The whole issue of "singularity" needs a bit of clarification. If this is a physical singularity, i.e. a breakdown of a theory's ability to predict, then this is in the reference class of "theories of society claiming current models have limited future validity", which makes it nearly certain to be true.

If its a mathematical singularity (reaching infinity in finite time), then its reference class is composed nearly solely of erroneous theories.

You can get compromises between the two extremes (such as nuclear chain reactions - massive self feeding increase until a resource is exhausted), but it's important to define what you mean by singularity before assigning it to a reference class.