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Re: [ontolog-forum] Ontological Assumptions of FOL

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Thu, 22 Mar 2007 14:39:02 -0500
Message-id: <FE0E21F9-36A9-4819-95C3-3FFE3352FF30@xxxxxxxx>
Whilst looking for a message in the ont-forum archives I just  
happened to notice that I asserted The False in a recent post; I wrote:    (01)

> John S. wrote:
>> The critical distinction between set theory and mereology
>> is that the axioms of set theory generate something new:
>>     For any x, the set {x} is distinct from x.
> Yes, in well-founded set theories like Zermelo-Fraenkel set theory,
> but singletons are perhaps the wrong thing to focus on to highlight
> the distinction in question, as there are in fact so-called non-well-
> founded set theories in which x = {x}.    (02)

That should have read "in which there are sets x such that x = {x}".   
That equation obviously does not hold across the board (consider,  
e.g., the empty set for a simple counterexample).    (03)

Chris Menzel    (04)

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