logic, mathematics

The Way Yablo Killed Infinity

It’s the best, if not the first infinity assassination.

Infinity is a very dear and fundamental concept to the majority of the people alive today. But I am sorry, it has to go for logic reasons.

Stephen Yablo, twenty years ago, created an infinite sequence of statements. Each of them stating, that all the following statements are wrong. So, the Nth is saying that N+1th is also wrong among all other after the Nth. But then, the N+1th is correct and therefore the Nth is wrong. So all of them are wrong, since N can be any number. But then, the Nth is correct.

And so on. We have encountered a paradox inside infinity, so it must be abandon like a rotten, rat and cockroach infested, sinking ship. No matter how many oceans we crossed with her. Or we think we did.

Note. This paradox isn’t reproducible inside a finite list of statements. If them all saying that all the higher are wrong, the last is true, others are all false, end of story. No paradox there.

But for the infinite series … Stephen Yablo taught us, 20 years ago. At least I took the lesson. Maybe because I didn’t believe infinity even then and it was easy for me.

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One thought on “The Way Yablo Killed Infinity

  1. Saladin says:

    A paradox or only a bad formulation or logical statement unrelated to a physical universe we live on?

    Mathematicians must learn to differentiate between pure mathematical/logical systems and physical/logical systems. Purely mathematically you can formulate a completely correct logical system that has nothing to do with a physical universe (like our own).

    And if it doesn’t relate to our physical universe – then it’s merit is by itself philosophical and not practical.

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