To infinity and beyond: The struggle to save arithmetic http://www.newscientist.com/article/mg20727731.300-to-infinity-and-beyond-the-struggle-to-save-arithmetic.html
<<Friedman's configurations, on the other hand, lay down an ultimatum: either admit large cardinals into the axioms of arithmetic, or accept that those axioms will always contain glaring holes. Friedman's own answer is unequivocal. "In the future, large cardinals will be systematically used for a wide variety of concrete mathematics in an essential, unremovable way," he says.>> <<Not everyone is happy to take that lying down. "Friedman's work is beautiful mathematics, but pure fiction," says Doron Zeilberger of Rutgers University in Piscataway, New Jersey. He has a radically different take. The problems highlighted by Friedman and others, he says, start when they consider infinite collections of objects and realise they need ever more grotesque infinite quantities to patch the resulting logical holes. The answer, he says, is that the concept of infinity itself is wrong. "Infinite sets are a paradise of fools," he says. "Infinite mathematics is meaningless because it is abstract nonsense.">> harry
