 A background issue in all of these debates concerns the extent to which each particular non-deductive method plays an essential role in the justificatory practices of mathematics. This question arises at both a local and global level. At the local level, a particular piece of reasoning to justify a given result may be unavoidably non-deductive, yet the result may also be established by some other, purely deductive piece of reasoning. At the global level, it may be that our only justification for certain mathematical claims is non-deductive. The extent to which our use of non-deductive methods is due to limitations in practice rather than limitations in principle remains an issue for further investigation.