@blinry Hmmm... I liked the prime numbers one. I'm not convinced by this one. You need a mathematical definition of interesting, I guess.

@noam @blinry The thing about mathematical definitions is that they do not explain what a thing "is", they list properties and relations to other things. The argument relies only on the statements "special is interesting" and "interesting implies not boring", to arrive at a proof by contradiction.

@noam @blinry So as a mathematical proof, it's perfectly fine. We do this all the time. When we evaluate the claim "The cat was in the bedroom, so it could not have eaten the lasagna in the kitchen" we do not rely on a full definition of what a cat "is", only properties such as "has only 1 location" and "can't walk through closed doors"

@noam @blinry We can however make new axiomatic systems where the proof does not hold. I state "If a number is interesting, it has its own wikipedia page".

@blinry @Eclogiter I understand the proof, but this isn't the same as defining what a cat or a lasagne is. The proof here rests on what makes a number interesting. It relies on the fact that having the property of being 'the smallest boring number' makes a number interesting. This implies that a number is 'interesting' if it has a unique or unusual property, but doesn't state it clearly.

For some reason, I'm reminded of the proof by induction that all people have ginger hair...
Sign in to participate in the conversation
chaos.social

chaos.social – a Fediverse instance for & by the Chaos community