We propose to run a pair of workshops on the theme of the title; in particular the area under discussion is the interaction between different formal frameworks for investigating the scope and limits of mathematical knowledge. The first workshop (Spring or Fall 2011) would be one exploratory of themes and assessing possible approaches; the second (Fall 2012) would be a finalising workshop, expounding on the collected problem areas identified in the first meeting and the results achieved. A number of potential participants are identified who have made contributions in this area. The meetings would be held in Bristol, England. It is anticipated that the two principal project leaders would potentially spend (up to 3) months each visiting a suitable department to work with experts or expected participants in the field, and funds are requested also for this. Publication of any results would then follow the second meeting.