Gregory Chaitin Lecture Mälardalen University 2005 Pt 4

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

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[gadionson1]

nice video..nice

[czubinm]

I do have to note to you that we people are inconsistent. We can for example believe in two things that contradict each other. However these things do obviously conflict with physical laws. We do not define what reality should be. Ex: Someone might not believe in gravity, but gravity won't care.

And still! you can model this is mathematics without contradictions. As an example: A quantum turing machine(i.e. a computer) can simulate the physical laws and every human being with all their flaws.

[czubinm]

Secondly, math is very rigor but we still allow to make conjectures (unproven mathematical statements) until proven consistent or false. However ideas should have be refined until they are rigor. But Chaitin is making an argument for his digital philosophy. But this is much outside of mathematics and not widely accepted. We still work on continuos mathematics, arithmetic hierarchy, turing degrees etc.

[czubinm]

To be very clear about this: if your formal theory has a paradox then it's inconsistent. You cannot make it go away by adding it as an axiom. Worse, anything you have shown to be true in your theory is automatically incorrect. For example if I allow a paradox in elementary arithmetic then I can prove 1 + 1 = 3 and 1 + 1 = 4 and 1 + 1 != 3 etc. The theory has become completely useless.

If there's a paradox in your theory then in it's inconsistent and should be modified to be consistent.

[agentredlum]

I would like to state 3 examples relative to our discussion. Plato imposed his restrictions because he wanted to find flaw in the Pythagoreans, Liebniz imposed his restrictions because he wanted to uncover flaws in his peers philosophy and Chaitin imposes his restrictions because he wants to uncover flaws in Arithmetic! "hey! I'm just an innocent victim here, I was attacked by a coked up whore and a crazy dentist!" (12 monkeys)

[agentredlum]

Should we disregard Euler's brilliant results because he wasn't as rigorous as K.F. Gauss? If only Gauss was more like Euler, our mathematics would be more advanced by 300 years. These are some of the reasons why, in my opinion, restrictions do more harm than good. Essentially restrictions are for pessimists looking to find flaws. When truth and understanding are concerned I prefer to remain an optimist.

[agentredlum]

Just kidding...we need some rigor but not too much. Look at someone like L. Euler. Every time I read some 'experts' explanation of some of his beautiful and brilliant arguments 'they' are quick to point out the 'shaky' part of the derivation. Euler posed no restrictions on himself, in a way he did say to hell with rigor, and look at all he accomplished (product formula for primes and 1/s^2=pi^2/6) many results too numerous to list here. e^(i8)=Cos(8)+isin(8

[agentredlum]

Here is where you and I differ. I say this with the utmost respect for you because I consider your goal a most noble one and your arguments convincing. You claim that imposing restrictions is a good idea (Chaitin and 99.9% of mathematicians and scientists would agree with you.) I claim that imposing restrictions is NOT a good idea because I think that they lead to paradoxes and wasted effort. TO HELL WITH RIGOR!

[agentredlum]

I think Russell got his paradox from the barber of seville paradox. If you insist that the barber be a male citizen of seville then it is impossible for him to shave ALL the men of seville who do not shave themselves. The problem arises when he considers himself subject to the rule. If he shaves himself then he must not shave himself, if he does not shave himself then he must shave himself. Notice he does very well with everyone except himself. No one bothers to point THAT out.

[agentredlum]

Here's what I'm afraid of, 'throwing the baby out with the bathwater' One should not throw away a theory because of a few paradoxes. One should do their best to make the theory as consistent as possible and then make a list of all paradoxes arising from the theory. If someone finds a new paradox, add it to the list. If someone comes up with a theory that explains exactly the same but with less paradoxes then that is a better theory.