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I think you need logic to support that claim, it is not the type of thing that can be studied. (Or you might find that kind of logic in academic philosophy.)
The logic is, you find it self-evident [requires no proof] that to quantify anything requires a method of measurement that consistently returns a unique position on a scale of possible values (or a tight range of values with minor measurement errors allowed). *['consistently' because it cannot give random values if the person and test conditions remain the same, e.g. an IQ test with randomized questions that returns 180 on Monday and 95 on Tuesday, for the same person under nearly identical conditions, is useless; no decisions should be made based upon such a test.]
Therefore to quantify 'knowledge', we need to define a scale of possible values and devise a method of measurement for knowledge.
That in turn logically demands a definition of what we mean by knowledge that constrains what we test to the consistently quantifiable.
Examples of what would be difficult to quantify is 'knowing what it is like to be in love.' On the other hand, it would be easier to devise tests, with experts, to quantify 'knowing how to play the piano'.
A more nuanced example might be 'Knowing the history of France.' Nobody can know the entire history of France and everybody that has lived there and what they have done. So in that sense, knowing the history of France is unquantifiable; a Frenchman may know enough facts about the history of his own family tree to fill several books, while knowing nothing of the political, economic, social or technological history of France. But if we define knowledge of the history of France to consist of the political history, we can devise a test to see what people know, and quantify this knowledge in that way.
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