[FOM] About Paradox Theory

[T.Forster at dpmms.cam.ac.uk]

I can believe there is a theorem of second-order logic corresponding to 
Mirimanoff's paradox... but a *first* order theorem..? I'd be very 
interested to see one.


On Sep 16 2011, hdeutsch at ilstu.edu wrote:

>
>
>There are first order theorems corresponding to the fact that  
>separation implies that there is no universal set (in ZF) and even one  
>corresponding to the paradox of grounded classes.  There is an  
>interesting list of such theorems in Kalish, Montague, and Mar:  
>Techniques of Formal Reasoning, but I'm sorry I don't have a copy  
>available so I can't give the page number right now.
>
>Harry
>
>
>
>
>
>Quoting David Auerbach <auerbach at ncsu.edu>:
>
>> James Thomson (Thomson, 'On Some Paradoxes', in Analytical  
>> Philosophy (Ist series) ed,. R. J. Butler, pp, 104-119) makes this  
>> point, with some nuances and somewhat long ago, in wonderful detail.  
>>  (It's a hard article to find, but I have a PDF if anyone wants it.)
>>
>>
>>
>> David Auerbach                                                       
>> auerbach at ncsu.edu
>> Department of Philosophy and Religious Studies
>> NCSU
>> Raleigh, NC 27695-8103
>>
>> On Sep 14, 2011, at 4:03 PM, charlie wrote:
>>
>>> 	I'm sure your project has merit, but I can never overcome  
>>> "Russell's Paradox" because of the following theorem of   
>>> first-order logic.
>>>
>>> 	   ~EyAx[F(xy) <--> ~F(xx)]
>>>
>>> 	       As a consequence, I tend to dismiss R's Paradox as having  
>>> nothing to do with sets or anything else in particular.   I'm sure  
>>> I must be wrong in this, as his paradox regarding classes or sets  
>>> enjoys such wide popularity, perhaps due to the Frege connection,  
>>> and was perhaps a guiding light for improved set theories.   So,  
>>> perhaps someone will please give me a good reason not to trivialize  
>>> it so.  Perhaps I'm making some significant mistake. I'd be glad to  
>>> be corrected.
>>>
>>> Charlie
>>>
>>>
>>>