Nic Weaver on the liar paradox

April 14, 2010

I have not yet read all of Nic Weaver’s comment on the liar paradox however the beginning is interesting enough to mention it here.

Edit: If I understand him correctly, then he claims that the law of excluded middle is not applicable for what he calls ‘heuristic concepts’, which are (and here I interpret freely) concepts with some immanent circularity.

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What is Your Dangerous Idea?

August 28, 2009

When I asked my guest about his opinion on this little booklet edited by John Brockman, he actually started to smile and answered something like: ‘These smart scientists have a lot of dangerous ideas and have you recognized, all of their ideas are dangerous for other people? Scientists surely must be very caring.’ By then I was already used to his interesting approach to the concept of humor and decided to ignore the last remark. Instead I wanted to know, whether he had his own dangerous idea, preferably an idea dangerous for science.

He told me, that the single most dangerous idea for science is:

There is no proof.

The danger of this idea, according to him, does not stem from the fact that it might be true. The problem is, that you, as a scientist, cannot argue scientifically against it.

I was not able to follow. The Pytagorean theorem is proved! There are dozens of proofs, some of them hundred and thousands of years old. I have checked a few myself and all experts agree on the truth of this theorem. After all, this is not the classification of all finite simple groups and even this is settled. At least I hope so. How can one seriously think that there is no proof?

In a deliberately patient sounding voice he explained again, that the possible truth of the idea is not the problem, but our wrong understanding of what science actually is. Even in this moment when I writing down this post, I have no idea of what he was talking about. My face must have expressed my ignorance and he began a monologue on proofs. In essence he claims, that to deserve its name

a proof has to prove that it is a proof.

Otherwise, it is obviously not a proof, but only some consensus among the participating players. You can call it peer review if you like, but don’t call it a proof.

I am completely lost. No mathematician has ever proved that his proof is indeed a proof. That makes no sense! Or, does it? And if yes, then it is surely impossible! What do you think?