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The above statement is correct. But instead of "conditional" I would rather use "contextual" or at the right level of abstraction. If we're talking about math, we don't need to bring in other subjects by fiat. Within math, 1+1 = 2 is 100% true. Of course that is in the context of the things being added are identical and the + sign is said to mean "collecting" or "adding." Now, this doesn't mean 1+1=2 is unquestionable, someone might say "what if we are adding an apple and an orange?" And this also doesn't mean that we get this empirically, it is still a guess. You can also know more about it. Like Brett talks about the Peano's axiom. At that point, you are going in more detail, which might be needed if it solves your problem.

My understanding so far is fallible means anyone can be wrong, which means that there is something to be right about, and as such one can be 100% right. y as things get complex and more detailed, it becomes to know which part you are 100% right about. And at that point, you go with what solves your problem, unless your problem is finding ideas that are 100% true, in which case the best you can do is guess how that idea can be false.