles meet Church's criteria for an intensional method of specification.  Those principles contain the real meaning, and the worlds themselves just disguise that source under an extensional veneer.


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