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“Appeal to authority” is a form of logical fallacy

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Religious adepts can be very easily identified by using the following diagnostic criteria:
1) they use the “appeal to authority” as an argument;
2) they are unable to provide scientific definitions for the terms that they use in their texts, and instead of scientific definitions they provide crackpot blabber;
3) they are totally incapable to provide the scientific arguments and instead of scientific arguments they actively use all sorts of bureaucratic muck (write complaints/denunciations, vote “against” at the polls/ratings, etc.).
4) and so on.

“Appeal to authority” is not a the scientific argument; “appeal to authority” is a form of logical fallacy.
“Appeal to authority” is the diagnostic criteria which identifies the religious adept.
Argument from authority, also ad verecundiam and appeal to authority, is a common form of argument which leads to a logical fallacy.

In informal reasoning, the appeal to authority is a form of argument attempting to establish a statistical syllogism. The appeal to authority relies on an argument of the form:
A is an authority on a particular topic
A says something about that topic
A is probably correct

Fallacious examples of using the appeal include any appeal to authority used in the context of logical reasoning, and appealing to the position of an authority or authorities to dismiss evidence, as authorities can come to the wrong judgments through error, bias, dishonesty, or falling prey to groupthink. Thus, the appeal to authority is not a generally reliable argument for establishing facts.

Let’s examine the “appeal to authority” in more detail using practical examples.

When discussing the functioning of the brain, the pseudoscientists very often appeal to the authority of Plato and Aristotle.
Let’s look more closely: what good advice in the field of brain functioning we can get from Plato and Aristotle?

Let’s raise a simple question: did Plato and Aristotle know that the brain is made up of cells (neurons)? Did Plato and Aristotle know anything about the neural signals?
They did not know and they could not know, because no one knew this until the 19th century.
The neuron doctrine is the now fundamental idea that neurons are the basic structural and functional units of the nervous system. The theory was put forward by Santiago Ramón y Cajal in the late 19th century. It held that neurons are discrete cells (not connected in a meshwork), acting as metabolically distinct units.

So what good advice in the field of brain functioning we can get from Plato and Aristotle?

We will remind that the eye is actually part of the brain:
The retina is actually part of the brain that is isolated to serve as a transducer for the conversion of patterns of light into neuronal signals. The lens of the eye focuses light on the photoreceptive cells of the retina, which detect the photons of light and respond by producing neural impulses. These signals are processed in a hierarchical fashion by different parts of the brain, from the retina upstream to central ganglia in the brain.

Now let's look more closely at the Plato’s and Aristotle’s advice about the functioning of the eye (i.e. the brain):
theory of visual perception suggested that sight occurs because rays emanate from the perceiver's eyes. After leaving the eyes, these rays explored the world, and upon encountering objects, the rays returned, carrying information about those objects. One of the foremost proponents of this theory was Euclid, whose contributions to geometry you probably know about; Aristotle and Plato also subscribed to this theory.
Theories of light; theories of vision
Robert Sekuler, for Npsy 12a, rev. 2004
What is unfortunate for the history of visual science is the fact that the idea of extramission was associated with the illustrious name of Plato (428-348 BC). Indeed Plato and before him Pythagoras (c. 532 BC), were the first to seriously propound the extramission theory. For Plato, the substance that was emitted by the eye was a kind of gentle "visual fire" or light, flowing forth out of the pupil, that combined with ambient light to generate a homogeneous "body of vision" (like a kind of disembodied tentacle controlled by the eyes) which encompassed or touched objects and thereby generated a medium between the object and the viewer which allowed aspects of the object to contact the soul.
Given Plato's great authority, the extramission viewpoint was adopted, with variations, by many thinkers after him. Of particular importance was its acceptance in the 2nd century AD by the great physician Galen, whose doctrines were to dominate medical thought throughout the middle ages. As we shall see below, up until the 17th century, the influencial medical community was wedded to the extramission hypothesis.
But in addition to weighing with his authority toward the extramission viewpoint, Plato probably contributed in other ways to hindering progress in the study of vision. One form of general hindrance created by Plato was not specific to his theory of vision, but derived from his general approach to science: in his opinion, observation of nature was a worthless pursuit -- progress could only come from logical reasoning and mathematical deduction. A more specific hindrance is suggested by one contemporary historian of science, who claims that for Plato, vision was not a very reliable sense. The "touch-at-a-distance" provided by vision was a poor relative of true manual touch. After all, contrary to the normal tactile sense, vision does not allow a whole object to be apprehended, since parts of it are always hidden from view. Judgements based on vision are subject to many types of errors, like those caused by changes in lighting and perspective viewpoint, by extraneous phenomena associated with shadows, transparency, reflection and refraction for example, not to mention the many well-known 'optical illusions' that give rise to errors in size and position judgement. In sum, for Plato, vision was unfit for doing science: tactile confirmation of visual impressions was essential.
Perhaps an example of Plato's negative influence on the pursuit of optical science is the history of lenses. It has been argued that, like hypnotism and paranormal phenomena today, the study of lenses was considered a disreputable pursuit in the Middle Ages. Even though magnifying lenses were probably used by craftsmen at least as early as the beginning of the christian era to make miniatures or to carve fine inscriptions on the moulds used to cast coins, and even though, starting in the 13th Century, a whole industry of artisans was manufacturing spectacles for correcting presbyopia (and later, myopia), it took another three hundred years until scientists deigned to study them. Even Kepler, in his revolutionary book Paralipomena published in 1604, merely devotes three pages to lenses, and then apologetically, with the justification that a mycene had been prodding him for three years to consider them. Only when Galileo's discoveries with the telescope caused a sensation and rendered more politic the serious consideration of lenses, did Kepler finally deign to give them proper treatment in his Dioptrica, published in 1609.
Ancient Visions

