Re: Troolean operators


Kilgore Trout wrote:
Although I think I understand your point, two-value logic has great
strength and utility. For instance, that computer you are using is
made possible because of this system of 0/1 - on/off - t/f logic.

The excluded middle is a concept which has great utility. Some situations are not only true/false. Especially complex ones.

Now, if your point is that these logical systems are incomplete, well,
perhaps you have heard of Gödel.

In the strictest sense, it is perhaps true that this logic simply
mimics our experiences (thus making it more inductive than deductive)
in the real-world, without saying anything really deep about that
world.

My understanding is that Gödel showed that within any deductive system
we can produce statements that basically claim to be decidable iff they
are not decided.

A rough (and somewhat crappy) analogy is the old statement: "This
statement is false", which cannot be assigned a truth-value.

Yes, Godel's theoerm is built on the Epimenides paradox, "This staement is false"; it is a very complex extension of it. And stictly speaking Godel's original theorem only appies to the Principia Mathematica. However, it has analogs in many different areas.

Anyways, it's been a long time since my last logic class, so I am
probably garbling some of this. But the basic idea that these systems
and even the meta-systems which analyze them are flawed is pretty much
accepted at this point.

Flawed, yes, but not unusable. GT is a self-referential paradox.. It's a consequence of a system being very rich and powerful. The key is to learn to deal with it. It's a small price to have to pay to have access to virtually unlimited knowldege, having to deal with self-ref messiness.. Self-ref is what makes us intelligent. It's what rose us above the apes.. Once a system achieves self-ref, stand back.

- Don

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