#57. Old chapter by Thoralf Skolem
Via Project Euclid, one can access Skolem's Abstract set theory (70-page lecture notes published by the University of Notre Dame). Its Chapter 18 summarizes very briefly Skolem's approach to proving the consistency of set theory within Lukasiewicz [0,1]-valued logic.
Just a curiosity, but--
Thoralf Skolem (1962). The possibility of set theory based on many-valued logic.
The whole volume can be downloaded chapter by chapter here.
Just a curiosity, but--
Thoralf Skolem (1962). The possibility of set theory based on many-valued logic.
The whole volume can be downloaded chapter by chapter here.
posted by Pedro Terán at 6:20 PM
2 Comments:
So, Zadeh wasn't the first scholar to investigate what a set theory would look like in a non-classical logic context. One could claim that Skolem originated the notion of a fuzzy set. Zadeh's original paper did contain notes on other operations than min and max (product, min(1, a+b)), however, it did not contain a hypothesis that one could use such operations in a similar way in a set theory. And no one did such until the late 70s or early 80s.
I agree Skolem definitely considers a set theory based on many-valued logic. It's not evident from the text but, yes, that's what I think.
Based on my memory, I'm not sure Zadeh didn't intend the `alternative' operations as set-theoretical. I'd have to check his paper carefully but maybe you're right at that as well.
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