For instance, it's authoritative that, "I believe 'Albert Einstein invented the theory of Relativity.'" The existence of this belief is foundational (i.e. properly basic or self-authenticating): I know that I believe some statement merely by virtue of the existence of that belief. The statement would be veridical if and only if the part with "stand-alone" propositional content (i.e. 'Albert Einstein invented the theory of relativity') were itself true absent the qualifier of my belief.
In science, experiments (public science) or experiences (phenomenal science) are authoritative by definition, but they are never assumed to be veridical. It is always a mistake in science to believe that any experience is foundationally veridical; the veracity of any experience is always a conclusion, never itself an authoritative fact. On the other hand, all experiences as experiences—including those experiences we conclude are hallucinations or illusions—are properly basic, self-authenticating, foundational and authoritative.
It is a tautology that using an epistemic method such as science which accepts experience as its sole foundation will always lead to the conclusion that most of our experiences are veridical. It is not, however, a tautology that a compelling account (evolution) will emerge to explain not only why most of our experiences are veridical, but also reinforce the principles which separate veridical from illusory experiences.
People, even scientists, are mostly inept at separating out experience as experience from our naive ontological interpretations of those experiences. Even a very superficial survey of cognitive science (or a reading of Quine) shows that our conscious minds (i.e. those mental events/brain structures associated with language processing) are not fed experiences, but are rather fed mechanical ontological interpretations by our preconscious and subconscious minds. Our conscious minds do not see a bunch of green and brown pixels; by the time our conscious minds are even aware of the outside world, our preconscious minds have already made the evaluation and supplied our conscious mind with "tree".
Even our conscious mind, which has, after all, been around for hundreds of millennia longer than we've understood the scientific method, mostly makes naive non-scientific ontological interpretations. Even so, our "unscientific" naive ontological interpretations at every level are mostly veridical, again by virtue of brute-force evolution: Organisms whose brains make certain kinds of non-veridical errors tend to get eaten by tigers.
It takes both considerable mental effort as well as strict mental discipline to override our naive ontological interpretations. Even scientists, engineers, police detectives and artists, all of whom must apply this effort and discipline in their professional work, tend to slip into unscientific thinking when they're "off the job".
Even worse, even on the job, even scientists do not really know how to think scientifically in general. I work with no small few scientists in my job, and I've concluded on the basis of my observations that most scientists simply learn by rote a set of rules about how to think about their area of specialty. These rules happen to be a good scientific way of thinking, because they've been established by people who can think scientifically in general, but most scientists seem unable to generalize those rules in a philosophical manner. In their defense, scientists are much more easily persuaded by a truly philosophically scientific argument than the average person.
To perform a scientific analysis we must do two things: We must accept the authority of experience, but we must reject a priori our naive opinions about the veracity of the experience. We must differentiate between the experience as an experience (authority) and our naive ontological interpretation of that experience (veracity).
Phenomenalism, i.e. applying the scientific method to our private, internal experiences, presents some challenges. We absolutely cannot escape many of our preconscious ontological interpretations, especially those supplied by the substantial fraction of our brain which is the visual cortex. The best we can do is override our semi-conscious biases (especially confirmation and selection bias); we might also, according to tantalizing hints from the cutting edge of cognitive science, consciously affect to a limited extent the most abstract levels of our visual and auditory cortices.
Hence pure phenomenalism can take us only so far. To go farther, we must employ "public" science: the scientific method applied to shared phenomena (stated phenomenally, those direct, perceptual experiences which strongly correlate to our phenomenal interpretation of experiences of hearing others' language). Phenomenal (private) and public science feed back to each other: We can't do public science at all without a phenomenal base, but we can go farther with public science than we can with pure private phenomena. Most especially, we can differentiate between those experiences which appear to be shared (correlate with language experience), and those which appear to be idiosyncratic (anti-correlate with language experience).
All this being said, we are in a position to scientifically analyze an account such as the Deacon's Demon boy episode.
(As a side note, phenomenally, we are interpreting our own experience of reading the Deacon's words. We'll assume as unproblematic that we are accurately interpreting his words, and further assume that he is not intentionally deceiving us: We may interpret a report of an experience as veridical in the sense that we'll conclude the Deacon does actually remember experiencing what he says he remembers experiencing. We will, however, treat critically his ontological interpretations of those experiences.)
