For Christmas, instead of writing about politics, I think it would be fun to write about the books I'm reading. Today I'm reading from: Metamagical Themas by Douglas R Hofstadter. It is a bit tougher going than his Godel, Escher, Bach. But it is fun trying to comprehend an intellect as profound and wide-reaching as Hofstadter's. The first chapter is on Self-Referential Statements. The discussion of such statements goes back to the Epimenides paradox where Epimenides (a Cretan says: "All Cretans are liars".
Hofstadter then provides an interesting collection of self-referential statements:
This sentence claims to be an Epimenides paradox, but it is lying.
Disobey this command!
As long as you are not reading me, the fourth word of this sentence has no referent.
The reader of this sentence exists only when reading this sentence.
If wishes were horses, the antecedent of this conditional would be true.
This sentence !!!! is a premature punctuator
This sentence no verb.
He spends quite a few pages describing different types of self-referential sentences and the logical implications behind them. An excellent example of how Hofstadter's brain works is found in this passage:
This issue is highlighted in the self-referential question, "Do you think anybody has ever had precisely this thought before?" To answer the question, one would have to know whether or not two different brains can ever have precisely the same thought (as two different computers can run precisely the same program). I have often wondered: Can one brain have the same thought more than once? Is thought something Platonic, something whose essence exists independently of the brain it is occuring in? If the answer is "Yes, thoughts are brain-independent", then the answer to the self-referential question would also be yes. If it is not, then no one could ever have had the same thought before--not even the person thinking it!
I think (this time) that one of the problems in analyzing law is that it is highly self referential, but we don't have a good method of analyzing it without resorting to further self-referential states. Take for example the urban legend of the man who goes to jail for murdering his wife when his conviction is based on the police finding her finger sawed off and in his refrigerator. 15 years later he gets out, finds his wife is alive (she framed him)and kills her. The police arrest him, but let him go because "Double Jeopardy" means that you can't be tried twice for the same offense. (The offense here being killing the particular woman who was his wife.)
I am not deeply knowledgable about double jeopardy jurisprudence, but I strongly suspect that the killing described in the legend would count as a separate offense. But figuring out why that would be true or false would lead through quite a thicket of law refering to itself. The definition between different offenses cannot be perfectly defined without running afoul of our intuitions of what offense means. If you were convicted of killing somone in a very specific way, and it turned out that you actually killed the person in a slightly different way, I think we we intuit that is the same 'offense'. But we can't expand it too far without allowing the man to kill his wife 15 years after being convicted of the offense of killing his wife. Any definition of 'offense' is going to draw on the jurisprudential history of offenses in a self-referential loop that can't be avoided. I'm not sure that the logic of self-referential systems has been exhaustively documented.
Anyone with better knowledge of the 'separate elements' test want to tell me if the urban legend is legally sound?