Thursday, 27 October 2011

Vanishing Foundations

One of the things mathematics taught me is that you have to start somewhere.  Some things you just have to accept.  Axioms are assumed to be true (usually because they are self evident) but are unprovable.

One thing discussions with atheists have taught me is that everyone (no one is excepted, here) finds it easier to see someone else's assumptions while often remaining ignorant of their own.

Let's have some fun seeing what that looks like.  David Hume raised the is/ought problem, also known as Hume's law or Hume's gillotuine.  When used in an argument, Hume's law might be deployed something like, "You can't get an ought from an is."

"School education is a shambles, we ought to put more money into schools."
This doesn't necessarily follow, for example
"School education is a shambles, we ought to stop wasting money on a broken system."

Which contention is correct needs to be established by further argument.

That's a simplified application.

But here's a really interesting application of Hume's law to Hume's law.

This is Hume's Law as he originally expressed it: