Thursday, May 05, 2005

Paradox Postponed

I've never thought up a paradox. I think almonst any philosopher worth his salt has thought up a paradox or two. I'm in my mid-thirties now and I haven't ever had a paradoxical thought. Maybe there's some variation of Russell's paradox for meta-ethics. Like suppose everyone who doesn't make their own values gets their values from God... Well it's not really a different paradox from Russell's. So, anyway, I want to think up a paradox but I don't know how. I've tried tweaking other's paradoxs. I've tried thinking really hard about hard problems. When I was in college I tried hallucinigens but that didn't worked either. What can I do?


Blogger Richard said...

There is a value-based variant of the liar paradox: suppose I desire that this desire be thwarted!

1:45 AM  
Anonymous saxon said...

isn't it somewhat paradoxical that a philosopher has never thought up a paradox?

12:53 AM  
Anonymous KK said...

Richard has provided a good starting point - why not try value-based variants of other paradoxes you know? Could you apply a similar twist to Russell's?

3:17 PM  
Blogger Brad said...

One thing that always ends up with paradoxes is looking into the widely ill-perceived distinction between theoretic and meta-theoretic. The liar paradox, Russell's paradox, Richard's paradox and the Grelling–Nelson paradox, Godel's Incompleteness theorems, and so on all have very similar themes in logic.

The liar paradox is an informal version of how semantics can form meaningless statements but if assumed to abide by the same semantical rules, create contradictions. Russell's paradox is an illustration of how theories should be formal (specifically set theory of mathematics), and definitive terms such as 'set' should be used cautiously in reasoning.

Richard's paradox and the Grelling–Nelson paradox are informal introspections into how expressiveness of a language makes it akin to the same consistency rules of a formal theory and thus show the 'meta-language' level of descriptions.

Godel's Incompleteness theorems are very general and the grandest two results in mathematical logic, which in a very mathematically convoluted way shows how formal theories must have necessary holes by lack of consistency or completeness, or else only be provable by even stronger theories which must also abide by the same incompleteness restrictions. This one is hard to tackle for amateurs in logic, but it should be simple enough to at least understand what it states after reading about terms such as omega-consistency, inference rules and axioms, effective computability a.k.a. computable recursiveness, etc.

So you can really look into how different levels can create misunderstandings, or 'paradoxes'. If you wanted to apply this to something outside of pure mathematics or logic itself (to something otherwise philosophical or practical even), you can look at the expressiveness of well-defined theories, and then try and find a way to make meta-descriptions about descriptions of the theory possible. This route need not be direct at all, but must confuse levels to confuse others.

5:05 PM  

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