[plt-scheme] The perfect teaching language--Is this too much to ask for?

From: Arthur Nunes-Harwit (anh at cs.rit.edu)
Date: Mon Jun 15 14:40:39 EDT 2009

> I guess it's analogous to the problem with "the set of all sets" that 
> led to Russell's paradox, the dismantling of naive set theory, the 
> _Principia Mathematica_, and thence to Goedel's incompleteness theorems.

I'd like to see some more dots connected.

While Russell & Whitehead's theory to avoid the paradox involved a 
hierarchy, the set theories that were widely embraced (eg Zermelo-Fraenkel 
and von_Neumann-Bernays-Goedel) had little or no hierarchy.

> I'll have to think about this: "type" as a type still seems so elegant, 
> so expressively efficient. ... Has somebody already proven that that's 
> unattainable too?

While Meyer and Reinhold's paper is suggestive, it doesn't appear to me to 
be the last word.  We want to avoid a system that can prove "bad" 
theorems.  Might there be other ways to avoid bad theorems other than 


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