Did Jesus Exist?

One of my favourite weblosophers gives his take on whether we can reasonably say that Jesus existed:
http://stephenlaw.blogspot.co.uk/2012/04/published-in-faith-and-philosophy-2011.html

Essentially, Law argues that while we do not have enough evidence to say with confidence that Jesus did not exist, nor do we have enough evidence to say with confidence that he did. 

I have long been sceptical of atheistic claims that Jesus did not exist - the existence of a real miracle-worker seems to me the most parsimonious way of explaining the existence of the early Christian documents and beliefs about Jesus.  However, Law does go some way to addressing some of my concerns, notably his 'principle of bracketing'.  Essentially, this says that if a high enough proportion of a story is miraculous in nature, we are not justified in separating out the non-miraculous portions and judging them by the usual standards.  The non-miraculous simply become a by-product of the miraculous, and if we are accepting that a large (miraculous) part of the story was invented from whole cloth, why should we not also accept that a smaller (non-miraculous) part was (or at least may have been) invented also?