I actually think that you're confusing a little bit of modern philosophy with a lot of "postmodernism." You have to be very careful there. Stove and Russell and Wittgenstein are "modern" philosophers. They also share a commonality in being founders of the school of analytic philosophy - the school most philosophy departments around the world are now centered on.

Postmodernism, on the other hand, has a comparatively small following. I'd make the exception for some of Stove's most criticized colleagues, including Feyerabend. There's no denying that he and his followers were influential, but I would not argue that they hold the "dominant" idea in modern philosophy. Their view is complex, but they certainly don't deny empirical knowledge, but instead aim to criticize certain points of empiricism which scientists generally regard as "solid." However, as you just read, Stove was one of many who sharply criticized him for "abusing" logical expressions.

I don't want this to turn into a really long argument, but I think you did make an interesting point. Many who believe that a posteriori knowledge is impossible are in opposition to many of the early philosopher/mathematicians of the early-mid 20th century. Some of the most notable are Russell, Whitehead, and Wittgenstein (and I also want to briefly mention Gödel, who was not very active in philosophy, but whose mathematics help the field immeasurably.

As opposed to Feyerabend and especially the skeptics, I would state that they have it all wrong. It is not a posteriori knowledge which is impossible, it is a priori knowledge which is impossible (or tautological, to be more accurate). Many of the early modern philosophers (especially the empiricists, like my heroes John Locke and David Hume) supposed that much of our knowledge comes from the outside - that is from our experience. As we now know today, they were largely correct. We gather a huge amount of our personality and view from our experiences, with very little "innate" knowledge. One of the main hold-outs from that time was in mathematics. Many believed that mathematics was something a priori solid. If you read Descartes's Meditations or Hume's Enquiry, you will see a lot of mention of Euclid, specifically his theories of geometry. Time and time again the philosophers used the example of basic addition or the laws of geometry as arguments for a priori knowledge. That is, even if I don't know that that tree exists, I can at least know that 2+2=4. This would seem to be an argument for the skeptics and idealists (like Berkeley), but instead it is an indictment. For, even mathematics is not safe from a posteriori reasoning. Why does 2+2=4? Because we have defined it to be so. We have come up with an algebra, the countable numbers, and defined addition using it. However, does this hold some innate truth, an a priori truth about the Universe? I would argue that no, it doesn't. This a priori knowledge is tautological -- math comes up with the "right" answer because we defined what the right answer in our consistent system is. Except, we really didn't. Gödel has helped here by proving that no moderately complex system can be both complete and consistent. This is one nail in the coffin of a priori math, but it continues. Eventually we reach some of our most basic axioms -- Peano arithmetic. It would seem that these are truly untouchable. a != !a. Who can disagree with this? Well, if you look closely, you'll see an assumption here. Or, more importantly, a definition. We define !a. We define these expressions. These are a priori, and many believe that you can build a priori systems out of them. The problem is -- you can't. Russell and Whitehead soon saw this after Gödel's insight, but it's still a contentious issue.

Well, I tried to keep that as brief as possible, but as you can see, philosophy tends to drone on and on. This isn't really a detailed analysis, but think of it as a footnote of my views on the issue.