And now let's look further at the Aristotle’s advice about the functioning of the brain.
According to Aristotle, the brain is just the heat sink which cools down the heat of the blood.
Aristotle thought that, while the heart was the seat of intelligence, the brain was a cooling mechanism for the blood. He reasoned that humans are more rational than the beasts because, among other reasons, they have a larger brain to cool their hot-bloodedness.

It is obvious that Plato and Aristotle are totally incompetent in neuroscience.
Despite this fact, the pseudoscientists insist on studying Plato’s and Aristotle’s writings about the functioning of the brain.
Pseudoscientists insist on studying “Stone Age” writings about the functioning of the brain.
That is the qualification level of pseudoscientists in the field of neuroscience.

It is interesting to note that history has hundreds of examples when religious adepts mimicking as “scientists” declared the real scientists as being “crazy”.
One such classical example is the case of Ignaz Philipp Semmelweis, who proposed the practice of washing hands before carrying out medical surgeries/procedures. The medical professors/surgeons/etc unanimously decided to lock up Ignaz Philipp Semmelweis into the lunatic asylum for his crazy/crank ideas. Ignaz Philipp Semmelweis died being locked up in the lunatic asylum.
Ignaz Philipp Semmelweis (born Semmelweis Ignác Fülöp; 1 July 1818 – 13 August 1865) was a Hungarian physician of German extraction now known as an early pioneer of antiseptic procedures. Described as the "savior of mothers", Semmelweis discovered that the incidence of puerperal fever (also known as "childbed fever") could be drastically cut by the use of hand disinfection in obstetrical clinics. Puerperal fever was common in mid-19th-century hospitals and often fatal, with mortality at 10%–35%. Semmelweis proposed the practice of washing hands with chlorinated lime solutions in 1847 while working in Vienna General Hospital's First Obstetrical Clinic, where doctors' wards had three times the mortality of midwives' wards. He published a book of his findings in Etiology, Concept and Prophylaxis of Childbed Fever.
Despite various publications of results where hand washing reduced mortality to below 1%, Semmelweis's observations conflicted with the established scientific and medical opinions of the time and his ideas were rejected by the medical community. Some doctors were offended at the suggestion that they should wash their hands and Semmelweis could offer no acceptable scientific explanation for his findings. Semmelweis's practice earned widespread acceptance only years after his death, when Louis Pasteur confirmed the germ theory and Joseph Lister, acting on the French microbiologist's research, practiced and operated, using hygienic methods, with great success. In 1865, Semmelweis was committed to an asylum, where he died at age 47 of pyaemia, after being beaten by the guards, only 14 days after he was committed.
Efforts to reduce childbed fever
Semmelweis demonstrated that puerperal fever (also known as childbed fever) was contagious and that this incidence could drastically be reduced by appropriate hand washing by medical care-givers. He made this discovery in 1847 while working in the Maternity Department of the Vienna Lying-in Hospital. His failure to convince his fellow doctors led to a tragic conclusion. However, he was ultimately vindicated. While employed as assistant to the professor of the maternity clinic at the Vienna General Hospital in Austria in 1847, Semmelweis introduced hand washing with chlorinated lime solutions for interns who had performed autopsies. This immediately reduced the incidence of fatal puerperal fever from about 10% (range 5–30%) to about 1–2%. At the time, diseases were attributed to many different and unrelated causes. Each case was considered unique, just as a human person is unique. Semmelweis's hypothesis, that there was only one cause, that all that mattered was cleanliness, was extreme at the time, and was largely ignored, rejected, or ridiculed. He was dismissed from the hospital for political reasons and harassed by the medical community in Vienna, being eventually forced to move to Budapest.
Semmelweis was outraged by the indifference of the medical profession and began writing open and increasingly angry letters to prominent European obstetricians, at times denouncing them as irresponsible murderers. His contemporaries, including his wife, believed he was losing his mind, and in 1865 he was committed to an asylum. In an ironic twist of fate, he died there of septicaemia only 14 days later, possibly as the result of being severely beaten by guards. Semmelweis's practice earned widespread acceptance only years after his death, when Louis Pasteur developed the germ theory of disease, offering a theoretical explanation for Semmelweis's findings. He is considered a pioneer of antiseptic procedures.