Presented by Verónica Becher.
We will be discussing how Gödel’s paradox “This sentence is false/non-demonstrable” leads to his well-known result on the limits of axiomatic reasoning. This will be compared and contrasted with Chaitin’s work, based on the paradox “The first non-interesting positive number”, which is already rather interesting given the fact that it is the first number not to be interesting. This paradox leads to the first of Chaitin’s results on axiomatic reasoning: that the majority of numbers are “non-interesting” or random, although it can never be proved in particular cases. These ideas led to his discovery that some mathematical statements are true for no reason, they are true by accident, or at random. Put it other way, not only does God play dice in physics, He also does so in pure mathematics, in logic, in the world of pure reason. Sometimes mathematical truth is completely random and has no structure or pattern we can ever get to understand. Straightforward, clear questions do not have straightforward, clear answers; not even in the world of pure ideas, let alone in the chaotic actual world of our everyday lives.


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