I mostly agree with Daniel Schoch’s analysis, Gods as topological invariants, except for part of its conclusion.
For a starters, Schoch is right to claim that theology is a mathematical problem. The same holds true for epistemology. Most areas in philosophy have successfully been annexed by mathematics.
In his analysis, it is not the Euler characteristic of the universe that matters, however, but the one of the domain of the Aristotelian causality function. If we assume that:
- Time is finite
- No two events can occur at exactly the same time
- There are no moments in time in which no event occurs
In that case, the domain of the causality function is homeomorphic with the topological space of a line segment, of which the Euler characteristic is one.
For the remainder of this reasoning, I just repeat more or less what Daniel Schoch says.
According to Lefschetz fixed-point theorem, a function mapping a topological space, with an Euler characteristic equal to one, onto itself, will have exactly one fixed point — which in the mapping of a topological space onto itself is indeed a topological invariant. As Schoch wrote, the fixed points in the Aristotelian causality function are indeed designated as gods.
Therefore, unlike what Schoch says, the correct conclusion is that there is exactly one God.
So, I agree with Daniel Schoch on his reasoning, except for the fact that he is looking at the wrong Euler characteristic. The domain for the Aristotelian causality function is not the universe but is time.