Gregory Chaitin Lecture Mälardalen University 2005 Pt 2

Västerås, Sweden, 2005, Alan Turing Lecture on Computing and Philosophy
European Computing and Philosophy Conference, Mälardalen University.

Epistemology as Information Theory: From Leibniz to O
G. Chaitin, IBM Research
Alan Turing Lecture on Computing and Philosophy, E-CAP'05, European Computing and Philosophy Conference, Mälardalen University, Västerås, Sweden, June 2005.
http://www.cs.auckland.ac.nz/~chaitin

Category:

Howto & Style

Tags:

• Gregory
• Chaitin
• lecture
• Epistemology
• Information
• Theory
• leibniz
• omega
• mälardalen
• university

[themfu]

@agentredlum correct, you cannot list the uncomputable ones, so you can't cover them with the epsilon argument.

[czubinm]

@agentredlum You could try to list them but I could simply construct out of them one that's not in your list. See "Cantor's diagonal argument" on wikipedia.

In sort the infinity of the real number is bigger than the infinity of integers/

Do not that this is no reason to not accept real numbers. However one must be wary of the difference between potential and actual infinities.

[agentredlum]

Thank you for your comment czubinm. Thanks to you I have discovered a flaw in my argument, I cannot cover the uncomputable numbers because they cannot be listed...is that right?

[czubinm]

@agentredlum uncomputable numbers are uncountable infinite, their sum would not equal to epsilon :P

[agentredlum]

What is going to stop me from using his brilliant argument to cover ALL real numbers computable and uncomputable? Using his argument the sum will again be € and so you can make it as small as you want not equal to unity. Now you have a problem, a number must be either computable or uncomputable. I have taken care of both of these cases and still failed to fill in the interval from 0 to 1. His method has a flaw, it seems he cannot fill anything in!