This strip is part of a trend that’s bucking the trend for me; I had the idea first and then went looking for a clip. Usually that creates all kinds of headaches for me, including sometimes having to commission a drawing to fit the script, but I was lucky enough that this one image in all the 600,000 in my collection would fit the bill.
The idea came to me in line at the supermarket. There was a young kid in one of the other lines who kept repeating something that sounded a lot like “I am sane.” I went from hoping my line would hurry up to hoping it wouldn’t move until I had locked down the idea.
I’ve also been reading a heavy book on game theory (which I understand about every other sentence of) and had the word “tautology” on my mind lately. Weird fusion.
Hi,
as a student of logic, i thought i would let you know that in first order theory contradictions are not statements – they are properties of sets of statements. i.e. if you have a set of statements Gamma, and Gamma proves both Alpha and (not)Alpha then we say Gamma is “inconsistent” i.e. at least one “contradiction” follows from it. Your definition of a tautology is more or less correct.
You might be interested to hear that inconsistent sets can prove any fact whatsoever. I.e. if Gamma is inconsistent and any contradiction whatsoever follows from it, Gamma proves every statement. E.g. if I am working with naturals, Gamma proves 1+1 = 3 for instance.
Bye!
Nice, now show me how to write “this sentence is false” in formal logic notation.
Douglas Hofstadter’s _Godel_Escher_Bach_ is a fun book to skim through if you’re interested in this sort of stuff. Godel has a nice proof of “this sentence is false”. It essentially changed the way we classify the world.
http://en.wikipedia.org/wiki/G%C3%B6del’s_incompleteness_theorems#Relation_to_the_liar_paradox