To All: Extending the Euthyphro dilemma

Most of us here will be familiar with the Euthyphro dilemma: "Is what is morally good commanded by God because it is morally good, or is it morally good because it is commanded by God?" This of course remains a vigorous topic of discussion, but I recently ran across an [interesting extension of the dilemma](http://philosotroll.com/2013/02/02/unmediated-presuppositional-silliness-biting-the-silver-bullet.aspx) that gets, I think, to the heart of many theistic arguments. It was brought up in the context of the increasingly popular presuppositional apologetics, but I think its applicability is more general.

There seems to be a view common among theists that abstract objects, however we might define them, necessitate theism. Concrete objects, no problem, atheists can account for those. But abstract objects can only be accounted for if we allow for a god, so the thought appears to go. We humans do not instantiate (i.e. give properties to) abstract objects (or at least *some* abstract objects), we simply observe them, but they must be instantiated by *something*, else they would not have properties. And the "something" that instantiates these abstract objects, theists call god.

However, there is a problem lurking at the heart of this claim. And it flows from the Euthyphro dilemma, because objective moral values are occasionally claimed to be such abstract objects. If *any* set of abstract objects are claimed to be non-arbitrary, then the form of the dilemma kicks in.

* P1: There is a set of abstract objects such that all beings stand in either an observer relation (OR) or an instantiating relation. (IR) * P2: If some being stands in IR to the abstract objects, then those objects are arbitrary. * P3: Those abstract objects are not arbitrary. * C1: Therefore, no being stands in IR. * C2: Therefore, God does not stand in IR.

Common "targets" include, of course, morality, but also such things as logic and mathematics. If it is claimed, as presuppositionalists tend to do, that the utility of logic depends on the existence of god, then they run into a problem if they also claim that logic is not arbitrary.