Introduction The existence of this meeting bears testimony to the anodyne remark that there is a continuing debate about what it means to say of a statement in mathematics that it is `true'. This debate began at least 2500 years ago, and will presumably continue at least well into the next millennium; it would be implausible and perhaps presumptuous to suppose that even the union of the talented and distinguished speakers that have been assembled here in Mussomeli will approach any solution to the problem, or even arrive at a consensus of what a solution would amount to. In the end, it falls to the philosophers, with their professional expertise and training, to carry forward the debate and to move us to a fuller understanding of this subtle and elusive matter. Indeed, we are hearing at this meeting a variety of contributions to the debate from different philosophical points of view; also, there is a good number of recent published contributions to the debate (see (Maddy 1990)