paolo wrote:
One of the holes in math which tormented Turing, Godel, and many eminent mathematicians was the liar’s paradox. If I say that I lie, am I not again lying? And again and again. And even 2+2=4 may be wrong. Wrong or irrelevant. You can say only irrelevant things or lies. Sometimes I feel plunged in this dilemma and that was part the reason of my demise Monday.
I don't understand
all of this, however-
In Wired I read about some new book by a guy named Hofstadter called "Strange Loop".
Excerpt from interview:
Q:"What is a strange loop ?"
A:"One good prototype is the Escher drawing of two hands sketching each other. A more abstract one is the sentence "
I am lying". Such loops are, I think anyone would agree, strange. They seem paradoxical and even strike some peopple as dangerous. I argue that such a strnge loop, paradoxical or not, is at the core of each human being. It is an abstract pattern that gives each of us an "I", or, if you don't mind the term, a soul."
Q:"You have a great line:'I am a mirage that perceives itself'. If our fundamental sense of what is real-our own existence-is merely a self-reinforcing mirage, does that call into question the reality of the universe itself ?"
A:"I don't think so. Even though subatomic particles engage in a deeply recursive process called renormalizaton, they don't contain a self-model..."
(I only cut out a piece of the brief blurb. Sure you can find out more about this if you want...)
An older curious & humorous logic book is "I Think, Therefore I Laugh" by John Allen Paulos.
_________________
*"I don't know what it is, but I know what it isn't."*