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Re: layer logic: a new dimension to logic?
Posted:
Oct 8, 2011 12:43 PM
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Hello,
at first sight, layer theory might look like Russell´s theory of types, but it is different in essential aspects:
Yes, the layers have a kind of hierarchy:
In layer t the truth values of (any) statement in layer t or higher are not ´known´:
The layers are ´blind´ to themselves or higher layers.
But as meta statements have to have the same truth values in all layers (except layer 0), there is an important exception.
In layer set theory sets can be elements of themselves and the set of all sets is a normal set,
antinmomies are avoided by respecting the layers.
The main price we have to pay is a more complicated construction of (logical) truth and truth values,
that become a kind of infinite truth vectors like (u,true,true,false,true,false,false, false,true, ...).
But if we get a theory without contradictions and a easier handling of infinity (just one kind),
this might be worth a try.
Yours
Trestone
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