I really disliked how the author randomly throws in opinions and beliefs like that in a context that didn't really warrant it. I thought I was going to read about epistemology; instead I got a summary of his worldview.
A learning strategy for history or literature: Subjective judgment is important; careful reasoning is not.
Really, careful reasoning is not required? This is patently false, and probably based on his English and History experiences in high school decades ago. I find that people who say such things rarely have adequate exposure to the subject area. Someone I encounter on a daily basis actually in the CS research community.
If you're not using deductive reasoning in the study of history or literature you're doing something horribly wrong. The authors statement is flat out wrong, no matter how you spin it.
But he isn't presenting some random opinion, he's claiming he's teaching how think clearly and one assumes he's trying to present well by example. Well, strike-three.
-- I think contrary to his rules, I don't think there is any set, global rules for presentation beyond the basic language skills he correctly says are rather in-born. What there are is a series of interlocking conventions and strategies on a per-subject and per-topic basis. Learning those well takes a long time and can't be summarized by a how-to...
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.
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'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.
Have to in this case is confined to context of the principle itself, it indicates that you have to do such and such in order to follow the principle.
I am holding a butter knife to my imaginary 3D-scanner: you have 64px^3 of the resultant image to determine the nature of the object. If you see the tip of my butter knife you'd assume it was a smooth, dull blade with a rounded form. If you saw the middle of the blade you'd know that it was serrated, but would have to speculate about the endpoints and the form of the knife. If you saw the end of the knife, you'd be hard pressed to determine its function; you'd only know that it is rounded, smooth, and roughly 1.5cm thick. Maybe you could guess that it was a knife, but you'd still remain ignorant of its greater nature.
Your knowledge consists of this tiny view of the knife, or else you're privileged to know all knowledge (so that you might approach it without a worldview or paradigm) or to know someone who does.
You cannot study knowledge without studying worldviews, or studying it with a worldview of your own.