In other words, Godel's theorem: all formal systems (including Deductive logic) will contain truths that are not provable from within the formal system.
The flip-side of "if you can't prove it false, I can believe it:" if you can't prove it false, that's no reason to disbelieve it.
Just because something
may be false is not a compelling reason to
assume it is false.
Just because it is a brilliant sentence.

He spanks Popper, Feyerabend, and Lakatos pretty soundly; but he grants Kuhn at least the courage of his convictions. Kuhn alone really believes there has been no scientific progress in 400 years, and wants others to believe it; the previous fellows are constantly aghast when people take their irrationalism seriously.
So how do we know something is true, if we can't prove it? Stove seems to imply that mere observation (as J.S. Mill argued) or assumptions about the consistency of the universe (Hume's "cement in the universe") isn't adequate, but I can't see where he provided any alternative.
My summation of his article: there are two kinds of people - those that think the world derives from truth, and those that think truth derives from the world.