Christ of Faith vs. Christ of History

I was reading Mark Strauss' excellent Four Portraits, One Jesus: An Introduction to Jesus and the Gospels and I came across an interesting discussion about the legitimacy of the quest for the historical Jesus. Strauss is worth quoting in full:

The foundational methodological question is whether a 'scientific' historical enquiry into Jesus is possible or even desirable. Scholars like Luke Timothy Johnson, echoing the work of Martin Kähler, reject any study of the historical Jesus which isolates him from the Christ of faith. The 'real Jesus' is discovered not through criteria of authenticity or historical methodology but through an existential faith-encounter with the risen Lord. On the other side, most scholars consider it both possible and necessary to investigate the historical Jesus using a rigorous historical method...

While it is certainly true that the 'real Jesus' cannot be known completely through historical investigation, this does not render historical-Jesus research misguided or invalid. The historical Jesus-defined as knowledge about Jesus which can be attained through historical research--is a subset of truth about the real Jesus. It is not a complete picture, since many questions remain unanswered about who Jesus was as a complex human being. Nor can historical research account for faith-encounters with the living Lord. In short, while conclusions about the historical Jesus are always partial and incomplete, this does not mean they are invalid or false. We can know much about the person of Jesus without knowing everything (359).