I asked:

Have any theologians tried to develop a theology without ontology, along lines suggested by 20th century mathematics?

As another example of "lines suggested by 20th century mathematics" I'll mention the theory of generalized functions, also called the theory of distributions, and the more recent wrinkle of Gaussian random fields. No longer do we specify a function by specifying what its values at specific points are; rather, we say what you get when you integrate the function against a test function. We do not concern ourselves with whether the Dirac delta function or other generalized functions "exist"; if we know how to integrate our function against every test function in some class, then we know everything about our function that we need to, and questions of existence become irrelevant. (A similar story can be told about the umbral calculus, which became respectable when most of it was reduced to linear algebra.) Of course, those who feel more secure when they can imaginatively construct the objects of their mathematical thought can (and do) construct generalized functions in a suitable dual space. But this just formalizes the original, operationalist insight that questions about what something *is* are better replaced by questions about what something *does*, or how something *interacts* with other things. Having a concrete model (like the dual space construction) is nice, especially because it affords a proof of consistency of all the properties you want these objects to have; but once you have established consistency, you can (and often do) ignore out the model and work in an operational (or, some might say, metaphysical) mode. In this paragraph I was going to close by talking about a belief that I suspect many modern mathematicians hold, namely that any interesting and consistent axiom system is going to turn out to be *about* something, and that asking whether those somethings exist in the mathematical universe is a senseless question (the answer is always "yes"), but I'd like to go a step further: Even before you've come up with axioms, when you're just messing about with objects of thought whose properties are a bit vague, and instead of propositions you're working with formal procedures or heuristics, if you start to find that what you're doing has a coherence to it, then I believe (and I suspect many other folks do to) that it is likely that one has gotten hold of fragments of a self-consistent theory that is yet to be created. Come to think of it, this lesson predates the 20th century; the calculus is a great example. So I wouldn't dismiss out-of-hand an interesting kind of theology that exhibited some logical inconsistencies as long as some non-trivial and surprising form of self-corroboration was also going on. Jim Propp