Measuring Knowledge

The medical profession, when it collects diagnostics, usually qualifies its findings by saying something like: “…these measures indicate that the patient has this condition…”  They are acknowledging the latitude that usually occurs in most physiological metrics; the measurements always have some finite “accuracy.”  They are also allowing for the fact that the interpretation—the diagnosis and subsequent prognosis and treatment—can vary considerably. So rather than being definitive which, in most cases is not indicated (sic), they correctly and appropriately hedge their bets by using the word “indicate.”

Indicators of Knowledge 
While we cannot directly measure knowledge, it does leave footprints that can act as indicators of the amount of knowledge.  Our examination processes are just such an activity.  If someone has passed their accredited baccalaureate examination in (say) physics, we can reasonably assert that that person is in possession of a quantity and quality of physics knowledge.  With, of course, all the caveats we have already mentioned and allowing for the fact that the degree may have been awarded a long time ago and that knowledge, stored as it is in the knowledge-volatile medium we call a brain, may have dissipated.   Additionally, the most recent or most “correct” physics knowledge (stored elsewhere) may well be different from the knowledge that was stored in the brain during the student’s college years.  If the person has a Master’s degree or a doctorate in physics, we can reasonably assert he or she likely has more physics knowledge than a person with just a bachelor’s degree.  

The awarding of these degrees is a reasonable indicator of both the quality and quantity of physics knowledge.

But they are only indicators and, generally, other metrics might need to be taken to truly assess the knowledge.  If someone has simply obtained a degree certificate online by paying a few dollars, or they have been awarded an honorary degree for contributions in some other field, they might claim to have a degree, but they probably don’t have the knowledge.   If one person obtained a doctorate 40 years ago and another a bachelor's degree last year, it might be that the more recent graduate has more and more correct knowledge. 

Multiple Indicators
The medical profession helps to qualify their diagnoses by collecting multiple metrics and using the collection of metrics to support the diagnosis.  If someone claims a degree in physics, can answer pertinent questions about the topic, is proficient at setting up and running physics experiments, can cogently document results, submits them through peer-reviewed channels, and gets them published in prestigious journals, it’s pretty reasonable to assert this person has a quantity of quality physics knowledge.

But, it is still not possible to empirically quantify that knowledge.