I fully agree with the premise that humanities aren't a science. In fact I am fairly certain that the current paradigm of science can not work for at least history, though I strongly suspect most of the humanities.
One of the problems is computability, when I try to build statistics on a space of human intentions, then I strongly suspect that this is at least as complicated as trying to build a measurable space atop the set of all Turing machines, and there I get immediately the issue of computability. (For example, calculating the average run time of halting Turing machines.) So, then assuming that one can meaningful build a statistic (just the claim that this is possible) will doom any too formal reasoning, by principle of explosion.
I disagree entirely, especially about history. You form hypotheses on the basis of evidence (literary, archaeological, documentary, etc), make predictions about the kinds of effects you’d expect to find in the historical record, and then modify those hypotheses based on what you find later.
No, predictions about what other undiscovered evidence you’d expect to find about the past. In a way this is like astrophysics in that you can’t conduct experiments, but you can predict that X is correlated with Y. Come to think of it, paleontology...
For example, take the Shakespeare authorship controversy; you could create a hypothesis that say “Shakespeare was indeed the author of Hamlet”. A prediction from this might be, “if a manuscript of Hamlet were ever found it would be in Shakespeare’s handwriting”. Not a really good example to be sure, but just off the top of my head...
One of the problems is computability, when I try to build statistics on a space of human intentions, then I strongly suspect that this is at least as complicated as trying to build a measurable space atop the set of all Turing machines, and there I get immediately the issue of computability. (For example, calculating the average run time of halting Turing machines.) So, then assuming that one can meaningful build a statistic (just the claim that this is possible) will doom any too formal reasoning, by principle of explosion.