Of course, there's a limit on how far we can drill down: The Deacon did not record the episode with a video camera. We are also relying on a verbal account of a decade-old memory of his experience. Such indirection does not preclude an analysis, but it does alert us to look for scientifically established distortions that can occur because of this indirection.
We can drill down in his story and extract (omitting those items of verisimilitude which establish the veracity of his account) the results of unproblematic superficial preconscious ontological interpretation (suspicious characterizations or ontological assumptions are highlighted in bold):
I left my friends sometime between 11 and midnight, and started walking back to St. George's. I remember that there was a bright moon in the sky, and I was struck by how utterly quiet and totally deserted the winding streets were. ...The bolded passages and elided conclusions certainly make the story vivid and interesting, but we must treat them with suspicion, and focus our analysis on our best effort to determine the experiences, not the immediate, unconsidered and naive conclusions (although we must also account for these secondary experiences (experiences of forming conclusions)).
I turned into a long alley that was arrow-straight for perhaps a hundred yards before curving gently to the right. Three- or four-story walls, the windowless and doorless backs of buildings, lined the alley on either side. ...
I'd walked about half the alley's length when suddenly, just on the other side of its bend, came the most uncanny wailing I've ever heard in my life. I just can't find words to describe it. It was a sort of ululating cry heavy with despair, fear, and loneliness. I remember thinking at the time that I'd never heard such a mournful sound [since the Deacon remembers thinking, this sentence is properly a description of his experiences]. It stopped me in my tracks.
And then, from around the bend in the alley, came the source of the wailing. It was a boy, maybe 12 or 13 years old. His head was bent down, so I couldn't see his face. He had thick, uncombed black hair... and his clothes were dirty and unkempt. One of his shirt tails hung out over his pants. He was shuffling toward me in a pigeon-toed way... He held his hands (which were also incredibly dirty) under his chin and was wringing them in frenzied syncopation with his wailing. ...
Despite his club foot, the boy was lopping toward me rapidly. When he was about a yard away, I called out: "Are you okay? Can I help you?"
The boy stopped, the wailing ceased, and he raised his head and looked me straight in the face. One of his eyes was clouded over, opaque, white, dead. The other, wide open, penned me with a stare of overwhelming hatred and malevolence. The boy's face was twisted in pain and rage, and his mouth was twisted wide, showing broken and black teeth... And then he snarled at me...
I was so startled, so completely weirded-out, that I recoiled and stumbled back out of his way. He stared at me with absolute hatred for a second or two longer. Then the wailing and hand-wringing recommenced and he pushed past me and ran off, in that broken way of his, down the long stretch of alley I'd just walked.
And before I could reflexively spin around to stare at his back--he was gone. No more boy, no more wailing. Nothing. He'd vanished. There was no way he could've sprinted down the entire 50-yard or so stretch of alleyway in the couple of seconds it took me to turn around. Even if he had, I'd still have heard the wailing. Nor were there any windows or doorways he could've slipped through. He simply vanished, leaving the alleyway just as silent and deserted as it had been a couple of minutes earlier.
We should first list those conclusions that we can trust. It's well known and scientifically established that people in general are good at recognizing the emotional content of expressions. Therefore, we can be moderately confident that the conclusions of hatred, malevolence, pain and rage in the boy—in the ordinarily human sense of these emotions—are plausibly accurate. We can conclude his physical description of the alley is accurate, as well as his reports of prosaic details such as the time of day.
There are other things we can conclude, though, that cast doubt on the veracity of the report, the memory and the experiences.
Most importantly, the Deacon is relating not just a memory, not just an almost decade-old memory, but a memory we can plausibly assume he has revisited with some frequency. It is again scientifically established that revisiting a memory can often adds vivid details to that memory. We cannot confidently conclude much from the mere vividness of his account that the original experience was as vivid.
The Deacon reports a "bright moon", but how bright? Full? Half? The level of illumination is critically important to determine the accuracy of the observation that "there [weren't] any windows or doorways he could've slipped through," or that the boy's expression in some way transcended the human norm. Shadows in low illumination can play funny tricks, and our evaluation of expression is definitely preconscious. Likewise, the acoustic properties of a long, even mostly door- and window-free alleyway can have a definite effect on our evaluation of sound.
Since the episode happened near a bend in the alleyway, it's plausible to suspect that the encounter might have happened not immediately before the bend, but during or immediately after the bend. This is precisely the sort of detail often elided by memory. This is an especially important consideration, given that the boy was wailing loudly; the Deacon would have heard the sound only so close only if the boy had coincidentally started wailing just before he encountered the Deacon.
