Hmm... yes. The basic idea seems to be that given any proposition, you can find a set of rules that make it valid/true or invalid/false, or some combination. From a mathematical point of view, this is not really a problem, and actually relates to one of my PhD interests, abstract interpretation, which seeks to relate alternative ways of interpreting mathematical constructs in a sound way, allowing more abstract interpretations to accurately predict the results of more concrete interpretations. With abstract interpretation, there's no particular problem with the idea that something might be true, false, either, or neither -- this kind of thing turns out to be necessary and useful in a variety of surprisingly fundamental ways.
For an example of abstract interpretation applied to a logic that is capable of handling all of that, as well as handling truth values that can change over time, see my SAS'04 paper. I don't know what the philosophers will make of my work, however -- as yet, it's only been peer reviewed by mathematicians and computer scientists.
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For an example of abstract interpretation applied to a logic that is capable of handling all of that, as well as handling truth values that can change over time, see my SAS'04 paper. I don't know what the philosophers will make of my work, however -- as yet, it's only been peer reviewed by mathematicians and computer scientists.
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