[FOM] Equivalence relation on sets of natural numbers

Richard Heck richard_heck at brown.edu
Wed Sep 12 12:48:36 EDT 2012

On 09/11/2012 02:14 PM, Stephen Yablo wrote:
> George Boolos considers this kind of relation in his "Bad Company" 
> objection to  Fregean platonism: two sets are the same "parity" if 
> their symmetric difference is finite and even.  This forces the domain 
> to be finite, if I remember right, assuming that parities "exist." 
>  See his  "Is Hume's Principle Analytic?"
Of course, this assumes (Robert Black made the same point) that the 
equivalence classes are supposed to get mapped back into the set of 
natural numbers (or whatever), which I'm not sure Tim was assuming. If 
we're working in ZF, e.g., then there is no problem about taking 
equivalence classes of this relation, over any set you wish, be they 
natural numbers or be they not.


> On Tue, Sep 11, 2012 at 10:37 AM, Timothy Y. Chow <tchow at alum.mit.edu 
> <mailto:tchow at alum.mit.edu>> wrote:
>     I want to declare that two sets of natural numbers are equivalent
>     if their symmetric difference is finite.
>     Is there a standard term for the resulting family of equivalence
>     classes, or for the equivalence relation?  I feel like I've seen
>     this somewhere before but I can't recall where.

Richard G Heck Jr
Romeo Elton Professor of Natural Theology
Brown University

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