I've thought a bit more about it, and concluded that while the above is a neat answer, it doesn't explain the question, and [thewarrior]'s remarks were nearer t

I've thought a bit more about it, and concluded that while the above is a neat answer, it doesn't explain the question, and [thewarrior]'s remarks were nearer the mark on that. So here goes. It's tempting to think of "knowledge" as some relationship between the mind and a single fact. But when we use the word "knowledge", what we actually mean is "an accurate world model" - a set of beliefs. This is the disconnect that Gettier cases are designed to expose - they construct scenarios where someone's mental model is inaccurate or incomplete, yet by sheer luck produce a single, cherry-picked correct prediction. We are uncomfortable calling these correct predictions "knowledge" because as soon as you start probing the rest of the mental model, it falls apart. Sure, they think there's a cow in the field, and there really is one. Ask them any more questions about the scenario though ("what color is the cow?") and they'll give wrong answers. From this perspective, "knowledge" as a "justified, true belief" is a perfectly coherent concept - the problem lies with the inadequacy of the word "justified" to describe the output of a complex decision procedure that incorporates many beliefs about the world, such that it could be expected to yield many other correct predictions in addition to the one in question, up to some arbitrary threshold. A thought experiment - suppose you tell the observer that the cow they see is made of paper mache. They no longer believe there is a cow in the field. Intuitively, has their knowledge increased or decreased?