To summarize, Sye wants to know how we justify reason itself, and hence our subjective view of the world which we base on our reason. However I take justification to be a part of our reason, and so this is akin to asking, how does a person justify justification? My position is that we don't need justification for using any particular standard of justification as long as that standard is consistent with itself, and with its own application. While this situation may not satisfy us completely, it's the best we have available to us, since any would-be justification for our standard of justification must necessarily have a circular character.
In Sye's view, though, not all circular reasoning is bad, or "vicious." According to him, we should instead use a good or "virtuous" kind of circular reasoning involving the existence of the Christian God. Recall from the podcast (~48:00):
SYE: We're saying that we have a justification---revelation from God.
BEN: Part of what we mean by justification is to satisfy our reason. How could you have a non-circular argument given that that's what we mean by justification?
SYE: We're not saying that our argument isn't circular. We're saying that it's virtuously circular in that God can justify reasoning.
So that's the background to the following discussion. Enjoy!