"All Cretans are liars", said Epimenides, a Cretan. But this means that his statement must be a lie too. But then it is false that Cretans are liars and the statement must be true. So what now?

For centuries, mathematics was seen as the one field built on absolute certainty. But a deeper look into logic reveals a flaw ...

The reticent and relentlessly abstract logician Kurt Gödel might seem an unlikely candidate for popular appreciation. But that’s what Rebecca Goldstein aims for in her new book Incompleteness, an ...

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Alan Saunders: Hi, this is The Philosopher's Zone, I'm Alan Saunders and let's take a walk with Albert ...

The Axiom of Choice became one of the most feared and contested ideas in mathematics. It created elegant theorems and ...

How Gödel Destroyed Search for Math's Theory of Everything | RealClearScienceMathematicians of the era sought a solid foundation for mathematics: a set of basic mathematical facts, or axioms, that was ...

Godel’s theorems on the incompleteness and undecidability of mathematical systems are among the deepest and most significant discoveries of the 20 th century. They represent a dramatic failure of one ...

Scientists at the University of British Columbia Okanagan say they’ve found a mathematical limit that shuts down the ...

When Gödel died in 1978, he left behind a tantalizing theory based on principles of modal logic -- that a higher being must exist. The details of the mathematics involved in Gödel's ontological proof ...

Mark Colyvan: That's right. So mathematical logic is just fleshing out that basic idea but using quite a bit of mathematical machinery to do it. And the other side of it is using that mathematical ...