what is the fallacy that declares the existence of finite absolutes

There is pastor who perpetually answers people who tell him there are no absolutes if they are absolutely sure.. It gets a big laugh.

Absolutes exist within the context of a given situation. If the room is warm and you say you are absolutely sure everyone is warm, are you considering those in the room who feel a chill?

What fallacy is the pastor using to declare that his all absolutes are finite? And that to consider exceptions to the rule is inviting sinful thought?

The pastor is pointing out what can possibly be a self-refutation . That is, if a person does declare that there are no absolutes, and they are "absolutely sure" about that, then the pastor might have been successful in pointing out a contradictory belief. However, even if the person did say they were "absolutely" sure it would be more like the atheist who says "God bless you" when someone sneezes. "Absolutely," in this context, is an expression of confidence and agreement; not a ontological claim about the universe. So we might be dealing with equivocation .

An interesting and revealing question, is WHY do people laugh at this? My take on this is that people assume that claims like this are made with certainty, and if they are not, then they are somehow more unlikely to be true than claims made with dogmatic certainty. Those who are laughing are likely confusing ontological claims with epistemic ones... showing their own lack of critical thinking skills.

I'm confused too. I understand the difference between ontological and epistemic claims but here we could say that saying that there are no absolutes can refer to claims themselves. We could rephrase it like this: there are no claims that are absolute (no claims that are always true). If this claim is always true then what it said is false and hence the laugh.