What are probabilities?

Mark Saward

"What are probabilities?  That is to say, what is it that makes our claims about probabilities true or false?  One popular view has been that probabilities just are relative frequencies.  The probability of a coin coming up heads just is the frequency of heads in coin tosses.  This particular interpretation has fallen on hard times because of its difficulty with dealing with, among other things: single cases (what's the probability for a single toss?); objective chances in Quantum Physics; uncondintional probabilities.  Alan Hájek declared frequentist interpretations "as close to being refuted as a serious philosophical position ever gets."  I hope to convince you that that reports of frequentism's demise have been greatly exaggerated."