Given all these things, supplying what is ambiguous or left unsaid, we can form a plausible, prosaic account of the Deacon's experiences.
The Deacon is walking home alone in the middle of the night, fatigued, perhaps mildly intoxicated (I don't know if the Deacon drinks; we can plausibly conclude, however, that he was not severely intoxicated) in a dark city (perhaps without streetlights?), a half or three-quarters moon (not all that much illumination). Furthermore, Jerusalem does not seem like a particularly safe city, so we can plausibly assume at least some degree of low-level apprehension.
He's walking through a supposedly door- and window-less alley, but can we absolutely rely on this evaluation? What's the orientation of the alley? Is one side shaded? Are there any obstructions or protrusions? He's either walking through this alley for the first time, or he has become used to it; neither case is especially conducive to the observation or memory of subtle details.
He hears an "uncanny" wailing and freezes in his tracks, but perhaps the wailing is farther away than memory recalls. He continues forward around the bend and only then encounters the boy. The boy is an unusual but otherwise prosaic person, blind in one eye and perhaps mentally ill. The general apprehension, the moonlight, the acoustics of the alley, the Deacon's general level of apprehension, and the boy's mental illness all conspire to heighten the spookiness and surreal quality of the actual encounter and the Deacon's evaluation of his facial and vocal expressions.
We can safely conclude from the Deacon's account that he is, at this point, scared shitless (and justly so!). Heart pumping, adrenaline flowing, perhaps in a state of near panic. This physiological condition is conducive neither to reliable memory formation nor an accurate time sense.
The boy has caused the Deacon considerable fright, so why should we assume that he follows the boy immediately? A perfectly natural reaction would be to run in the opposite direction. To follow the boy immediately he would have to anticipate the boy's mysterious disappearance, else why attempt to confirm it?
So perhaps the Deacon waits for an unknown length of time, just around the bend from the straight stretch of the alley. Perhaps he waits until the wailing abruptly stops, and then (showing more courage that I would have), steps back around the bend. The wailing might have stopped precisely because the boy had taken an unobserved exit, or perhaps he just stopped wailing and was momentarily obscured by a shadow, obstruction or some sort of protuberance. The Deacon, being merely courageous and not suicidal, does not make a thorough inspection of the alley, but merely glances, does not immediately see the boy, and, given his fear and the spookiness of the situation, sensibly moves quickly in the opposite direction.
I don't of course know what actually happened; there's not enough information to conclusively resolve this mystery. But consider: While critical of his interpretation, this account gives full weight and authority to the Deacon's experiences as experiences; it does not deny that he is fabricating anything of substance, either in his report, his memory or his experiences at the time. For instance, we are entitled to interpret the ontological statement that the boy "simply vanished" as an experiential statement, "I lost sight of the boy."
Furthermore, his emotional state of fear accounts for his immediate ontological interpretations, and his predisposition to theism (confirmation bias) accounts for the paranormal interpretation.
Of course, the Deacon's memory might well be perfectly accurate, and his experiences entirely veridical. But is that the simplest explanation which accounts for the actual facts? Remember, the actual facts specific to the story, the only basis we have for examining this episode, comprise our linguistic understanding of the Deacon's report of a memory of an experience.
If we accept his story as absolutely veridical, we call into question all our prosaic experiences regarding human-appearing experiences: People simply do not usually vanish into thin air. The simplest explanation of just our prosaic experiences is that people cannot vanish into thin air, which accords well with our scientific knowledge about things like the conservation of mass.
To accept the Deacon's report as thoroughly veridical, we are forced to explain not only the report and underlying experiences themselves, but we must also explain why those experiences contradict the interpretation of our prosaic experiences. We must not only explain why the boy actually did vanish, but also why human-appearing ordinarily don't ever otherwise vanish, since to accept the report as veridical we must reject the conclusion that human-appearing object cannot vanish.
As Hume notes, it is always the simpler explanation to conclude that either this singular memory, experience or even the report itself are somehow in error than to contradict the interpretation based on an enormously large number of consistent observations. Even if we were unable to otherwise find an interpretation consistent with our well-established understanding of scientific universals, we would still be more rationally justified in concluding the experience was a pure hallucination or (speaking only hypothetically; there's compelling evidence that the Deacon is an entirely honest man) the report was a pure fabrication.