“Falsifiability” is a word with meaning. If you identify a single counter example to a mathematical conjecture, the conjecture is wrong. That is not true for history, philosophy, psychology, or the other liberal arts.
Two Dogmas would be a good place to end up.
It's also weird to suggest that no historical claims are falsifiable. That seems to put real history on a par with nutty conspiracy theories.
In my humble opinion the scarceness of falsifiability in history is the reason why it is so easy to create nutty conspiracy theories about history vs, say, mathematics or physics.
> But then why do you judge the conspiracy theories to be nutty, if they are on just as firm an epistemological footing as actual history?
But to elaborate on your argument: Because of the dubious epistemological footing indeed "actual history" has not the highest reputation to me. The reason I disregard lots of "nutty conspiracy theories" rather lies in the fact that many "conspiracists" have a tendency to find conspiracies in other topics, too, where falsification is much better possible. Thus I tend to judge by looking at the track record of the respective person.
This is exactly one example for my "where falsification is much better possible" - in this case because of physics.
But by picking over the details of a particular example you're missing the point. Surely you don't want to say that you can reject crazy historical claims solely because the proponents of those claims make outragerous claims in other areas too. If you think the moon landings are an exception, for some reason, then let's look at other examples. E.g. Holocaust denial.
History is roughly as falsifiable as astronomy or biology.
At least for mathematics I have hardly seen any "nutty mathematical theories" (I am a PhD student in mathematics, but not a physicist, so I cannot say anything about physics here). The reason that I see is that for a math text to be considered as solid, it has to contain good, understandable proofs - which are hard to write by "crackpots". To be more precise: On sceptic's blogs I have of course seen links to papers containing "mathematical crackpottery", but I have hardly ever seen those "in the open countryside".
Ask your favorite well-known professor how many proofs of P=NP, the Riemann hypothesis, or whatever they get per week. Sure, they're all Time-Cube level crazy, but most off the wall theories are, too.
My PhD advisor actually works in an area that is related to complexity questions that are related to P=NP. So if he would get spammed a lot with this kind of papers, I am pretty sure that I would know. Similar statements hold for other researchers who work on the same floor.
You might object that even though they might work on questions that are related to complexity theory, they are perhaps simply not the people that an "ordinary crackpot" thinks of as target reader for their texts - in other words one has to know a little bit about mathematics to know that the questions these people work on are actually related to P=NP. I will not disagree with this objection.
You may also object that the respective persons are well-known and well-regarded in their respective community, but the general public is not so much aware of them. I also will not disagree with this objection.
Nevertheless I strongly believe that if your claim were true in general, I would probably know.
Falsifiable means subject to test. It doesn't mean provabe on the sense of math. Only math is provable like math.