I suggest constitutional law, itself another approach to generating knowledge, if only because I'll enjoy having Jay patiently explain to me how wrong I've got it all.
Only insofar as such a derail would be tolerated.
Separation of powers, typically between executive, legislature and judiciary, is seen as a vital aspect of a free society, and the fact that there is no single overriding authority to rule between the three is not a stumbling block but a strength.
You have to distinguish between the concept of separation of powers and the corollary concept of checks and balancers. The U.K. for many years separated the judiciary from the legislative
powers, but vested them both to a certain extent in the House of Lords. The U.S. Constitution inaugurated the form of separated government with mutual checks and balances among the branches.
Taking this approach, then, we have no need even to ask what is the criterion by which different forms of acquiring knowledge are assessed. We simply employ them all, indiscriminately, at any and all times. This may or may not result in any useful results...
Criminal law provides a much more interesting example since it is an attempt to implement a moral philosophy—philosophical "knowledge" that our OP assures us is non-empirical and does not require an explicit epistemological foundation.
We were presented with the moral proposition, "It is blameworthy to torture an innocent person." Well, yes. Also, water is wet. Maybe a less childish example would serve.
In American criminal law we have the notion of strict liability.
Let's say Tom, Dick, and Harry conspire to steal money from a bank. Tom agrees to drive the getaway car. Dick and Harry will enter the bank at night, when it's closed, and pilfer the vault. Unbeknownst to Tom, Dick and Harry have obtained handguns and in the process of opening the vault they shoot and kill the night watchman. Tom was outside waiting in the car the whole time.
Under the doctrine of strict liability, Tom can be charged with murder even though he was in no way involved with
that offense. His willing involvement in the felony of burglary makes him liable for the death, even though he did not intend for anyone to die, nor did he take any specific steps toward that outcome.
Quite a lot of people think this is very unfair, including a lot of moral philosophers. Yes, Tom should be charged with his participation in the burglary, but only Dick and Harry are guilty of murder. "Knowledge" from moral philosophy is divided on whether blameworthiness should be outcome-based or intent-based. In Roman law, the doctrine is
nullum crimen sine culpa—there is no crime in the absence of guilt.
If you drink to excess and drive home, but do not hurt anyone, you are blameworthy for your intent. But no harm followed. Are you guilty of anything? Conversely if a sober driver accidentally hits and injures a pedestrian, the driver is blameworthy for the outcome, but not for the intent. What's the right answer?
Advocates of strict liability warn that Tom willingly exhibited a depraved mind and a willingness to commit crime. Some moral philosophers believe that's blameworthy with respect to any
potential outcome. Strict liability therefore serves to put citizens on notice that by deciding to be criminals, they have crossed a line and have accepted a moral risk. In Tom's case, an undesirable and avoidable outcome occurred as the unintended (but very real) consequence of a willful immoral act, whether the consequence was intended or not =
actus rea alone determines blame.
The opposite question occurs in police stings. Police officers, say, posing as minors lure sexual predators into unlawful interactions and proposals. Here only the
mens rea is enough to convict. No child was ever actually in danger—there is no
actus rea. But people have no problem assigning blame to such entrapped perpetrators, generally claiming that if not the undercover police officer, then some actual child would have been endangered or harmed. Again, in Roman law
iniuria (actual injury) was a thing. While crimes against "the people" were a thing (
crimina publica), the prosecution still had to show an actual injury. Under Roman law, the fact that the "victim" was an adult playing along would void the charge.
Now we can (and do) debate the moral underpinnings of crime and punishment until the cows come home. The point is where this falls in the taxonomy of knowledge. If we "know" two completely opposite things (
solos actus rea = crime,
sola mens rea = crime) is it really knowledge? What kind of knowledge is it? Is it congruent with knowledge like, "Statistically significant impairment begins at a blood alcohol level of 0.05%?" That was determined empirically. Does it have sufficient epistemological foundation and authority to be "knowledge?"
That's why I want to talk about the paranormal.
Whether Tom should go to prison for murder is a hard question, unlike "Don't beat up the weak kids." Similarly, the inability to prove empirically that there are an infinite number of primes—you do it by mathematical induction—is a given. A hard question is whether there exists a class of hypotheses that sound in ordinary phenomenology (e.g., ghosts, UFOs) but which cannot be rightly investigated with reliable tools of empiricism—a proper paranormal claim. If pragmatic empirical science rejects the existence of ghosts, does it do so with the same authority by which it rejects luminiferous ether? If not, what other source of knowledge should we invoke?