Plato, Meet Russell

           Plato, Meet Russell

 

 

Plato spoke of ideal Forms, of which the entities around us are imperfect examples. Thus there are frogs, and there is the Form of all frogs, and the Form of all frogs is not a frog.

But there is also the Form of all Forms, which is itself a Form. Therefore some Forms are examples of themselves, and some are not.

 

Now consider the Form of all Forms, and only those Forms, that are not examples of themselves. Call it Russell’s Form R:

 

For any form F,  

F is an example of R    =    F is not an example of F

 

What of R? Is it an example of itself? Substitution yields:

 

R is an example of R    =    R is not an example of R

 

A Russellian paradox!

 

So the world of Platonic Forms is paradoxical or incomplete.