Neil Barton (Birkbeck) gives a talk at the MCMP Colloquium (14 January, 2016) titled "On the Relationship Between Intrinsic and Extrinsic Justifications". Abstract: Recent discussions of the justification of new axioms for set theory have often focussed on a distinction between two different kinds of justification. Intrinsic justifications argue that putative axioms are implied by an underlying mathematical conception, whereas extrinsic justifications concern the consequences of said principle. In this paper, we argue that intrinsic and extrinsic justification as it has been explained in the literature is unsatisfactory. In its stead we propose a new account of intrinsic and extrinsic justification, one which develops a harmony between the two notions and avoids the problems we see for extant accounts.