1. How does that prove anything? What you are effectively saying is that standing in front of a bus will only kill you in an objective universe.

2. The comment you replied to did not state that the commentator holds that view, it was merely an observation that they didn't expect certain content in the article.

The point is not whether or not he's right (which is an incredibly tricky question, actually, when you stop generalizing in a cartoonish way), it's that he's presenting something as fact which is definitely not provable.

Provability (that is, being able to be proved by deductive means) is not generally taken to be a requirement for asserting a fact. To prove something is to demonstrate that it could not be otherwise (that it is necessary, given the logic employed and that that the premises are true).

For example, I might assert that "Tomorrow, the gravitational constant be the same as it is today." This seems like a fact: we have pretty strong theoretical justification for it, given certain empirical evidence, an assumption of regularity in nature, and the continued predictive success of the general theory of relativity. However, if tomorrow the gravitational constant is slightly different to what it is today, then although no (deductive [1]) logical law has been contravened (as would have to be the case if a provable statement turned out to be untrue), my assertion was clearly not a fact.

However, proofs (as in mathematical or logical proofs) are obtained through deductive reasoning, not inductive reasoning, as my statement was. Thus, I would argue, there is nothing wrong with presenting something as a fact which is not provable. Otherwise, we wouldn't be able to assert very much at all: the restricted epistemology obtained would rule out all of science, for starters, and might even cast doubt on certain classes of observation statements.

Of course, you may have meant something other by 'provable' than I do, in which case clarification would be appreciated, since you presumably meant something by your assertion that facts must be provable, and it would be nice to know what it was!

[1] It is controversial as to whether a general inductive logic can be formulated.

I think he is getting at the epistemological problem of first premises. If the only fact of epistemology that I accept is "I exist", the statement "Objective reality exists" cannot be proved.

I'm sure there's better formal language for this, but we could benefit by making a distinction between "facts in principle" and "facts in practice". Let's say a fact in principle is derived from a priori knowledge, whereas a fact in practice is one that we have accepted and depend on in order to make pragmatic decisions and survive. In principle, I believe that I exist but that I cannot prove objective reality exists. In practice, I accept that objective reality exists and that if I stand in front of a bus I will be hit.

His problem is even more basic than that. Axioms+rules+theorems make up a formal system, not a universe. (I can see how it's easy to confuse the two.) At some point, you must use induction & associate/identify some of its elements with observable quantities; that's what makes it a physical theory instead of a purely mathematical theory. Deduction alone gets you nowhere in the real world. And in its own domain the most it gives is consistency, not truth. I can't for the life of me understand why it's desired, or why its absence is relevant.

In my experience, the trickiness mostly comes down to disagreements over definitions.

Well, you can not prove that the bus would run over him every time he tries it.

How is that a coherent statement? Even if a "proof" was possible (which it isn't by definition), you could just pick a different set of axioms & arrive at a different conclusion.

From the OP: The evidence for one side can still be a lot stronger than the evidence for the other.

Did you mean a moving bus?