[peritonlogon]

There is an entire field of philosophy called epistemology that addresses this question.

One thing that I will actually add though, is that the latter portions of modernity stopped putting the question in terms of knowledge and started putting it in terms of "understanding." And not to quote any, but some of your examples simply employed different uses of the word "know" in different gramatical forms and, in light of this, would be simply considered semantic differences.